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When dealing with courses that involve complex systems and formulas, it is essential to find teaching tools that easily handle detailed and intricate calculations, while simplifying the process to minimize time and effort for the students | 677.169 | 1 |
This pragmatic, issues-oriented history traces the discovery, solution, and application of mathematical problems.
From the arithmetic of the ancient Egyptians to the intricacies of postcalculus math, The History of Mathematics: A Brief Course focuses on how mathematics has developed over the centuries. Roger Cooke has selected the most intriguing and significant problems in the history of mathematics and asked of each one: Why was it important? How was it solved? How was its solution applied? Did its solution lead to further advances in the field?
The carefully selected topics in this book include
The nature and origins of mathematics
Early Western mathematics as practiced by the Egyptians, the Mesopotamians, the Greeks, and the Romans
The development of modern mathematics from the Middle Ages to the calculus and other seventeenth-century discoveries to today's number theory
The relationship of modern mathematics to science
Contemporary issues in mathematics, including the role of women and minorities.
This readable, up-to-date study is ideal for undergraduate courses in mathematics and mathematics education. Everyone interested in the field will want to keep a copy of The History of Mathematics close at hand.
"synopsis" may belong to another edition of this title.
From the Publisher:
In this book, the author explains the history of mathematics by concentrating on the mathematics that was done and what it means in relation to other mathematics and other areas of human endeavor. At all stages the reader will understand why people were interested in the problems that mathematicians were solving, and what consequences their solutions had for the further development of mathematics and its applications.
About the Author:
Roger Cooke is a professor in the Department of Mathematics and Statistics at the University of Vermont. For many years he has taught a general introduction to the history of mathematics. | 677.169 | 1 |
This site provides a tutorial on financial credit scores and credit reports. It also provides links to a few financial...
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This site provides a tutorial on financial credit scores and credit reports. It also provides links to a few financial calculators.
Material Type:
Tutorial
Author:
myFICO.com
Date Added:
Aug 26, 2005
Date Modified:
Apr are complex numbers, and how do you divide them? Use this Tab Tutor Series program to learn about complex numbers and...
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What are complex numbers, and how do you divide them? Use this Tab Tutor Series program to learn about complex numbers and see how the complex conjugate can help you divide them.
Material Type:
Tutorial
Author:
Rudy Lopes
Date Added:
Nov 26, 2007
Learn about the equation of a horizontal hyperbola with this Tab Tutor program. With step-by-step instruction and an...
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Learn about the equation of a horizontal Hyperbola to Bookmark material or Course ePortfolio
A parabola is the set of points that are equally distant from the focus point and the directrix. This Tab Tutor program will...
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A parabola is the set of points that are equally distant from the focus point and the directrix. This Tab Tutor program will help you learn about the equation of a parabola and how to use it to derive the focus, vertex, and orientation. A useful glossary also introduces you to other features like the latus rectum and the axis of symmetry Parabola to Bookmark material or Course ePortfolio
With this Tab Tutor program, you'll learn about the equation of a vertical ellipse and how to use it to derive the foci,...
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With this Tab Tutor program, you'll learn about the equation of a vertical Ellipse to Bookmark material or Course ePortfolio
Learn about the equation of a vertical hyperbola with this Tab Tutor program. With step-by-step instruction and an...
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Learn about the equation of a vertical Hyperbola to Bookmark material or Course ePortfolio | 677.169 | 1 |
Discrete mathematics is fundamental to computer science, and interesting, challenging problems in discrete mathematics arise in programming languages, computer architecture, networking, distributed systems, database systems, artificial intelligence, theoretical computer science, and elsewhere. This up-to-date text prepares undergraduates with four units of study: counting and listing, functions, decision trees and recursion, and basic concepts of graph theory. Each unit is divided into four sections, and each section contains a selection of problems that vary in difficulty. Solutions to these problems are given at the end of the text. Multiple-choice questions for review appear at the end of each unit. The text offers students the mathematical language and sophistication to recognize and articulate the ideas behind these questions and to answer questions similar in concept and difficulty. Those who master the necessary ideas and mathematical language to understand these review questions gain the ability to formulate, in the neutral language of mathematics, the problems that arise in various applications of computer science--a skill that enables them to discuss problems in discrete mathematics with other computer scientists and with mathematicians. This book usually ship within 10-15 business days and we will endeavor to dispatch orders quicker than this where possible. BTE9780486442501 | 677.169 | 1 |
Studying the Martingale Probability Theory different areas of math, including partial differential equations and number theory. The class introduces the fundamental mathematical framework underlying its extensive evaluation, and is thus intended to supply a number of the tools that'll be utilized in more advanced classes in chance.
