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How to Become a Pure Mathematician Page 2 of 66
It's like if you want to be a good pianist, you have to do a lot of scales and a lot of practice, and a lot of that is kind of boring, it's work. But you need to do that before you can really be very expressive and really play beautiful music. You have to go through that phase of practice and drill.
Here is a guide to study pure mathematics.html).nl/~thooft/theorist. • Assumed knowledge. Note the highlighted list does NOT indicate those books are good for beginners. I don't claim that this list makes you a good pure mathematician. Yup. Shouting eureka is the high point of a mathematician. I listed more than enough so that you can scout around to find one that you feel comfortable with. since I belong to the complement of good pure mathematician.. I also highlighted several books that you would really like to keep in your own library.. beware of the symbols from different books in such cases. or even more. Scientists in other fields and engineers may skip first or second stages and begin at later stages. especially in higher level courses. Euclidean geometry. It relies on two factors: well written or cheap. I list more material in each field for more advanced studies). It takes approximately one year for each stage (except for stage 4. These two factors are not mutually exclusive. for a full time student.phys. and recommended a few notes or texts. Moreover. This list is written for those who want to learn mathematics but have no idea how to start.geocities. a list for beginners. Some people like to consult a few books. My selection will not be bounded by any publication press. perhaps. Part time students may double the time. Things may come to your head suddenly. The aim of this page is to introduce what different branches of mathematics are.e. If you decided to attend a class.How to Become a Pure Mathematician Page 5 of 66 About this article: What for? OK. basic trigonometry.uu. I shall try to keep this list up to date whenever I exist. sometimes I get a HK $2xx book and Amazon says its US $1xx (~HK $7xx). What's the order of courses to study within a stage doesn't really matter. • Time.. • "Axiom of choice". don't expect the professor can teach. Free material excluded. Moreover. it always happen. But its better for anyone to understand most parts of stage n before proceeding to n+1. Note the price factor may by irrelevant. but hopefully it will be clear as you proceed. there is a way to become a good theoretical physicist ( some Chinese press in mainland China it often happens that you couldn't solve a problem within an hour. One doesn't need to read every listed book within a subject to master the subject.htm
•
. I assumed you have high school mathematics background (i. You probably like to read those books again and again in your life.com/mathphyweb/puremath. usually. I make no attempt to define what pure mathematics is. with the only difference is. I treat "free" as an element in "cheap". I got the international edition.. It's not surprise to spend a week or more to tackle one problem. 3. 2. 4}. author's nationality or religion.. for some integer n in {1. etc). according to their prior knowledge.
mhprofessional. • Comments. Google books ( ask yourself.. In contrast. Also.cs.wikibooks. Links to Amazon for most of the listed book are included. So.edu/OcwWeb/Mathematics/index. Note that the comments are sometimes quite extreme: for the same book.com/products/acrobat/readstep2. you know.htm
. I've taken all undergraduate core pure mathematics and statistics courses there. The list below aimed to recommend books or (usually) printable notes. Sydney.adobe.edu/pub/mirrors/ghost/AFPL/gs853/gs853w32. If they can't pass the exam. probability and statistics books. Principia Mathematica.com/category/?cat=4234) series are cheap. UNSW. or visit While for literature or philosophy.exe and ftp://mirror.. with all pure mathematics courses in higher level.edu/pub/mirrors/ghost/ghostgum/gsv48w32.com/download/dl_options. To view [.mit. especially for introductory discrete mathematics. Gottfried Leibniz's student Jacob Bernoulli's student Johann Bernoulli's student Leonhard Euler's student Joseph Lagrange's student Simeon Poisson's student's student's student's student's student's student's student's student's student. why do you study? • Other resources. I was Terry Tao's teacher's student. but I seldom include them.org. etc) is optional. most pure mathematics students study because they like the subject and enjoy it.wisc.djvu] get Michael Artin's student's student. These are excluded in the following list.archim. • Me. reading the classics (the Elements. Large proportion of these readers are lack of mathematical maturity. Schaum's Outlines ( provide another great sources of materials. Perhaps Terry Tao is an exceptional case. Although I'm not into reading books online. to view [.uk/notes/) and Wikibooks ( I wonder if any well educated student has never study Shakespeare or Plato. the Principia.exe. To study science. Dialogo sopra i due massimi sistemi del mondo.cs. so that you have an easy access to other users' comments.google. Just feel get Adobe Reader ( I should remind you that MIT's open recourse ( whenever they exist. to view [.com/mathphyweb/puremath.lizardtech. they want to apply mathematics.php?page=doc. the Archimedeans ( Australia. Disquisitiones Arithmeticae. It seemed to me that lots of people study these subjects because they need to. you may search the relevant if you like.htm). Bear in mind that. just because one is a good mathematician doesn't imply he's a good author or educator.How to Become a Pure Mathematician Page 6 of 66 published photocopied of English text with a relatively cheap price.com/) allow you to preview sections from a book.wisc. Max Planck's student's student's student's student and Thomas Kuhn's student's student.edu/~ghost/gsview/.ps] download ftp://mirror. A product of School of Mathematics and Statistics.html). one rated it with 5 star (with dozens of people supporting) and at the same time another rated 1 star (with dozens of people supporting again).
geocities. contact can be found in the main page ( • Disclaimer.htm
. just email me.How to Become a Pure Mathematician Page 7 of 66 like I'm an idiot. etc.
• Comments/suggestion for a book. I'm not responsible for any external link.com/mathphyweb/puremath.
Basic Concepts of Mathematics (FREE! to Become a Pure Mathematician Page 9 of 66 Zakon E. Halmos P. Velleman did a good job for beginners here.A. and Givant S.millersville.T.com/zakon1.edu. Logic for Everyone (FREE! Elements of Set Theory Halmos P. Naive Set Theory .Don't misinterpret the word naive. A Problem Course in Mathematical Logic (FREE! In general: Anderson I. though he propose the honest title as An Outline of the Elements of Naive Set Theory.org/abs/math. Introduction to Logic Velleman D.L. Notes on Math Proof (FREE!
. Background and Fundamentals of Mathematics (FREE! . Functions (FREE! Connell E.trentu. Abstract Set Theory (FREE! Discrete Mathematics (FREE! surjective. Logic and Set Theory: Bilaniuk S.cosc. introductory graph theory and number theory. and Franklin J.tw/~htchen/dm/index.geocities. A First Course in Discrete Mathematics Chen H. nPr) etc in this course. Relations.au/~wchen/lndmfolder/lndm. Proof in Mathematics: An Introduction Düntsch I.math.com/mathphyweb/puremath.ndml/1175197470) Suppes P.H.html) Enderton H.html) Skolem T.miami. part in higher mathematics. Discrete Mathematics (see the Lecture Notes section) (FREE! Logic as Algebra Herrmann R.ca/~duentsch/papers/methprimer1. Daoud A. How to Prove It: A Structured Approach .A short chapter from the author's algebra book.Let me warn you: proof is a crucial.html) Sets.R. if you are serious about it. discrete probability (counting.trillia. Only for Proof. You will also study proofs. The concepts you learnt here will play a key role in your later studies and improve your thinking skill.org/euclid.html) 陳旭東:離散數學 Chen W. Set theory plays a significant role in mathematics.R. functions (injective.html) Introductory Discrete Mathematics: You will study logic and set theory in an introductory discrete mathematics. bijective inverse). nCr. This is not those books for dummies nor complete idiot's guide.W. crucial. Halmos is one of the better expositors of mathematics.J.maths. I repeat.edu. Euclid's algorithm.GM/0601709) Ikenaga B.
W. hyperbolic functions. If you prefer it.math. Calculus (FREE! Undergraduate Algebra . double.com/calc/) Dawkins.geocities.edu/~garrett/calculus/) Ghorpade S.umn.html) Courant R.R. It is not only important in advanced mathematics but also can be applied to many other fields. Introduction to Calculus and Analysis I . First Year Calculus (FREE! say vector calculus.math. you would like to leave a few section. P Calculus I and Calculus II (FREE! learn the epsilon and delta proof.edu/~djoyce/complex/) Lang S.He's a member of the Bourbaki and wrote many books. limit of sequences. line and surface integrals. Algebra (FREE! Elementary Linear Algebra (FREE! If you learn first year calculus in a college.How to Become a Pure Mathematician Page 11 of 66 Garrett P.L. Linear Algebra and Its Applications Wedderburn J. inverse trigonometric functions.B. Matthews K.maths.aspx and it is colorful and quite detailed.V. basic idea of several variables.etsu.math.edu.lightandmatter. and John F.ams.in/~srg/acicara/) for errata.iitb.edu/classes/alg/alg.edu.org/online_bks/coll17/) Introductory Calculus: As you may have seen. triple.H. 1 Burn R. Crowell B. This is a standard modern text. Calculus Vol. The first thing we need to fix up is the definition of limit. logarithm and exponential functions. infinite series. Linear Algebra Notes (FREE! to the next stage.au/~wchen/lnmtfymfolder/lnmtfym. This book is thick.lamar.openmathtext.M.E. Linear Algebra (FREE! indeterminate form. Not friendly for beginners.html) Dawkins P.lamar. that's fine.org/lecture_notes/new_linearalgebra.mq. Calculus (FREE! Gardner R. fundamental theorem of calculus. A Short Course on Complex Numbers (FREE! but you should get use to it.math. I would suggest a few non-standard texts and notes.edu/classes/calcII/calcII. Other key concepts are the mean value theorem.See their web ( Stewart's Calculus. Numbers and Functions: Steps into Analysis Chen W. A Course in Calculus and Real Analysis .pdf) Strang G. Joyce D.htm
. calculus is crucial. of the better calculus text in print. Lectures on Matrices (FREE! basic differential equations. your suggested text is probably J.htm) Leave Chapter 6 and 7 to the next stage.org/book/) Santos D.P. and Limaye B.lamar. Apostol T.
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.com/mathphyweb/puremath.How to Become a Pure Mathematician Page 19 of 66
topological space. every steps in a proof should be logically related and everyone can go easily from the previous step to the next. they can be applied to other graduated level science subjects.' Also get maturity and learn how to write mathematics. '[t]he serious student will train himself to look for gaps in proofs. swallowed. etc. These can be generalised. It often happens in advanced text that the author skips some steps in a proof or calculation. Yup. 1) talks about liminf. and one too seldom emphasized. You will study the idea of several spaces (metric space.
Introductory Analysis: At this stage you should have learnt limits. Don't expect you can solve a problem by plugging numbers into formulae.geocities. '[i]t is a basic principle in the study of mathematics. 40. As you may see. But as G. limsup. one is just ignorant. Focus on the proof. I can show you a copy of full mark statistics assignment consists work of mere calculation and computation. No. A proof should be chewed. Vol. (Of course not done by me!) I had tried to list more books so that you can compare and choose one or two that fit you. I don't bother to argue with those people anymore. weak topology and stuffs like that. compactness.F. If you insist. connectedness.F. while elementary text gives detail explanations. Banach. In the analysis class. much more is necessary than merely following the individual steps in the reasoning.How to Become a Pure Mathematician Page 20 of 66 Stage 3 At this stage. In achieving this end. The point is. that a proof is not really understood until the stage is reached at which one can grasp it as a whole and see it as a single idea.htm
. linear operators.' Moreover. Hilbert). and 2) they don't bother to explain to others. measure. Kolmogorov and Fomin's text fits this stage this is the beginning. If one insists that the pure stuff is useless.com/mathphyweb/puremath. and should regard them as tacit invitations to do a little thinking on his own. Simmons has said. elementary Lebesgue theory and measure theory. over the reals. This is not the case for non-pure mathematics. I don't think Gauss or Galois can get full mark in mathematics assignments these days. and this process of assimilation should not be abandoned until it yields a full comprehension of the overall pattern of though. and Metrens J. by reading good books (?). Despite that most of following courses are 'pure'.e. This is only the beginning. and digested. for 1) something obvious to them may not be obvious to everyone else. continuity and convergence. These are central concepts of calculus in both one and several variables.). you begin to learn modern Pure Mathematics. Upper Hemi-continuity of the Equilibrium-set Correspondence for Pure Exchange Economies. Contents of analysis courses varies almost everywhere (a. Ian Doust even showed us an article in the Econometrica (Hildenbrad W. the term analysis appear in the first and second year calculus to forth year analysis.
R.W. A Course in Modern Analysis and its Applications Davidson K.edu/~bass/meas.M. Elements of the Theory of Functions and Functional Analysis .L.R.mq.html) Chen W.edu. and Fomin S.F. and Fomin S.pdf) Beals R. It seems that this is a more popular edition.aspx) Chen W.au/~wchen/lnilifolder/lnili. A Second Course in Mathematical Analysis Giles J. they cover most of the above topics. Real Analysis (Measure Theory) (FREE! continuity.W. Several books entitled analysis are indeed advanced calculus (stage two calculus) or not aimed for mathematicians.ohio-state.mq. and Burkill H.L. Searcóid M. One feature is that proofs are often left behind examples. Real Analysis with Real Applications Jost J. Stay away from Mathematical analysis for business and finance or the like. Banach spaces and Hilbert spaces.uconn.B.It covers a lot of stuff and hence too concise for an introductory text.Ó. etc: Apostol T. Bruckner A.C. Treat this as a reference. Postmodern Analysis Kolmogorov A.The material is based on lectures given by the authors in the Moscow State University.N.and Thomson B. Real Analysis (FREE! Only for metric spaces and topological spaces (also consult the list of Topology below): Burkill J. Mathematical Analysis . and Donsig A.com/download.edu. Silverman.V. and Simmons make good references. 2 in stage 2. Bass R.This version is translated and edited by R.A. Bruckner J. Elementary Classical Analysis . Introduction to the Analysis of Metric Spaces . Introduction to Metric and Topological Spaces Also deals with Lebesgue theory. Introductory Real Analysis . Apostol. Metric Spaces Sutherland W.P.One of the Australian Mathematical Society Lecture Series.S. See the typo by Edgar ( Introduction to Lebesgue Integration (FREE! to Become a Pure Mathematician Page 21 of 66 well. then you should go for this.L.M. and Hoffman M..math. Marsden and Hoffman.maths.geocities. Solution by Shin-Yi Lee can be found here. compactness and metric topology.This book sits somewhere between the stage 2 calculus and stage 3 analysis in this list. maybe.html) Cohen G. Marsden J.htm
. 1 in stage 1 and Calculus Vol. gives nice discussion on limit processes.If you enjoy his Calculus Vol.maths.edu/~edgar/752_06/errata. Linear Functional Analysis (FREE! Kolmogorov A. Analysis: An Introduction .
Rings and Fields Mitchell J.pdf) In general: Group Theory (FREE! to Become a Pure Mathematician Page 22 of 66 Rudin W.ac. like Platonic solid and wallpaper patterns.uk/~anskor/notesM2P4. Bergman's supplement exercises ( Real Analysis/Advanced Calculus (FREE! Tao T.phtml) Milne J.pdf) Saxe K. Topics to be covered are basic group.uk/~ajb/2q/index.org/math/CourseNotes/math594g. Groups and Symmetry . Baker A. Groups. Introduction to Topology and Modern Analysis .harvard.ps).hndts/06x2+03F_104_q+a.ac. You will see how we study symmetry.mcs.ucla.tcd. Principles of Mathematical Analysis .A.com/mathphyweb/puremath. This book deals with several topics. A modern classic.maths.math. Rings and Fields Lecture Notes (FREE! Rings and Fields (FREE! and Evelyn Silvia's Companion Notes ( ring and field theory.txt).maths. Simmons F.math.ac. See also George M. notes ( Symmetry and Fractals (FREE! Beginning Functional Analysis . Analysis 2 (FREE! Skorobogatov A.edu/~emsilvia/math127/math127.Baby Rudin.berkeley. Sternberg S. Only discuss Groups: Armstrong M.st-and.html) Rings and Fields: Chambert-Loir A. General Topology and Real Analysis (FREE!
.edu/~gbergman/ug.N.jmilne.edu/~tao/resource/general/131bh.openmathtext.edu/~gbergman/ug.' said the author.Nice mathematical writing.R. groups measure symmetry.edu/~shlomo/docs/Advanced_Calculus.G.hndts/m104_Rudin_notes.gla.html).math. Santos D.'Numbers measure size.ie/~dwilkins/Courses/221/) Abstract Algebra: One of the beautiful branches of mathematics.hndts/m104_Rudin_exs.Large proportion of this book can be studied at this stage. Advanced Calculus (FREE! http:/www. which introductory abstract algebra texts usually skip.geocities. Get a copy and play around with it. A Field Guide to Algebra Ellis G.edu/~gbergman/ug.03s/) Wilkins D.ps) and q&a (
pdf). Artin was his supervisor.If you could afford this. and Foote R. See also Afra's incomplete notes ( hundreds of figures.D. Abstract Algebra Done Correctly (FREE! A First Course in Abstract Algebra . you may simply follow his list at this stage.B. Contemporary Abstract Algebra .dartmouth. biographies. Higher Algebra Lecture Notes (FREE! it's best to attend Daniel's lecture. Basic Algebra I . Abstract Algebra .pdf) Gilbert W. Goodman F.html) Herstein I. Ideal for a first coures. Modern Algebra with Applications Gillian J. A First Course in Abstract Algebra: Rings. See the author's website ( Abstract Algebra (FREE! the author have said. and numerous tables and charts.New edition of his Lectures in Abstract Algebra. dozens of photographs. Garrett P.pdf) Artin M.html) Jacobson N.edu/~afra/goodies/abstract.edu/~ec/book/) Dummit D.H. Read sections recommended by the authors in the preface. Groups. Connell E. he gives a good introduction abstract algebra for newbie. Abstract Algebra Online Study Guide (FREE! but this is the one you like to keep in your own library.dir/algebrabook.uvm. and Fields Arapura D.uiowa.math. My lecturer recommended this partly because M.torget.au/~danielch/algebra07a/qinnotes.cs. See Foote's web ( Algebra: Abstract and Concrete (FREE! Clark A." If you prefer those things. Standard recommended text in the U.htm) Chan D. Artin.pdf) . and Blair W. historical notes.S.M. As M.Diagram omitted.Kind of handbook.edu/~garrett/m/intro_algebra/notes.edu/~jgallian/) for resources.emba. Algebra . and Mac Lane S.d. this book includes 'lines from popular songs.A.umn. Fraleigh J. Beachy J.math. Elements of Abstract Algebra . Artin states in "A Note for the Teacher" that several sections would make a coherent course.se/users/m/mauritz/math/alg/index.Not aimed at this level.html) Birkhoff G. Elements of Abstract and Linear Algebra (FREE! quotations.edu/~foote/) for errata. and Feil T.htm
.maths. Abstract Algebra Ikenaga B.M. I recommend this but I have no direct relationship with M.How to Become a Pure Mathematician Page 23 of 66 Anderson M.miami. A Survey of Modern Algebra Blomqvist C.edu. Intro to Abstract Algebra (FREE! made it. leave others to the next stage. Algebraic Systems (FREE! poems.math.
How to Become a Pure Mathematician Page 24 of 66 Knapp A.W. Basic Algebra - See the web ( for correction. Rotman J.J. A First Course in Abstract Algebra - Check out Rotman's page ( for errata. Shahriari S. Lectures on Algebra I (FREE! 李華介:大學基礎代數 (FREE! - The best free material on introductory abstract algebra I have seen so far, provided you can read Chinese. Introductory Number Theory: Gauss once said "mathematics is the queen of sciences and number theory the queen of mathematics." G..H. Hardy once said in A Mathematician's Apology that, "If the theory of numbers could be employed for any practical and obviously honourable purpose, if it could be turned directly to the furtherance of human happiness or the relief of human suffering, as physiology and even chemistry can, then surely neither Gauss nor any other mathematician would have been so foolish as to decry or regret such applications. But science works for evil as well as for good (and particularly, of course, in time of war); and both Gauss and less mathematicians may be justified in rejoicing that there is one science at any rate, and that their own, whose very remoteness from ordinary human activities should keep it gentle and clean." He wrote it on November 1940. It turned out coding theory, where algebra and number theory are applied, played a key role in the World War II. Adler A. and Cloury J.E. Theory of Numbers: A Text and Source Book of Problems Baker A. Algebra and Number Theory (FREE! Burton D.M. Elementary Number Theory - One of the better books for an introduction. Chen W.W.L. Elementary Number Theory (FREE! Clark W.E. Elementary Number Theory (FREE! Coppel W.A. Number Theory: An Introduction to Mathematics: Part A, B - You may leave Part B to the next stage. Dantzig T. and Mazur J. Number: The Language of Science - Non-mathematical treatment indeed. Dirichlet P.G.L. Supplements by Dedekind R. Lectures on Number Theory Erdos P. and Suranyi J. Topics in the Theory of Numbers Everest G. and Ward T. An Introduction to Number Theory Fine B. and Rosenberger G. Number Theory: An Introduction via the Distribution of Primes Ikenaga B. Number Theory (FREE!
How to Become a Pure Mathematician Page 25 of 66 Joens G.A. and Jones J.M. Elementary Number Theory Moser L. An Introduction to the Theory of Numbers (FREE! Nathanson M.B. Elementary Methods in Number Theory Niven I., Zuckerman H.S. and Montgomery H.L. An Introduction to the Theory of Numbers Parent D.P. Exercises in Number Theory Redmond D Number Theory Rosen K.T. Elementary Number Theory - See the website ( for supplementary material. Santos D. Number Theory Notes (FREE! Sato N. Number Theory (FREE! - IMO level. Shoup V. A Computational Introduction to Number Theory and Algebra (FREE! Silverman J.H. A Friendly Introduction to Number Theory - See the web ( for extra material. Stein W. An Explicit Approach to Elementary Number Theory (FREE! Stein W. Elementary Number Theory (FREE! 李華介:基礎數論 (FREE! Introductory Topology: Topology is an extension of geometry and built on set theory, it's about continuity. There is a joke that topologists are those who cannot distinguish between a doughnut and a coffee or tea cup. Wikipedia has a [.gif] to demonstrate this ( You may have studied open sets, open neighbourhood, interior, closure, boundary, basis, continuity, compactness and connectedness etc. in the analysis course, move on to homemorphism, homotopy and fundamental group. As in abstract algebra and analysis, several selected books or notes cover more than enough. You may leave a few sections to study at the next stage. Crossley M.D. Essential Topology - Undergraduate introductory level, detailed explanation. Davis S.W. Topology - It's like lecture notes, many proofs are left as exercises and many exercises are proofs. Dugundji J. Topology - Another topology text with quality. Engelking R. General Topology Gemignani M.C. Elementary Topology Henle M. A Combinatorial Introduction to Topology - Plenty of illustrations. Indeed many
How to Become a Pure Mathematician Page 26 of 66 concepts in this subject can and should be visualised. Ikenaga B. Notes on Topology (FREE! McCluskey A. and McMaster B. Topology Course Lecture Notes (FREE! Mendelson B. Introduction to Topology - Very nice introduction to the metric spaces, topological spaces, connectedness and compactness. Recommended for first reading. Moller J.M. General Topology (FREE! Morris S.A. Topology Without Tears (FREE! Munkres J.R. Topology - Another nice introduction. Go further than Mendelson's one. Also cover topics like the Tychonoff theorem, metrization theorems, complete metric spaces and function spaces, the fundamental group and covering spaces. Singer I.M. and Thorpe J.A. Lecture Notes on Elementary Topology and Geometry Steen L.A. and Seebach J.A. Counterexamples in Topology Strickland N. Topology Notes (FREE! Thurston W.P. The Geometry and Topology of Three-Manifolds (FREE! Ward T.B. Topology Lecture Notes (FREE! Wilkins D.R. Topology (FREE! Differential Geometry: You may wonder, geometry takes up a large portion in high school mathematics, why isn't there any geometry course in the first two stages? In fact, geometry is kind of imbedded in stage two calculus (several variables) and linear algebra courses, they are usually assumed and will be used for this course. Here differential calculus is used to study geometry. Key things to study: multilinear algebra, curvature and torsion, Serret-Frenet equation, fundamental theorem of curves, Poincaré Index theorem (plane and surface), exterior calculus, Gauss' theorema egregium, geodesics, Gauss-Bonnet theorem. Moving frame, due to Élie Cartan, is an approach to geometry of surface. According to my lecturer John Steele, it is "computationally the easiest, notationally the neatest, aesthetically the best, makes the definitions more natural and the proofs of the two major theorems easier. The moving frame method also points the way towards several important ideas in modern differential geometry and theoretical physics. The downside (if there is one) is the reliance on exterior calculus of differential forms." O'Neill, for example, uses this approach and he manages to prove Gauss' theorema egregium in half page, see p.281. In general:
Fowler A.stat. you will learn here the Cramer-Rao bound.edu/~r-ash/Stat. introductory non-parametric (including the sign test.pdf) Statistical Inference (optional): Build upon stage 2 statistics. Wilcoxon signed rank test.B. sort of.Detail explanation.ac. Used widely in grad school. The Nature of Mathematical Modeling Giordano F. and Fox W. Unlike the rest recommended texts for this course.P.T. Weir M.pdf) Fowler A.17) and Statistical Swindles (p.cmu. but perhaps too concise as a textbook. partly because people from other fields only learn this material in graduated schools.. Spearman's R and Kendal's Tau). An Introduction to Mathematical Modelling (FREE! Geometry of Differential Forms Mathematical Modelling (optional): "All models are wrong. stage 2 stuff) for them.J. Lectures Notes on Mathematical Modeling (FREE! basic bootstrap and robustness. Wald-Wolfowitz runs test.. etc.geocities.D. stage 2 probability and statistics is the assumed knowledge for this text.H. Statistical Inference . Kolmogorov-Smirnov two-samples test. Can be served as a reference.A standard text.J.html) Bain L. Jolliffe I. for example: "Probability Zero Does Not Mean Impossible" (p. some are useful. as a result the texts have to set up basic probability and statistics (you have done it.uiuc.45). uniform minimum variance unbiased estimators.pdf) Gershenfeld N. but not the main concern of pure mathematician.pdf). and Schervish M.How to Become a Pure Mathematician Page 28 of 66 Morita S. McNemar's chi-square test.M." George Box.edu/~mark/degroot/typos/typos. Check out the typo page ( a few good comments.H.R. Mann-Whitney U test. Introduction to Probability and Mathematical Statistics Casella G. and Engelhardt M. Garthwaite P.maths. Mathematical Modeling Veeh J. Probability and Statistics . Lectures on Statistics (FREE! Techniques in Applied Mathematics (FREE! and Jones B.uk/~fowler/courses/o11intro/o11notes. Bayesian inference.html). Statistical Inference . Neyman-Pearson theory.C.ox.htm
. and Berger R. Ash R.math.com/mathphyweb/puremath.uk/~fowler/courses/tech/technotes.ox. Solutions Manual available on web ( Common misconceptions are mentioned. A First Course in Mathematical Modeling Meerschaert M. DeGroot M. Using mathematics to model real world phenomena is useful. Kruskal-Wallis analysis of ranks.L.C. Note a few texts say they are aimed at graduated level.
htm
. 1 . Random Variables.R. it's a pain for customers to correct such long list of typos. See also left material from stage 2 probability. This topic is particularly useful for electrical and computer engineers. and Taylor H. Schaum's Outline of Probability. reliability theory. Quite professional.html) Grimmett G.ellerman. If you want to learn this with measure. Check the at: Tutorial Notes (FREE! Introduction to Statistical Signal Processing (FREE! S1 S12. and Davisson L. Poisson process.pdf) Young G. Graybill F.M.ndml/1175196978) Weber R. Statistical Inference in Science Wald A. see stage 4 probability list. Statistics (FREE! bit advanced for a first course. Markov chains.V.stat. not so user friendly for people from other fields.. Introduction to the Theory of Statistics .edu/~lebanon/notes/) . On the Principles of Statistical Inference (FREE! text modernised. and Stirzaker D.M.geocities.G.T. An Introduction to Probability and Statistical Inference Sprott D. Mathematical Statistics and Data Analysis .As my lecturer Spiridon Penev have said. Lebanon G.edu/~gray/sp.com/mathphyweb/puremath.html Roussas G. and Random Processes Karlin S."A colorful and rich introduction to probability theory and its applications" according to Karlin and Taylor.W. queueing theory.berkeley.edu/lowry/webtext.org/euclid. Essentials of Statistical Inference . Mukhopadhyay N.A.purdue.G. Probability and Statistical Inference Rice J." Gray R. McKean J.pdf) Feller W. Probability and Stochastic (Random) Processes (optional): Conditional expectation. and Rota G. and Boes D.How to Become a Pure Mathematician Page 29 of 66 Hogg R.A.The main feature of this book is that it contain lots of figures. Brownian motion and stationary processes.. Baclawski K.A.uk/~rrw1/stats/notes. and Smith R.C.wmich. 11 pages of errata ( perhaps.stanford.D.stat..R.L. A Course in Mathematical Statistics Roussas G. Concepts and Applications of Inferential Statistics (FREE! A First Course in Stochastic Processes Mood A.vassar.M.-C.ac. Introduction to Mathematical Statistics . Probability and Random Processes Hsu H.statslab.cam. An Introduction to Probability Theory and Its Applications Vol. renewal theory..edu/mckean/HMC/). and Craig A. finance or things like that. Lowry R. An Introduction to Probability and Random Processes (FREE! actuarial study. this text is a bit outdated but it contains useful exercise problems. If you are serious about Statistics. but it "is limited in that it deals only with discrete probabilities.
stat.edu/~wlr/126notes. analyses and examples from the book are available at Lecture Notes on Probability Theory (FREE! to Become a Pure Mathematician Page 30 of 66 Krishnan V.pdf) 《R 導論》《R 文檔》(FREE! , Venables B.ps) Papoulis A. Dalgaard P. in practice.et. so he includes the topic survival analysis in this introductory text.J.bs. Mörters P. and Hothorn T.org/).D. not an introduction to basic probability theory. so I recommend books of this kind.The author is a biostatistician.edu/~lebanon/notes/) .stat. Tutorial Notes (FREE! no graph has been used when the author introduce Markov chains for the first time.See their web ( Walrand J.mhhe.es/~etptupaf/pub/R/Rlecturenotes. Also note that. A Handbook of Statistical Analyses Using R . Ross S. and Olson M.pdf) Spector P.edu/users/rice/Stat230A/SpectorIntroR.pdf) Yates R.org/pages/newhtm/r/tchtml/ and Probability. An Introduction to R: Software for Statistical Modelling and Computing (FREE! and Smith D.Note this is an introduction to probability and stochastic processes. R Tutorial (FREE! and Venables B.r-project.Read R1 R5. Introduction to Probability Models .ehu.M. Random Variables and Stochastic Processes .com/mathphyweb/puremath.D. data sets.pdf) Ripley B.eecs.org/web/packages/HSAUR/index.uk/maspm/prob.org/R/R-doc/) An Introduction to R (FREE! This text could be quite hard to follow without knowing very basic probability theory.M. R 丁國徽譯: Probability and Random Processes Lebanon G.edu/stat/SPLUS/library/sguide.pdf) Spector P.html .berkeley.ac. An Introduction to R (FREE! you can't do statistics without computer. Introductory Guide to S-Plus (FREE! S-PLUS uses the same language.edu/users/rice/Stat230A/SpectorRtutorial.M. The Basics of S and S-Plus Kuhnert P.com/engcs/electrical/papoulis/) for resources. Krause A. in particular the section "an Introduction to R" is completely included free on web.bath.berkeley. Everitt B. and Smith D.biosino.Many functions. and Goodman D. Probability and Stochastic Processes: An Friendly Introduction for Electrical and Computer Engineers Statistical Computing (optional): These days.berkeley. R is a freeware ( Introductory Statistics with R .geocities.r-project.htm
.pdf) Venables B. Lecture Notes on Probability Theory and Random Processes (FREE!