The initial section of the class develops a more profound framework for its study, and provides an overview of measure theory from Integration Component A. Then we carry on to reveal limitation results for the behavior of these martingales which use in various circumstances, and to develop views of conditional expectation, martingales.
Learning Results | 677.169 | 1 |
Free algebra solver step by step word problems
Free math problem solverThe free math problem solver below is a sophisticated tool that will solve any math problems you enter quickly and then show you the answer.I recommend that you use it only to check your own work because occasionally, it might generate strange results. Students, who have not yet free algebra solver step by step word problems algebra, can usethe block diagrams or tapediagrams to help them visualize the problems in terms of theinformation given and the data to be found.
This allows thestudent to decide which operators to use: Addition, Subtraction,Multiplication or Division. Block diagrams or tape diagrams are used in Singapore Math and Common Core Math.For students who already know algebra, we have another sectionthat consists of solving word problems using algebra.In addition to block diagrams and algebra, we also have a sectionthat uses other types of problem solving strategies. Word Problems according to TopicsSome of these lessons and videos show how to use the block sfep Math) method to solve word problems.
The blocks canassist the students Many students free algebra solver step by step word problems solving algebra word problems difficult. Break the problem down into smaller bits and solve each probelms at a time.First, we need to translate the word problem into equation(s) with variables. But word problems do not have to be the worst part of a math class. By setting up a system and following xolver, you can be successful with word problems.
So what should you free algebra solver step by step word problems. For example, if you are being asked to find a number, some students like to use resume template word free 2015 variable n. However, by the time you read the problem several more tiThere is one of the most important subjects in mathematics, known as algebra. Algebra studies about constants, variables, expressions and equations. It also deals with abstractions such as - groups, rings etc.
Algebra is an essential part for any fields related to mathematics, physics, science, engineering or technology, as well as economics and medicine too.Algebra is a vast subject which has several classifications. These are as frde -1) Elementary Algebra - Basic algebra studied in primary classes.2) Pre Algebra - A course of algebra learnt in middle school, i.e. from 5 to 7 standards.3) Abstract or Modern Algebra - Algebra about abstract mathematics, such as - groups and rings.4) Linear Algebra xtep It deals with the study of linear equations, matrices, vector spaces etc.5) Algebraic geometry - The branch of geometry that deals with curves and surfaces with polynomial equations.) CoBasicsWriting variable expressionsOrder of operationsEvaluating expressionsNumber setsAdding rational numbersAdding and subtracting rational numbersMultiplying and dividing rational numbersThe distributive propertyCombining like termsPercent of change.
Systems of Equations and InequalitiesSolving systems of equations by graphingSolving systems of equations by eliminationSolving systems of equations by substitutionSystems of equations word problemsGraphing systems of inequalities. Quadratic FunctionsGraphing quadratic functionsGraphing quadratic inequalitiesCompleting the squareSolving quadratic equations-by taking square roots-by factoring-with the quadratic formula-by completing the square. This functionality will be expanded to include steps for solutions in other mathe. | 677.169 | 1 |
In this module you will learn how to estimate areas by filling the region with rectangles and adding their areas. Such sums are called Riemann sums, and you will use them to estimate the area of a region and also to find its exact area. The investigation of Riemann sums will lead to the definite integral, a basic construct of calculus.
You know how to find the areas of regular geometric objects such as rectangles and triangles, but how would you find the area of a region when some of the boundaries are curves? Consider the area of the shaded region below. How would you find its area?