Modern Applied Statistics with S .More advanced topics are covered.pdf).htm
.edu/~calvinw/MthSc885/yakirsplus.ox.clemson. See also B.N. See their web (
to Become a Pure Mathematician Page 31 of 66 Venables W.ces.stats. Yakir's notes ( for extra material. and Ripley B.ac.geocities.D.com/mathphyweb/puremath.
G. Principia Mathematica (FREE! Mathematical Logic . Crossely J. Set Theory.umich.edu/simpson/foundations. I'm far from being an expert. or the basic graduated year in other places. further reading in Number Theory and algebraic geometry in Geometry.PDF)
Foundations and Discrete Mathematics: Foundation: Courant R.edu/AAT3201. e.org/bertrand-russell/the-principles-of-mathematics/) Simpson S. and Russell B.math.. let me know if you have a suggestion! Note that at this stage. and Hodges W. and Russell B. and Williams N. mind you.ac..Interested reader may find his paper Logic and Mathematics ( What is Mathematical Logic? Barwise J. Wittgenstein L.C.psu. Mathematics: Form and Function Russell B.html) worth reading.Oxford Texts in Logic 3.How to Become a Pure Mathematician Page 32 of 66 Stage 4 Equivalent to the (fourth) honours year in Australia. Stillwell J. Remarks on the Foundations of Mathematics Logic.First part of the landmark work.shef.Not for beginners. A few subfields may be highly related. The Principles of Mathematics (FREE! Bornat R.N.com/mathphyweb/puremath. the levels or difficulties of books within a certain topic may vary a lot. Set Theory (FREE! I shall outline the key topics and give short lists of references. Moreover.pdf) . Chiswell I.. What Is Mathematics? An Elementary Approach to Ideas and Methods Mac Lane S.N.: Ash C. Brickhill C. Whitehead A.0001.G. Introduction to Mathematical Logic Dixon P.H. Church A.) Handbook of Mathematical Logic . etc.J. Principia Mathematica to *56 . Foundations of Mathematics (FREE! (ed.umdl. Proof and Disproof in Formal Logic: An Introduction for Programmers .Oxford Texts in Logic 2.math.uk/teaching/STDN. you may scout around to see what makes you interest.htm
.staff.001) Whitehead A.psu. further reading should belong to stage 5.J. and Robbins H.
Prime Numbers: A Computational Perspective Guy R.u-bordeaux1. Introduction to Homological Algebra (FREE! Freyd P. algebraic number theory employs algebra result to number theory.rutgers.math.H. A Course in Homological Algebra Kashiwara M.utwente.math.html consists links to online number lecture notes. Crandall R. Algebraic Number Theory Archives ( Number Theory: Volume I: Tools and Diophantine Equations Cohen H. Ireland K.mta. Categories and Sheaves Lawvere F. Fermat's last theorem and the Poincaré conjecture have been solved.pdf) Fokkinga M.J. A Concise Introduction to the Theory of Numbers Cohen H.edu/Algebraic-Number-Theory/) provide papers for further study. and Rosen M.A. In general: Baker A.numbertheory.ac.tac.geocities.This site ( An Introduction to Homological Algebra – Correction: Introduction to Modern Number Theory: Fundamental A Gentle Introduction to Category Theory: The Calculational Approach (FREE! Hilton P. It is recommended you have a solid background of algebra before you begin to study algebraic number theory. Conceptual Mathematics: A First Introduction to Categories Mac Lane S.html Number Theory: There are several branch of Number Theory and we focus in algebraic and analytic here.html Solution by Jinhyun: and Pomerance C. Abelian Categories (FREE! Homology Rotman J.M.W.org/ntw/lecture_notes.edu/~weibel/Hbook-corrections.html) .com/mathphyweb/puremath.math.K. Riemann hypothesis is one of the Millennium Prize Problems.M.ca/tac/reprints/index.ca/tac/reprints/articles/3/tr3abs.A must have for this field.I.nl/~fokkinga/mmf92b.uiuc.html) consists dozens of Reprints in Theory and Applications of Categories for further reading.See his web ( and Schapira P. and Schanuel S.math.htm
.H.purdue.edu/~jinhyun/sol2/weibel. Categories for the Working Mathematician Mac Lane S. Unsolved Problems in Number Theory Hardy G.maths. and Wright E.A. An Introductory to the Theory of Numbers . and Panchishkin A. analytic one applies analysis theory. Number Theory: Volume II: Analytic and Modern Tools .cs. and Stammbach U.J.tac. As the title indicated.uk/personal/ibf/ha/ha.How to Become a Pure Mathematician Page 42 of 66 Fesenko I.fr/~cohen/) for errata list. Introduction to Homological Algebra Weibel C. A Classical Introduction to Modern Number Theory Manin Y.mta. this is probably the biggest challenge to date.
info/Mathematics.geocities.edu/OcwWeb/Mathematics/index.ams. and possibly more than that.htm
•
•
.cambridge.emis. Several books in the list above give suggestions for further reading.How to Become a Pure Mathematician Page 65 of 66 Stage 5 By completing stage 4.org/uk/series/sSeries. a.html FreeScience • Cambridge University Press: Cambridge Studies in Advanced Mathematics etc) Moreover.org/uk/series/sSeries.'s Modular Abelian Varieties page Now you probably know what's going on and you should have an idea what you can read.65/mathdoc/ • Stein W. you may refer to them according to your interest.com/mathphyweb/puremath. My list ends here.com/west/home/math?SGWID=4-10042-69-173621337-0 • Springer: Grundlehren der mathematischen Wissenschaften (I've listed a few of them in the above list) List of books: American Mathematical Society: Graduate Studies in Mathematics The Electronic Library of Mathematics Riesz and Sz.asp?code=CSAM • Cambridge University Press: London Mathematical Society Student Texts Yosida.springer.springer. You've completed an undergraduate mathematics program (who cares about certificate?). This is (partly) because the entry requirement of mathematics degree is usually not so high (but don't expect it's easy) and folks fall into such program accidentally and they don't have to pick those abstract courses.cambridge. e.g. Baby Rudin and Big Rudin.php Scanned text (mostly Chinese.38.math. abstract algebra or topology courses. you should be ready for graduated schools.cambridge. check out: American Mathematical Society Books Online: • • • • MIT's graduate courses list: • Springer: Universitext • Springer: Graduate Text in Mathematics GTM I've seen mathematics graduates haven't taken any analysis. Harthsorne. choices decrease as stages increase. For more advanced FREE! materials.e. Believe it or not.asp?code=LMST • Cambridge University Press: London Mathematical Society Lecture Notes Series Halmos.126.
How to Become a Pure Mathematician Page 66 of 66 • Dover books in mathematics Harvard Mathematics Qualifying Exam what can you do with your mathematical knowledge? There are a few options (ideas by James Franklin.maths.cam.org Project Euclid
. better diagnosis Teaching.math.html#past After several extra stages.edu/ arXiv.edu/graduate/index. etc) Optimization for resources planning Statistical research on effectiveness of drugs and medical procedures. if it turned out that you're not going to further your study in pure mathematics. weather prediction.com/by-subject-science-and-mathematics-mathematics.princeton.com/mathphyweb/puremath.html Want challenging questions? See: Mathematical Tripos Examination Papers given in the 'Professional Issues and Ethics in Mathematics' course): Modelling of environment (related areas are global warming.org/
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After all. try: Annals of Mathematics to inspire (or corrupt?) the next generation
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if you feel like you are ready to read journals. | 677.169 | 1 |
The third quarter has started and run from January 20 - April 10, 2015
Algebra 1:The third quarter will be spent studying linear functions. Students will be tasked with numerous studies and activities that allow them to delve into what functions are and how they behave when being manipulated. In addition students will learn about slope, independent and dependent variables, time versus distance graphs, and how to represent functions in various way to convey a message. This is the first time students will represent solutions to sequences and patterns in a visual way by using graphs and linear models. Pre-Algebra: The third quarter will focus on building up the students' ability to reason and make connections between various mathematical concepts. This is a critical time in the students' life, as it will serve as the base for higher mathematical learning. Students will begin their studies of linear functions by analyzing them piece-by-piece before putting it all together toward the end of the quarter. Some of the topics that students will analyze are slope, proportional relationships, graphing, and linear relationships.
Please feel free to contact me with any questions of concerns you may have. | 677.169 | 1 |
Yeah, start easy
I agree that the switch of notation is the biggest obstruction. You will probably find a book like "Foundations of higher mathematics" by Fletcher and Patty quite useful. It's an introduction to things like logical statements, ways to prove something, sets, functions and all the other basic things you encounter anywhere in mathematics, introducing a lot of notation.
About the Greek alphabet, don't worry - you'll get used to it. You will learn the letters as you go; the most common ones such as [itex]\phi, \psi, \alpha, \beta, \theta[/itex] you will pick up rather soon, others you will only encounter only much later (some fellow students who didn't take Greek only learned some of them in the third year in university).
I'm about to learn advances of mathematics. However, notations, symbols, such as Greek, etc, makes me MORE difficult to learn it. Does anyone here know the way to solve this problem and get easier?
Your worry expressed indicates the stress of transitioning from "Basic Mathematics" to Introductory Algebra. Maybe you are really trying to transit from Introductory Algebra into Geometry. What you need is the ability to read critically and practice. Notation will always be important. Mathematics works like a written language. It is not the same to use as a natural human language. Mathematics is nearly always handled in written form, and so notation, just as in written English, will always be important for clear communication.
Yeah, it's probably the subtle difference between "advances" and "advanced" that I initially missed as a non-native English speaker, mainly looking at the title
I admit it is a bit ambiguous though. So sorry if I misinterpreted your question. | 677.169 | 1 |
Function Graphing
fKey Template Designer v2.1 - $40 from SigmaTech Software. A design tool to construct and print a keyboard template of a programs function key and shortcut key combinations. The program presently can print a template to fit all known keyboard layouts. You may have up to six rows of function key combinations and 24 shortcut key combinations. The template may be adjusted for three row function key combinations with either an alt key or ctrl key.
GraphSight is a feature-rich comprehensive 2D math graphing utility with easy navigation, perfectly suited for use by high-school an college math students. The program is capable of plotting Cartesian, polar, table defined, as well as specialty graphs. Importantly, it features a simple data and formula input format, making it very practical for solving in-class and homework problems. The program comes with customizable Axis options, too.
Turns your PC into an incredible math machine! Have fun with live interactive graphing tools for linear functions, parabolas, ellipses, circles and more! Use any of 5 parameters simultaneously in graph and function definintions to model real life problems and create working demonstrations! Many interactive tools for tracing around functions, finding integrals, roots, turning points and more. Calculate statistics with full working steps shown!...
SPROC Function Builder is a tool for writing functions to access SQL Server stored procedures (SPROCs). The program is not limited to any specific language so you can write your code in ASP,.NET or pretty much any other language and still save hours with this little utility. SPROC Function Builder uses an easy to learn template syntax, that is also available from the right click menu in the built-in editing screen (with syntax highlighting).
active graph rotation, fogging effect, cubic draw, unlimited space ploting, four view plot screen, auto rotate animation, drawing many curves in the same screen,working with many graph screen est.Math Function Mania is a fun multimedia game for grades 7-12 that teaches functions, algebra and problem solving skills. You must first detect which function is being used, and then solve it by clicking on the correct answer. Includes a head-to-head combat option for two-player competition. This game will take some of the mystery out of functions | 677.169 | 1 |
Keith Erich Johnston, KS
The program helped my son do well on an exam. It helped refresh my memory of a lot of things I forgot. Leilani Jekar, CA Alan Cox, TX
Thank you! I was having problems understanding exponential expressions, when my friend told me about the Algebrator Software. I can't believe how easy the software made it for me to understand how each step is preformed | 677.169 | 1 |
Course Description
From the course catalog:
Introduction to the mathematics fundamental to all phases of computer
science, from the formulation of problems to the understanding of
their underlying structure, to the comparative analysis of the
complexity of algorithms that can be used to solve these problems. The
course introduces combinatorics, first-order logic, induction, set
theory, relations and functions, graphs, trees, and number theory.
Grading | 677.169 | 1 |
Pre-Calculus – Segment 1
Feb 24, 2016
Credits: 0.5 Term: Fall 2017, On Demand Prerequisites:
Algebra I, Geometry, Algebra II
Course Description:
Students, as mathematic analysts, investigate how advanced mathematics concepts are used to solve problems encountered in operating national parks. As students venture from algebra to trigonometry, they analyze and articulate the real-world application of these concepts. The purpose of this course is to study functions and develop skills necessary for the study of calculus. This course includes algebra, analytical geometry, and trigonometry.
eBook needs to be purchased. To purchase, visit Cost of eBook is $30.90 | 677.169 | 1 |
MATH281 Introduction to Mathematical Reasoning, Fall 2007
Objectives
Introduce the student to mathematical reasoning and proof. Present techniques
and methods which are necessary for higher level math courses.
Enforce a better understanding of logic, different kinds of numbers, notation,
concepts from analysis, number theory, algebra and combinatorics.
Enhance the understanding of functions and relations between arbitrary sets. | 677.169 | 1 |
Calculus offers some of the most astounding advances in all of mathematics—reaching far beyond the two-dimensional applications learned in first-year calculus. We do not live on a sheet of paper, and in order to understand and solve rich, real-world problems of more than one variable, we need multivariable calculus, where the full depth and power of calculus is revealed.
Understanding Multivariable Calculus: Problems, Solutions, and Tips, taught by award-winning Professor Bruce H. Edwards of the University of Florida, brings the concepts of calculus together in a much deeper and more powerful way. Building from an understanding of basic concepts in Calculus I, it is a full-scope course that encompasses all the key topics of multivariable calculus, together with brief reviews of needed concepts as you go along. This course is the next step for students and professionals to expand their knowledge for work or study in mathematics, statistics, science, or engineering and to learn new methods to apply to their field of choice.
The Larson CALCULUS program has a long history of innovation in the calculus market. It has been widely praised by a generation of students and professors for its solid and effective pedagogy that addresses the needs of a broad range of teaching and learning styles and environments. Each title is just one component in a comprehensive calculus course program that carefully integrates and coordinates print, media, and technology products for successful teaching and learning. | 677.169 | 1 |
Survey of Mathematics
MAT 101
Science, Technology, Engineering & Math
Credits: 3
Students will discover the power of mathematics as a foundation for lifelong learning. As they explore various real world applications, students will strengthen their critical thinking, quantitative analysis, and problem-solving skills, as well as discover connections between mathematics and other disciplines. Topics will include logic, probability, statistics, and personal finance. Additional topics may include voting and social choice, geometry, graph theory, and symmetries. This course is intended for students who do not need higher level mathematics for their program. Prerequisite: MAT 098, placement in MAT 100 or higher or by permission of instructor. | 677.169 | 1 |
"How To Solve It" by George Polya, a classic book published in 1945, suggests steps in solving a problem – mathematical or otherwise. The book includes advice for teaching students of mathematics and a mini-encyclopaedia of heuristic terms. Teachers and parents would find it easy to explain problem solving discipline to children. Students will benefit by using the simple framework and tips from Polya. In schools, mathematics question papers contain only problems. In science, a sure way to score better is by attempting all the numerical problems in question papers.
I strongly suggest that parents, teachers and students study "How To Solve It."
While teaching a few lessons to high school students, I used a modified approach and found it simple and effective. I have tried this approach to teach solving problems in a chapter on heat in Physics text book and a chapter on Equity Shares in Mathematics text book. Let us trace the steps in solving a problem on heat.
Preparatory step:
Identify the chapter of the problem.
List all the formulae in the chapter. A problem from the chapter would certainly use the formulae partly or fully.
3. Make a table with one column per variable in the set of formulae. Include the units of measure for each variable, in SI units. In the table, t1 is the starting temperature and t2 is the ending temperature of the process in a step.
m Kg
c : J/(kg*K)
ΔQ J
t1 OC
t2 OC
ΔT
L J/Kg
Understand the Problem
The following diagram summarises the theory the student has studied in the chapter on Heat.
Example Problem: Calculate the total amount of heat energy required to convert 100 g of ice at -10OC completely into water vapour at 150OC.
4. Values in the problem would map to one of the variables in the formulae. Make one row per sample item in the problem and enter the values under appropriate variables.
In the problem above, we have 5 samples representing each phase of the conversion of sub-zero ice and super-heated steam: heating ice, melting ice, heating water, vaporising water, and heating steam. Thus we would have 5 rows. Add a row for Total values as the problem requires us to find the total energy.-10
0
melting ice
0.1
0
0
3,36,000
heating water
0.1
4,200
0
100
vaporising water
0.1
0
0
22,60,000
heating steam
0.1
2,000
100
150
Total
Values of specific heats and latent heats may be given in the problem or the student may be expected to know them.
Important: If the problem has given values in different units, convert to SI units. This applies to values of specific heat and latent heat in the current problem. A common cause of error is using inconsistent units for variables
5. Picking up values of different variables from the table, calculate and fill values in empty cells.
– I have made a copy of the table to demonstrate the steps. In practice, we would fill the values in the table of the previous step.
– Here, I show the derived values in blue. While working on paper, we may encircle the interim results from solution steps.
– From t1 and t2, calculate ΔT for each row.
– Energy required to bring the temperature of heating ice from 10 to 0 OC
ΔQ = c m ΔT = 2,100 * 0.1 * 10 = 2,100 J
– Energy to convert melting ice to water at 0OC
ΔQ = m L = 0.1 * 3,36,000 = 33,600 J
– Energy to heat water from 0OC to 100OC
ΔQ = c m ΔT = 4,200 * 0.1 * 100 = 42,000 J
– Energy to vaporise the water at 100OC
ΔQ = m L = 0.1 * 22,60,000 = 2,26,000 J
– Energy to heat steam from 100OC to 150OC
ΔQ = c m ΔT = 2,000 * 0.1 * 50 = 10,000 J2,100
-10
0
10
melting ice
0.1
33,600
0
0
0
3,36,000
heating water
0.1
4,200
42,000
0
100
100
vaporising water
0.1
2,26,000
0
0
0
22,60,000
heating steam
0.1
2,000
10,000
100
150
50
Total
3,13,700
6. From the interim results, calculate the final answer and insert in the table. On paper, we could underline the final answer, which is shown in red here.
Total energy spent = 3,13,700 J
7. Review the answer. Before re-calculating, compare the relative energy spent in various phases, recorded in ΔQ column, and check if they conform to the relative lengths of X axis in the picture for different phases.
With a different approach, we have used tables to teach and summarise lessons from other subjects like History and languages. We can discuss about them in another blog.
In the mean time, if you would try this approach as parents, teachers, students or out of curiosity, and give feedback at bhat.pg@gmail.com , I shall be grateful. The feedback will help refine the approach.
2 Responses to Tabulate Early
The approach i recollect having used in school didn't use tables but was similar in approach. Example, delQ = m*c*delT
Given information:
delQ?
m = 0.1 KG
c = 2400 J/(Kg*K)
delT = 10K
Substituting into, formula, we get delQ = 0.1*2400*10 = 2400J
I wonder if you agree that the tabular approach is similar. Or does it do anything different?
Also, I agree that the tabulation approach might help structure the information for students.The key with new learning methodologies is that it is worth testing with a set of students. Example, 2 sections of the same class in the same school can use two different approaches (9A Vs 9B). One gets taught the regular method and another the tabular approach. One can get concrete data on the impact. I imagine it's hard to rope in teachers willing to experiment. In its absence, some anecdotal evidence would be useful.
There is no difference in the steps in solving the problem. I hope that the tables would help in visualising the relations by putting all the data in one place. It could prompt to convert all the values to SI units.
Informal feedback from the students and teachers was encouraging. That could also be out of their personal regard for me. I have to try this in a school that does not know me.
Now it is very close to the final examination for the students. I would like to try this approach on one section of a class and then compare with the other that does not use the approach. | 677.169 | 1 |
Further reading
Other events
The course covers the following essential topics in mathematics: back to basics (percentages, proportions, averages), data and tables, describing and visualising data, measures of spread, transforming data, concepts in algebra and common symbols, geometry of a straight line, limits and continuity, derivatives and more, maximisation in statistics, correlations, vectors and matrices, solving a multivariate regression problem.
There will be exercises and examples of the use of these concepts in mathematics for statistical applications.
The course is designed for those interested in pursuing more advanced courses on statistical methods for the social sciences. Some basic understanding of research methods in statistics is required, eg. regression modeling. It is recommended that the students carry out pre-reading according to the reading list below in preparation for the course. | 677.169 | 1 |
Matlab英文教材3
发布时间:2013-10-23 13:44:15
Mathematical Methods (10/24.539)
III. Overview of Linear Algebra
Introduction
The subject of Linear Algebra, in general, covers a broad range of topics. Our goal in this unit is simply to review the standard concepts needed for other subjects in this course. In particular, we will first cover the basic notation and operations associated with vector and matrix algebra and then focus on systems of linear equations, including both inhomogeneous and homogeneous equations. The homogeneous systems, of course, also lead to the important subject of
eigenvalues and eigenvectors of a matrix. The classification of matrices based on the properties of their eigenvalues and eigenvectors is also discussed briefly. Finally, a demo is provided to illustrate how to perform many of the analytical operations outlined in this unit within the Matlab programming language.
The subjects reviewed here are treated as part of most undergraduate engineering programs (although you may not have had a formal course in Linear Algebra). As such, this section of notes is primarily intended as review material. Students already comfortable with this subject material should quickly browse this section to become familiar with the specific notation used here, and also to become acquainted with performing many common and very useful matrix-vector operations within the Matlab environment. Students weak in this subject are encouraged to study these notes thoroughly and to consult other reference books on this subject as needed. The key topics treated here are: ? General Notation
? Gauss Elimination
? Determinant of a Matrix
? Matrix Inverse
? Rank of a Matrix
? The Case of n Equations and n Unknowns ? Overview
? An Example ? Three Special Classes
? Quadratic Forms
? Similar Matrices
Math Methods -- Section III: Overview of Linear Algebra 2
Basic Notation and Operations
This section introduces some terminology and notation from linear algebra and also outlines some basic arithmetic operations with vectors and matrices. Let's start by defining some notation associated with vectors and matrices.
Note: In the technical literature, vectors and matrices are usually written with bold lower and upper case letters or as variables with a single underline or double underline, respectively, for 1-D vectors or 2-D matrices. In my courses, I use both of these notation schemes so that the students become familiar with a variety of forms for representing these quantities. In this section, however, I have tried to use the underline notation consistently so that it is not too confusing for the student who has not used their linear algebra background for some time…
A vector is simply an ordered set of numbers or quantities. A column vector is usually written as ?x1?
=?x2? ????x3??
and a row vector is given by =[x1x2Tx3]
where the length of the vector is equal to the number of elements. The usual notation, without the superscript T, refers to the multiple row, single column format - thus, the vector quantity is referred to as a column vector. Similarly, the row vector has only one row but multiple columns. ?x1??y1?
Given two column vectors, =?x2? and y=?y2?, the most common arithmetic operations are ???????x3???y3??
where the number of columns of the first matrix must be equal to the number of rows of the second matrix, or × = (m×n)(n×p)=(m×p)
where the notation m×n, for example, implies that the matrix has m rows and n columns. Matrix-Vector Multiplication y= or yi=∑aijxj
j (3.8)
Matrix Transpose =T or cij=aji (3.9) Also there are a number of special matrices of interest. For example, some of these matrices include diagonal, triangular, square, and identity matrices, as well as symmetric and skew
symmetric matrices, etc.. Most of the names for these matrices are self-explanatory. A square
Math Methods -- Section III: Overview of Linear Algebra 4matrix is one with an equal number of rows and columns. A lower triangular matrix is a square matrix with all zero elements above the diagonal elements. Also, a real symmetric matrix is one that satisfies T= or aji=aij
T=? or aji=?aij (3.10) and a real skew-symmetric matrix satisfies the relationship (3.11) Other relationships will be defined as needed in subsequent subsections.
and, using the definitions of matrix multiplication, we have = (3.14) Gauss Elimination
Most direct methods for solving systems of equations involve a sequence of elementary row operations. These operations represent legal algebraic manipulations that do not alter the basic equality associated with the original equations. The purpose of the row operations is to take the original equations and put them into a form that is easier to solve than the original equations. There are three row operations that are used to systematically simplify the original system of equations:
1. Interchange two rows. 2. Multiply a row by a constant. 3. Add a constant times one row to another row.
The Gauss Elimination Method is the most well known method that implements these row operations in a systematic manner to take the original system and convert the matrix to upper triangular form. In this form, back substitution is used to evaluate the unknown solution vector . The elimination step can be represented symbolically using an augmented matrix notation, ??=??, or, for example, a 3x3 system would be transformed as follows: ??
Math Methods -- Section III: Overview of Linear Algebra 6where the x notation implies a general entry and the last column in the original matrix contains the right hand side vector . Of course, after transformation, the entries in the resultant matrix are different from the original case. However, this upper triangular form (for the n×n part of the augmented matrix), which is also known as echelon form, is an equivalent representation of the original equation. Once in this form, one can easily use back substitution to solve for the unknown vector .
As a simple example of this method, consider the following 3x3 system: = b
?219??x1??1???23?1??x?=?2?
???2?????421????0???x3???
?2191???23?12? ????4210??
?2191??0483? ????4210??
1??219?0483? ????00?17?2??
?22= ?1717 Written in augmented matrix form, this becomes Now, as our first row operation, take row 1 added to row 2 to give Note that only row 2 is modified in this step. Now take -2 times row 1 added to row 3 to give This system is now in echelon form. Using back substitution gives
x3=x2=x1=[3?8x3]=35 468[1?x2?9x3]=?239 136
A quick check shows that this is indeed the correct solution to the original system of equations. The reader is referred to the section on Numerical Solution of Algebraic Equations (Section VI of these Lecture Notes) for a more detailed treatment of the Gauss Elimination Algorithm and other techniques for solving systems of linear algebraic equations on the computer.
Math Methods -- Section III: Overview of Linear Algebra 7Determinant of a Matrix The determinant of a matrix, denoted as det or , appears frequently in applications of matrix equations. It is sometimes thought of as a measure of the size or magnitude of a matrix. Independent of its formal interpretation, it does appear in many formal definitions of other quantities and we must be able to compute det in lots of situations. For hand manipulation of low order systems, Laplace's expansion for det is the best way to evaluate this quantity (computer computation is done differently and more efficiently by other means). Laplace's expansion can be written in terms of an expansion along any row i as det=∑aijcij for any i
j (3.15)
or down any column j as det=∑aijcij for any j
i (3.16)
where cij is the cofactor of element aij. The elements of the cofactor matrix are defined as
cij=(?1)i+jMij (3.17) where Mij is referred to as the minor of the aij element. Mij is defined as the determinant of the matrix formed by deleting the ith row and the jth column from the original matrix. For example, given a general 3x3 matrix ?a11a12
=?a21a22???a31a32a13?a23? ?a33??
we can expand down column 1 (for example), giving
where
det=a11c11+a21c21+a31c31 c11=(+1)M11=a22
a32
a12
a32a23a33=a22a33?a23a32 =?a12a33+a13a32 c21=(?1)M21=?
c31=(+1)M31=a13a33a13
a23 a12a22=a12a23?a13a22
Note that this is exactly the same result as if one expands along row 1 (or any other row or column).
Math Methods -- Section III: Overview of Linear Algebra 8The determinant of a matrix may or may not be altered under certain variations to the original matrix. Several important relations are as follows: 1. The det is not altered if the rows are written as columns in the same order. Therefore,
det=det T (3.18) 2. If any two rows or columns are interchanged, the value of det is multiplied by -1. 3. The value of det is not altered if the elements of one row are altered by adding any constant multiple of another row to them.
4. The determinant is multiplied by a constant α if any row is multiplied by α.
5. The determinant of a diagonal matrix is simply the product of the diagonal elements. This is also true for triangular matrices. 6. For square matrices,
det()=det()=det
Matrix Inverse (3.19)
The matrix inverse, denoted as , is a quantity used in the formal manipulation and solution of systems of equations. is defined such that ==. This says that a square
matrix multiplied by its inverse gives the identity matrix. Also, the identity matrix operating on a matrix or vector of appropriate size does not alter the original quantity. These facts can be used to write the formal solution to a system of equations. In particular, given =, a formal solution for can be developed as follows: Starting with =, pre-multiply both sides by to give
?1?1?1?1?1?1= ?1?1but =, and =, therefore we have = ?1 (3.20) This formal solution is very important, since it provides a basis for discussing the uniqueness and existence of solutions and it also allows for various manipulations of matrix equations.
However, the reader should be cautioned that this formulation is not the most efficient procedure for actually computing the solution vector . For computer implementation, especially for large systems, other techniques are far more efficient (see Section VI on Numerical Solution of Algebraic Equations).
There are many cases, however, when it is useful to actually evaluate the inverse matrix. There are a variety of ways to do this. For low order systems, the following formula is often applied, CT
Math Methods -- Section III: Overview of Linear Algebra 9where C is the matrix whose elements are the cofactors of automated implementation on the computer, some form of the Gauss-Jordan Method is often used. The Gauss-Jordan Elimination Method (which is just an extension of the Gauss
With this symbolic notation, we see that the original matrix is augmented with the identity
matrix. Extending the notation from before, this says we are trying to evaluate a matrix equation of the form, =, for the unknown matrix inverse matrix, that =. We can solve for by performing row operations on the augmented matrix ????. ?, finally putting it into the form ???
Let's illustrate these two methods for finding the inverse matrix using the following 3x3 matrix, ?3?22?A=?12?3? ????412???1
A couple of convenient relationships that should also be noted are as follows: 1. If is a diagonal matrix (a square matrix with all zeros in the off-diagonal locations), then
?1? ?1=?aii?? (3.22)
2. The inverse of a product of matrices is simply the product of the individual inverses in the opposite order, or ()?1= ?1?1 (3.23) To show this last relationship (as an example of manipulating matrix equations), we have
()=C ()()== ?1?1
Thus =?1, or =?1?1, which proves the above statement.
Rank of a Matrix
The rank of a matrix is defined as the maximum number of linearly independent rows or columns in the matrix. It is important to note that elementary row operations do not alter the Trank of a matrix. Also it should be noted that and have the same rank.
Math Methods -- Section III: Overview of Linear Algebra 12one can make the following statements concerning the existence and uniqueness of solutions for this matrix system: ?? are equal. 1. This system has nontrivial solutions only if rank and rank 2. The system has precisely one solution if rank is n, where n is the number of unknowns in vector . 3. The system has infinitely many solutions if rank is less than n.
In general, if m > n, we have an over-determined system, and usually no solutions exist. If rank is m, then there are m linearly independent rows and only n unknowns; thus, there are no nontrivial solutions that can satisfy m independent equations with n unknowns (with n < m). In this case one usually uses the method of least squares to find the best solution based on some specific objective criterion (the reader is referred to the literature for further information on this subject).
If m < n, we have an under-determined system and usually an infinite number of solutions will satisfy these conditions. If m = n (i.e. a square matrix) and rank = m = n, there is a single unique solution. This is normally the case of interest. If =0 (homogeneous system), then for a nontrivial solution, rank A must be less than n. This says that the system matrix must have linearly dependent rows (which implies that the determinant is zero - see below).
The Case of n Equations and n Unknowns
For the usual case of n simultaneous equations with n unknowns, we have = and =?1where?1CT
= detNow two situations can occur:
I. Non-Homogeneous Problems: In this case, ≠0, and this system is said to be a non-homogeneous system. For this situation, there is only a single non-trivial solution if we have n linearly independent rows, which implies ?1?1that rank = n, that the det is nonzero, and that exists. When exists, is said to
be non-singular.
II. Homogeneous Problems: If =0 , then = implies, at first glance, that must be the null vector since we are multiplying the inverse matrix and the =0 vector. However, if det=0, then does not exist, and the solution form, =, leads to an indeterminate form, which could lead to a nontrivial solution. In fact, this is indeed the situation, and we can argue that there are nontrivial
From the discussion in the previous subsection on Systems of Linear Algebraic Equations, we saw that homogeneous equations with n equations and n unknowns require that the system matrix be singular for the existence of nontrivial solutions. The classical eigenvalue problem is a special case that falls into this class of problems and it arises from the general problem given by = when =λ (that is, the right hand side vector is some constant times the solution vector ). With this substitution, we have =λ (3.24) These systems occur frequently in applications and are usually written as (?λ)=0
det(?λ)=0 (3.25) which is a homogeneous system of equations. Therefore, for non-trivial solutions, we require that (3.26) which is referred to as the characteristic equation. This gives rise to an nth order polynomial in λ which has n roots -- the n eigenvalues of a square matrix of order n.
Note that the eigenvalues may be real and distinct, complex conjugates, repeated, or some combination of these. Note also that the sequence λ1,λ2,"λn is called the eigenvalue spectrum, with the magnitude of the largest eigenvalue denoted as the spectral radius, or λmax=spectralradius The eigenvector associated with the ith eigenvalue, λi, is found by evaluating the homogeneous equation (?λi)i=0 (3.27) An Example
As an example, let's find the eigenvalues and eigenvectors of the following matrix: ?2?10?A=??12?1? ????0?12??
Now, the eigenvector associated with the ith eigenvalue can be determined by solving the matrix equations with the specific eigenvalue inserted into the equation. For example, for λ1=2, we have
?0?10??x1??0???10?1??x?=?0? ???2?????0?10????0???x3??1?
?x2=0 , ?x1?x3=0 , and ?x2=0 which gives three equations
Clearly, the first and third equations are redundant, as expected. These equations, along with the second equation, which implies that x3=?x1, identify the first eigenvector as ?1?=?0? ?????1??
where we have chosen the first component to be unity. Clearly there is an arbitrary
normalization associated with the eigenvector (because a homogeneous system of rank n-1 will always have an infinite number of solutions that simply differ by a single normalization
parameter). One common practice is to normalize the magnitude of the vector to unity to force some specificity for the normalization constant. If this is done, the above eigenvector becomes
?1??==0 ??1??
are valid eigenvectors for this eigenvalue (differ only by a normalization). Note Both and that normalization of the eigenvectors is usually not a requirement in most applications -- it is often done, however, in computer calculations for consistency among various computer codes.
1 = x3 and x2 is the arbitrary normalization. For convenience, we choose x2
=, which gives
?1??=?
?
1???
?1?=
?1???Similarly, the third eigenvector can be determined to be
using the same method as above.
Summary Note
The capability to do computations of this type is built directly into Matlab and other similar programs and, in practice, automated routines like those in Matlab (see the Matlab demo in a later subsection) are used in day-to-day engineering applications as needed. However, the student should definitely know the fundamentals of these numerical algorithms (although the details are not always necessary). By assuring that you can do the above manipulations by hand for low order systems, you will gain the confidence and experience necessary to intelligently and efficiently use the automated software. Thus, you should make sure you understand the above example, and be able to perform similar manipulations on small systems as verification of the computer tools that simply automate the procedures.
There are a number of matrices that deserve some special mention. In particular, of interest here are three classes of matrices -- Hermitian, Skew-Hermitian, and Unitary Matrices.
Hermitian matrices satisfy the relationship ??T= or a??ji=aij (3.28) where the wavy line over an element implies that one should take the complex conjugate of that quantity. An example of a hermitian matrix is 1?3i??4=?? 1+3i7??
??ii=aii for the Note that the diagonal elements of hermitian matrices must be real, since a
diagonal elements.
Skew-hermitian matrices are similar to the above definition except for a negative relationship, ??T=? or a??ji=?aij (3.29)
??ii=?aii along the diagonal. In this case, the diagonal elements must be pure imaginary, since a
This really says that (α?jβ)=?(α+jβ), which clearly implies that α=0. As an example, consider the following matrix, 2+i??3i =????2+i?i?
??T=?1 A unitary matrix is one that satisfies the expression (3.30) ??1As an example, if
? and ????T. As a check, let's compute the product ??T and see if it gives the should be the same as identity matrix, or
Note that hermitian, skew-hermitian, and unitary matrices are, in general, complex matrices. However, a subset of each of these classes exists for the case of all real elements, and they go by the names symmetric, skew-symmetric, and orthogonal, respectively.
Math Methods -- Section III: Overview of Linear Algebra 18The nice thing about matrices within these classes is that we can characterize their eigenvalue spectrum, as follows:
1. The eigenvalues of a hermitian (or real symmetric) matrix are real.
2. The eigenvalues of a skew-hermitian (or real skew-symmetric) matrix are imaginary or zero.
3. The eigenvalues of a unitary matrix (or real orthogonal) matrix have absolute value of unity. For the examples given above we can compute the eigenvalues, giving
Hermitian matrix λ2?11λ+18=0 and λ1,2=9,2
λ2?2iλ+8=0 and λ1,2=4i,?2i
λ2?iλ?1=0 and λ1=1
2Skew-hermitian matrix Unitary matrix
+i,λ2=)1i 2()
where this last set of eigenvalues was obtained from Matlab. Also note that the magnitude of each eigenvalue for the unitary matrix is indeed unity. For example, the magnitude of λ
1 is given by
λ1===1 Quadratic Forms The form is a common combination of terms that occurs frequently in applications. In particular, if and are both real, then the combination is referred to as a quadratic form. Also if is hermitian, then is real for any , and if is skew-hermitian, then TTT
is pure imaginary for any . These summary properties can be useful in some cases. Similar Matrices
One final set of terminology related to the eigenvalues of a matrix still needs to be discussed – that is the concept of similar matrices and related subjects. In particular, two matrices,
A and B, are said to be similar if they satisfy the relation T= ?1 (3.31) where is a transformation matrix. This transformation is said to be a Similarity
Transformation. The important point here is that similar matrices have the same eigenvalues. In addition, if is an eigenvector of , then y=?1 is the eigenvector of corresponding to that same eigenvalue. We can show this by the following manipulations:
This set of expressions shows that λ is indeed an eigenvalue of and that y=?1 is the eigenvector of that corresponds to eigenvalue λ.
If λ1,λ2,"λn are distinct eigenvalues of an n×n matrix, then the corresponding eigenvectors ,2,3,"form a linearly independent set and they represent a basis of eigenvectors in n dimensional space.
The modal matrix is a special matrix whose columns contain the linearly independent eigenvectors/basis vectors, or =[2"n] (3.32) Also we should note that any vector, y, has a unique representation in n dimensional space simply as a linear combination of the basis vectors, or y=c1+c2+c33+"cnn (3.33) Also note that a linear transformation, =, in terms of the basis vectors, becomes
or =c1λ1+c2λ2+"cnλnn (3.34) ==[c1+c2+c33+"cnn] Now if we let the transformation matrix, , in the above similarity transformation expression
[see eqn. (3.31)] be composed of the basis vectors for the n-dimensional problem, or
then, ==[2"n] ?1= (3.35) which is a diagonal matrix with the eigenvalues of along the diagonal of similar relationship that is often used is = ?1 (3.36)
A proof of the first relationship can be demonstrated as follows: =[2"n]=[λ1λ2"λnn]
A short Matlab demo has been prepared to illustrate some of the matrix/vector operations that can be performed within this programming environment. A few quantities are defined ?2?=?1? ?????1???0? y=??4? ????3???105? =?04?2? ????132???6?22? =?? 832??
and then several manipulations are performed with these variables and related quantities. The Matlab commands are stored in the file linademo.m and a diary file is created during the run and saved as linademo.out. The actual m-file has several comments and it also displays (via the disp command) various comments to the output diary file. With this information, the Matlab file is very easy to follow and is quite self-explanatory. These files (the main program linademo.m and the diary file linademo.out) are listed in Table 3.1 and Table 3.2, respectively.
This demo only touches on a few of the matrix operations that can be accomplished with the Matlab package. If you are a new Matlab user, you should use this as a start, and then build upon this capability as needed for specific applications. The Matlab documentation is a good source of information as you become more experienced and your needs grow. I think you will find that Matlab is extremely powerful and quite easy to use for typical linear algebra
applications.
Table 3.1 Listing of Matlab file linademo.m.
%
% LINADEMO.M Linear Algebra Applications in MATLAB
%
% This file simply demonstrates several linear algebra operations that can be
% performed in Matlab. This area is, in fact, one of Matlab's greatest strengths,
% since the base element is a 2-d array and all operations are, by default, matrix
% manipulations. In addition to the basic arithmetic operations, Matlab also has
% m-files for just about any matrix application or operation you can imagine. | 677.169 | 1 |
subject of partial differential equations holds an exciting place in mathematics. Inevitably, the subject falls into several areas of mathematics. At one extreme the interest lies in the existence and uniqueness of solutions, and the functional analysis of the proofs of these properties. At the other extreme lies the applied mathematical and engineering quest to find useful solutions, either analytically or numerically, to these important equations which can be used in design and construction. The book presents a clear introduction of the methods and underlying theory used in the numerical solution of partial differential equations. After revising the mathematical preliminaries, the book covers the finite difference method of parabolic or heat equations, hyperbolic or wave equations and elliptic or Laplace equations. Throughout, the emphasis is on the practical solution rather than the theoretical background, without sacrificing rigour.
Book Info
Presents a clear introduction of the methods and underlying theory used in the numerical solution of partial differential equations. Provides a complete introduction to partial differential equations. Softcover. DCL: Differential equations, Partial--Numerical solutions | 677.169 | 1 |
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Circuit Training - Linear, Quadratic and Exponential Regression
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Give your students engaging practice with the circuit format! Students will need to use technology (graphing calculator, on-line software) to calculate regression equations to advance in the circuit. At first students will be told what kind of regression, but towards the end of the circuit students need to try several regressions and compare the r-value to see which is the best fit. 16 equations total. Can be turned into task cards or even a scavenger hunt. | 677.169 | 1 |
Description: This book describes what has for many years been the most important part of the regular course in the Calculus for Mechanical and Electrical Engineering students at the Finsbury Technical College. The students in October knew only the most elementary mathematics, many of them did not know the Binomial Theorem, or the definition of the sine of an angle.
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Introduction to Computational Engineering by Steven J Cox - Rice University We strive to speak the Matlab language free of syntactic error, to confidently translate English simulation and/or design questions, to identify the proper numerical method for the job, and to represent the solution in a visually striking way. (4364 | 677.169 | 1 |
No, i want to learn the underlying mathematics with some applications(which do not use algorithms and stuff)Why did you add the word "Extra"? One can not learn by only using those books?
Because they aren't as comprehensive as the books I'd recommend as primary sources for learning modern differential geometry, and their pedagogy is aimed in a different direction.
For primary books, I'd recommend John M Lee's three textbooks on manifolds. Topological, then Smooth, then RiemannianAll the books I mentioned are famous in their class and are usually recommended. But I think Schutz's is more proper for you.
You can't have it both ways. Either you learn the underlying mathematics, which will take several books. Or you take the physicists approach which will teach you how to teach the computations but not the underlying math. | 677.169 | 1 |
About the Book
Mathematical Reasoning: Writing and Proof is designed to be a text for the ?rst course in the college mathematics curriculum that introduces students to the processes of constructing and writing proofs and focuses on the formal development of mathematics. The primary goals of the text are to help students:
Develop logical thinking skills and to develop the ability to think more abstractly in a proof oriented setting. | 677.169 | 1 |
Developmental Math
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Let the ACC Mathematics faculty be your guide to preparing for and choosing a path that is right for you. Whether your math skills are a little rusty or you have a few trouble areas, we'll provide you with the tools you need to succeed at ACC and beyond. We're here to get you ready for college level math courses so you can Move Mountains to achieve your educational and career goals. Get the confidence and the skills you need to take the next step in your journey.
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Math III Technical Readiness and Math IV Technical Readiness are course options (for juniors and seniors) built for the mathematics content of Math III through integration of career clusters. These courses integrate academics with hands-on career content. The collaborative teaching model is recommended based at our Career and Technical Education (CTE) centers. The involvement of a highly qualified Mathematics teacher and certified CTE teachers will ensure a rich, authentic and respectful environment for delivery of the academics in "real world" scenarios.
All West Virginia teachers are responsible for classroom instruction that integrates content standards and mathematical habits of mind. Students in this course will make connections and applications the accumulation of learning that they have from their previous courses, with content grouped into four critical units. Students will apply methods from probability and statistics to draw inferences and conclusions from data. They will expand their repertoire of functions to include polynomial, rational and radical functions and their study of right triangle trigonometry to include general triangles. Students will bring together their experiences with functions and geometry to create models and solve contextual problemsInferences and Conclusions from Data
Summarize, represent, and interpret data on a single count or measurement variable.
M.3HS.1 (*)
Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets and tables to estimate areas under the normal curve.
Understand that statistics allows inferences to be made about population parameters based on a random sample from that population.
M.3HS.3 (*)
Decide if a specified model is consistent with results from a given data-generating process, for example, using simulation. (e.g., A model says a spinning coin falls heads up with probability 0.5. Would a result of 5 tails in a row cause you to question the model?)
Make inferences and justify conclusions from sample surveys, experiments, and observational studies.
M.3HS.4 (*,^)
Recognize the purposes of and differences among sample surveys, experiments and observational studies; explain how randomization relates to each.
M.3HS.5 (*,^)
Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.
M.3HS.6 (*,^)
Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.
M.3HS.7 (*,^)
Evaluate reports based on data.
Use probability to evaluate outcomes of decisions.
M.3HS.8 (+, ^)
Use probabilities to make fair decisions (e.g., drawing by lots or using a random number generator).
M.3HS.9 (+, ^)
Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, and/or pulling a hockey goalie at the end of a game).
Polynomial, Rational and Radical Relationships
Use complex numbers in polynomial identities and equations.
Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.
Interpret the structure of expressions.
M.3HS.12 (*)
Interpret expressions that represent a quantity in terms of its context.
Interpret parts of an expression, such as terms, factors, and coefficients.
Interpret complicated expressions by viewing one or more of their parts as a single entity. (e.g., Interpret P(1 + r)n as the product of P and a factor not depending on P.)
M.3HS.13 (*)
UseWrite expressions in equivalent forms to solve problems.
M.3HS.14 (^)
Derive the formula for the sum of a geometric series (when the common ratio is not 1), and use the formula to solve problems. (e.g., Calculate mortgage payments.)
Perform arithmetic operations on polynomials.
M.3HS.15 (*)
Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction and multiplication; add, subtract and multiply polynomials.
Understand the relationship between zeros and factors of polynomials.
M.3HS.16 (*)
M.3HS.17 (*)
Identify zeros of polynomials when suitable factorizations are available and use the zeros to construct a rough graph of the function defined by the polynomial.
Use polynomial identities to solve problems.
M.3HS.18 (^)
Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x2 + y2)2 = (x2 – y2)2 + (2xy)2 can be used to generate Pythagorean triples.
M.3HS.19 (+,^)3HS.20 (*)
Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.
M.3HS.21 (+)
Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply and divide rational expressions.
Understand solving equations as a process of reasoning and explain the reasoning.
M.3HS.22 (*)
Solve simple rational and radical equations in one variable and give examples showing how extraneous solutions may arise.
Represent and solve equations and inequalities graphically.
M.3HS.23 (*,^) (e.g., using technology to graph the functions, make tables of values or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential and logarithmic functions.
Analyze functions using different representations.
M.3HS.24 (*,^)
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Graph polynomial functions, identifying zeros when suitable factorizations are available and showing end behavior.
Trigonometry of General Triangles and Trigonometric Functions
Apply trigonometry to general triangles.
M.3HS.25 (+,^)
Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.
M.3HS.26 (+, ^)
Prove the Laws of Sines and Cosines and use them to solve problems.
M.3HS.27 (+,^)
Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems and/or resultant forces).
Extend the domain of trigonometric functions using the unit circle.
M.3HS.28 (*)
Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.
M.3HS.29 (*)
Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.
Mathematical Modeling
Create equations that describe numbers or relationships.
Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
M.3HS.32 (*,^)
Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
M.3HS.33 (*,^)
Represent constraints by equations or inequalities and by systems of equations and/or inequalities and interpret solutions as viable or non-viable options in a modeling context. (e.g., Represent inequalities describing nutritional and cost constraints on combinations of different foods.)
M.3HS.34 (*,^)
Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. (e.g., Rearrange Ohm's law V = IR to highlight resistance R.)
Interpret functions that arise in applications in terms of a context.
M.3HS.35 (*)
or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.
M.3HS.36 (*)
Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. (e.g., If the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.)
M.3HS.37 (*)
Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
Analyze functions using different representations.
M.3HS.38 (*,^)
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
M.3HS.40 (*,^)
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). (e.g., Given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.)
Build a function that models a relationship between two quantities.
M.3HS.41 (*)
Write a function that describes a relationship between two quantities. Combine standard function types using arithmetic operations. (e.g., Build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.)
Build new functions from existing functions.
M.3HS.42 (*)
Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
M.3HS.43 (*)
Find inverse functions. Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. (e.g., f(x) = 2 x3 or f(x) = (x+1)/(x-1) for x ≠ 1.) | 677.169 | 1 |
Guide to Mathematical Modelling is a book designed for students and professionals interested in an introduction to mathematical modelling. It explains the concept of a mathematical model, examines why mathematical modelling is important, and presents several different modelling situations, ranging from simple to very complex. The book also discusses communication and the art of presenting and reporting on modelling activities. | 677.169 | 1 |
Benchmarks 9B (The Mathematical World: Symbolic Relationships)
Grades 9-12, page 220
Symbolic statements can be manipulated by rules of mathematical logic
to produce other statements of the same relationship, which may show some
interesting aspect more clearly. Symbolic statements can be combined to
look for values of variables that will satisfy all of them at the same
time.
Appreciate that seemingly different mathematical systems may be essentially
the same
Benchmarks 9A (The Mathematical World: Numbers)
Grades 9-12, page 214
Numbers can be written with bases different from ten (which people
probably use because of their 10 fingers). The simplest base, 2, uses just
two symbols (1 and 0, or on and off)
and so that, in addition, college-intending students can:
Develop the complex number system and demonstrate facility with its
operations
Prove elementary theorems within various mathematical structures, such
as groups and fields
Develop an understanding of the nature and purpose of axiomatic systems | 677.169 | 1 |
The significance of arithmetic competitions has been well known for 3 purposes: they assist to enhance creative skill and considering abilities whose worth a ways transcends arithmetic; they represent the simplest manner of learning and nurturing mathematical expertise; they usually offer a method to strive against the universal fake photo of arithmetic held through highschool scholars, as both a fearsomely tough or a lifeless and uncreative topic. This ebook presents a finished education source for competitions from neighborhood and provincial to nationwide Olympiad point, containing thousands of diagrams, and graced through many light-hearted cartoons. It incorporates a huge selection of what mathematicians name "beautiful" difficulties - non-routine, provocative, interesting, and difficult difficulties, frequently with based ideas. It gains cautious, systematic exposition of a variety of an important issues encountered in arithmetic competitions, assuming little previous wisdom. Geometry, trigonometry, mathematical induction, inequalities, Diophantine equations, quantity concept, sequences and sequence, the binomial theorem, and combinatorics - are all built in a steady yet full of life demeanour, liberally illustrated with examples, and continually influenced by way of beautiful "appetiser" difficulties, whose resolution seems after the correct conception has been expounded.
Each bankruptcy is gifted as a "toolchest" of tools designed for cracking the issues accumulated on the finish of the bankruptcy. different themes, similar to algebra, co-ordinate geometry, sensible equations and likelihood, are brought and elucidated within the posing and fixing of the massive selection of miscellaneous difficulties within the ultimate toolchest.
An strange function of this ebook is the eye paid all through to the background of arithmetic - the origins of the information, the terminology and a few of the issues, and the social gathering of arithmetic as a multicultural, cooperative human achievement.
As an advantage the aspiring "mathlete" could stumble upon, within the most pleasurable means attainable, a few of the issues that shape the middle of the normal tuition curriculum.
The development of recent Mathematical wisdom in school room interplay bargains with the very particular features of mathematical conversation within the lecture room. the overall examine query of this e-book is: How can daily arithmetic instructing be defined, understood and built as a instructing and studying surroundings within which the scholars achieve mathematical insights and lengthening mathematical competence by way of the teacher's tasks, deals and demanding situations?
Five points are marked in the area bounded by the line AB, BC and AC (points may also be marked on any of the boundary lines). 3 (E) cannot be determined Solution: A 1/2 1/2 1/2 CЈ BЈ 1/2 1/2 1/2 1/2 B 1/2 AЈ 1/2 C Geometry The triangle is shown above with medians AA , BB and CC . Using Theorem 1, we see that BC =AC =AB = 1 . 2 Now we have four smaller congruent equilateral triangles making up the larger triangle as shown above. We are now going to use the pigeon-hole principle (see Toolchest 8 for more): if k+1 letters are posted into k pigeon-holes, then at least two letters will share the same hole. | 677.169 | 1 |
Introduction to Maple in the Undergraduate Computer Lab
by James A. Carlson and Jennifer M. Johnson
Department of Mathematics, University of Utah
December, 1995
This document tells how to open a Maple file on the
undergraduate lab machines,
how to save and reopen files, how to print Maple sessions and plots,
and introduces a few basic Maple commands. For further information
about Maple commands see
Maple is a general purpose software package containing tools
useful in the study of a wide variety of problems. We can use
Maple like a calculator to carry out numerical computations or
we can use the programming features of Maple to produce a more
complicated sequence of computations. In addition to numerical
computation, we can do symbolic or algebraic computations in
Maple. This software package has built-in functions for solving many
kinds of equations, for working with matrices and vectors, for
differentiation and integration. It also contains functions
which allow us to create visual representations of curves and
surfaces from their mathematical descriptions.
Using a software package like Maple gives new ways to think
about problems. For example, we can use the computer to run
numerical experiments. This means that we can not only look at
more realistic versions of standard problems, but we can easily
look at many more examples, in the process developing a better
intuitive feel for the essential features of a general problem
and its solutions. Often these experiments suggest further
questions or interpretations that might otherwise go
unnoticed. Patterns that appear in these experiments give
insight into and motivation for the standard approaches to these
problems --- and frequently highlight the limitations of these
methods.
In many situations the graphics features of Maple are a useful
tool for visualizing the geometric ideas behind important
definitions and standard techniques. Again, this goes a long
way toward giving a better feeling for the essentials.
In the beginning computing can be frustrating because we are
used to dealing with people, who are intelligent and cn
undrstond whot u meen evn if it isn't quite right from a
literal point of view. Anyway, you will soon get past this
stage as the right moves become automatic. Eventually computers
will be smarter and better designed, and this will make life
easier for all of us.
Move the cursor into the local window and
type xmaple & to open a Maple window.
Presently the ghost of a new window will appear in a kind of
``dotted outline form.'' Move the mouse to position this window
and click with left mouse button when satisfied.
(Try to place windows so that part of the title bar is visible
for each window. Sometimes the mouse
gets a bit wild and hard to control so you may end up with a
window whose title bar is completely obscured. In that case,
you can move and resize windows to get
access to the title bar.) If you need help, ask! Getting used
to the mouse and multiple windows can be very frustrating at
first, especially if you are unwilling to get help when you need
it.
At the top of your Maple window you
will see several menus. Click on the File
menu with the
left mouse button. To name a Maple file click on the option
Save As with the left mouse button.
A Save Session
window appears: If the box labelled Selection
near the bottom of this window is empty
and you want to save your Maple file under the name hw1
(for example), then click anywhere
in the Selection box with the left mouse button and
type hw1. Then press the return key or click on the
Save box at the bottom of the
Save Session window.
(It sometimes happens that the Selection box appears
containing your full computer address. In that case you must place
the cursor at the end of the name that appears in the box (after
the /) and type your file name, etc.)
If this process was successful the name hw1.ms should
appear at the top of the Maple window. Maple adds the .ms
extension to identify the saved file as a Maple file. To avoid
headaches you should use some care in naming your files. Keep
it simple. Use only letters and numbers in your file names.
Don't use any special symbols and in particular, avoid using
spaces, periods, and hyphens.
All you have done so far is save a blank file. As you
continue working you will need to update your saved file. Do
this by clicking on the File menu and then the option
Save in that menu. Do this frequently. Power
failures or Maple memory failures can occur without
warning at any time. In that case you will lose all work done
since the last time you saved the file.
The following examples give an introduction to a few basic
Maple commands and further technical details of using Maple
in the Undergraduate Lab.
Example: Find the point of intersection of the two lines
defined by 3x + 2y = 5 and 2x + 4y = 5 in the plane. Use Maple to
find the intersection algebraically and graphically.
Solution:
It is of
course an easy matter to solve this system by hand, but for
larger systems with more equations the help of a machine will be
very welcome.
The first line of your Maple window should contain
the symbol >. This is called the Maple prompt. It is an
indication that Maple is waiting for your next command.
To solve in Maple, we write:
> solve( { 3*x + 2*y = 5, 2*x + 4*y = 5 } );
and Maple
responds with this:
{ x = 5/4, y = 5/8 }
Except for minor (but important) differences of punctuation,
we formulate the problem for Maple in the same way as we do for
a fellow mathematician. Note that we give the system of
equations as a set: a list of items separated by commas
and enclosed by curly braces. This tells Maple to apply the
function solve simultaneously to both equations. Typically, a
Maple command takes a set as its argument if the order of the
elements is not important --- in other words, since nothing
about this problem changes if we give the equations in the
other order, we give the list of equations as a set. The
solution is also a set --- its elements are the simplified
equations.
Notice that Maple commands end with a semicolon. Maple is very
finicky about such things. It will not carry out any of your
instructions until you end the command properly.
For the most part, spacing is not important in a Maple command,
although generous use of the space bar makes your commands much
easier to read.
If you made some typing mistakes in your command you may have
gotten a syntax error. This means that Maple doesn't
understand your command. With practice you will be able to use
Maple's error messages to get clues about what kind of mistake
you have made but at first they will probably be a bit
mysterious. For example, you may see that you left out one of
the * symbols or that you have typed =
instead of +. To
correct this kind of error you need not retype the entire
command.
You can use the arrow keys to move the cursor back into the
line and then use the backspace key to erase your mistake.
Insert the missing symbol and
press Return. Maple will attempt to carry out your
instructions.
(You don't need to move the cursor to the end of the line.
Maple will just look at the line the cursor is in.) Another
common error is to forget to type the semicolon at the end of
your command. You can move back into the line and add the
semicolon as with the other typos. However, for a mistake like
this you will probably have to enter the command twice before
Maple gets it straight.)
Often you will want to enter a command that is a small variation
on an earlier command. In that case instead of retyping you
can use the mouse to copy an old command and then paste it onto
a new command line. Then you can move the cursor into the
command and make modifications.
Press the left mouse button at the beginning of the
text you want to copy.
Hold the button down and drag the mouse until you have
blackened the desired text. Release the mouse button.
Move the cursor to the position where you want to paste.
Click the left mouse button to mark this spot.
Click the middle mouse button to paste.
For example, notice that in our intersecting line problem Maple
gave the result in fractional form. If possible, Maple tries
to use algebraic methods to find solutions exactly. If we
rephrase the question using decimals instead of integers for
even one of the coefficients, then Maple approaches the question
very differently and we get answers in decimal form:
> solve({3*x + 2*y = 5.0, 2*x + 4*y = 5});
gives
(1.250000000, 0.6250000000) as the point of intersection.
Use the mouse to copy and modify the solve command
above to get an
answer in decimal form as described above.
You can paste repeatedly---the copied text stays in memory and
anytime you press the middle mouse button it will be pasted at
the current cursor position. (This can cause some problems for
you if you accidentally hit the middle mouse button later on so
you may want to copy some blank space to clear the copied text.)
Another way we could use the solve command is to solve the
equation 3x + 2y = 5 for y as a function of x:
> solve( 3*x + 2*y = 5, y);
We see that the line 3x + 2y = 5
is the graph of the function
f1(x) = -3x/2 + 5/2. Maple has a built-in command plot for
producing graphs of curves in the plane. To obtain a graph of
the line for
x in [-2, 2] we use the command:
> plot( -3*x/2 + 5/2, x = -2..2);
In this command we see an example where spacing is
important in Maple; no space is allowed between the dots
in this command. A new window, called a plot window
should appear in response to this command. This plot can be
printed by itself or it can be pasted into your Maple window to
be printed later (see below).