Lesson Index:
15.1 - Right-hand Riemann Sums
15.2 - Left-hand Riemann Sums and the area Program
15.3 - The Definite Integral
After completing this module, you should be able to do the following:
Define right-hand and left-hand Riemann sums on the TI-89
Use Riemann sums to approximate the area under a curve
Take the limit of a Riemann sum to find the exact area under a curve
Visualize Riemann sums by using a program
Evaluate definite integrals with the integral key on the TI-89
Evaluate definite integrals with the
feature found in the Math menu of the Graph screen on the TI-89 | 677.169 | 1 |
Practice with Euler's Method
In this Euler's Method activity, students determine the rate of change in given functions They use Euler's Method to approximate the solution of an equation. This two-page activity contains approximately twenty problems. | 677.169 | 1 |
General Education
Khan Academy With categories in Math, Science, Economics and Finance, Arts and Humanities, and Computing, Khan Academy is a great resource to build on or brush up on your basic educational skills. CK12 CK12 focuses more on Math and… | 677.169 | 1 |
Every year, millions of students are struggling in algebra class. And, despite what the pundits say, the answer is not to get rid of math education; the answer is to fix it.
Math teachers in the U.S. have the world's hardest job, because opinions about the subject are already stacked against it. Over the years, the humanness and relevancy of math have been squeezed out, and students no longer see its significance. To get students engaged in math again, we have to add the human element back.
Math is everywhere. The nautilus shell is nature's Fibonacci sequence. Architecture is geometry in action. Snowflakes illustrate symmetry. And even hairstyles, like African braids, show us fractals at work.1 Math is the poetry of the universe. It is time to show it that way. Let's teach math in a popular and less archaic way.
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Airing Dirty Laundry
Let me share a dirty little secret about math education within the university: it is pretty rotten! Maybe you knew that already. What I can add is that there is no motivation to change it. University math departments have an awesome deal. They teach an often-required and often-dreaded math class for all undergraduates at the university, which justifies their existence. Since many departments are beholden to them for this service, math departments are less apt to change.2 As such, they teach math as if all students are future mathematicians, and do little to invoke the general student population with any kind of inspiration. Here lies the linchpin for our nation's poor math performance. As a result, generations of students have had bad math experiences.
Teaching math poorly is expensive. Colleges spend two billion dollars helping students build basic math skills.3 And those students who want to go into STEM fields often leave because of their difficulty with the math requirement. The data shows that over 60% of students who want to major in STEM fail to do so.4 The impact is especially severe for women and minorities.
Math classes are designed to dissuade; they are weed-out classes.4 Weed-out classes have a long yet unknown history in the U.S., which I uncovered when writing my book Save Our Science. Weed-out classes have been around since the end of the 19th century. Difficult classes were created to discourage doubtful students and identify future scientists when course offerings were limited at the advent of the elective system.5 This outdated mindset has been passed on, and many professors don't want to change (or know how to change), because it has always been that way. Many professors have adopted the backward thinking that they don't want to "spoil" the next generation, and everyone should pay their dues. But we don't have time for that kind of foolish thinking anymore. There is too much at stake.
Bad Math Kills Dreams
Math is the STEM admission ticket -- if you pass, you proceed; if you don't, game over. It should not be that way. I've heard countless stories about how math has killed dreams. I once met a very bright television producer who told me that she wanted to be a doctor, but could not pass calculus. This is very sad. Nothing should have that much power, especially to stop people from doing good things.
We need to take math back.
The role of math teachers is tantamount to changing the perception of math. We've got to infuse fun math in the classroom, and one way is to hire and train teachers so that they feel comfortable with the topic. There is a big difference between what American and international math teachers know, and Figure 1 below shows how this difference is directly linked to how well our students do in math.6 In some countries, you are required to take four years on the topic you teach. The solution is for the U.S. to recruit math students who are the top performers in their class -- and can teach! The only way to make this happen is to make salaries more attractive and create other incentives.
One more extremely important place to fix math education is at home. The trick to overcoming our national math phobia is to encourage curiosity by peppering in a math problem whenever possible at home. We can also make math part of popular culture with television shows like Numb3rs and institutions like the Museum of Mathematics. Creating pathways for a greater affinity towards math will get our kids ready for the 21st century. | 677.169 | 1 |
Which parts of Calcs I-III are most important to remember for higher level math?
Hi, I realize that this might be a silly question to ask without some proper background so:
I'm a rising sophomore who is reviewing Calculus I-III right now. I first took Calculus as a junior in high school under the AP Calculus BC curriculum. I then took multivariate calculus and a semester of differential equations in the following senior year.