We have graphed the line given by the first equation and we can
modify our work above to get a plot that contains both lines.
> solve( 2*x + 4*y = 5 , y);
tells us that the second line
is the graph of the function f2(x) = -x/2 + 5/4 and we can
tell Maple to graph f1 and f2 together:
> plot( {-3*x/2 + 5/2, -x/2 + 5/4}, x = -2..2);
Again notice the use of
braces to tell Maple to apply the command plot to both
functions. We see from the resulting plot that the lines meet at
the point (5/4, 5/8)= (1.25, 0.625) as expected. Use the
left mouse button to click on the intersection point; the
coordinates of this point will then appear in the upper left
corner of your plot window.
The quotation mark here is the backquote, located in the
upper left corner of the lab keyboard; don't confuse it with
the single quote. Also, note that this command is too long to
fit on a single line. To enter a multiline command in
Maple just press the Enter key instead of Return when you finish
typing the first line of the command. When the command is
complete and you are ready for Maple to carry it out, press the
Return key.
You should be aware that Maple chooses the scale on the
x-axis and the y-axis independently. To force Maple to
use the same scale on both axes you can choose the option
Constrained in the Projection
menu in the plot window.
Another way to achieve the same thing is to specify the range
of variation for y in your Maple command:
If you click on the box labelled Confirm or hit the
return key you will create a printable file named
plotoutfile.ps.
To actually print the plot you must return to the
local window and type print plotoutfile.ps . The plot will
be enlarged to fill one standard size page.
To give the printable version of your plot a name of
your own choosing -- for example, intersection.ps -- click in
the box labelled Output Filename, backspace to erase
plotoutfile.ps and type intersection.ps instead. Then
press Return or click to Confirm. Then print by typing
print intersection.ps in your local window.
This is useful if
you want to delay printing. Any time you save a plot under the
name plotoutfile.ps you replace the last plot you did with the
new plot. So if you want to save several plots for later
printing you need to give the files different names.
Remark: The extension .ps after a file name should mean
that the file is a postscript file. All your plot files and
the printable version of your Maple file are of this type. It
is very helpful to indicate the file type with an appropriate
extension as part of the file name.
Rather than printing
the plot out separately you may prefer to include the plot in
your Maple window and then print out your entire Maple session
instead. This has the advantage that the plot appears with the
commands that produced it. To do this
Click on the Edit menu in the plot
window.
Click on the option Copy.
Go to your Maple window and place the cursor
anywhere
in the line that contains the command which produced the plot.
Click on the Edit menu in your Maple
window
and choose the option Paste.
The plot should then appear in your Maple window. To
continue working just use the arrow keys or click to move the
cursor into the next command line. (It may happen that you don't
see a Maple prompt > at the end of your file. You can get a
new prompt by going to the Edit menu and selecting the
option Insert Prompt. This can also be achieved using key
commands---hold down the
``compose character'' key (referred to as ``Alt" in the
instruction in the Maple menus) while you press the ``I'' key
and a new prompt will appear below the line the cursor is in.)
Your plot will take up about half a page in the printed
version. Often you won't need the plot to be so large. You can
make the plot smaller (see directions above for resizing a
window) before you paste it into your Maple file.
To get rid of a plot window click on the
File menu
in the plot window and choose the
Exit option. If
you change your mind and you want to get the plot back, just
move the cursor into the command line that produced the plot and
press Return.
In the example above we saw two ways
to use the solve command in Maple. Are there others? We can
ask Maple for more information about the solve command by
typing ? solve or ?solve after the prompt.
If we do this a
help window will appear, containing a lot of (probably)
incomprehensible information about the command solve. If you
scroll to the end of the help window then you will see a
list of examples. At first these examples won't be very easy to
use but as you get more familiar with Maple these will become
quite useful for figuring out how to get Maple to work for you.
So far we have looked at lines in the plane and we've seen an
example of two useful Maple commands---plot and solve.
Next we look at some three dimensional examples.
Example: Let P be the plane given by the equation 3x + y
-2z = 2. Use Maple to plot this plane.
Solution: Maple has a built-in command
plot3d for drawing
surfaces in 3-space, but we have to describe the surface in the
terms Maple expects. Although we can specify our plane with a
linear equation as above, the command plot3d will not accept
this description of P (we would get a syntax error).
However, this plane can also be described as the graph of a
function of two variables, namely as the graph of
f(x,y) = (3x + y - 2)/2. From this description we can get a
plot of P if we specify a range of x-values and of
y-values over which to graph the function f:
> plot3d( (3*x + y - 2)/2, x = -3..3, y = -3..3);
This command
produces a 3d-plot window containing a graph of P, but
without axes it is difficult to get any information from this
picture. We cannot see how the plane lies in 3-space. At the
top of the 3d-plot window are several menus. Choose the
option Normal in the Axes menu. The
plane disappears
and is replaced with a box. Click anywhere in the plot
window with the middle mouse button to redraw the plane
P, now with axes. It is still difficult to interpret this
picture
because it is difficult to see how the axes as drawn relate to
the plane. Try some other choices of axes style from the
menu. The options Boxed and
Framed are often better
choices for surfaces. We can tell Maple to include axes by
adding an option to our plot3d command. (This is a good
chance to practice using the mouse to copy and modify an earlier
command.)
> plot3d( (3*x + y - 2)/2, x = -3..3, y = -3..3, axes = boxed );
The surface in this case is very simple, but
we also need to understand how this 2-dimensional object sits in
3-space. To get a better understanding of this we can turn
the surface and look at it from different angles. Click on the
plot with the left mouse button. The box should reappear.
Hold down the left mouse button and drag to move the
box. Click with the middle mouse button to redraw the
plot. Experiment with different views of the plane. Experiment
with the choices in the other menus as well. Recall that the
option Constrained in the Projection
menu forces
Maple to use the same scale on all the coordinate axes.
Try ?plot3d to bring up the plot3d help file;
the examples there give some more interesting surfaces.
Warning: Assignment statements are the source of two very
common and hard-to-spot syntax errors --- typing = instead
of := and typing : = instead of :=.
Geometric Solution: We can solve the system above
by finding the intersection of the three planes defined by equations
e1, e2, e3 . To do this we need to
plot these three planes together; the best approach is to
describe each plane as the graph of a function of
two variables and then use plot3d to produce the
picture:
In our examples we have seen a few of the built-in features of
Maple. For a list of the functions available in Maple type
> ?library
In addition to this standard library of functions
there are specialized packages of functions for working with
special topics--- for example there is a collection of
functions, called the linalg package for working with
matrices and vectors and there is also a collection of plotting
functions in the plots package. We will frequently use
both these packages. To use the functions in these packages you
must load them into Maple's working memory at the beginning of
your Maple session using the with command.
> with(linalg); # the warning you see is normal --- ignore it
> with(plots);
Often it will take more than one
session at the computer to complete
your analysis. You will need to save your
work and come back to the lab and open
your Maple file again to continue
working. Often it will be useful to take with you a printed copy
of your Maple session so you can think about what you have done
so far and how you want to continue when you come back to the
lab or so that you can talk to your instructor or your lab
partner about any questions you may have.
Before you learn how to print your Maple session
you should
learn how to clean it up a bit.
In the Edit menu of your
Maple window you will find some useful commands for this
purpose. For example the option Delete Cursor Region
will delete whatever line the cursor is in. Note that holding
down the "control" key while you hit the "delete" key will
have the same effect. This gives you a quick way to erase your
mistakes.
Also in the Edit menu you find the option
Delete by
Type. Choosing this option brings up another menu. Most of
these choices are rather drastic and self-explanatory. Try the
option Delete all Separators.
It is also a good idea to include some explanations with your
work. There are two ways to do this.
First you can use comments. In any command line, Maple ignores
anything typed after the symbol #. So inserting a line like
> solve( 3*x + 2*y - 5*z = 1, z); # Get z in terms of x and y:
makes your work much easier to follow. Notice that you can move
anywhere you like inside your Maple window with the arrow
keys or the mouse and the option Insert Prompt in the
Edit menu allows you to insert a command line.
Also in the Edit menu you find the option
Insert
Text. This allows you to type some explanations into your
Maple file. However, editing is very crude and there is no way
to get decent looking mathematical formulas with Maple's text
mode so if you want to say something complicated you may be
better off with a handwritten note. Also be careful using
Delete Cursor Region with text. Maple will delete the
whole section of text rather than the line the cursor is in.
(Try Display Region Boundaries in the View
menu of
your Maple window.)
Click on the File menu and choose the option
Save to update your file.
Click on the File menu; again choose the option
Print. A Page Setup Dialog window will appear.
Click on the box labelled OK at the bottom of this
window to create a printable version of your Maple session and
store it in a file named hw1.ps (assuming that your Maple file
is named hw1.ms as in the example above).
To actually print your Maple session, you must go to your
local window and type print hw1.ps.
Alternatively, you could click on the option Printer
Command in the Page Setup Dialog window
to send your
Maple session directly to the printer.
In your work above you created a Maple file and saved it under
the name hw1. Our task now is to reopen that file and get
back to where we left off.
Go to your local window and open a
Maple
window.
Click on the File menu with the left mouse button
and select the option Open. A Load Session
window
will appear.
In the middle-right of this window you should see a list
of Maple files, including your file hw1.ms. Click on this
file name with the left mouse. Then press the Return key or
click on the box labelled Load.
Your Maple window should now look like it did
the last time you saved your file hw1. However, you are not
quite ready to continue working. For example in your first
session you made some assignments (using :=). Maple displays
a record of these commands but it does not remember any of
the assignments you made last time. Also, if you loaded a
package of functions using with, the command will be there on
your screen, but Maple will not have any of the functions of
that package in its working memory.
The easiest way to get Maple to remember what happened last time
is to go to the beginning of your file and hit the Return key
until you get to the last line of the file.
(You might want to use the arrow keys to skip the lines that
displayed plots or requests for help files). This will ensure
that Maple's memory of your last session is restored. The most
important lines to re-enter are the lines where you loaded a
package or read in a file (using the command with or
read) or
lines where you made assignments (using :=).
Remark: You will find it inconvenient to work with a Maple
session file that is more than a few pages long. It is a good
idea to start a new Maple file when you begin a new section of
problems. | 677.169 | 1 |
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Make use of the Nutritional supplements That include Your Textbook
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Study In advance To remain Forward
If you want to reduce your in-class workload or perhaps the time you spend on homework, use your free time immediately after faculty or over the weekends to study in advance to your chapters and ideas which will be coated the following time you are in school.
Review Aged Exams and Classroom Examples
The perform you need to do in school, for homework, and on quizzes can present clues to what your midterm or last examination will glance like. Use your previous assessments and classwork to create a own research information on your approaching exam. Seem with the way your trainer frames queries – this is probably how they can seem on your own examination.
Learn how to Do the job Via the Clock
It is a well-known review suggestion for persons taking timed examinations; especially standardized exams. When you have only forty minutes for your 100-point test, then you can optimally expend four minutes on each 10-point concern. Get data regarding how extensive the exam is going to be and which forms of thoughts might be on it. Then system to attack the better inquiries 1st, leaving you enough time to shell out to the extra demanding kinds.
Improve your Resources to have math research enable
If you are acquiring a hard time comprehending ideas in class, then make sure you get assistance outside of course. Ask your friends to produce a study team and stop by your instructor's business several hours to go in excess of challenging troubles one-on-one. Attend examine and evaluation classes whenever your instructor announces them, or retain the services of a personal tutor if you want just one.
Speak To You
After you are examining problems for an examination, consider to explain out loud what approach and solutions you accustomed to get the answers. These verbal declarations will arrive in useful for the duration of a check once you need to recall the techniques you need to take to find a answer. Get extra observe by seeking this tactic having a mate.
Use Study Guides For More Follow
Are your textbook or course notes not supporting you understand everything you must be mastering in class? Use review guides for standardized tests, such as the ACT, SAT, or DSST, to brush up on previous product, or . Research guides ordinarily arrive geared up with comprehensive explanations of tips on how to fix a sample dilemma, , therefore you can generally come across wherever would be the greater obtain mathcomplications. | 677.169 | 1 |
Mighty Math Astro Algebra CD-ROM for Win/Mac - NEW CD in SLEEVE
Details
Mighty Math Astro Algebra CD-ROM for Win/Mac - NEW CD in SLEEVEDescription Mighty Math Astro Algebra CD-ROM for Windows & Macintosh Copyright Year: 1996 Publisher: Edmark / Riverdeep Interactive / SelectSoft Publishing Ages 12-14 Grades 7-9 Provides a Strong Foundation for Algebra Success! Alien Friends in Trouble! Algebra to the Rescue! Astro Algebra teaches the concepts and problem-solving skills necessary to learn basic algebra! Students learn how to graph functions, translate word problems into solvable equations, and represent algebraic expressions using the program's Virtual Manipulatives. Hundreds of problems in over 90 space missions provide students with a solid foundation for success in algebra and beyond. Play with the Basic Building Blocks of Algebra You understand equations better when you can build them with VariaBlox. Manipulate the Blox to combine like terms, substitute or solve for a variable and multiply, and factor simple algebraic expressions. An alert warns you when your equation is out of balance! Capture Satellites, Meteoroids and Unusual Outer-Space Treasures Drag objects into the Cargo Bay to sort them and solve a mathematical problem. Use the special sorting bins for translating between fractions, decimals, and percents and identifying equivalent rational numbers or exponential expressions. The Proportion Tool can help you solve scale factor, equivalent ratio, proportion, and percent problems. Represent Multiple Points and Graphs of Linear Equations and Inequalities Use the Grapher Station to solve problems and complete missions by identifying slopes and intercepts and solving systems of equations and inequalities. In some missions, a Number Line replaces the coordinate grid and you can graph fractions, decimals, expressions, and inequalities. Special Features! The math fun in Astro Algebra takes place in two modes, On-Duty Mode and Off-Duty Mode. You begin the program in On-Duty Mode, where you are directed through missions. You can also go into Off-Duty Mode at any time in order to freely explore the tools and stations at your own pace, view trophies or play Equation of Mystery in the Cargo Bay. Surf the AstroNet, a simulated universe-wide Internet* that contains data on math topics and terms. Learn about important algebra concepts before or during a mission. Use the Calculator to evaluate functions, compute solutions, and create tables of values. Astro Algebra's Grow Slide automatically records your progress and adjusts to guide your learning. The activities in Astro Algebra offer dozens of math topics and hundreds of problems in 7th, 8th and 9th grade algebra. As you learn and progress, the Grow Slide advances, offering more challenging problems. Students, parents, or teachers can also set the difficulty of each activity or choose a specific topic related to schoolwork. System Requirements: PC: Windows 95/98/Me, 486, Pentium or better (33Mhz or faster) , 9MB Hard Disk space, 8 MB RAM, Super VGA graphics (640x480 with 256 or more colors), Double-speed (2X) or faster CD-ROM drive, Windows-compatible sound card. Optional: Windows-compatible printer, Edmark TouchWindow. MAC: OS 7.5.6 - 9.x, 68030(25 MHz or faster), 68040 or PowerPC, 9MB Hard Disk space, 8 MB memory (RAM), 16 MB for PowerPC, 13" monitor or larger, 256 or more colors, Double-speed (2X) or faster CD-ROM drive. Optional: Printer, Edmark TouchWindow. NEW CD-ROM ONLY in protective windowed paper sleeve! NOT as pictured! Pictures are for illustration purposes only. Unless otherwise noted, you will receive a genuine factory CD in a sleeve. It does not include any documentation, paperwork, Jewel Case, or Box.Payment and Shipping Info In some instances, picture may differ from actual item. Domestic US S&H for this item is $0.00, or $0.00 if shipped with another item. Canada S&H for this item is $3.99, or $2.99 if shipped with another item. International S&H for this item is $5.99, or $4.99 if shipped with another item. NOTE: WE ship all items within 24 hours (usually the same day, within hours!) except on weekends & Holidays! If the USPS takes a long time to get it to you, it is not our fault! Depending on Weight, most items will be shipped by First Class Mail (usually takes 2-3 days) or Media Mail (usually takes 2-9 days) for Domestic orders. Some items may ship by Priority Mail. Delivery Confirmation is included in S&H for US orders. Delivery Conf. & Ins. is available for Int'l orders shipped by First Class Mail or Flat-Rate Priority Mail. You will get proof that we mailed your package through the Stamps.com & USPS. If you prefer another shipping method through the USPS, please ask for rates before paying. When in doubt, please contact us for S&H rates before looking/buying the item. We accept Credit Card & eCheck payments through PayPal. 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Example: Listing says Windows 3.1 or higher or Windows 95, and you have Windows 7, then there is no guarantee that this will work on your system and if you purchase it, it will be at your own risk! Anytime the listing says "Windows 3.1 or higher" means it is still for Windows 3.1 or higher (meaning Windows 3.11, etc.) not Windows 95/98/Me/2000/XP/Vista/7 or 8, same goes for all other Operating Systems including Macintosh. In many instances older software may or may not run in newer operating systems and again, if you purchase it, it will be at your own risk! There are no returns if you purchase the software for any other operating system than it was intended to be used on. All software sold are brand new & sealed unless otherwise stated, therefore we cannot be held accountable if your PC refuses to run the software due to system requirements not met or other incompatibility issues. Feel free to contact us if you need more info. Please research the software title you are interested in prior to looking or buying the item. Make sure your computer meets the requirements described in every item and be sure to note the packaging details included in the description of every item we sell. It is the customer responsibility to verify system compatibility and product needs before purchasing software products. For technical questions regarding a product, please contact the software publisher. There are no returns on software. Please contact us if you have an issue with your transaction and we will be happy to assist. IMPORTANT LEGAL NOTICE: Please note that your buy is a legal and binding contract to purchase the item. DO NOT buy OR BUY if you're unable to pay or have no intention of completing the transaction. Non-completion of transaction will be reported for further action. Please pay for your purchases in a reasonable time frame within 7 days. FEEDBACK: POSITIVE feedback: If you are satisfied with your transaction, please leave a positive feedback. We feel our part of the transaction is complete when we receive your positive feedback, and will give you instant positive feedback as soon as your feedback is received. Positive Feedbacks are left AUTOMATICALLY. NEGATIVE/NEUTRAL feedback: We encourage you to contact us in order to resolve any issues regarding the transaction before placing negative or neutral feedback. INTERNATIONAL BUYERS: We ship all items by First Class International Mail unless otherwise requested. It is trackable up to when it leaves the USA, but not thereafter and we will provide proof of mailing through the USPS. Therefore, we cannot be held responsible if the package gets lost or stolen in your country. SELLER POLICIES: By looking or buying, you accept ALL terms and policies listed in this listing. Minor errors or omissions do not invalidate the stated purchase terms. In the rare case of a major or gross mistake as determined by the seller or his representative, we will typically go beyond the stated purchase terms. Buyer agrees not to leave negative feedback until they have contacted us and provided us with an opportunity to resolve any issues. | 677.169 | 1 |
NCERT Solutions For Class 8
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The concept of the modern syllabus has changed. An important development in this discipline has been its orientation to global problems. such a concern about the environment or global level.
NCERT Solution For Class 8 Geography
NCERT Solutions For Class 8 Hindi
NCERT Solutions For Class 8 English
NCERT Solutions For Class 8 Maths
NCERT Solutions Class 8 is revised and includes many new things which will help students to update with the concept. Every single note has been dispatched after the end of the chapter. Also, previous year questions added. 1 marks questions has been added.
I am grateful to all the experts who built these solutions. I am also thankful to all the teachers and students. | 677.169 | 1 |
The course focuses on introducing important mathematical concepts through the development of mathematical techniques. The intention is to introduce students to these concepts in a comprehensible and coherent way, rather than insisting on the mathematical rigour required for mathematics HL. Students should, wherever possible, apply the mathematical knowledge they have acquired to solve realistic problems set in an appropriate context. The internally assessed component, the exploration, offers students the opportunity for developing independence in their mathematical learning. Students are encouraged to take a considered approach to various mathematical activities and to explore different mathematical ideas. The exploration also allows students to work without the time constraints of a written examination and to develop the skills they need for communicating mathematical ideas. This course does not have the depth found in the mathematics HL courses. Students wishing to study subjects with a high degree of mathematical content should therefore opt for a mathematics HL course rather than a mathematics SL course. This is a demanding course for those with a sound level of competency in using and applying basic mathematical skills. There is a minimum requirement for entry into this course and a list of mathematical prior learning can be found here. Students who choose this option should enjoy the challenge of problem solving and appreciate the need for good mathematical knowledge to support their current or future courses. The course involves solving realistic problems in appropriate contexts. There are 7 areas of compulsory study as with the higher level course. Students should be aware that in a small number of cases, this is the lowest accepted level for some courses at university, you are advised to discuss this with your college counsellor.
Formula Book
Introduction
Educating for a future that has yet to be invented. Mathematics. Technology. Pedagogy. | 677.169 | 1 |
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Variables aren't much good unless you can do math with them. Who knew your math classes could be useful? This video is part of a Virtual high school course at Divine Child High School. physcomp.flosscience.com
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An informal introduction to why we need to learn about fractions. Lesson 6 consists of providing you with a Self-Tutorial on all about fractions. This lesson is different from the previous ones in that the use of printed Notes is integrated with the Video (other Notes may be used independently of the videos). This lesson is VERY detailed and covers the necessary areas to help students review the many aspects of fractions and fraction conversions. I also show you how to perform all the many...
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Summary: An Introduction to Units, with some useful illustrations Series: Practical Math Duration: 00:42:47 Source: Introduction: Units are the bridge from learning abstract arithmetic operations on numbers to actually using maths to navigate the world of objects, distance, time, rates, volume, temperature, heat, current, voltage, and even cooking using recipes. Goal for the series: Embracing units, and carrying them along as you go, can help you... Topics: maths, units
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Starting from the basic ideas of mathematica, we give a detailed description about the way of linking of external programs with mathematica through proper mathlink commands. This article may be quite helpful for the beginners to start with and write programs in mathematica. In the first part, we illustrate how to use a mathemtica notebook and write a complete program in the notebook. Following with this, we also mention elaborately about the utility of the local and global variables those are... Source:
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This learning module, a continuation of the math I module, provides review and practice of the concepts explored in the earlier module at an intermediate level involving workplace problems. The following concepts are covered: instruction in performing basic computations, using general numerical concepts such as whole numbers, fractions, decimals, averages, ratios, proportions, percentages, and equivalents in practical situations. The problems are relevant to all aspects of the printing and... Topics: ERIC Archive, Adult Basic Education, Behavioral Objectives, Community Colleges, High School...
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This basic skills learning module includes instruction in performing basic computations, using general numerical concepts such as whole numbers, fractions, decimals, averages, ratios, proportions, percentages, and equivalents in practical situations. The problems are relevant to all aspects of the printing and manufacturing industry, with emphasis on basic measurement skills, converting fractions to decimals, reading a ruler, and figuring cost information that might be used in a customer... Topics: ERIC Archive, Adult Basic Education, Basic Skills, Behavioral Objectives, Community Colleges, High...
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Sets, numbers, geometrical figures, equations etc. are what mathematicians are talking about. Logic is their language. You cannot talk about any mathematical property without using the terminology of logic. There are a few quite fundamental logical concepts which everybody who wants to talk about math needs to know. This is a brief introduction to these concepts. TRUE or FALSE - this is the question most mathematicians are concern about. They express certain statement about some properties of... Topics: Unizor, Math, Math4teens, Lecture, Function, Algebra, Geometry, Graph, Invariant, Transformation,...
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Math Into LaTeX is for the mathematician, physicist, engineer, scientist, or technical typist who needs to quickly learn how to write and typeset articles and books containing mathematical formulas, and requires a thorough reference book on all aspects of LaTeX and the AMS packages (the enhancements to LaTeX by the American Mathematical Society). Key features of Math Into LaTeX: 0130091154.pdf 059a.pdf 1 10 100 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 101 1010 1011 1012 1013 1014 1015... Topics: ", Mathematics and LateX
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This booklet is intended to help mainstreamed mentally retarded, emotionally disturbed, or learning disabled high school students acquire a basic understanding of the responsibilities and working conditions of painters and to practice basic math skills necessary in the occupation. The first section provides a brief introduction to the occupation by focusing upon those job tasks of a painter with which the student is likely to be familiar. The next two sections deal with the work environment of... Topics: ERIC Archive, Career Awareness, Career Education, Disabilities, Emotional Disturbances, Employment...
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This booklet is intended to help mainstreamed mentally retarded, emotionally disturbed, or learning disabled high school students acquire a basic understanding of the responsibilities and working conditions of cashiers and to practice basic math skills necessary in the occupation. The first section provides a brief introduction to the occupation by focusing upon those job tasks of a cashier with which the student is likely to be familiar. The next two sections deal with the work environment of... Topics: ERIC Archive, Career Awareness, Career Education, Disabilities, Emotional Disturbances, Employment...
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This booklet is intended to help mainstreamed mentally retarded, emotionally disturbed, or learning disabled high school students acquire a basic understanding of the responsibilities and working conditions of machinists and to practice basic math skills necessary in the occupation. The first section provides a brief introduction to the occupation by focusing upon those job tasks of a machinist with which the student is likely to be familiar. The next two sections deal with the work environment... Topics: ERIC Archive, Career Awareness, Career Education, Disabilities, Emotional Disturbances, Learning...
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This booklet is intended to help mainstreamed mentally retarded, emotionally disturbed, or learning disabled high school students acquire a basic understanding of the responsibilities and working conditions of plumbers and to practice basic math skills necessary in the occupation. The first section provides a brief introduction to the occupation by focusing upon those job tasks of a plumber with which the student is likely to be familiar. The next two sections deal with the work environment of... Topics: ERIC Archive, Career Awareness, Career Education, Disabilities, Emotional Disturbances, Employment...
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NASA's Smart Skies™ features an interactive Air Traffic Control Simulator that enables students to apply proportional reasoning to make decisions and resolve conflicts in realistic air traffic control problems involving two or more planes. "Line Up With Math" is an introduction to the module for student in grades 5 through 9, where students are challenged to line up the planes safely, with proper spacing, on time, at a given intersection of jet routes. For more information about the... Topics: nasa, ames, nasa ames, smart, skies, smart skies, airplanes, aviation, math, education, students,... Source:
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This booklet is intended to help mainstreamed mentally retarded, emotionally disturbed, or learning disabled high school students acquire a basic understanding of the responsibilities and working conditions of electricians and to practice basic math skills necessary in the occupation. The first section provides a brief introduction to the occupation by focusing upon those job tasks of a electrician with which the student is likely to be familiar. The next two sections deal with the work... Topics: ERIC Archive, Career Awareness, Career Education, Disabilities, Electricians, Electricity,...
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This booklet is intended to help mainstreamed mentally retarded, emotionally disturbed, or learning disabled high school students acquire a basic understanding of the responsibilities and working conditions of programmers and to practice basic math skills necessary in the occupation. The first section provides a brief introduction to the occupation by focusing upon those job tasks of a programmer with which the student is likely to be familiar. The next two sections deal with the work... Topics: ERIC Archive, Career Awareness, Career Education, Computer Science Education, Disabilities,...
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This booklet is intended to help mainstreamed mentally retarded, emotionally disturbed, or learning disabled high school students acquire a basic understanding of the responsibilities and working conditions of cooks and to practice basic math skills necessary in the occupation. The first section provides a brief introduction to the occupation by focusing upon those job tasks of a cook with which the student is likely to be familiar. The next two sections deal with the work environment of the... Topics: ERIC Archive, Career Awareness, Career Education, Cooking Instruction, Cooks, Disabilities,...
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This booklet is intended to help mainstreamed mentally retarded, emotionally disturbed, or learning disabled high school students acquire a basic understanding of the responsibilities and working conditions of carpenters and to practice basic math skills necessary in the occupation. The first section provides a brief introduction to the occupation by focusing upon those job tasks of a carpenter with which the student is likely to be familiar. The next two sections deal with the work environment... Topics: ERIC Archive, Building Trades, Career Awareness, Career Education, Carpentry, Disabilities,...
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A project adapted an existing problem-solving curriculum to help unemployed or underemployed displaced homemakers and single parents qualify for job placement and training. Forty-five adult learners from the New Choice program participated. Handouts adapted from a prior Math Employment project and instructor-created materials were used. Handouts from level 1 of the previous project were simplified even further. Instruction was supplemented with self-help groups. Findings indicated the... Topics: ERIC Archive, Adult Basic Education, Curriculum Development, Displaced Homemakers, One Parent...
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This is an introduction to the theory of Shimura varieties, or, in other words, to the arithmetic theory of automorphic functions and holomorphic automorphic forms. Lecture Notes Collection FreeScience.info ID2322 Obtained from Topics: Abelian Varieties, "
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These self-paced student training modules on linear measurement and whole numbers are two of a number of modules developed for Pre-apprenticeship Phase 1 Training. Purposes of the modules are to teach students the necessary math concepts in linear measurement to enable them to read and use those concepts; and to teach students the necessary math concepts in the addition, subtraction, multiplication, and division of whole numbers to enable them to compute math problems in which these concepts... Topics: ERIC Archive, Addition, Behavioral Objectives, Division, Individual Instruction, Learning Modules,...
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The Conscience and the Fury 002: In Remembrance of Fuzzy Math Today's episode bought to you by: Harold Camping's lack of Rapture I. Introduction II. News of the Flesh The Libyan Dictator (Former) Dead OWS: One week anniversary, Naomiâs Arrest Cheesy Bacon Bowl III. Righteous Indignation Here is how it works. I bring on a friend to guess which story Jesse will find to be the worst of the week. This Week: Republican Debate 10/18/11 Quotes IV. Dirty Thoughts Testament of Political Views V.... Topics: c&F Podcast, occupy wall street, political testimony
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This paper provides for the elementary school teacher an introduction to the problem of mathematics readiness. The first part outlines the four developmental stages as seen by Piaget, and the manner in which schemata develop through the process of assimilation and accommodation. The second part consists of seven Piagetian tasks which a teacher may use to assess a child's stage of development. (MM) Topics: ERIC Archive, Child Development, Cognitive Development, Concept Formation, Developmental...
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2010May19 - Human Psychology â Vivekananda Institute of Human Excellence, Ramakrishna Math, Hyderabad This is a live recording of the speech, in English, [with a liberal sprinkling of Telugu and Hindi], given to a group of participants of a one-week programme on Mind Management, at Vivekananda Institute of Human Excellence, Ramakrishna Math, Hyderabad. This session, titled Human Psychology, was a part of the programme intended to motivate the participants. Human Psychology is a very... Topics: Human Psychology, selfishness, double standards, mind, behaviour, thinking, thoughts, improving the...
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We have expanded a set of numbers we deal with from natural to integer to rational. Every time this expansion was caused by something mathematicians wanted to do with existing numbers but could not because the result of a reverse operation was not always defined in the existing set of numbers. Thus, zero and negative numbers had to be added to natural ones to enable to define unrestricted subtraction. Rational numbers had to be added to enable division. Now consider an operation of squaring a... Topics: Unizor, Math, Math4teens, Algebra, Invariant, Transformation, Equations, Geometry, Graph, Complex,...
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This is an expanded version of a lecture given at the {\it Workshop on Theoretical Methods for Strongly Correlated Fermions}, held at the {\it Centre de Recherches Math\'ematiques}, in Montr\'eal, from May 26 to May 30, 1999. After general comments on the relevance of field theory to condensed matter systems, the continuum description of interacting electrons in 1D is summarized. The bosonization procedure is then introduced heuristically, but the precise quantum equivalence between fermion and... Source:
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The purpose of this case study is to highlight the integral role that progress monitoring (PM) plays throughout any Response to Intervention (RTI) process. This example uses a three-level, responsiveness-to-intervention (RTI) method for identifying students with learning difficulties. Using a fictional first-grade classroom as the setting for this example, readers are provided with a framework of the RTI identification process, along with frequent opportunities to test their comprehension of... Topics: ERIC Archive, Prevention, Learning Problems, Intervention, Case Studies, Identification, Grade 1,...
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The purpose of this case study is to highlight the integral role that progress monitoring (PM) plays throughout any response to intervention (RTI) process. This example uses a three-level, responsiveness-to-intervention (RTI) method for identifying students with learning difficulties. Using a fictional third-grade classroom as the setting for this example, readers are provided with a framework of the RTI identification process, along with frequent opportunities to test their comprehension of... Topics: ERIC Archive, Learning Problems, Intervention, Learning Disabilities, Case Studies, Grade 3,...
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This document is the teacher's edition of a learning module designed to help nonnative English speakers develop basic workplace mathematics skills. This module was developed by educators from the Emily Griffith Opportunity School. The math curriculum presented in how math might be taught to nonnative English speakers at a manufacturing worksite. Included in the manual are an introduction outlining the module's objectives and scope, eight session outlines, an appendix explaining basic... Topics: ERIC Archive, Adult Basic Education, Behavioral Objectives, Cultural Differences, Learning...
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A solid background in math, science, and technology is vital to competing in today's workforce, as well as necessary to understanding the world in which we live. Mastery of technology is now necessary even in traditionally vocational careers, as some of today's automobiles have more computing power than a personal computer. New York City private sector job growth has been concentrated in areas which require a foundation in math, science, and technology. This report looks at recent steps taken,... Topics: ERIC Archive, Academic Achievement, Educational Change, Elementary Secondary Education, Higher...
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We have expanded our choice of numbers from natural (1, 2, 3 etc.) to integer (adding 0 and negative numbers), to rational (adding fractions), to real (adding irrational numbers like square root of 2). Every expansion we made was initiated by a desire to do something that seemed to be reasonable but impossible to accomplish in the old framework. The last step on this way is introduction of complex numbers which will open one more previously closed door - extracting roots of any even degree from... Topics: Unizor, Math, Math4teens, Algebra, Invariant, Transformation, Equations, Geometry, Function, Graph,...
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This booklet is intended to help mainstreamed mentally retarded, emotionally disturbed, or learning disabled high school students acquire a basic understanding of the responsibilities and working conditions of motor vehicle mechanics and to practice basic math skills necessary in the occupation. The first section provides a brief introduction to the occupation by focusing upon those job tasks of a motor vehicle mechanic with which the student is likely to be familiar. The next two sections deal... Topics: ERIC Archive, Auto Mechanics, Career Awareness, Career Education, Disabilities, Emotional...
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This booklet is intended to help mainstreamed mentally retarded, emotionally disturbed, or learning disabled high school students acquire a basic understanding of the responsibilities and working conditions of sheet metal workers and to practice basic math skills necessary in the occupation. The first section provides a brief introduction to the occupation by focusing upon those job tasks of a sheet metal worker with which the student is likely to be familiar. The next two sections deal with... Topics: ERIC Archive, Blueprints, Career Awareness, Career Education, Disabilities, Emotional Disturbances,... | 677.169 | 1 |
Parabola Lesson Plan
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Here is my parabola lesson plan. This lesson is designed to help students understand how the variables change when a parabola is moved or flipped. This lesson can be used with geogebra.org as I have designed or with a graphing calculator or how you see fit. Enjoy! | 677.169 | 1 |
This book provides a combination of theoretical and
practical tools from which any advanced undergraduate and graduate student, professional quant and researcher will benefit. It differs from existing books in quantitative finance from the ready-to-use software
and accessible theoretical tools provided as a complete package. As a bonus, the book also gives a detailed exposition on cutting-edge theoretical techniques published here for the first time | 677.169 | 1 |
Algorithmic Graph Theory
Algorithmic Graph Theory is that branch of Mathematics that deals with mathematical structures that are used to model pairwise relations between objects from a certain collection, together with algorithms used to manipulate these models. Algorithmic Graph Theory is used to model many types of relations and process dynamics in physical, biological and social systems. This course helps students develop the mathematical underpinnings of the theory of graphs and algorithms, a branch of discrete mathematics. This course provides an excellent background to an exciting area of mathematics that has applications in fields like computer science, economics, and engineering. Prerequisites: CSC 233, foundations of computation or MATH 270, linear algebra or MATH 223, foundations of advanced mathematics. It will be beneficial for the student to be fluent in a programming language for this course.
Fall Semester information
323A: Algorithmic Graph Theory | 677.169 | 1 |
Handbook Of Mathematics And Computational Science
Hardcover | July 23, 1998"It is the best text of its type that I have come across to date...an excellent resource for anyone involved in mathematical practice up to and including degree standard...it is a pleasant experience to flick through it at leisure, dropping in here and there on some of the thousands of results the book holds. It is beautifully illustrated and set out...we have here a comprehensive volume whose worth will not readily fade with time...If you feel the need to own a mathematical reference to see you through school and university mathematics to graduation, you couldn't do much better than to buy this one." --Mathematics TodayA complete desk-top reference for working scientists, engineers, and students, this handbook serves as a veritable math toolbox for rapid access to a wealth of mathematics information for everyday use in problem solving, examinations, homework, etc. Compiled by professional scientists, engineers, and lecturers and internationally renowned for its clarity and completeness, The Handbook includes hundreds of tables of frequently used functions, formulae, transformations, and series, plus many applications. The layout, structured table of contents, and index make finding the relevant information quick and painless.
Mathematicians, students and researchers constantly refer to various sources for different formulas, equations, etc. "The Handbook of Mathematical Formulas" puts up-to-date equations, formulas, tables, illustrations, and explanations in one invaluable reference volume. Fully up to date, this handbook will quickly become the standard reference for mathematicians and students. 545 illus
Editorial Reviews
From the reviews"It is the best text of its type that I have come across to date - an excellent resource for anyone involved in mathematical practice up to and including degree standard (...) it is a pleasant experience to flick through it at leisure, dropping in here and there on some of the thousands of results the book holds. It is beautifully illustrated and set out (...) we have here a comprehensive volume whose worth will not readily fade with time (...) If you feel the need to own a mathematical reference to see you through school and university mathematics to graduation, you couldn't do much better than to buy this one" (MATHEMATICS TODAY) | 677.169 | 1 |
Course Summary
The MTLE Middle Level Mathematics exam is used to license current and future Minnesota teachers wanting to teach grades 5-8 mathematics. This study-guide course will help you prepare for this exam by reviewing with you the properties and procedures used in arithmetic, algebra, geometry, probability and statistics. | 677.169 | 1 |
Math 20: Discrete Probability
Course Information
In this class we cover discrete probability, which might be described as the study of experiments with a discrete (usually finite) collection of possible outcomes. Some familiar examples of such experiments include flipping coins and shuffling cards. Through both rigorous mathematical reasoning and looking at simulations of events, we will gain a better understanding of the way probability works.
An online version of the textbook is available (free-of-charge) here and a printed version is available at Wheelock Books.
A nice feature of this book, from the perspective of Dartmouth students, is that many of the examples and exercises are set at Dartmouth. Both of the authors of this textbook were Dartmouth professors at some point.
In order to get a good intuition about probability, it will be important to test out some simulations on your own. Here are some python scripts I have written that will allow you to simulate various probabilistic experiments. If you have a python interpreter on your computer, you can copy and paste them into that interpreter. If not, you can either download one (recommended!) or else use one online. (Be sure to set it to run in Python; it won't work if you run it in C!) Some of these programs include graphics. These will not run in the online interpreter. They will run if you have an interpreter on your computer and install the matplotlit and numpy packages.
Feel free to modify these programs and try other experiments if you know how.
You are allowed, and even encouraged, to work with other students on the homework problems, but you must write up your solutions independently and in your own words. You may also consult other people or sources other than the course text, your class notes, and the instructor when working on the problems. However, you are expected to understand the solutions you write.
All exams are closed book, with no notes or calculators allowed. No help will be given or received | 677.169 | 1 |
Advanced Trigonometry
This volume provides a welcome resource for teachers seeking an undergraduate text on advanced trigonometry. Ideal for self-study, this text offers a clear, logical presentation of topics such as the properties of the triangle and the quadrilateral; sub-multiple angles and inverse functions; hyperbolic, logarithmic, and exponential functions; much more. | 677.169 | 1 |
T.G., Florida
I am actually pleased at the content driven focus of the algebra software. We can use this in our secondary methods course as well as math methods. Keith Erich Johnston, KS
A plane flying with the wind can cover a certain distance in 2 hours. The return trip against the wind takes 2.5 hours. How fast is the plane and what is the speed of the air, if the one -way distance is 600 miles?
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practice sums on the topic - algebraic expressions and identities for class viii | 677.169 | 1 |
Synopses & Reviews
Publisher Comments
This book contains selected topics from the history of geometry, with "modern" proofs of some of the results, as well as a fully modern treatment of selected basic issues in geometry. The book aims at future teachers of mathematics. All too often the geometry which goes into the syllabus for teacher-students presents the material as pedantic and formalistic, suppressing its dynamic character and its role as part of the foundation for our common cultural heritage. The motivation for the book is to open up these aspects of the field. Another motivation is to provide an invitation to mathematics in general. It is an unfortunate fact that today, at a time when mathematics and knowledge of mathematics are more important than ever, phrases like math avoidance and math anxiety are very much in the public vocabulary. An important task is seriously attempting to heal these ills. Thus the book also aims at an informed public, interested in making a new beginning in math.
Synopsis
Mathematics is more important than ever, but phrases like "math avoidance" and "math anxiety" are very much in the public vocabulary. In addition to providing an invitation to mathematics in general, this book emphasizes the dynamic character of geometry and its role as part of the foundation for our cultural heritage. Aimed at an informed public and future teachers of mathematics, it seeks to heal the ills of math phobia in society. | 677.169 | 1 |
Gcse maths data handling coursework
Study Guides. Tough GCSE topics broken down and explained by out team of expert teachers. Learn more. Support information for GCSE Maths students Coursework : Home. Outline for Handling data coursework:. Saturday 07/02/04 Deal class coursework workshop at Dover. GCSE DATA HANDLING handling data coursework maths COURSEWORK. GCSE Maths (Re-sits only) learning resources for adults, children, parents and teachers organised by. Gcse maths coursework handling data if you are This will stop any Some advisors are willing to offer a choice of two or greatest challenge threw dissertation topics. With over 20 years of trust in our products, the international boating community knows that when it comes to a mount for electronics, they choose 'a Scanstrut'.
Support information for GCSE Maths students Coursework : Home. Outline for Handling data coursework:. Saturday 07/02/04 Deal class coursework workshop at Dover. Home ; GCSE Maths ; Handling data ; Handling data. The final topic we cover is handling data. This topic will also be useful to you if you are taking the GCSE. Study Guides. Tough GCSE topics broken down and explained by out team of expert teachers. Learn more. With over 20 years of trust in our products, the international boating community knows that when it comes to a mount for electronics, they choose 'a Scanstrut'.
GCSE Coursework. GCSE students no longer have to complete Maths coursework tasks. The following is left as a guide to investigative tasks and data handling projects.
This web page contains a lot of revision material aimed at students preparing for their GCSE Maths examination GCSE DATA HANDLING COURSEWORK. For your GCSE.
GCSE Data Handling Coursework. Stage 1: Set up a discussion about how to make inferences from statistical data. Especially making statements about differences between. GCSE Data Handling Coursework. Stage 1: Set up a discussion about how to make inferences from statistical data. Especially making statements about differences between. Coursework in Mathematics A discussion paper October 2006. students are unaware of the excitement of studying maths and. GCSE data handling coursework with the. I've posted here before about the incompetant maths teacher I have for my final GCSE year, but now it is becoming more crucial that I understand what I nee. | 677.169 | 1 |
You are about to embark on the course which lays the foundation for virtually all of higher mathematics. In previous courses you have occasionally used a letter to stand for a number you seek to find. Now you will be less concerned about what number the letter represents, and will concentrate on things that are true just because it is a number. The letters used will be called variables, because they can stand for different numbers at different times. Expressions containing these variables can represent quantities in the real world, such as how high a ball is above the ground at various times after it was thrown. By learning how to operate with such expressions, you will be able to predict such things as how to operate with such expressions, you will be able to predict how high the ball is at a given time, how long it takes to reach a given height, and when it will be back down. | 677.169 | 1 |
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Description
"GCSE Modular Mathematics for Edexcel" is the perfect preparation for the two-tier modular GCSE examination from Edexcel. This book has been written especially for Edexcel students and their teachers and provides complete coverage of Foundation Unit 4 of the modular specification. The course comprises student textbooks, teacher's resources, and digital resources. | 677.169 | 1 |
Find a Camp Strake, TX MathLinear Algebra is the study of matrices and their properties. The applications for linear algebra are far reaching whether you want to continue studying advanced algebra or computer science. I studied logic, as math major, both in the context of my courses requiring proofs, as well as a separat... | 677.169 | 1 |
1.Ability to understand the concept of
function, and functional attributes such as domain, range, oddness/evenness,
increasing/decreasing, and symmetry.Ability to determine these attributes for a function given its
graph and/or equation.Ability to
perform the algebra of functions: sum, difference, product, quotient,
composite, and inverse.
2.Ability to graph absolute value,
reciprocal, square root, polynomial, rational, piecewise defined, logarithmic,
exponential, and trigonometric functions and the ability to use such graphs to
solve applied problems and to understand the significance of attributes of the
graph to such applied problems.
3.Ability to solve appropriate applications
of determining maximum or minimum of a quadratic function,
zeros of polynomials, compound interest, and exponential growth and decay.The ability to identify and
articulate the significance of graphical components such as x-intercepts,
horizontal asymptotes, intervals of increasing or decreasing in a mathematical
model/application.
You will also need one Math 1127 Course Packet with my
name listed on the cover.
Calculators:A graphing calculator is highly
required. I recommend a TI-83 or TI-86.
MathCenter: Help is available in the MathLearningCenter.The hours are M-Th: 9-6, and F: 9-1.
Grading Criteria:
Quizzes:worth
approximately 100 points (no make-ups)
Classwork/Projects:worth approximately 100 points
Exams:4 exams each worth 100 points
(no unexcused make-ups)
Final Exam:worth 200 points
Grade Scale:A = 90-100%
B = 80-89%
C = 70-79%
D = 60-69%
F = Below 60
P = Minimum of 70
Important Dates:
January 12, Classes beginMarch 16-20,
Spring Break
January 19, No classApril
17, No Class
February 16, No ClassApril
24, No Class
February 24, Student Success
DayApril 22, Last Day to
Withdraw
February 27, No classMay 5/13,
Final Exam 7-10 am
Homework:
Homework will not be graded
on a regular basis, but a list of homework problems will be provided.It is expected that students do the homework
problems so that they have a solid understanding of the material.If you have questions on any homework
problems it is your responsibility to ask for help in class, during office
hours, or in the math center.Keep up
with your assignments, because daily work done completely will make test and
quiz preparation significantly easier.Occasionally problem sets, supplemental worksheets and review sheets for
exams will be collected and graded for accuracy.
Quizzes:
Quizzes are given about once
a week and cover the previous week's material.These may be in-class quizzes or take-home quizzes.Each is worth 10 points. Keeping up with
daily work will give you better success on these weekly quizzes! The lowest
quiz score during the course will be dropped and the remaining scores will be
averaged together for approximately 100 points.IF YOU ARE ABSENT FOR A QUIZ, THEN THIS WILL BE COUNTED AS YOUR DROPPED QUIZ.NO MAKE-UP QUIZZES WILL BE GIVEN!Situations (e.g., extended illness, death
in family, etc.) that cause many missed classes will be dealt with on a
student-by-student basis.
Classwork:
Occasionally there will be
individual or group assignments during the class period that will be
collected.These are meant for
additional practice and problem solving.They will be graded on completeness and correctness.If you
are absent for a classwork assignment, it is your
responsibility to make it up in a timely manner.There may also be take-home assignments
or group projects that will be graded as well.These assignments will total no more than 100 points of your final
grade.
Exams:
There will be four exams
worth 100 points each.There will be one
graphing gateway exam worth 50 points.The
final exam will be comprehensive and worth 200 points.YOU
MUST CALL OR SPEAK TO ME WITHIN 24 HOURS OF THE EXAM DAY IN ORDER TO BE ALLOWED
TO SCHEDULE A MAKE-UP EXAM.All make-up
exams need to be completed before I hand back the exams.IF NO CONTACT IS MADE, THEN NO MAKE-UP WILL
BE ALLOWED.
Attendance:
Even though no official
attendance is taken, regular attendance is recommended and crucial in a
mathematics class since subsequent classes are based on ideas developed in
previous classes.If you do have to miss a class, you are still responsible for learning
the material that was taught in that class and for any exams, quizzes, classwork or homework missed or due the next class.YOU
WILL STILL BE EXPECTED TO TAKE AN EXAM OR QUIZ ON THE SCHEDULED DAY EVEN IF YOU
WERE ABSENT THE DAY BEFORE.All make-up work needs to be completed in
a timely manner at the discretion of the instructor.If an absence is unexcused, then make-up work
may not be accepted.
Other Policies:
As a courtesy to all, please
be sure that your cell phone and pager are turned off during class.
Be on time.It is very disruptive to those around you if
you come in late.
Be courteous.
Be in class to be
successful.
You are responsible for what
happens in class whether you are in attendance or not.
Do not cheat.Any cheating will result in a zero on that
test, quiz, homework or classwork. Other actions may
be taken at the discretion of the instructor.
Access/Accommodations:
Any student who feels that he
or she may need an accommodation for a disability can contact the Disabilities
Service Office at (651) 450-8628, or visit them on the second floor of the
Library Building.
Satisfactory
Academic Progress:
Students
need to maintain both a cumulative GPA of 2.0 and cumulative completion rate of
at least 67% of all attempted credits for each term of attendance.If a student fails to meet these
requirements, they will be placed on academic and/or financial aid probation. | 677.169 | 1 |
Sunday, April 23, 2017
Gratuit Mathwords: Index for Advanced Algebra Pre Calculus Index for Advanced Algebra Pre Calculus Math terminology from Pre Calculus, Advanced Algebra, Functions, and Analytic Geometry. Communications in Algebra: Vol 45, No 10 tandfonline.com Point primitive linear spaces with number of points being a product of two primes Calc101.com Automatic Calculus, Linear Algebra, and ... derivatives, integrals, graphs, linear equations, matrix algebra automatic calculus help on the web NOW... no software download, no sign up hassle How to solve simultaneous equations by substitution. This topic is part of the TCS FREE high school mathematics 'How to Library', and will help you to solve simultaneous equations by substitution. Linear Algebra Toolkit Step by step solutions of problems such as Gauss Jordan reduction, calculating the determinant, and finding a basis of a space spanned by given vectors. Linear Algebra Toolkit Old Dominion University This Linear Algebra Toolkit is composed of the modules listed below. Each module is designed to help a linear algebra student learn and practice a basic linear ... Algebra Augmented Matrices Cheat Sheets Tables Algebra, Trigonometry and Calculus cheat sheets and a variety of tables. Class Notes Each class has notes available. Most of the classes have ... Inverse of a matrix by Gauss Jordan elimination Math Help To find the inverse of matrix A, using Gauss Jordan elimination, we must find a sequence of elementary row operations that reduces A to the identity and then perform ... Algebra More on the Augmented Matrix Current Location : Algebra (Notes) Systems of Equations More on the Augmented Matrix Types of Matrices vitutor.com Types of matrices, row, column, rectangular, square, zero, upper triangular, lower triangular, diagonal, scalar, identity, transpose, regular, idempotent, involutive ... Solving linear equations A complete course in algebra 9. LINEAR EQUATIONS. The law of inverses. The four forms of equations. Transposing. A logical sequence of statements. Transposing versus exchanging sides Read/download Matrix Algebra (Econometric Exercises, Vol. 1) ebook full free online. | 677.169 | 1 |
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Prentice hall algebra 2 homework help
Engage your students with Prentice Hall Mathematics: Algebra 1, Geometry, Algebra 2, a Pearson Math Curriculum. Arson is your one stop shop for classroom? Always, please. ClassZone Book Finder? Hi i am writing u to ask what is the state requirments while growing for person medical needs. Thousands of users are using our software to conquer their algebra homework. At will make it completely legal where if visited by the law i wanna. Ad educational articles, parenting articles, more . We have made some important updates to Pearson SuccessNet. Llow these simple steps to find online resources for your book. Welcome to Pearson SuccessNet. Please see the Feature Summary for more details. Re are some of their experiences:Education and parenting articles offer expert tips and information on raising kids!
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Technology can be used to supplement a modern algebra course
to increase exploration of the relationship of
abstract algebraic structures to real life problems.
We will look at the effectiveness of this in a Spring 2000 course (see
).
We will explore Maple demos on the applications of modular arithmetic
to check digits for money orders,
and the application of the direct product of cyclic groups
to HBO cable security. We will then talk about followup WebCT
quizzes and activities, and discuss the students' experiences with the
Maple demos and WebCT activities.
This past spring I taught modern algebra to 12 students. The class was a first proof-writing
course for many of them. Most of them wanted to be future high school teachers and this
would be the only algebra course that they would take. The focus of the course was on
proof-writing and a sampling of algebraic structures.
Assignments were mainly standard
problem sets with one or two revisions allowed. We also did
group work and presentations in class.
I also wanted students to learn some
applications of algebraic structures to real life. This
was done mainly via Maple demos, which are accessible from my web page.
We also
learned about the history of algebra through algebraists and their
mathematical
accomplishments.
During this talk, we'll examine my use of technology in the course, specifically Maple and
WebCT, and the effect it had on the students.
Our first Maple demo took place during class in the computer lab about 5 weeks
into the course. It was on modular arithmetic and was based on a section from Joe
Gallian's Contemporary Abstract Algebra. Students were to work with one other person
and each group was to type in their answers to questions on the computer. We first defined
a mod n as the remainder of a divided by n, and we had some questions on this, which they
did well on.
The demo explained that the US post office uses mod 9 for the check digit on money
orders. The US post office check digit is a 10-digit number mod 9. So, you hand me any
10-digit number, for example, the number in this demo. You look at the remainder of it
divided by nine and the answer, in this case 2, is the check digit.
The post office then uses the 11-digit number formed by a 10-digit code with the check
digit appended onto the right side. The post office puts this 11-digit number on its money
order.
So, if we wanted to check for a forgery or if a money order number was incorrectly entered
into a computer, the program would remove the last digit and check to see that it equals the
remaining 10 digits mod 9.
During the rest of the demo, students were asked whether certain typing errors could be
detected via the check digit. As I came around the computers and looked at their answers, I
noticed that they did very well. We went over the demo the next class day.
Subsequently they had a generalized version of check digits as a problem on their problem
set. They had their first test a couple of weeks later that did not include this material. This
first test, on proof writing, sets functions and rationality was based on class work and
standard problem sets. Even though they had done a couple of revisions on each problem
set, the material still had not sunk in - they did not do very well.
So, I decided to try something new with them to help them jell the material -
WebCT.
WebCT is a web program designed for teaching online. It is available
at numerous unniversities and can be used by and department whose university
has a site license. I mainly used the online quiz and bulletin board
features of WebCT, which are also available in other software.
This is what the students would see once they logged in using their password. I mainly
used the bulleting board and online quiz features of WebCT to supplement the standard
problem sets and Maple demos, which I kept doing.
If I student clicked on online quizzes from this page, they would see the following:
This is a list of quizzes available.
The instructor can set the number of tries allowed from 1 to 5 for each quiz.
Notice that the first quiz was not
offered until the end of
March. That is because I decided to use WebCT for drilling material because of the results
of the first test. I learned about WebCT details over spring break in a workshop my
university offered. We are going to look at the short answer part of test 2, given a week
after I started using WebCT in the course.
Question 4 asked about the check digit. Student's
should have marked no to answer the
question. There were 5 questions on this part of the test.
If I have time at the end of the
talk,
I'll show you how I used multiple choice and matching to test on
proof writing skills. (see below)
The great advantage of WebCT quizzes is that when the students are
finished with the quiz, they click "Finish" and then
WebCT instantly grades their work and offers instant feedback.
The students did better on this test than on test 1, especially on proof wiring questions.
They said that the ability to keep redoing
quiz 1 and the instant feedback had helped them a
lot.
But, I decided to rethink my Maple demo strategy of having them answer questions and also
going over the demo in the next class, since they did terribly on this problem on the check
digit.
This Maple demo on the application of direct products of cyclic groups to data security,
based on Gallian's Contemporary Abstract Algebra, was made with questions the students
would andwer, similar to the other demo that we examined. But, this time, I directed them to
not only type their answers into Maple, but also for students to post their answers to the
WebCT bulletin board.
We'll carefully examine one of the questions that I asked them and their posted answers
and discuss how their posts helped me identify problems tha they were having.
A binary string is a string of 0s and 1s. We can think of this as an element of the direct
sum of Z_2, the cyclic group of order 2. Then, we can define an operation, *, on bineary
strings via adding corresponding digits mod 2.
We noticed via examples that 2 strings
sum mod 2 to the 0 string exactly when they are
identical to each other.
I wanted to prove this for them, since this is the bases of a data
security system used by
HBO to protect its television signals.
I just did one direction of the proof and asked the students if it was correct.
They had been asked similar questions in the past, with my proofs sometimes
correct but sometimes incorrect (ie they were not necessarily expecting
to find an error).
So, we want to prove that if 2 binary strings sum mod 2 to the 0 string,
then each corresponding binary string digit is equal.
So, I assume that the if part of the statement is true, ie we are given that 2 binary strings
sume mod 2 to the 0 string. And, I want to show that each corresponding binary string digit
is equal. So, in my notation here, we want to show that a_i=b_i for all i, and our asumption
that the 2 binary strings sum mod 2 to the 0 string tells us, after rewriting this using
definitions, that a_i +b_i mod 2 = 0 for all i.
So fix i. Now a_i, b_i in {0,1} means that we have 4 cases for a_i+b_i mod 2.
So we look at our 4 cases and compare them with the fact that our given statement implied
that a_i +b_i mod 2 = 0. This is only true in cases 1 and 4. In both of these cases, a_i
=b_i , which is what we wanted to prove.
I asked the students if my proof was correct.
Notice my typo of 2 instead of 4. I
announced this typo in class when a student asked if this was the mistake they were
supposed to find.
The rest of the Maple demo is about the relation of this to HBO scrambling. You can
access this demo from my web page.
When I went around the room and talked to them about this question they told me that they
thought the proof was correct except for the typo.
For this question, Alan posted:
"Other than the fact that it should say cases 1 and 4 rather
than cases 1 and 2, the proof seems to be correct".
While Anna wrote: "The proof is more than likely
correct since you have shown that 1 and
4 work, but what about 2 and 3? Would that not show a contradiction?"
In Monday's class we went over the fact that the given info told us that
we had to be in
either case 1 or 4.
A number of students had been confused about this, but hadn't
brought it up in their group
or to me. I was pleased they they brought it up in the newsgroup posts instead of just
agreeing with other posts. For some reason, for certain, often quite, students, posting felt
like a safe place for them to post their questions.
WebCT really helped the students in this course.
They loved being drilled on webCT
quizzes, and felt in evaluations that they learned a lot from this.
It revitalized the class, which had been tired from working hard to learn
proof-writing skills via standard problems sets and classroom presentations
and group work.
This newfound energy helped the class continue
to work hard and succeed at proofs.
I think that it was a good
supplement to the problem sets and Maple demos and did help to
jell the material for them.
The Maple demos enabled me to communicate interesting
topics to the students that
would have taken a long time to do by hand. Maple
was used interactively as much more than just a calculator
(see
below)
While the bulletin board was used lightly,
it also helped to reach more students by forcing
them to communication their ideas in a different forum that especially normally quiet
students found less intimidating.
Click "OK" if a box pops up with a message which might
resemble:
Time remaining: blah minutes.
OR
Your time is up. Please submit your quiz now. For all but the "final exam", you are seeing what the
students see when they begin taking the quiz.
Note that the grading, submitting and other features
accessible via buttons will not work here since you are not in WebCT.
If you would like to try WebCT for yourself and take a quiz, e-mail me
at greenwaldsj@appstate.edu and
I will create a guest password into WebCT for you.
Quiz 1 Solution by radicals, Fermat's Last Theorem,
definitions of function, one-to-one, onto, and the negation of the
definition of continuity.
Quiz 2 Groups Test 2 short answerInduction, real numbers,
modular arithmetic applications and Fermat's Last Theorem biographies. Test 2 long answer Induction.
Note that WebCT can't
grade this to give instant feedback -
the instructor must go into webct to grade long answer problems
. Quiz 3 Groups and Rings
Quiz 4 Algebraic Structures
Quiz 5 Algebraic Structures
Graded WebCT section of the final exam
What the students see after they submit. (This is set to reveal the
answers although usually I turn this feature off.) The remainder of the final
exam consisted of standard proof-writing problems.
E-mail questions or comments about these pages to
Dr. Sarah Greenwald, greenwaldsj@appstate.edu | 677.169 | 1 |
Citation Machine helps students and professionals properly credit the information that they use. Te sources in APA, MLA, Chicago, Turabian, and Harvard for free. ..