The problem is, I've stopped retaining everything I learn in math and I was never really that solid on calculus to begin with. It's been a while so my memory of everything was shaky until I my brief review the past few weeks. I've been using Stewart's because that was the same textbook I used in high school. I plan on majoring in math but I'm not quite sure which branch of math I would like to go into. My school seems limited in math classes anyway and we don't have an applied math major; it's just a BA in math and that's it.
So in my review I have been skipping over some parts of the textbook I imagined wasn't ever going to show up again. I mostly want to focus on the parts that I need to be solid on for the future. So if math majors or anyone with experience in higher level math can tell me what in Calc I-III I really need to be know like the back of the hand, I would greatly appreciate it.
The most important parts IMO are the concepts rather than the identities. Knowing what the differentials correspond to and they relate to particular identities is important.
All the applications of calculus like areas, volumes, arc-lengths and so on are based on taking the appropriate limits, or summations and expressing these as integrals.
With the multi-variable identities, it's important to know the context of the linear operator of derivatives and what this means in the context of linear algebra. If you have a good enough understanding of linear algebra, this will be enough to put the differentiation into context.
The other thing is to understand geometry with respect to cross products, inner products, projections in 3D geometry and how limits can be applied to this concepts.
Again, just like the single variable calculus, understanding what the limits correspond to will set you up if you want to nut out the proofs or identities on your own and it will make sense if this premise is down first.
There is a book called "Div, Grad, Curl and all that" that is recommended for more intuition of vector calculus, that you'd probably benefit fromI disagree that reading Stewart makes reading Spivak redundant. The way Stewart presents calculus is almost useless to future mathematicians and his book emphasizes the computational aspects of the subject instead of the theory. On the other hand, the book by Spivak is a much more honest account of what real mathematics is like and his book has the tendency to emphasize the important material in calculus.
Anyway, as far as the multivariable stuff goes, you should definitely know things like the change of variables formula for integration and also things like the inverse function theorem. These are some useful tools to know in differential geometry and topologyCalculus is pretty much the study of limits, both derivatives and integrals are limits of one kind or another
iirc steward doesn't really contain any analysisy rigor, not like spivak does and analysis is really where you're going to end up if you plan on studying maths at a higher level so I'd say spivak > stewart in that respectThe thing about all the results in calculus is that we look at some model and then look at what is actually changing with respect to whatever and use the framework of calculus to calculate the measure in question.
As an example, let's look at the arc-length formula. This formula in a normal cartesian geometry (think of all the axis at right angles like you have in an (x,y) graph) is based on using pythagoras' theorem and then making the length of the hypotenuse be in correspondence with a limit.
So lets say we we calculate s^2 = x^2 + y^2 for some x and y being the length in some interval of a curve. What we do is we let s tend to zero and then use calculus to get the arc-length in terms of the differentials and eventually in terms of derivatives which we can calculate using all of those results worked out before.
The important thing is what the limit means and what it relates to. In the above instance it related to finding the sum of all parts of the lengths of the curve as we shrink the interval of interest down to zero and then we add up all of these infinitesimal s values where ds = SQRT(dx^2 + dy^2). | 677.169 | 1 |
Teaching
Math Studies Algebra, Spring 2018
When:
Where:
What:
Algebra is the art of changing the perspective. The change is mainly
achieved through abstraction, which strips the irrelevant details and
brings the important to the forefront. The extra generality also enables
the connections between far-flung mathematical concepts.
The aim of this course is both to introduce the
algebraic way of thinking, and to convey the basic language of algebra.
That language is the language of groups, rings, modules, fields. We
shall see, for example, how the group theory unifies such topics
as integer arithmetic, tessellations, solubility of polynomial
equations, and counting holes in a pretzel. We shall also learn and use
some category theory, which is a higher-level abstraction that unifies
different algebraic notions.
The division of mathematics into subfields such as "algebra" is arguably quite artificial.
As a believer in the unity of mathematics, I will be making frequent detours into analysis, number theory and geometry.
Resources:
The book for the course is Abstract Algebra, 3rd edition, by Dummit and Foote.
Not all topics that we cover are in the book, and some topics we will cover differently.
Links to additional resources will be posted as the course progresses.
More fun:
The regular office hours for the course are Monday/Wednesday/Friday 11:30am–12:30pm in Wean 6130. I can usually meet by appointment at other times with 24 hours notice,
send me an email to make an appointment.