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Llow these simple steps to find online resources for your book. Notice that the ball covers an equal distance between flashes. ClassZone Book Finder. En the. Lone Star College Online provides distance learning for students wishing to earn college credit with Lone Star College. Improve your skills with free problems in 'Translations: graph the image' and thousands of other practice lessons. T's assume this distance equals 20 cm and display the ball's behavior on a graph plotting its x? What is 'Demand' Demand is an economic principle that describes a consumer's desire and willingness to pay a price for a specific good or service. Is wikiHow teaches you how to use spreadsheet data to create a graph in Microsoft Excel or Google Sheets. L designed to be highly modular, quick to execute, and simple to use via a clean and. Dlib contains a wide range of machine learning algorithms. How to Create a Graph Using a Spreadsheet. Fun math practice. Homepage of GraphCalc The ultimate windows graphing calculator softwareLone Star College Online provides distance learning for students wishing to earn college credit with Lone Star College. Product information from this developer of mathematical educational software for colleges and universities. | 677.169 | 1 |
Welcome to Math for Teachers!
This is the course homepage and syllabus for Math 1136,
Measurement and Geometry for Teachers. Here you will find our course
calendar, current assignments, basic course information, and links to
additional content of interest. This syllabus may need to be updated
as the course progresses, and you will always find the current version
at
Excellent math teachers have been far too scarce in American
education. This course and its prequel, Math 1135, give you the keys
to how and why elementary mathematics works. We
will develop a thorough understanding of the ideas, how they are
related to eachother, and how they are related to more advanced ideas.
This is the basic knowledge which underpins truly great teaching!
Course Objectives
The course consists of fundamental topics in geometry and
measurement. This includes the concepts of length, area, volume,
angles, units of measurement, precision and error. Algebraic
expressions and functions, primarily in the linear case, are
introduced to express geometric relationships.
The basic properties of two and three dimensional geometric shapes
and their relationships are a central part of the course. Special
emphasis is put on geometric reasoning through problem solving,
including unknown angle, length, area, and volume. The course also
covers topics on transformations in the plane, symmetries, congruence,
and similarity. Some geometric constructions and basic geometric
proofs are included. The skills developed throughtout the course are
applied at the end in a brief introduction to probability.
Homework 19 due Friday, 04/15
Homework 18 due Friday, 04/08
Turn in problems from the review sheet.
Homework 17 due Monday, 04/04
Problems 14.1.8 — 14.1.13
Additional problem: Plot a line of slope 2/3 and write an equation
for it. Rotate the line by 90 degrees around the origin. What is
the slope of the rotated line?
You can use this link to
download graph paper.
Homework 16 due Friday, 04/01
Problems: 13.4.1, 14.1.4, 14.1.5, 14.2.2, 14.2.3
You can use this link to
download graph paper.
Additional problem: Draw a pattern which, when cut out and folded
up, makes an oblique rectangular prism.
Homework 15 due Monday, 03/28
Problems: 13.2.14, 13.2.17, 13.3.19
Writing Assignment due Wednesday, 03/23
See guidelines and suggested topics in class email or here. I've opened a
dropbox in our Carmen course for you turn your papers in. Please
submit your document in pdf and use a filename that begins with your last name.
Midterm Exams (3):
Final Exam:
Attendance
Active participation in class is an essential part of this course,
and so attendance every day is required. Please let Niles know as
soon as possible if an illness or other commitment will prevent you
from attending. Homework is due at the beginning of each class, and
late homework cannot be accepted unless prior arrangements have been
made. See full late policy below.
Calculators and Mathematical Software
There are a variety of modern tools which support mathematics
learning and application. We'll use several of them in this course,
but no technology will be used on the quizzes or exams. In particular,
calculators and cell phones will not be permitted. The only materials
you'll need are writing instruments and your mind.
Assessment
Your final grade will be based on written homework, written and
oral in-class participation, quizzes, midterms, and a final exam. The
precise breakdown is as follows:
In-class participation: 12%
Homework: 6%
Quizzes: 13%
Writing Assignments: 4%
Midterm exams: 15% each, for a total of 45%
Final exam: 20%
Participation
Thoughout this semester we will be focused on the how
and why of elementary mathematics. This means that you will
be responsible both for knowing the content and for knowing how to
explain the content. We will practice this in a variety of
ways, and much of this practice will take place in class.
Teaching mathematics requires listening carefully to students,
assessing their ideas, and responding in ways that make sense. Our
class participation is designed to practice these essential skills.
You will have opportunities on a daily basis to listen to your fellow
classmates explain ideas and ask questions. You will be asked to
respond with your ideas and with additional questions. Together we
will see how and why mathematics works! Participating in this course
includes all of the following:
Show interest in mathematical ideas.
Show interest in different ways of approaching mathematical ideas.
Listen carefully to different ways of solving a problem.
Carefully evaluate a proposed method of solution.
State whether you agree or (respectfully) disagree with a statement.
Show interest in learning with and from others.
Homework and Quizzes
Homework and Quizzes will be scored using the rubric below. Scores
are based both on mathematical correctness and quality of
explanations. Homework should be typed and presented as you would an
essay. If necessary, you may draw diagrams by hand on separate pages.
Quizzes will be hand-written during the first 10 or 15 minutes of
class.
The homework is intended to give you time to develop your
explanations and understanding of the content. You are encouraged to
work with your classmates on this, but you must write your own
explanations. Homework is designed to help you learn, and not as an
assessment tool. Therefore grades for homework will be recorded on a
complete/incomplete basis (scores of 3 and higher are complete). The
numerical scores are given only for your information.
The weekly quizzes are opportunities to evaluate your current grasp
of the material. They will be very short and based on previous
homework problems or class activities. Quiz grades will be recored as
scored.
Late Work Policy
If you miss class on the day homework is due, or forget to bring a
printed copy of your homework, you may send me a copy by email the
next day. I will accept up to three homeworks this way.
If you must miss class on the date of a quiz or exam, please do the
following:
Contact me before the time of the assessment to let me know
you will be away.
Make up the assessment within two days of your return to campus,
and before the next class if possible.
Miss no more than two assessments this way.
If you do each of the items above, you will have no penalty. For
each item that you do not complete there will be a 10% reduction in
your final score.
Exceptions may be made in the case of an emergency; please contact
me as soon as you are able.
Grading Rubric
The descriptions on the rubric below are meant as a guide to help
answer the question What constitutes a good explanation of
mathematics? This is a subtle and challenging
question—one that is worthy of considerable time and energy.
As you write your explanations, consider the distinction between
Procedure and Conceptual Meaning. A complete
explanation addresses both of these, but the conceptual meaning is
essential. Explanations that address procedure only are a
disservice to students and do not support their future learning.
They are also much less interesting!
Quizzes and exams will follow this scale; Niles will use these
for comments on homework too, although homework grades are recorded
on a complete/incomplete basis. Homework will be considered
complete if the average score is R (3) or higher.
G++
Exemplary
Excellent work that exceeds the assignment guidelines.
G+
Good plus (10)
Correct procedure with an explanation that effectively
addresses relevant definitions and concepts.
G
Good (9)
Correct procedure with nearly complete explanation.
Em/G
Emerging/Good (8)
Well-developed but incomplete explanation.
Procedural errors are minor or nonexistant.
GEC Information
This Mathematics course can be used, depending on your degree
program, to satisfy the Quantitative and Logical Skills category of
the General Education Requirement (GEC). The goals and learning
objectives for this category are:
Goals:
Courses in quantitative and logical skills develop logical
reasoning, including the ability to identify valid arguments, use
mathematical models and draw conclusions based on quantitative
data.
Learning objectives:
Students comprehend mathematical concepts and methods adequate to
construct valid arguments and understand inductive and deductive
reasoning, scientific inference and general problem solving.
Support Services
All students are encouraged to take advantage of campus support
services. These include tutoring, academic advising, counseling, and
the math learning center! A complete list is available at
Accommodation Statement
If you need accommodations due to a disability, you must first
register with the Office for Disability Services (ODS) at 226 Warner
Center, ext. 441. After you receive your authorized accommodation from
ODS, you should show me your access plan and discuss your needs with
me. Ideally, we should meet within the first week of class.
Academic Misconduct Statement
It is the responsibility of the Committee on Academic Misconduct to
investigate or establish procedures for the investigation of all
reported cases of student academic misconduct. The term "academic
misconduct" includes all forms of student academic misconduct wherever
committed; illustrated by, but not limited to, cases of plagiarism and
dishonest practices in connection with examinations. Instructors shall
report all instances of alleged academic misconduct to the committee.
For additional information, see the Code of Student Conduct: | 677.169 | 1 |
LAPLACE TRANSFORMATIONS aims to present elementary theories of Laplace transforms in the forms suitable for use of students whose main interest in the subject are based on simple mathematical ideas. The book has been organized in a logical order and the topics are discussed step by step in a systematic manner. Simplicity of presentation differentiates this book from several others.
Key Features
• Variety of Exercises in each section and sub-section
• Worked out examples illustrated according to the theories developed in the book with possible alternatives
The book will be helpful to the students of Mathematics, Physics, Engineering and different competitive examinations. | 677.169 | 1 |
Laplace transforms continue to be a very important tool for the engineer; physicist and applied mathematician. They are also now useful to financial; economic and biological modellers as these disciplines become more quantitative. Any problem that has...
Spivak's celebrated textbook is widely held as one of the finest introductions to mathematical analysis. His aim is to present calculus as the first real encounter with mathematics: it is the place to learn how logical reasoning combined with fundamental
OverviewJames Stewart's Calculus; Early Transcendentals; International Metric Edition texts are widely renowned for their mathematical precision and accuracy; clarity of exposition; and outstanding examples and problem sets. Millions of students worldwide...
Calculus Single and Multivariable 6th Edition has been designed to provide you with a comprehensive understanding of mathematics. The textbook presents concepts from a verbal; algebraic; visual and numerical point of view; recognising that students learn...
For ten editions; readers have turned to Salas to learn the difficult concepts of calculus without sacrificing rigor. The book consistently provides clear calculus content to help them master these concepts and understand its relevance to the real world.
For freshman/sophomore; 2-semester (2-3 quarter) courses covering applied calculus for students in business; economics; social sciences; or life sciences. Calculus with Applications; Eleventh Edition by Lial; Greenwell; and Ritchey; is our most applied...
Complex Variables and Applications; 9e will serve; just as the earlier editions did; as a textbook for an introductory course in the theory and application of functions of a complex variable. This new edition preserves the basic content and style of the...
This introductory graduate text is based on a graduate course the author has taught repeatedly over the last ten years to students in applied mathematics; engineering sciences; and physics. Each chapter begins with an introductory development involving...
The calculus of variations is one of the oldest subjects in mathematics; yet is very much alive and is still evolving. Besides its mathematical importance and its links to other branches of mathematics; such as geometry or differential equations; it is... | 677.169 | 1 |
Geometry
Description
The CliffsStudySolver workbooks combine 20 percent review material with 80 percent practice problems (and the answers!) to help make your lessons stick.CliffsStudySolver Geometry is for students who want to reinforce their knowledge with a learn-by-doing approach. Inside, you'll get the practice you need to learn Geometry with problem-solving tools such asClear, concise reviews of every topicPractice problems in every chapter — with explanations and solutionsA diagnostic pretest to assess your current skillsA full-length exam that adapts to your skill levelExample problems, work problems, worked solutions, and an appendix of postulates and theorems help you get the practice you need to learn Geometry. In this book, you'll explore many aspects of Geometry, including the following:Basic concepts: Points, lines, planes, line segments, midpoints, and raysAngles and angle pairs, and parallel linesMeasuring angle sumsTriangles, polygons, and circlesDetermining perimeter and area, and ratio and proportionSolid figures and measurementCoordinate geometryPractice makes perfect —and whether you're taking lessons or teaching yourself, CliffsStudySolver guides can help you make the grade.Author David Alan Herzog has written more than 100 books and education software programs concerned with test preparation in mathematics and science. He taught math education at Fairleigh Dickinson University, was a mathematics coordinator for New Jersey's Rockaway Township Public Schools, and taught in the New York City public schools.show more | 677.169 | 1 |
Mathematical Structures / Edition 6
Discrete Mathematical Structures, Sixth Edition, offers a clear and concise presentation of the fundamental concepts of discrete mathematics. Ideal for a one-semester introductory course, this text contains more genuine computer science applications than any other text in the field.
This book is written at an appropriate level for a wide variety of majors and non-majors, and assumes a college algebra course as a prerequisite.
Preface
Discrete mathematics is an interesting course to teach and to study at the freshman and sophomore level for several reasons. Its content is mathematics, but most of its applications and more than half its students are from computer science. Thus careful motivation of topics and previews of applications are important and necessary strategies. Moreover, there are a number of substantive and diverse topics covered in the course, so a text must proceed clearly and carefully, emphasizing key ideas with suitable pedagogy. In addition, the student is often expected to develop an important new skill: the ability to write a mathematical proof. This skill is excellent training for writing good computer programs.
This text can be used by students in mathematics as an introduction to the fundamental ideas of discrete mathematics, and a foundation for the development of more advanced mathematical concepts. If used in this way, the topics dealing with specific computer science applications can be ignored or selected independently as important examples. The text can also be used in a computer science or computer engineering curriculum to present the foundations of many basic computer-related concepts and provide a coherent development and common theme for these ideas. The instructor can easily develop a suitable course by referring to the chapter prerequisites which identify material needed by that chapter.
Approach
First, we have limited both the areas covered and the depth of coverage to what we deem prudent in a first course taught at the freshman and sophomore level. We have identified a set of topics that we feel are of genuine use in computer science andelsewhere and that can be presented in a logically coherent fashion. We have presented an introduction to these topics along with an indication of how they can be pursued in greater depth. This approach makes our text an excellent reference for upper-division courses.
Second, the material has been organized and interrelated to minimize the mass of definitions and the abstraction of some of the theory. Relations and digraphs are treated as two aspects of the same fundamental mathematical idea, with a directed graph being a pictorial representation of a relation. This fundamental idea is then used as the basis of virtually all the concepts introduced in the book, including functions, partial orders, graphs, and mathematical structures. Whenever possible, each new idea introduced in the text uses previously encountered material and, in turn, is developed in such a way that it simplifies the more complex ideas that follow.
What Is New in the Fifth Edition
We continue to believe that this book works well in the classroom because of the unifying role played by the two key concepts: relations and digraphs. In this edition we have woven in a thread of coding in all its aspects, efficiency, effectiveness, and security. Two new sections, Other Mathematical Structures and Public Key Cryptology are the major components of this thread, but smaller related insertions begin in Chapter 1. The number of exercises for this edition has been increased by more than 25%. Whatever changes we have made, our objective has remained the same as in the first four editions: to present the basic notions of discrete mathematics and some of its applications .in a clear and concise manner that will be understandable to the student.
A cryptology thread begins in Chapter 1 and presents the basic ideas of the field. The thread concludes in Public Key Cryptology. Included now is coding in all its aspects, efficiency, effectiveness, and security.
A new section, Other Mathematical Structures, introduces the basic concepts of rings and fields, in particular Zp.
More opportunities for students to build modeling skills are provided. Whether seen as modeling, abstraction, pattern recognition, or problem solving, the ability to see the mathematical bones of a problem is a critical factor for success in higher-level mathematics courses.
Understanding proofs and writing simple proofs are important course goals. More occasions for students to read, analyze, complete, and produce proofs are presented throughout the text, not just in the sections that introduce formal proofs.
More applications are included. Among these are relational databases, check digits, a variety of ciphers, and weighted voting systems.
New exercises have been added to each chapter. Greater emphasis has been placed on multiple representations of concepts. There are approximately 400 more exercises than in the fourth edition.
A brief historical commentary opens each chapter and introduces some of the major contributors to that chapter's topics.
Isomorphism is presented in more contexts than before throughout the book.
Additional student experiments have been developed on weighted voting systems, Petri nets, and Catalan numbers. Experiments have been integrated into appropriate chapters and others are gathered in Appendix B. These assignments provide opportunities for exploration and discovery, as well as for writing, and are designed for collaborative work.
This edition continues to weave the discussion of proofs and proof techniques throughout the book with comments on most proofs, exercises related to the mechanics of proving statements, and Tips for Proofs sections. Many of the new exercises provide more practice in building proof-reading and proof-writing skills.
Each chapter now has a set of review questions. These are mainly conceptual in nature and help students identify the "big" ideas of the chapter.
A glossary for quick reference is now included.
The index contains approximately 100 new entries related to both new concepts and to new examples for material in previous editions.
Exercises
The exercises form an integral part of the book. Many are computational in nature, whereas others are of a theoretical type. Many of the latter and the experiments, to be further described below, require verbal solutions. Exercises to help develop proof-writing skills ask the student to analyze proofs, amplify arguments, or complete partial proofs. Guidance and practice in recognizing key elements and patterns have been extended in many new exercises. Answers to all odd-numbered exercises, review questions, and self-test items appear in the back of the book. Solutions to all exercises appear in the Instructor's Solutions Manual, which is available (to instructors only) gratis from the publisher. The Instructor's Solutions Manual also includes notes on the pedagogical ideas underlying each chapter, goals and grading guidelines for the experiments, and a test bank.
Experiments
Chapters 1 through 10 each end with a student experiment. These provide opportunities for discovery and exploration, or a more in-depth look at topics discussed in the text. They are designed as extended-time, out-of-class experiences and are suitable for group work. Each experiment requires significantly more writing than section exercises do. Some additional experiments are to be found in Appendix B. Content, prerequisites, and goals for each experiment are given in the Instructor's Solutions Manual.
End-of-Chapter Material
Each chapter contains Tips for Proofs, a summary of Key Ideas for Review, a set of Coding Exercises, an Experiment, a set of conceptual Review Questions, and a Self-Test covering the chapter's material.
Organization
Chapter 1 contains material that is fundamental to the course. This includes sets, subsets, and their operations; sequences; properties of the integers, including base n representations; matrices; and mathematical structures. A goal of this chapter is to help students develop skills in identifying patterns on many levels. Chapter 2 covers logic and related material, including methods of proof and mathematical induction. Although the discussion of proof is based on this chapter, the commentary on proofs continues throughout the book. Chapter 3, on counting, deals with permutations, combinations, the pigeonhole principle, elements of probability, and recurrence relations.
Chapter 4 presents basic types and properties of relations, along with their representation as directed graphs. Connections with matrices and other data structures are also explored in this chapter. Chapter 5 deals with the notion of a function and gives important examples of functions, including functions of special interest in computer science. An introduction to the growth of functions is developed. Chapter 6 covers partially ordered sets, including lattices and Boolean algebras. A symbolic version for finding a Boolean function for a Boolean expression joins the pictorial Kamaugh method. Chapter 7 introduces directed and undirected trees along with applications of these ideas. Elementary graph theory with applications to transport networks and matching problems is the focus of Chapter 8.
In Chapter 9 we return to mathematical structures and present the basic ideas of semigroups, groups, rings, and fields. By building on work in previous chapters, only a few new concepts are needed. Chapter 10 is devoted to finite-state machines. It complements and makes effective use of ideas developed in previous chapters. Chapter 11 finishes our discussion of coding for error detecting and correction and for security purposes. Appendix A discusses algorithms and pseudocode. The simplified pseudocode presented here is used in some text examples and exercises; these may be omitted without loss of continuity. Appendix B gives some additional experiments dealing with extensions or previews of topics in various parts of the course.
Editorial Reviews
A text for a first course at the freshman and sophomore level, incorporating topics useful in computer science, for use in mathematics, computer science, and computer engineering programs. Chapters on subjects including logic, digraphs, trees, and finite- state machines include computational and theoretical exercises and answers, chapter reviews, and group experiment assignments. This third edition contains new material on mathematical structures and graph theory, coding exercises, and revised exercises. Annotation c. Book News, Inc., Portland, OR (booknews.com) innovative new introduction to Mathematical Statistics covers the important concept of estimation at a
point much earlier (Chapter 2) than others on this subject. Applies mathematical statistics to topics such as insurance, Pap smear tests, estimating the number of ...
Linear programming finds the least expensive way to meet given needs with available resources. Its
results are used in every area of engineering and commerce: agriculture, oil refining, banking, and air transport. Authors Kolman and Beck present the basic notionsThis edition features the same content as the traditional text in a convenient, three-hole-punched, loose-leaf
version. Books a la Carte also offer a great value–this format costs significantly less than a new textbook. Before you purchase, check with your instructor ... | 677.169 | 1 |
Paperback | September 14, 2012
Pricing and Purchase Info
about
The only DP resources developed with the IB.Uniquely developed with the IB curriculum team, this fully comprehensive student book will ensure your students achieve their best. Fully capturing the IB philosophy via lots of TOK, a huge bank of practice, a free eBook on CD-ROM and dedicated support for the Exploration will set you and yourlearners up to succeed Mathematics as the science of patterns2. Mathematics as a language3. The long journey of mathematics4. Modeling the real world5. Aesthetics in mathematics: an introduction to mathematical explorations6. Exploring randomness: statistics and probability7. The origins of calculus8. Ancient mathematics and modern methods: trigonometry and its multiple applications9. Further calculus10. Modeling randomness11. Inspiration and formalism12. Multiple perspectives in mathematics13. Exploration14. Prior learning
Editorial Reviews
"We have adopted most of the Oxford course books for our schools. We find them well written, well linked to TOK issues and age appropiate." --Sheta Saha, IB Coordinator, Chatsworth International School, Singapore | 677.169 | 1 |
The goal of Pre-Algebra is to develop fluency with rational numbers and proportional relationships. Students will extend their elementary skills and begin to learn algebra concepts that serve as a transition into formal Algebra and Geometry.The major emphases of the Pre-Algebra course are rational numbers, proportionality, measurement, data collection and analysis, probability, and beginning algebra concepts that serve as a transition into formal algebra and geometry.
Students in Elementary Algebra will learn algebra as a style of thinking for formalizing patterns, functions, and generalizations. In this course, students will expand previously learned quantitative rational number relationships to include the irrational numbers.
Students will explore geometry through inductive and deductive processes, technology, constructions, manipulatives, and algebraic connections.The main goal of Geometry is for students to develop the structure of Euclidean geometry logically and apply the resulting theorems, proofs, and formulas to address meaningful problems. Students will use experimentation and inductive reasoning to construct geometric concepts, discover geometric relationships, and formulate conjectures. Students will employ deductive logic to construct formal logical arguments and proofs.
This Financial Math course combines essential math skills and personal financial planning to teach students how to manage their income, make a budget, consider types of insurance and investments, and plan for expenditures like higher education and retirement.
In this course, students will build upon the knowledge previously learned in Algebra I and Geometry, expanding their ability to understand, perform operations and solve problems with real numbers. Students will focus on the importance of linear relations; develop fluency with the language and operations of algebra to analyze and represent relationships; and perform exercises in statistics and statistical methods to solve problems.
Pre-calculus fills the minimum mathematics course requirement for students who plan to participate in post-secondary training. It also serves as the prerequisite for Advanced Placement Calculus or Statistics courses. In preparation for this course, students should have mastered linear and quadratic functions, concepts from discrete mathematics involving sequences and series, and data analysis and probability techniques. They should also be able to confidently work with expressions containing rational exponents and radical and rational terms.
In this course, students will complete statistical evaluations through advanced math calculations. Statistics coursework will explore a wide variety of data systems and models, and utilize statistical systems to graph, interpret, and draw conclusions from data. Additionally, students will further develop skills in calculating probability, mean, and understanding the distribution of data within a system. | 677.169 | 1 |
For over fifty years, the Mathematical Association of America (MAA) has been engaged in the construction and administration of challenging contests for students in American and Canadian high schools at every level of ability. This is the ninth book of problems and solutions from the American Mathematics Competitions 12 (AMC), aimed at students of high school age, and featuring 325 problems from the 13 AMC contests held in the years 2001-2007. Graphs and figures have since been redrawn to make them more consistent in form and style, and the solutions to the problems have been both edited and supplemented. The Problem Index contained classifies the problems into the following major subject areas: Algebra and Arithmetic, Sequences and Series, Triangle Geometry, Circle Geometry, Quadrilateral Geometry, Polygon Geometry, Counting Coordinate Geometry, Solid Geometry, Discrete Probability, Statistics, Number Theory, and Logic. These are then broken down into subcategories and cross-referenced for ease of use. | 677.169 | 1 |
Discrete Mathematics Assignment Help
Discrete math, also recognized as "math for CS" is generally a necessary course for a scholar of computer science. The material normally covered in this division for CS scholar overlaps with fields such as cryptography, judgment, information theory, artificial intelligence, plan of algorithms, & others, and teaches the crucial language and structures utilized by computer scientists.
Sometimes discrete math is programmed as a mathematics course. Discrete mathematics is a modern field of mathematics that is extensively used in business and commerce. It is occasionally called the mathematics of computers, or the math used to optimize limited systems. Discrete Mathematics is the study of the subject in discrete mathematics generally includes the study of algorithms, their implementations, & efficiencies.
What is difficult about discrete mathematics homework?
Discrete mathematics deals mostly with the learning of discrete mathematical structures & countable number order. It is also closely related to additional mathematical subjects that are why thriving accomplishment of discrete mathematics assignments need sufficient discrete mathematics familiarity, skillfulness, and certain practice. Almost all discrete mathematics Homework includes the application of diverse discrete mathematics formulas, equations in addition to the understanding of discrete mathematics' graphs & integers.
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Overview: This course is concerned with abstract algebra. This is one of the most fundamental areas of modern mathematics. The idea is to study mathematical structures with simple rules---so simple that they may be found in many different areas---and yet to see that these simple rules impose a rich structure upon the objects. Much of the course will be concerned with Group Theory. Groups are behind games such as the Rubrik's cube, and they are also behind the study of symmetries in physics and secure data transmission in computer science. They play a central role in modern mathematics. We will also study objects called Rings. These objects mimic the integers, and yet may be subtly different. Their properties will allow us to discover new facts about the integers themselves. Finally, we will study Fields. These are Rings with extra structure. They are important in understanding the solutions to equations and are also used in coding theory and in cryptography.
This is a foundational upper division course covering one of the subjects which is at the center of modern mathematics. But it is intrinsically sophisticated stuff. You can't get by just studying right before the test. You need to go over your notes after each lecture. Learn the definitions by heart. Work through the examples (in both text and lecture) until you understand them thoroughly. Then learn the proofs as well as the Theorems. If you put this off, you'll find that the lectures make use of material you have not yet worked through, and you'll get behind rapidly. But if you keep up---and don't hesitate to ask questions in class or in office hours if you're confused by something---then the course will work well. The material is intrinsically beautiful, and you'll be introduced to the power of modern abstract mathematics.
Note: This course satisfies the algebra requirement for the B.A. degree in mathematics. Students considering the B.S. degree should take MT3311 and not this course.
Lectures: MWF 1:00-1:50 in GASSON 210.
I am very happy to answer your questions and to help you with the homework during these office hours. These times are always reserved for you and there is no need for an appointment. I am also available on other times by appointment. Please email me for one. I am always happy to work with students, so don't hesitate to contact me (email is also good for short questions).
Textbook:Abstract Algebra: A First Course by Dan Saracino, Second Edition. Waveland Press
Grading: Homework 30%; Each midterm 20%; Final 30%.
Exams: Two in-class exams (Wed. Feb. 10 and Wed. Mar. 23) and one final exam (Wed. May 11 at 12:30).
Homework: There will be weekly homework assigned and collected every week. HOMEWORK WILL NOT BE ACCEPTED AFTER THE DAY IT IS DUE!
You are encouraged to typeset your HW in LATEX. Though it takes a while to get the hang of it, this is recommended as it will help you write mathematics clearly. If you want to give it a try, here are some helpful resources
Mac OSX: Download MacTeX. For an introduction,
see "Trying out TeX" and its links. Windows: Download proTeXt and follow the
installation instructions.
See also
LaTeX manual (math symbols on page 60) and
LaTeX Wiki Book
for more information Homework problems:
Assignment 1: Problems 0.4, 0.9, 0.16, 0.17, 0.18, 1.3, 1.4, 1.5, 1.6, 1.9 from the text. Due Friday Jan 29 in class. (If you want to typeset your solution, you can use the following TEX template). | 677.169 | 1 |
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In Exercises 24 and 25, find answers to maths questions the following information. For the same chapter all lessons are 1-day lessons : 5. The contents of any site or link not maintained by CRSD does not necessarily reflect the opinions, standards, or policies of CRSD, its officials, agents, or employees. We are often asked if homeschoolers can study perpendicular algebra content at HippoCampus and then just take and pass the AP exam. Learn about Pearson's Terms of Use And what we're doing to protect your privacy. Also helpful is a listing of their most popular Math books. Practice continued For use with pages 336-345 Graph the polynomial function. It would be a sellout instantly. A list of the topics covered in this game can be found on the Directions page. Teachers can follow the teacher tips and post parent and student Tips of the Week to their runescape classic quest guide webpages or include them in newsletters or updates sent out regularly. Write the letter of the answer in each box containingthe number of the exercise. Solving expressions and representing functions take too many clicks. Miss Sullivan came to the Keller home to be six-year-old Helen Keller's teacher. Math with Pizzazz Book Students work develop their graphing linear equations and inequalities skills Subjects: Math, Algebra, Algebra 2 Grades: 7th, 8th, 9th, 10th, learner driving test online, 12th Projects, Activities, Handouts 8. These printable practice worksheets are organized by both topics and grades for easy navigation. Algebra related rates worksheets Final, find the value of x, myalgebra. Beginning and Intermediate Algebra was designed median wikipedia reduce textbook costs to students while not median wikipedia the quality of materials.
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Asked by free halloween reading comprehension worksheets on June 16, it is assumed that you know Algebra and Trig prior to reading the Calculus I notes, know Calculus I prior to reading the Calculus II notes, etc. Matlab solve numerically, algebrator, Algebra Slope Projects, how to do math problems, maths simplifying equation answers. What is the coefficient of the squared term in the parabola's equation. If you have forgotten your password, enter your username or email address to have your password sent to you. The other important factor to increase demand is the actual usage of the coin in terms of exchange of value. But, I think it's more than that. Virtually every puzzle can be matched with a particular lesson in recent editions of popular textbooks. Think median wikipedia it as an alternative teacher for homework problems. Middle School Math with Pizzazz free ebook how did zonnique dog die Middle School Math with Pizzazz. | 677.169 | 1 |
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Evaluation Notes The Evening In advance of Class
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The thought of doing research each individual night time could appear annoying, however, if you would like to succeed in , it is actually important that you constantly practice and grasp the problem-solving techniques. Make use of your textbook or on line guides to work by means of leading math problems over a weekly basis – even when you've got no research assigned.
Use the Dietary supplements That come with Your Textbook
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Read In advance To remain In advance
If you want to minimize your in-class workload or perhaps the time you commit on research, make use of your spare time just after university or on the weekends to browse ahead for the chapters and concepts that will be covered the subsequent time that you are in class.
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After you are reviewing issues for an examination, consider to explain out loud what strategy and solutions you accustomed to get your remedies. These verbal declarations will occur in useful in the course of a take a look at if you have to remember the ways you should consider to find a remedy. Get additional follow by seeking this tactic with a mate.
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Algebrator truly is a must-have for us algebra students. As already said in the post above , not only does it solve questions but it also explains all the intermediary steps involved in reaching that final solution . That way you don't just get to know the final answer but also learn how to go about solving questions from the scratch , and it helps a lot in working on assignments.
I remember having often faced difficulties with exponent rules, rational expressions and function definition. A truly great piece of math program is Algebrator software. By simply typing in a problem from workbook a step by step solution would appear by a click on Solve. I have used it through many algebra classes – Pre Algebra, College Algebra and Basic Math. I greatly recommend the program. | 677.169 | 1 |
Geogebra files designed for class lessons on electronic board but also useful for individual students at home or in school.
Other collected files at and
The free Geogebra software at
Three worksheets on integrating powers, sums and differences, trigonometric functions, exponential and logarithmic functions and using the reverse of the chain rule. Detailed solutions are included. From
This is three lessons designed to tackle the different areas of differentiation for AS Level.
1. Introduction and Basics
2. Applications
3. 2nd Differential
NOTE: Feel free to browse my shop for more free and premium resources and as always please rate and feedback, thanks.
This is a whole lesson (3rd) on differentiation and looks at differentiating twice. Looking at why and how and its applications in real life and in terms of exam questions.
This lesson comes with a starter, plenary, some excellent clear teaching slides and teaching. I have included some exam questions that will test everything that the pupils have learnt at the stage.
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This is a whole lesson (second) that builds on my the first lesson introducing the topic of differentiation. It builds on the first lesson by looking at slightly more tricky examples of differentiation and how to re-arrange indices in particular.
It then looks at applications of differentiation in terms of finding the gradient of curves. The lesson comes with a starter, lots of teaching examples, notation explanations, answers and plenary. It also includes some excellent exam practice to help pupils practise directly the style they will have to face as well as a jargon-busting sheet to help them with marking.
NOTE: Feel free to browse my shop for more excellent free and premium resources and as always please rate and feedback, thank you. | 677.169 | 1 |
Course Description
The goal of this course is to develop a precise understanding of the concepts that underlie calculus including the real numbers, continuous functions, sequences and their limits, the derivative, and the integral. Using this precise understanding, we will then rigorously prove many of the major results from single-variable calculus such as the Intermediate Value Theorem, the Mean Value Theorem, and the Fundamental Theorem of Calculus.
In this course, you will improve your understanding of mathematical proofs. You will also gain lots of experience constructing mathematically rigorous arguments using proof techniques both new (e.g. epsilon-delta proofs) and familiar (e.g. proof by contradiction, inductive proofs).
Text
We will be using Analysis with an introduction to proof (4th Edition) by S. R. Lay. Some other introductory books on the subject include Principles of mathematical analysis (3rd Edition) by W. Rudin and Real Analysis and Foundations by S. Krantz.
Grading
Your grade in this course will be based on the following:
Homework: 20%
Starred problems: 10%
Midterm 1 (Feb. 20): 20%
Midterm 2 (Apr. 3): 20%
Final exam (May 5, 1:30 pm - 4:00 pm): 30%
Homework
Every week you will have a written homework assignment, which will give you an opportunity to practice constructing and writing proofs using the concepts, definitions, theorems and techniques we have learned. These will be posted on the course website. Late homework will not be accepted.
Homework should be legible, have your name on it, and be stapled in order to ensure that you get credit. A primary goal of this course is for you to improve your ability to write clear, precise proofs; the homework (and the exams) will be graded accordingly.
I encourage you to discuss the homework problems with your classmates, tutors, or me (or any other resources you find helpful). However, the Honor Code requires that the solution you turn in must be in your own words and reflect your own understanding.
Starred problems
Each week, (at most) one problem on the homework assignment will be starred (e.g. Chapter 6, problem 4*). These problems will usually be more challenging than the rest of the homework. The starred problem should be turned in on a separate page from the rest of the written homework. I will grade these problems myself on a credit/no credit basis (but with comments so that you know what you need to fix). If you receive a score of no credit, you can resubmit the problem the next week along with that week's homework assignment, and you can continue this process until you receive credit. The primary point of these problems is to make sure that everyone learns to write good proofs. The secondary point is to encourage you to solve problems which might require more than one week of thinking -- although not all of the starred problems will be that hard.
Practice
Course policies
Honor Code
Student classroom and course-related regarding classroom behavior and student conduct.
Religious obligations
Campus policy regarding religious observances requires that faculty make every effort to deal reasonably and fairly with all students who, because of religious obligations, have conflicts with scheduled exams, assignments or required attendance.
If a religious observance conflicts with a scheduled exam or other course activity, please let me know during the first two weeks of the semester so that we can make alternate arrangements.
Statement on discrimination and harassment
The University of Colorado Boulder (CU-Boulder) is committed to maintaining a positive learning, working, and living environment. The University of Colorado does not discriminate on the basis of race, color, national origin, sex, age, disability, creed, religion, sexual orientation, or veteran status in admission and access to, and treatment and employment in, its educational programs and activities. (Regent Law, Article 10, amended 11/8/2001). or veteran status. Individuals who believe they have been discriminated against should contact the Office of Discrimination and Harassment (ODH) at 303-492-2127 or the Office of Student Conduct (OSC) at 303-492-5550. | 677.169 | 1 |
Math for Liberal Studies. A cable company wants to set up a small network in the local area This graph shows the cost of connecting each pair of cities.
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Presentation on theme: "Math for Liberal Studies. A cable company wants to set up a small network in the local area This graph shows the cost of connecting each pair of cities."— Presentation transcript:
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Start with none of the edges being part of the solution Then add edges one at a time, starting with the cheapest edge… …but don't add an edge if it would create a circuit Keep adding edges until every vertex is connected to the network | 677.169 | 1 |
DESCRIPTION
This easy-to-use guide identifies and addresses the areas where most students need help with basic mathematical problems that occur in everyday life and academic study and provides straightforward, practical tips and solutions that will enable you to assess and then improve your performance.
CONTENTS
Preface and acknowledgementsHow to use this bookTimes tablesArithmetic1 - Basic Arithmetic and the ¬ BODMAS¬ rule. Getting used to basic arithmetic and simple calculations, and making sure you perform them correctly2 - Negative numbers. Understanding negative numbers and dealing with them accurately.3 ¬ Fractions. Understanding what fractions mean and being able to manipulate them correctly.4 ¬ Percentages, ratios and proportions. Using percentages and ratios to describe and compare values.5 ¬ Decimals, decimal places and significant figures. Using decimal numbers and rounding numbers to a certain number of decimal places.6 ¬ Scientific notation. Representing very small and very large numbers using scientific notation7 - Indices. Writing repeated multiplications easily, roots and the laws of powers. Algebra8 ¬ An introduction to algebra. Using symbols to represent numbers and an introduction to algebra9 ¬ Brackets in algebra. Using brackets in algebraic expressions10 ¬ Solving linear equations. Solving simple equations using algebra.11 - Transposition and algebraic fractions. Rearranging expressions using basic rules of algebra.12 - Simultaneous equations. Solving two equations at the same time.Data13 ¬ Presentation of data. Using various types of graphs and charts to illustrate data visually.14 ¬ Measures of location and dispersion. Working out ¬ averages¬ and a measure of the spread of a set of data.15 - Straight Lines. Linear data and calculating the equation of a straight line.16 ¬ Introduction to probability. Working out probabilities - the chances of something happeningOther topics17 ¬ Areas and volumes. Calculating the areas and volumes of basic shapes18 ¬ Logarithms. Calculating logarithms - the opposite of powers19 ¬ Quadratic equations. Solving equations involving powers of x. 20 ¬ Trigonometry. Calculations with triangles, including angles and trigonometric functions.21 ¬ Inequalities and basic logic. Using mathematical symbols to represent inequalities and basic logical conceptsSummaryFurther work on our websiteGlossaryIndex
We use cookies to provide you with a better service. By continuing to browse the site you consent to our use of cookies. Click Continue to close this notice or read more about our cookies and how to manage them. | 677.169 | 1 |
This comprehensive and stimulating introduction to Matlab, a computer language now widely used for technical computing, is based on an introductory course held at Qian Weichang College, Shanghai University, in the fall of 2014.
This revision and work book offers a very specific concept for learning the finite element method applying it to problems from statics of: It skips all the classical derivations and focusses only the essential final results. Based on these `essentials', fully solved example problems are presented. To facilitate the initial learning process, the authors compiled 10 recommended steps for a linear finite element solution procedure (`hand calculation') and all the solved examples follow this simple scheme | 677.169 | 1 |
Projects for Precalculus
by Janet Andersen, Robert Keeley and Todd Swanson
Saunders College Publishers
Instructor's Edition ISBN 0-03-024966-X
Student Edition ISBN 0-03-020444-5
Projects for Precalculus is a set
of supplementary projects. These projects were designed to be used at both the
high school and college level. Two versions of Projects for Precalculus
are available from Saunders College
Publishing. One version contains 26 projects, complete with solutions and
teacher's notes. The other version contains 13 projects without solutions.
The materials cover a wide range of topics that are typical to many precalculus
courses. These projects are designed to help teach new topics or can be used
for longer explorations into topics already covered in classes. We have designed
the projects to help students as they prepare for some of the new emphases currently
being used in calculus.
Projects for Precalculus was an award winner in the 1996-97 Innovative Programs
Using Technology (INPUT) Awards Competition.
The authors of Projects for Precalculus
have written a text, Precalculus, A Study of Functions and Their Applications
published Fall 2000 by Harcourt College Publishers (now part of Thompson
Learning). To read more about it go here. | 677.169 | 1 |
Shows the two different methods of solving simultaneous equations - by elimination and substitution. Each method is clearly explained in a step by step manner. The elimination method of adding the equations vertically makes solving simultaneous equations fast and easy.
SimulEquations can generate hundreds of pairs of simultaneous equations for drills to ensure that the student masters the methods learnt. There are two levels of difficulty to choose from: average for beginners and challenging for advance learners. The student may also key in his own sums and let the guide help him solve them.
There are many worked examples to provide help for students who have difficulty in doing the sums.
You can print out a report at the end of each practice session. The report shows each sum with its correct answer and the student's answer marked. It also includes the percentage score, the average time taken to do each sum and other details.
FEATURES:
· A step by step interactive guide is provided to help the student solve the equations if he has difficulties. The guide does not solve the equations for the student but guides him along, providing feedback on his working for each step.
· A student can key in his own equations and let the guide help him solve it. This feature can help the student do his homework.
· Two players may compete with each other on one computer, reducing the number of computers required for a class by half. Each player can do the sums at his own pace.
Mathematics
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Math-o-mir 1.61
Basically an equation editor, however not focused over one single equation, but you can write your mathematical artwork over several pages. You can easily move and copy your equations and expressions by mouse touch. Illustrate your equations using...
Modules
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WPMathPublisher 0.4
The equation needs to be enclosed within the [m]equation[/m] tags.InstallationUnpack and upload it to the /wp-content/plugins/ directory.Activate the plugin through the 'Plugins' menu in WordPress. Requirements: - WordPress 2.0.2 or higher
Productivity
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Physics Helper 1.0.0.0
Physics Helper is similar to a calculator as it will take in information that you have and spit out the answer. You can choose which common, beginner physics equation you need to solve and then input what you know. With this, Physics Helper will...
Games
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ChemIQ 1.1
The objective of the game is to solve (balance) a chemical equation. You will be presented with one or more molecules, break the bonds of the molecule by swiping across the bond link and get the atoms/elements. Now, combine the correct...
8.6 MB
Business
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Laredo Group Media Calculator 1.0
The Laredo Group Media Calculator has 6 different modules. Each module will solve a different advertising equation: calculating the CPM, ad impression level, media costs, Click-Through Rate (CTR), and 2 Return on Ad Spend (ROAS) calculators....
8.6102.4 KB
Education
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Learn Sorting 1.0
The Learn Sorting app is designed to teach children how to sort different objects. You can choose to sort by shape, sort by color, or to sort coins. A random number of objects to sort, and a random number of presorted examples are chosen | 677.169 | 1 |
This booklet is designed as a handout for a workshop with The Geometer's Sketchpad or for use, in conjunction with the Instructor's Evaluation Edition of The Geometer's Sketchpad, in evaluating the pr... More: lessons, discussions, ratings, reviews,...
Students move two ghost characters (Doug and Linda) around the screen to explore geometric concepts. Students discover connections between the ghosts' constructed paths by comparing them and looking f... More: lessons, discussions, ratings, reviews,...
In this activity, students create their own Sketchpad kaleidoscopes. In the process, they learn about rotation and reflection, as well as gaining some skill using Sketchpad's transformation features. More: lessons, discussions, ratings, reviews,...
These activities provide students with the opportunity to explore geometric concepts such as symmetry, transformations, and even fractal geometry in a way no other teaching tool can. The dynamic ca... More: lessons, discussions, ratings, reviews,...
This book guides students as they construct and manipulate geometric figures, and discover relationships and theorems on their own. It features over 100 activities covering virtually every concept st... More: lessons, discussions, ratings, reviews,...
In this activity, students will construct a golden section and a golden rectangle and study their characteristics and connections with the Fibonacci series. They will import pictures from the Internet... More: lessons, discussions, ratings, reviews,...
Students investigate parametric functions in rectangular and polar coordinates. The link to the tool itself is to a zip file that contains both the sketch and a pdf file of the corresponding activi... More: lessons, discussions, ratings, reviews,...
Students investigate parametric functions in rectangular and polar coordinates. The link to the activity itself is to a zip file that contains both the activity in pdf format and the corresponding ... More: lessons, discussions, ratings, reviews,...
This sketch allows the manipulation of a parabola in factored form. On the first page, the coefficients a and b are restricted to multiples of 0.5. On the second page, they are unrestricted and can be... More: lessons, discussions, ratings, reviews,...
This sketch allows the manipulation of a parabola in standard form. On the first page, the coefficients a, b, and c are restricted to multiples of 0.5. On the second page, they are unrestricted and ca... More: lessons, discussions, ratings, reviews,...
This sketch allows the manipulation of a parabola in vertex form. On the first page, the coefficients a, h, and k are restricted to multiples of 0.5. On the second page, they are unrestricted and can ...Download this Sketchpad file to investigate the definite integral using a model of a car accelerating from rest. Students explore the graph of the car's speed as a function of time, and use Sketchpad'... More: lessons, discussions, ratings, reviews,...
Students identify and measure corresponding angles, alternate interior angles, and alternate exterior angles, and determine which angles are congruent to each other. The link to the tool itself is ... More: lessons, discussions, ratings, reviews,...
Students identify and measure corresponding angles, alternate interior angles, and alternate exterior angles, and determine which angles are congruent to each other. The link to the activity itself... More: lessons, discussions, ratings, reviews,...
This activity builds on the previous activity, Limits with Tables. Students investigate limits using tools for controlling delta and epsilon, giving them a concrete, hands-on understanding of the form... More: lessons, discussions, ratings, reviews,...
Download this Sketchpad file to investigate the concept of a limit numerically using tables. Students encounter a function that's undefined at a particular value of x, but whose limit exists at that v... More: lessons, discussions, ratings, reviews,...
Sketchpad Activities for Introducing Calculus Topics is a series of five activities designed to introduce students to the basic concepts of calculus. Use these activities near the end of Precalculus c... More: lessons, discussions, ratings, reviews,...
This is a one page activity that includes how to construct a kite on Sketchpad, along with a kite that is ready to be manipulated. The kite sketch is followed by 8 questions that lead the student to ... | 677.169 | 1 |
Ausgew?hlte Algorithmen in der Computergraphik
The course covers certain fundamental and advanced methods which provide the basis of various applications in computer graphics and geometry processing. Focus is on practical application of (numerical) algorithms including efficient implementation in C/C++ and Matlab | 677.169 | 1 |
More Links for Students
The primary purpose of WeBWorK is to let you know that you are getting the
correct answer or to alert you if you are making some kind of mistake.
Usually you can attempt a problem as many times as you want before the due
date. However, if you are having trouble figuring out your error, you
should consult the book, or ask a fellow student, one of the TA's or your
professor for help. Don't spend a lot of time guessing -- it's not very
efficient or effective.
Give 4 or 5 significant digits for (floating point) numerical answers. For
most problems when entering numerical answers, you can if you wish enter
elementary expressions. Here's the list
of the functions which WeBWorK understands.
You can use the Feedback button on each problem page to send e-mail to the
professors.
WeBWorK summary for students
is a must-read!
More Links for Instructors
WeBWorK (ww) is a system that lets students answer questions online.
WeBWork is being developed by an NSF funded group (headed by Arnie
Pizer and Mike Gage) at
Rochester University, and it's in the public
domain. It is not tied to specific publishers or textbooks.
You can find more details at WeBWork Main Page | 677.169 | 1 |
Galois Theory
Galois Theory by Emil Artin In the nineteenth century, French mathematician Evariste Galois developed the Galois theory of groups-one of the most penetrating concepts in modem mathematics. The elements of the theory are clearly presented in this second, revised edition of a volume of lectures delivered by noted mathematician Emil Artin. The book has been edited by Dr. Arthur N. Milgram, who has also supplemented the work with a Section on Applications.The first...
Elements of Abstract Algebra
Elements of Abstract Algebra by Allan Clark This concise, readable, college-level text treats basic abstract algebra in remarkable depth and detail. An antidote to the usual surveys of structure, the book presents group theory, Galois theory, and classical ideal theory in a framework emphasizing proof of important theorems.Chapter I (Set Theory) covers the basics of sets. Chapter II (Group Theory) is a rigorous introduction to groups. It contains all the results... | 677.169 | 1 |
Top Math Software for Windows
A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. Prime Number Counter is a small utility to calculate the prime numbers. You can make the software count until a specified number or...
Program that enables you to draw mathematical functions. It can also generate functions using the Newton interpolation algorithm.
You can navigate through the graph, zoom in, zoom out and add/remove points (magnet mode). In the functions created by...
Simple Grapher is an application that enables you to create advanced plots and graphs using mathematical functions. The program allows you to graph 2D and 3D drawing for educational purposes and could be a helpful tool for teaching mathematics in middle...
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HomeHelp was created to help children learn math through practice. Once the subject has been chosen, and the level selected, then you can print a worksheet, out with or without answers, for the student(s) to fill in. HomeHelp keeps a track of the child or...
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Algematics can actually do your high school algebra, one step at a time! You can finish your work without waiting to ask your teacher. Enter equations and expressions straight out of your book or from your homework sheet. Simply point and click to... | 677.169 | 1 |
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My study methods have never been quite good; that is way I always look for an easier learning method, and I strongly recommend the Algebrator. Maria Lopez, CA
You guys are GREAT!! It has been 20 years since I have even thought about Algebra, now with my daughter I want to be able to help her. The step-by-step approach is wonderful!!! Maria Lopez, CA Maria Leblanc
Absolutely genius! Thanks!04-10:
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Help me with my math
Pearson Prentice Hall and our other respected imprints provide educational materials, technologies, assessments and related services across the secondary curriculum. CalcChat.com is a moderated chat forum that provides interactive calculus help, calculus solutions, college algebra solutions, precalculus solutions and more. You'll Succeed Even if the deadline is hard on heels! Professional Essay Writer from essaycapital.org will help you. Coffee won't help you to write a good essay. Covers the basic materials for algebra, calculus, and differential equations. Includes examples, review questions, common errors, study tips and formula tables(PDF. Weekly Tips CPM has created weekly tips for teachers, parents and students, written to help everyone be successful in math. Teachers can follow the teacher tips and. HELP US HELP YOU. The majority of math worksheet sites require you to pay a monthly fee for use. Math Fact Cafe is proud to have provided awesome free math.
Our goal is to help every student succeed. We're working with educators and institutions to improve results for students everywhere. Learn more. Eureka Math is America's #1 Math Curriculum. Eureka Math, only three years old, is now the most widely used math curriculum in the United States, according to a new. Weekly Tips CPM has created weekly tips for teachers, parents and students, written to help everyone be successful in math. Teachers can follow the teacher tips and. Revolutionary Digital Learning for Science, Engineering, and Math Math Snacks: Animations and Games for Middle School. Ask Dr. Math a question or browse the archive of previous questions and answers. Get fired up about math teaching and learning with our Ignite! videos. The Math Forum Is the home of 2017 Mathematics Game The Art of Math Challenge. Get Your Kolbe A™ Result It all starts with "A" Learn what's RIGHT about you. Taking a Kolbe A™ Index will help you identify your own natural strengths and talents.
Help me with my math
For technical operation, usability problems with the OJUSD ENY Math Homework Help website, please use the Contact Webmaster Form. ClassZone Book Finder. Follow these simple steps to find online resources for your book Math-Whizz improves students' math ability. Find out more about our virtual online math tutor learning methods for 5 - 13 year olds. Essay writing can be a piece of cake. Hard to believe? Then try our essay writing service and see yourself. Samedayessay.org writers can master any assignment in any.
Achieve. More than 20 million students and 10,000 different schools worldwide have benefited from the First In Math Online Program and 24 games. Get fired up about math teaching and learning with our Ignite! videos. The Math Forum Is the home of 2017 Mathematics Game The Art of Math Challenge. ClassZone Book Finder. Follow these simple steps to find online resources for your book. Ask Dr. Math a question or browse the archive of previous questions and answers. Essay writing can be a piece of cake. Hard to believe? Then try our essay writing service and see yourself. Samedayessay.org writers can master any assignment in any. Eureka Math is America's #1 Math Curriculum. Eureka Math, only three years old, is now the most widely used math curriculum in the United States, according to a new.
CalcChat.com is a moderated chat forum that provides interactive calculus help, calculus solutions, college algebra solutions, precalculus solutions and more. AAA Math features a comprehensive set of of interactive arithmetic lessons. There is no cost or registration required to practice your math on the AAAMath.com site. Teacher Login / Registration : Teachers: If your school or district has purchased print student editions, register now to access the full online version of the book. Times Tables. Print out The Times Tables and stick them in your exercise book. Test Your Tables with an interactive quiz. Teacher Login / Registration : Teachers: If your school or district has purchased print student editions, register now to access the full online version of the book. HELP US HELP YOU. The majority of math worksheet sites require you to pay a monthly fee for use. Math Fact Cafe is proud to have provided awesome free math.
AAA Math features a comprehensive set of of interactive arithmetic lessons. There is no cost or registration required to practice your math on the AAAMath.com site. By enrolling my child in XtraMath, I give my consent for XtraMath to record my child's skill progress, generate reports summarizing my child's progress, and use. The Everyday Mathematics eSuite is an award winning online curriculum for teachers, students and parents. Developed through research and field testing over 25 years. The Everyday Mathematics eSuite is an award winning online curriculum for teachers, students and parents. Developed through research and field testing over 25 years. Find math jobs at the Math.com Career Center. We hope your visit to math.com brings you a greater love of mathematics, both for its beauty and its power to help solve. Times Tables. Print out The Times Tables and stick them in your exercise book. Test Your Tables with an interactive quiz. | 677.169 | 1 |
Mathematics Methods for Elementary and Middle School Teachers
Paperback | November 2, 2007
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about
Always on the cutting-edge of mathematics teaching, the new Sixth Edition continues to integrate technology with hands-on experience and the latest research and standards. The CD packaged with this book features videos with guiding questions to analyze real teacher-student interaction in the hard-to-teach math concepts. It also includes colored patterns to download that will help readers practice hands-on manipulations as they prepare for interactive test items.
About The Author
Applied entomologists, research entomologists, agricultural entomologists, entomologists involved in advisory work in horticulture, and in insect and identification and taxonomy. Terrestrial ecologists and employees of the agricultural chemical industry. Academic scientists studying weeds and wild plants and their roles in biodiversity... | 677.169 | 1 |
This study aims to determine the mathematical concepts and skills needed in a beginning course in educational statistics, to ascertain the common mathematical difficulties of students of statistics, to indicate the relationship between mathematical ability and success in statistics, and to suggest measures for mitigating difficulties of a mathematical nature. | 677.169 | 1 |
Math 370 (Precalculus Mathematics) | 677.169 | 1 |
Despite the increasing use of computers, the basic need for mathematical tables continues. Tables serve a vital role in preliminary surveys of problems before programming for machine operation, and they are indispensable to thousands of engineers and scientists without access to machines. Because of automatic computers, however, and because of recent scientific advances, a greater variety of functions and a higher accuracy of tabulation than have been available until now are required. In 1954, a conference on mathematical tables, sponsored by M.I.T. and the National Science Foundation, met to discuss a modernization and extension of Jahnke and Emde's classical tables of functions. This volume, published 10 years later by the U.S. Department of Commerce, is the result. Designed to include a maximum of information and to meet the needs of scientists in all fields, it is a monumental piece of work, a comprehensive and self-contained summary of the mathematical functions that arise in physical and engineering problems. The book contains 29 sets of tables, some to as high as 20 places: mathematical constants; physical constants and conversion factors (6 tables); exponential integral and related functions (7); error function and Fresnel integrals (12); Bessel functions of integer (12) and fractional (13) order; integrals of Bessel functions (2); Struve and related functions (2); confluent hypergeometric functions (2); Coulomb wave functions (2); hypergeometric functions; Jacobian elliptic and theta functions (2); elliptic integrals {9); Weierstrass elliptic and related functions; parabolic cylinder functions {3); Mathieu functions (2); spheroidal wave functions (5); orthogonal polynomials (13); combinatorial analysis (9); numerical interpolation, differentiation and integration (11); probability functions (ll); scales of notation {6); miscellaneous functions {9); Laplace transforms (2); and others. Each of these sections is prefaced by a list of related formulas and graphs: differential equations, series expansions, special functions, and other basic relations. These constitute an unusually valuable reference work in themselves. The prefatory material also includes an explanation of the numerical methods involved in using the tables that follow and a bibliography. Numerical examples illustrate the use of each table and explain the computation of function values which lie outside its range, while the editors' introduction describes higher-order interpolation procedures. Well over 100 figures illustrate the text. In all, this is one of the most ambitious and useful books of its type ever published, an essential aid in all scientific and engineering research, problem solving, experimentation and field work. This low-cost edition contains every page of the original government publication. Preface by A. V. Astin. Foreword by Advisory Committee, Conference on Mathematical Tables. Editors' Introduction. Indices to Subjects, Notations.
Click on the below link below for Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables pdf free download, whole book
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Know your limits!
It is important to know your (not only mathematical) limits – when you know what you can do and what you can't do (yet), you know where you need to focus your efforts to improve your skills. This applies to everything in life, not just mathematics.
Have you spent time analysing your own skills in mathematics? Have you looked at the list of skills that you are expect to have (and be able to demonstrate in a test) as you complete each section of study? If you haven't you can (and should!) read the study design document at this link.
In the early days of television, there was a programme that became very popular – an early horror/thriller called The Outer Limits:
As the intro says:… The Outer Limits.
You are going on an adventure from your inner mind to the outer limits – and you will have control the vertical and the horizontal with crystal clarity – if you want to pass the calculus component of Mathematical Methods!
You have already studied an introduction to calculus last year, particularly the concept of limits and derivatives from first principles, leading to the general theory of differential of polynomials:
Calculus is central to almost all mathematics that has been developed in the last 400 years of mathematical thought – and as far as you continue into mathematics (whether that be in engineering, architecture, economics, medicine, or almost any other professional field) you will need to master this area of study. To assist you in this, I have compiled a video course to support your classroom instruction. There are three playlists – I advise you to consider carefully the time needed to view these videos (approximately an hour per playlist) and plan when you will watch which ones.
A warning to all students – this topic is the most critical aspect of Year 12 Mathematical Methods. You must bring your best efforts or all your work to this point will be devalued. Ask questions – practice – work and you will be successful.
2 Comments on "Know your limits!"
You may be slightly confused after being told that we would continue to circular functions (chapter 7). In consultation with other teachers, I have decided that it is better to continue to introductory calculus (chapter 9). You should be beginning your own revision at this time by beginning to work on chapter 8. Start making your plans for end of unit 3 assessment by working on this chapter. | 677.169 | 1 |
8th Grade Math
Welcome to Math!
Overview for 8th Grade Math
In this year of mathematics, middle school students will expand their mathematical skills, especially relating to algebraic reasoning, representing functions and equations, and probability. This course will prepare students to succeed in Algebra 1 as freshmen in high school.
This Week in 8th Grade Math
This week, the 8th Graders are learning about transformations of plane figures in the coordinate plane. They have a test on all of Chapter 2 on Thursday.
Syllabus
Google Classroom
Join Code for students: 4qhuxeh
I use Google Classroom (click here for link) as my main way to communicate with students during the school year. I post things such as2.7 Workbook activities
Tuesday
text pp. 87-89 #3, 7-25 odd
Wednesday
Study for test
Thursday
None
Friday
Chapter 3 Fair Game Review | 677.169 | 1 |
Mathematics of Personal Finance
Core
Course materials required. See 'Course Materials' below.
Mathematics of Personal Finance focuses on real-world financial literacy, personal finance, and business subjects. Students apply what they learned in Algebra I and Geometry to topics including personal income, taxes, checking and savings accounts, credit, loans and payments, car leasing and purchasing, home mortgages, stocks, insurance, and retirement planning.
Students then extend their investigations using more advanced mathematics, such as systems of equations (when studying cost and profit issues) and exponential functions (when calculating interest problems). To assist students for whom language presents a barrier to learning or who are not reading at grade level, Mathematics of Personal Finance includes audio resources in both Spanish and English.
This course is aligned with state standards as they apply to Mathematics of Personal Finance | 677.169 | 1 |
Measuring is a challenging math skill, but it is also an important one. Early learners are introduced to basic measurement concepts that they can explore on their own or with an adult. Simple, clear text explains different units of measurement, supporting essential math curriculum topics. Familiar examples presented with full-color photographs help readers understand how to apply what they have learned in the world around them. Young readers will become measuring masters in no time thanks to these engaging and relatable examples. Activities, Detailed Table of Contents, Full-Color Photographs.
The fastest way to learn algebra is to build a solid foundation in the basics. Inside this book you won't find a lot of endless drills. Instead, you get an original, step-by-step approach to learning algebra. In your first steps, you are introduced to essential concepts, allowing you to grasp the subject almost immediately. You will gradually progress to more challenging skills. Along the way, the authors show you how to solve practical problems using clear, step-by-step instructions. Exercises for each section, with detailed, worked-out solutions, will let you check your progress. In no time at all, you will have acquired the knowledge and skills you need to solve algebraic problems with confidence. --Publisher
Part one: Becoming Fermi. Prodigy ; Pisa ; Germany and Holland ; Quantum breakthroughs ; Of geckos and men -- Part two: The Rome years. Family life ; The Rome School ; Beta rays ; Goldfish ; Physics as soma ; The Nobel Prize -- Part three: The Manhattan Project. The New World ; Splitting the atom ; Fermi meets the Navy ; Piles of graphite ; The move to Chicago ; "We're cookin'!" ; Xenon-135 ; On a mesa ; An unholy Trinity -- Part four: The Chicago years. Return to Chicago ; In the public eye ; A patent fight ; Brilliant teacher, beloved mentor ; Travels abroad ; Home to die ; Fermi's legacy.
"In December 1942, a team at the University of Chicago achieved a milestone in human history: a nuclear chain reaction. At the forefront of this breakthrough stood Enrico Fermi, the father of the nuclear age. But as David N. Schwartz shows in this groundbreaking biography, Fermi's impact goes well beyond this epochal event. With his theory of beta decay and his development of quantum statistics, Fermi revolutionized modern physics. Straddling the classical and quantum ages, equally at ease with elegant mathematics and grubby experiments, Fermi truly was the last man who knew everything--at least about physics. In [this book], Schwartz draws from newly discovered archival material and exclusive interviews with those who knew Fermi to reveal the complex figure behind these historic contributions. A reluctant member of the Italian Fascist party, Fermi escaped to New York when Mussolini promulgated a series of anti-Semitic laws that put his wife, Laura, at risk. A citizen of an Axis power at the heart of the US government's most secret war effort, the Manhattan Project, he became one of its leading lights. A less-than-ideal father and husband, he was nevertheless one of history's greatest scientific mentors and teachers. He was also a deep thinker, as perspicacious about extraterrestrial life as he was about quantum field theory. The Last Man Who Knew Everything brings Fermi's brilliant, complex genius to life in a profound and consuming read."--Dust jacket flap.
A celebrated mathematician traces the history of math through the lives and work of twenty-five pioneering mathematicians. In Significant Figures, acclaimed mathematician Ian Stewart introduces the visionaries of mathematics throughout history. Delving into the lives of twenty-five great mathematicians, Stewart examines the roles they played in creating, inventing, and discovering the mathematics we use today. Through these short biographies, we get acquainted with the history of mathematics from Archimedes to Benoit Mandelbrot, and learn about those too often left out of the cannon, such as Muhammad ibn Musa al-Khwarizmi (c. 780-850), the creator of algebra, and Augusta Ada King (1815-1852), Countess of Lovelace, the world's first computer programmer. Tracing the evolution of mathematics over the course of two millennia, Significant Figures will educate and delight aspiring mathematicians and experts alike.
Foreword: Six things you may not know about gravity -- Part one: Newton. The Moon is falling ; The last of the magicians ; Beware the tides of March ; Map of the invisible world -- Part two: Einstein. Catch me if you can ; Ode to a falling man ; Where God divided by zero -- Part three: Beyond Einstein. A quantum of space-time ; The undiscovered country.
Discusses the concept of gravity from its earliest recognition in 1666 to the discovery of gravitational waves in 2015, and explains why gravity holds the key to understanding the nature of time and the origin of the universe.
Lamentation. Mathematics and culture ; Mathematics in school ; The mathematics curriculum ; High school geometry : instrument of the devil -- Exultation.
Lockhart speaks "against the way mathematics is taught in too many schools--as a rigid system of mindless algebraic rules with little meaning and very little beauty. Lockhart who has been a math researcher as well as a K-12 math teacher."--Publisher's description.
" Our user-friendly techniques break complicated problems down into their basic parts, so that you don't waste your time memorizing dozens of long formulas and equations" -- Provided by Amazon.
Wheeler's watch -- The only particle in the universe -- All the roads not to paradise -- The hidden paths of ghosts -- The island and the mountains: mapping the particle landscape -- Life as an amoeba in the foamy sea of possibilities -- Time's arrow and the mysterious Mr. X -- Minds, machines, and the cosmos -- Conclusion: The way of the labyrinth.
"In Fall 1939, Richard Feynman, a brash and brilliant recent graduate of MIT, arrived in John Wheeler's Princeton office to report for duty as his teaching assistant. The prim and proper Wheeler timed their interaction with a watch placed on the table. Feynman caught on, and for the next meeting brought his own cheap watch, set it on the table next to Wheeler's, and also began timing the chat. The two had a hearty laugh and a lifelong friendship was born. At first glance, they would seem an unlikely pair. Feynman was rough on the exterior, spoke in a working class Queens accent, and loved playing bongo drums, picking up hitchhikers, and exploring out-of-the way places. Wheeler was a family man, spoke softly and politely, dressed in suits, and had the manners of a minister. Yet intellectually, their roles were reversed. Wheeler was a raging nonconformist, full of wild ideas about space, time, and the universe. Feynman was very cautious in his research, wanting to prove and confirm everything himself. Yet when Feynman saw merit in one of Wheeler's crazy ideas and found that it matched experimental data, their joint efforts paid off phenomenally"--Provided by publisher.
Foreword / by Larry Gonick -- The coin-tossing prisoner of the Nazis -- What the Law of Averages really means -- The dark secret of the Golden Theorem -- What are the chances of that? -- Thinking independently is no yolk -- Random lessons from the lottery -- Warning : there's a lot of X about -- Why the amazing so often turns ho-hum -- If you don't know, go random -- Doing the right thing isn't always ethical -- How a lot of bull sparked a revolution -- How to beat casinos at their own game -- Where wise-guys go wrong -- The Golden Rule of Gambling -- Insure it-- or chance it? -- Making better bets in the Casino of Life -- Tell me straight doc-- what are my chances? -- This is not a drill! : Repeat: this is not a drill! -- The miraculous formula of Reverend Bayes -- When Dr. Turing met Reverend Bayes -- Using Bayes to be a better judge -- A scandal of significance -- Dodging the Amazing Baloney Machine -- Making use of what you already know -- I'm sorry professor, I just don't buy it -- The Amazing Curve for Everything -- The dangers of thinking everything's Normal -- Ugly sisters and evil twins -- Going to extremes -- See a Nicolas Cage movie and die -- We've got to draw the line somewhere -- Playing the markets isn't rocket science -- Beware geeks bearing models.
"Over the years, some very smart people have thought they understood the rules of chance--only to fail dismally. Whether you call it probability, risk, or uncertainty, the workings of chance often defy common sense. Fortunately, advances in math and science have revealed the laws of chance, and understanding those laws can help in your everyday life. In Chancing It, award-winning scientist and writer Robert Matthews shows how to understand the laws of probability and use them to your advantage. He gives you access to some of the most potent intellectual tools ever developed and explains how to use them to guide your judgments and decisions. By the end of the book, you will know: how to understand and even predict coincidences; when an insurance policy is worth having; why "expert" predictions are often misleading; how to tell when a scientific claim is a breakthrough or baloney; when it makes sense to place a bet on anything from sports to stock markets. A groundbreaking introduction to the power of probability, Chancing It will sharpen your decision-making and maximize your luck."--Jacket.
Educator Paul Lockhart's goal is to demystify arithmetic: to bring the subject to life in a fun and accessible way, and to reveal its profound and simple beauty, as seen through the eyes of a modern research mathematician. The craft of arithmetic arises from our natural desire to count, arrange, and compare quantities. Over the centuries, humans have devised a wide variety of strategies for representing and manipulating numerical information: tally marks, rocks and beads, marked-value and place-value systems, as well as mechanical and electronic calculators. Arithmetic traces the history and development of these various number languages and calculating devices and examines their comparative advantages and disadvantages, providing readers with an opportunity to develop not only their computational skills but also their own personal tastes and preferences. The book is neither a training manual nor an authoritative history, but rather an entertaining survey of ideas and methods for the reader to enjoy and appreciate. Written in a lively conversational style, Arithmetic is a fun and engaging introduction to both practical techniques as well as the more abstract mathematical aspects of the subject.-- Provided by publisher.
"Featuring Einstein's Classic Text, The Meaning of Relativity, in its Historical Context" -- title page.
Einstein's first trip to America -- Structure and contents of the meaning of relativity -- Physics and geometry -- The principles of general relativity -- The first solutions and the challenge of their interpretation -- Einstein and astronomers -- The genesis of relativistic cosmology -- The controversy over gravitational waves -- Philosophical debates on general relativity -- The quest for a unified field theory -- Early monographs on relativity -- Beyond the formative years -- Pre-relativity physics -- The theory of special relativity -- The general theory of relativity -- The general theory of relativity (continued)..-- Provided by publisher
This resource was created in response to the requests of teachers--those who want to implement number talks but are unsure of how to begin, and those with experience who want more guidance in crafting purposeful problems.
Part I. Atom and void -- The quiet citadel -- Things-in-themselves -- An impression of force -- The sceptical chymists -- Part II. Mass and energy -- A very interesting conclusion -- Incommensurable -- The fabric -- In the heart of darkness -- Part III. Wave and particle -- An act of desperation -- The wave equation -- The only mystery -- Mass bare and dressed -- Part IV. Field and force -- The symmetries of nature -- The Goddamn particle -- The standard model -- Mass without mass.
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"Zapped tells the story of all the light we cannot see, tracing microwaves, X-rays, gamma rays, radio waves, infrared, ultraviolet, and other forms of radiation from their historic, world-altering discoveries in the nineteenth century to their central role in modern life"--Provided by publisher.
We live in a world that is not quite 'right'. The central tenet of statistical inquiry is that Observation = Truth + Error because even the most careful of scientific investigations have always been bedevilled by uncertainty. Our attempts to measure things are plagued with small errors. Our attempts to understand our world are blocked by blunders. And, unfortunately, in some cases, people have been known to lie. In this follow-up to his acclaimed best-seller, The Lady Tasting Tea, David Salsburg opens a door to the widespread use of statistical methods by looking at historical examples of errors, blunders and lies from areas as diverse as archaeology, law, economics, medicine, psychology, sociology, Biblical studies, history, and war-time espionage. In doing so, he shows how, upon closer statistical investigation, errors and blunders often lead to useful information. And how statistical methods have been used to uncover falsified data. Beginning with Edmund Halley's examination of the Transit of Venus and ending with discussions of how many tanks Rommel had during the Second World War and whether modern African censuses contain falsified data, the author invites the reader to come along on this easily-accessible and fascinating journey of how to identify the nature of errors, minimize the effects of blunders, and figure out who the liars are.
Algorithmic thinking in everyday life -- Match those socks -- Find your size -- Pop to the shops -- Bring him home -- Sort that post -- Be more hip -- Update that status -- Get the jobs done -- Fix that necklace -- Locate that box -- Fill those shelves -- Navigate those aisles -- Final thoughts.
An introduction to algorithms and their problem-solving potential in the everyday world outlines alternative methods for managing twelve different scenarios using the same systems that underline a word processor, a Google search engine, or a Facebook ad.
Dr. Judy Willis presents this informative guide to getting better results in math class. Willis presents a practical approach for how we can improve academic results by demonstrating certain behaviors and teaching students in a way that minimizes negativity. | 677.169 | 1 |
Extract of sample Discrete Mathematics(Mathematical Algorithms)
The comprehensive study of how discrete objects come together through one another and the likelihoods of a diversity of outcomes is acknowledged as combinatory. Further areas of mathematics which are known to be component of discrete mathematics comprise graph theory as well as the theory of computation. In addition, subjects that are related to number theory like that resemblances and recurrence relations are as well renowned as a division of discrete mathematics (Wolfram Research, Inc. , 2010). This paper presents a detailed analysis of the existing one of most famous paradigms of discrete mathematics which is known as "Mathematical Algorithms". Mathematical Algorithms are presently one of the hot areas in discrete mathematics because of their extensive and effective use in the field of computer and information technology. This paper will provide comprehensive analysis of main features and areas of "Mathematical Algorithms".
The comprehensive study and areas of interest in discrete mathematics generally comprise the analysis and systematic study of algorithms, their efficiencies and implementations in various fields of life. Discrete mathematics is also acknowledged as the language of mathematics used in conjunction with computer science, as well as its significance has increased noticeably in recent few decades (John & Weisstein, 2010). In a broad sense, an algorithm can be thought as instruction (or a set of commands or course of actions) according to that a specific procedure has to take place. We can say that a computer program is an illustration or an accomplishment of an algorithm. This command/instruction has to be organized in such an accurate manner so that it is proficient to be executed by an operator that is capable to comprehend as well as efficiently run the algorithms commands. Several cases of consideration of algorithms are the strategies planned for summing up and finding difference between two or more
...Show more
Summary
Discrete mathematics is a section or element of mathematics that is concerned with the objects which are capable of assuming just divided, distinctive values. The concept of discrete mathematics is thus applied in distinction with continuous mathematics, that is the subdivision…
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Hashing algorithms are generally categorized based on the type of data in which they are used. The most popular hashing algorithms include SHA algorithms which work on the basis of the bit length of the text. Another commonly used algorithm is MD5 and its basic function is to generate hash values to encode and decode the given information.
Thus, the breaker failure relay opens adjacent breakers to isolate the problem. Fast and secure breaker failure detection algorithm would be a critical challenge facing a numerical BF relay. In the first part, it presents the need for breaker failure protection.
One would be expecting players in various retail supply chains to habitually misjudge demand, creating shortages or inventory surpluses at diverse stages in the supply chain. Changes in demand patterns also affect the supply chain of different manufacturing environments.
The compression can be lossless or lossy. Lossless compression lessens bits through identification and elimination of statistical redundancy. There is no information that is lost in the lossless compression. In contrary, lossy compression lessens bits through identification of marginally vital information and eliminates it.
Models provide an essential link between mathematics and other study disciplines such as economics and philosophy. Models reflect real world phenomenon and this can be confirmed through a suitable test. However not all models can be tested for their application or capability of providing solutions to real world problems.
This paper discusses the aspects of floating-point computer scientist should know to avoid some petty mistakes than can rather cost him a lot. Goldberg (1991) states that discrete mathematics is what distinguishes old computers from scientific computing. He adds that digital computers does not signify exactly all real numbers and therefore new things would be faced when designing computer algorithms for exact numbers.
Short time durations to wait for fortification are the best for children with ADHD (Moore, 2001).
This is the punishment the child gets whenever he or she deviates from the desired behavior. For example, it could be
pression of automata is in respect with the minimization, determination, primeness, and the extension on output feedback, observability, stability, and invertibility regarding the framework. The approach resembles that used by Mon-talbano's and Giammarresi in the illustration
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e, there were two different developments that were taking place that directly affected both the content and balance of these books, particularly those produced in the United States and Britain (Graham, 2012).
The discoveries of ancient mathematics on clay tablets in Mesopotamia | 677.169 | 1 |
Books
Mathematical Physics
Gauss's law for electric fields, Gauss's law for magnetic fields, Faraday's law, and the Ampere-Maxwell law are four of the most influential equations in science. In this guide for students, each equation is the subject of an entire chapter, with detailed, plain-language explanations of the physical meaning of each symbol in the equation, for both the integral and differential forms. The final chapter shows how Maxwell's equations may be combined to produce the wave equation, the basis for the electromagnetic theory of light. This book is a wonderful resource for undergraduate and graduate courses in electromagnetism and electromagnetics. A website hosted by the author at contains interactive solutions to every problem in the text as well as audio podcasts to walk students through each chapter.
want to learn probability and statistics quickly. It is suitable for graduate or advanced undergraduate students in computer science, mathematics, statistics, and related disciplines.
The book includes modern topics like non-parametric curve estimation, bootstrapping, and classification, topics that are usually relegated to follow-up courses. The reader is presumed to know calculus and a little linear algebra. No previous knowledge of probability and statistics is required. Statistics, data mining, and machine learning are all concerned with collecting and analysing data.
The purpose of this book is to provide an introduction to the concepts of statistical analysis of data for students at the undergraduate and graduate level, and to provide tools for data reduction and error analysis commonly required in the physical sciences. The presentation is developed from a practical point of view, including enough derivation to justify the results, but emphasizing methods of handling data more than theory. The text provides a variety of numerical and graphical techniques. Computer programs that support these techniques will be available on an accompanying website in both Fortran and C++.
Quantum mechanics and the Schrodinger equation are the basis for the de scription of the properties of atoms, molecules, and nuclei. The development of reliable, meaningful solutions for the energy eigenfunctions of these many is a formidable problem. The usual approach for obtaining particle systems the eigenfunctions is based on their variational extremum property of the expectation values of the energy. However the complexity of these variational solutions does not allow a transparent, compact description of the physical structure. There are some properties of the wave functions in some specific, spatial domains, which depend on the general structure of the Schrodinger equation and the electromagnetic potential. These properties provide very useful guidelines in developing simple and accurate solutions for the wave functions of these systems, and provide significant insight into their physical structure. This point, though of considerable importance, has not received adequate attention. Here we present a description of the local properties of the wave functions of a collection of particles, in particular the asymptotic properties when one of the particles is far away from the others. The asymptotic behaviour of this wave function depends primarily on the separation energy of the outmost particle. The universal significance of the asymptotic behaviour of the wave functions should be appreciated at both research and pedagogic levels. This is the main aim of our presentation here.
Features:
Asymptotic Methods in Quantum Mechanics Application to Atoms Molecules and Nuclei Springer Series in Chemical Physics
Going beyond the conventional mathematics of probability theory, this study views the subject in a wider context. It discusses new results, along with applications of probability theory to a variety of problems. The book contains many exercises and is suitable for use as a textbook on graduate-level courses involving data analysis. Aimed at readers already familiar with applied mathematics at an advanced undergraduate level or higher, it is of interest to scientists concerned with inference from incomplete information.
Achieve success in your physics course by making the most of what PHYSICS FOR SCIENTISTS AND ENGINEERS has to offer you. From a host of in-text features to a range of outstanding technology resources, you''ll have everything you need to understand the natural forces and principles of physics. Throughout every chapter, the authors have built in a wide range of examples, exercises, and illustrations that will help you understand the laws of physics AND succeed in your course!
Riemannian Geometry is an expanded edition of a highly acclaimed and successful textbook (originally published in Portuguese) for first-year graduate students in mathematics and physics. The author's treatment goes very directly to the basic language of Riemannian geometry and immediately presents some of its most fundamental theorems. It is elementary, assuming only a modest background from readers, making it suitable for a wide variety of students and course structures. Its selection of topics has been deemed "superb" by teachers who have used the text.
A significant feature of the book is its powerful and revealing structure, beginning simply with the definition of a differentiable manifold and ending with one of the most important results in Riemannian geometry, a proof of the Sphere Theorem. The text abounds with basic definitions and theorems, examples, applications, and numerous exercises to test the student's understanding and extend knowledge and insight into the subject. Instructors and students alike will find the work to be a significant contribution to this highly applicable and stimulating subject.
This textbook gives a comprehensive review of the new approach to group representation theory developed in the mid 70's and 80's. The unique feature of the approach is that it is based on Dirac's complete set of commuting operators theory in quantum mechanics and thus the representation theories for finite groups, infinite discrete groups and Lie groups are all unified. The new approach is easily acceptable to physicists, yet powerful and versatile for practical calculations. The development of the theory is from special to general, supplemented with abundant illustrative examples. The Clebsch-Gordan, Racah and subduction coefficients and isoscalar factors are discussed in detail for point groups, permutation groups, unitary groups and space groups. Tables of several useful coefficients are included. The theory on roots and weights in Lie groups is reformulated in the spirit of representation theory of quantum mechanics. The applications of group theory to many-body problem are introduced with emphasis on the various dynamic symmetry models of nuclei. There should be no difficulty for the readers of this book to understand the conclusions derived in other textbooks or literature, although the process of derivation may be entirely different from the conventional one
Roger Penrose, one of the most accomplished scientists of our time, presents the only comprehensive and comprehensible account of the physics of the universe. From the very first attempts by the Greeks to grapple with the complexities of our known world to the latest application of infinity in physics, The Road to Reality carefully explores the movement of the smallest atomic particles and reaches into the vastness of intergalactic space. Here, Penrose examines the mathematical foundations of the physical universe, exposing the underlying beauty of physics and giving us one the most important works in modern science writing.
If Albert Einstein were alive, he would have a copy of The Road to Reality on his bookshelf. So would Isaac Newton. This may be the most complete mathematical explanation of the universe yet published, and Roger Penrose richly deserves the accolades he will receive for it. That said, let us be perfectly clear: this is not an easy book to read. The number of people in the world who can understand everything in it could probably take a taxi together to Penrose's next lecture. Still, math-friendly readers looking for a substantial and possibly even thrillingly difficult intellectual experience should pick up a copy (carefully--it's over a thousand pages long and weighs nearly 4 pounds) and start at the beginning, where Penrose sets out his purpose: to describe "the search for the underlying principles that govern the behavior of our universe." Beginning with the deceptively simple geometry of Pythagoras and the Greeks, Penrose guides readers through the fundamentals--the incontrovertible bricks that hold up the fanciful mathematical structures of later chapters. From such theoretical delights as complex-number calculus, Riemann surfaces, and Clifford bundles, the tour takes us quickly on to the nature of spacetime. The bulk of the book is then devoted to quantum physics, cosmological theories (including Penrose's favored ideas about string theory and universal inflation), and what we know about how the universe is held together. For physicists, mathematicians, and advanced students, The Road to Reality is an essential field guide to the universe. For enthusiastic amateurs, the book is a project to tackle a bit at a time, one with unimaginable intellectual rewards. --Therese Littleton
A two-volume set, consisting of the latest editions of the two volumes (4th edition (2017) for Vol. I, and 4th edition (2012) for Vol. II). Much supplementary material can be found at the book's web page. The first volume is oriented towards modeling, conceptualization, and finite-horizon problems, but also includes a substantive introduction to infinite horizon problems that is suitable for classroom use, as well as an up-to-date account of some of the most interesting developments in approximate dynamic programming. The second volume is oriented towards mathematical analysis and computation, treats infinite horizon problems extensively, and provides a detailed account of approximate large-scale dynamic programming and reinforcement learning. This is a textbook on the far-ranging algorithmic methododogy of Dynamic Programming, which can be used for optimal control, Markovian decision problems, planning and sequential decision making under uncertainty, and discrete/combinatorial optimization. The treatment focuses on basic unifying themes, and conceptual foundations. It illustrates the versatility, power, and generality of the method with many examples and applications from engineering, operations research, and other fields. It also addresses extensively the practical application of the methodology, possibly through the use of approximations, and provides an introduction to the methodology of Neuro-Dynamic Programming, which is the focus of much recent research. | 677.169 | 1 |
Download E-books Mathematical Reflections: In a Room with Many Mirrors (Undergraduate Texts in Mathematics) PDF
A peaceful and casual presentation conveying the enjoyment of mathematical discovery and perception. common questions lead readers to work out arithmetic as an obtainable international of suggestion, the place realizing can flip opaque formulae into appealing and significant rules. The textual content provides 8 themes that illustrate the cohesion of mathematical idea in addition to the range of mathematical principles. Drawn from either "pure" and "applied" arithmetic, they comprise: spirals in nature and in arithmetic; the trendy subject of fractals and the traditional subject of Fibonacci numbers; Pascals Triangle and paper folding; modular mathematics and the mathematics of the limitless. the ultimate bankruptcy provides a few rules approximately how arithmetic can be performed, and for this reason, the way it might be taught. offering many contemporary discoveries that bring about fascinating open questions, the booklet can function the most textual content in classes facing modern mathematical themes or as enrichment for different classes. it might even be learn with excitement by means of an individual drawn to the intellectually interesting points of arithmetic.
An creation to the speculation of Numbers by way of G. H. Hardy and E. M. Wright is located at the analyzing record of just about all hassle-free quantity conception classes and is greatly considered as the first and vintage textual content in straight forward quantity concept. built below the suggestions of D. R. Heath-Brown, this 6th variation of An advent to the speculation of Numbers has been generally revised and up-to-date to lead modern day scholars throughout the key milestones and advancements in quantity concept.
Extra resources for Mathematical Reflections: In a Room with Many Mirrors (Undergraduate Texts in Mathematics) | 677.169 | 1 |
Hey there, I've just bought the lovely new Casio fx-9860GII SD, Casio's latest graphic calculator. It does NOT have CAS, therefore I can use it in A-level exams, but after spending so much money I was wondering if I'll be able to use it next year? I've heard unis are quite tight on calculator usage, so should I be holding on to my old fx-991 ES (the standard one everyone seems to have for A-levels now) and just selling my old graphic calc? Cheers
We're not allowed to use calculators at all. I suggest you look at each of the universities in question, given I'm aware that some only allow you to use certain models which you must buy from them, or get yours approved (then a sticker is applied). MostWe have to use the fx-115MS. It's basically the calculator from high school (the one before that blue natural display one, which everyone uses at college), however it also does complex numbers and calculus. Downside is it isn't natural display which is VERY annoying if you're doing say continued fraction expansions or just any job requiring accuracy and/or surds.
Although to be honest, I just use that silver casio calc which everyone uses. The version of the blue one i mentioned that does complex numbers/vectors/matrices/calculus etc etc. I even used it in our maths exams in jan (took both in just in case) and noone said anything.
However as others have said, you don't need a calc that much tbh. I needed it for calculus and the calculations fit of proof.
Also to do basic sums because I still have to count up in my head for the times tables and/or count on my finger. My excuse is I do maths degree not mental arithmetic and I have said calculator for any problems (or pen and paper) :P
at uni we have 2 different models of calculator we're allowed to use in exams. and thats it.
graphical calculators are still useful to have outside the exam room when you're working through problems etc so i'd say keep it. but do expect to have to buy a uni approved calculator when you get there
(Original post by orionmoo)
Although to be honest, I just use that silver casio calc which everyone uses.
Yeah that's the fx-991ES which I was contemplating selling as the new one does everything it does.
(Original post by jayshah31)
Most(Original post by korobeiniki)
Yeah that's the fx-991ES which I was contemplating selling as the new one does everything it doesThanks to all.
Keep one for spare at least. But it is best just buying the one the uni advises/requires. The universities shop should sell it once you get there..
(Original post by korobeiniki)
This is exactly what I thought before I came to university. I haven't needed a calculator once in these ~5 months simply because the mathematics doesn't require it. I guess you'll only see this once you start. | 677.169 | 1 |
The Complete Mathematics (Extended) Teacher's Resource Pack provides invaluable support for Cambridge IGCSE Mathematics teachers as well as ways to prepare students for the examinations. The printed Teacher's Guide provides a wealth of lesson ideas and resources to save you time - such as lesson plans with starter and plenary activities, and a guide to assessment. It also includes all answers to the students' book questions. The Teacher's CD provides customisable versions of the lesson plans so that you can make them even more relevant to your students and classroom situation, and use them as a basis for new ideas. The CD also provides suggestions for tackling tricky ideas, additional support to stretch your higher ability students. Fully endorsed by Cambridge International Examinations. This book usually ship within 10-15 business days and we will endeavor to dispatch orders quicker than this where possible. BTE9780199138753 | 677.169 | 1 |
Algebra Equations short 3.0
5018 algebraic equations from basic to advanced with fully explained solutions, related math theory and easy-to-use test preparation options This bilingual problem-solving mathematics software allows you to work through 5018 algebra equations with guided solutions, and encourages to learn through in-depth understanding of each solution step and repetition rather than through rote memorization. The software includes linear, quadratic, biquadratic, reciprocal, cubic and fractional algebraic equationsVP Algebra 1.1 - Individuals who are pencil impaired (blind, motor impaired, or learning disabled) have a very difficult time writing and manipulating Algebraic equations, since operating a pencil effectively is very difficult if not impossible. ...
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Hands-On Equations 1 - The Fun Way to Learn Algebra 3.4 - Teach your children the joys of learning algebra with Hands-On Equations 1 the algebra app for children as young as eight! ...ingenious app...makes it exceptionally easy to learn algebra..."- Dr. Alex Davidovic, former International Chess Master ... ...
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ENGINEERING MATHEMATICS I.
(Prof Evbogbai Edekin Jacob Mariekpen)
Intended Learning Outcome At the completion of the lecture, it is expected that the students should be able to: (i)Understand that operator j stands for ?1 and be able to simplify powers of j to ±???? ???????? ±1 (ii)Understand that complex numbers consist of (real part) + j(imaginary part) (iii)Add, subtract, multiply and divide complex number. (iv)Determine the conjugate of a complex number (v)Know the conditions for the equality of two complex numbers (vi)Complex numbers can be represented graphically using… READ MORE Download Staff Profile | 677.169 | 1 |
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Summary
With more than five hours of video instruction, the Digital Video Companion CD-ROM is the ideal study companion. The CD-ROM is based on three solid educational principles: Motivation, Instruction, and Evaluation. Instruction is at the core of the Digital Video Companion, so each section of McKeague's texts are covered by a 5- to 10-minute video lesson. The problems worked during the video lesson are listed next to the viewing screen, so students can try working them in advance. A slider bar gives immediate access to any part of the video lesson. In order to help students evaluate their progress, each chapter of the Digital Video Companion contains a chapter text with answers. To further assist students, MathCue tutorial software is now integrated into the Digital Video Companion. MathCue Tutorial lets students practice with problems, then scores them and offers annotated, step-by-step solutions. | 677.169 | 1 |
Take the stress out of high school math
The curriculum-based lessons are designed by educators to help students understand and avoid common algebra mistakes. Plus, special tips and tricks give students the edge in mastering key concepts.
Includes helpful tips and tricks, plus how to avoid common errors
Features animation and live voices from friendly tutors
Multi-step quizzes and fun games provided for each concept
System Requirements for Windows | 677.169 | 1 |
Math 60 is an introductory course on probability.
The course will have two components an exploratory simulation based
component where we will explore several interesting advanced probability
ideas and a more "down to earth" traditional component where we will
familiarize ourselves with the basics of mathematical probability.
One of the main goals of the exploratory aspect of this course is to leave
with you with tools that will enable you to set up and simulate your own
probability experiments. In the process of developing these tools we will
take a look into some interesting advanced topics ideas like Brownian
motion, streak theory and stochastic differential equations. In the "down
to earth part of the course" we will
introduce to the basic mathematical
concepts used in probability and in the process
develop a consistent way to articulate and interpret the results
of our simulations. In order to accomplish this we will be
covering chapters 1-9 of this
book (scroll down to see the table of contents). | 677.169 | 1 |
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