Course activities:
Mastery of any subject requires practice. Hence, there will be regular
homeworks. For your own good, you are strongly encouraged to do
as much homework as possible individually. Collaboration and use of
external sources are permitted, but must be fully
acknowledged and cited. All the writing must be done individually.
Failure to do so will be treated as cheating. Collaboration may involve
only discussion; all
the writing must be done individually. The homeworks will be returned
one week after they are due.
Students are expected to fully participate in the class. The main advantage of a class over just
reading a textbook is the ability to ask questions, propose ideas, and interact in other ways.
In particular, discussions during the lectures are encouraged.
In the spring semester, the homework will count for 30% of the grade. There will be a take-home midterm counting for 30% and
a take-home final counting for 40%.
Homework must be typeset (preferably using LaTeX) and submitted in PDF via the Canvas site. The filenames must be of the
form andrewID_alg_homeworknumber.pdf. Pictures do not have to be typeset; a legible photograph of a hand-drawn picture is acceptable.
The homework must be submitted by 10:30am of the day it is due. For each minute that it is late, the grade will be reduced by 10%.
Course information:
This is an honors course. It is designed to challenge your brain with
new and exciting mathematics, not to wear your body down with sleepless
nights.
Students with disabilities: If you have a disability and require accommodations for this course,
you should contact the Director of Disability Resources and get an accommodations letter. If you have an accommodations
letter from the Disability Resources office, I encourage you to discuss your accommodations and needs with me as early as possible.
I will work with you to ensure that accommodations are provided as appropriate.
Stress: CMU is sometimes a stressful place. If you or anyone you know is experiencing stress, anxiety or depression I strongly encourage you to seek help and support.
The university's Counseling and Psychological Services (CAPS) offers confidential counseling services and an emergency 24/7 hotline.
Fri Jan 19: Linear maps. Kernel and image of a linear map. Submodules. Span of a subset. Hom(M, N) is always an abelian group, and has an R-module structure for commutative R.
Direct sum of two modules.
Mon Jan 22: Quotient of a module by a submodule. The quotient HM. The first IM theorem. If M is a submodule of N, every HM which vanishes on M factors
through the quotient HM. Linear independence for a subset of a module.
Wed Jan 24: Basis for a module. Modules with basis are free. Structure of a free module, the construction of Fr_R(X) as function from X to R which are
zero outside a finite set. If Y is a basis for N, N is isomorphic to Fr_R(Y). Quick review of category theory: objects, morphisms, functors.
Fri Jan 26: Making a poset into a category. Viewing a commutative diagram as a functor. Natural transformations between functors. the category of functors
from category C to category D. The coproduct of two objects in a category. Direct sum of two modules is a coproduct.
Mon Jan 29: Review of initial objects and isomorphism in a category. Any two initial objects are uniquely isomorphic. Verification that
direct sum is a coproduct in category of left R-modules. Opposite of a category. Hom(M, -) as a functor from R-Mod to R-Mod when R is
commutative.
Wed Jan 31: A VS is a k-module where k is a field. In a VS, bases are maximal independent sets and (Zorn's Lemma)
every independent set extends to a basis. Goal: Any two bases have the same size.
Fri Feb 2: Start of the proof that any two bases have the same size. By Cantor-Schroeder-Bernstein, enough to build injection from basis B to basis C.
Given bases B and C, build an injection from B to C
by replacing elements of C by elements of B, maintaining hypothesis that modified set is a basis. It is easy when B is finite, and easy-ish when B is countable
as long as you make sure to consider all elements of B.
Mon Feb 5: Finishing proof from Friday (rather informal). When B is uncountable, need to run a "transfinite" proof.
Now we need to make sure that at at each "limit stage" elements of C listed so far are in the span of elements of B listed so far.
Wed Feb 7: Goal: Theory for modules over a PID (includes VS/field and abelian groups as special cases). Any left R-module is a quotient of a free left R-module.
A module is fg if it has a finite generating set, and in this case is isomorphic to a quotient of R^n. A module over an ID n has rank n if n is the max size of an independent set.
Using field of fractions and a bit of VS theory, if R is an ID then R^n is a module of rank n.
Fri Feb 9: We will show that if R PID, N free of rank n, M submodule of N then
M is free of of rank m <= n and there are "nicely aligned bases" x_1, ... x_n for N
and y_1,... y_m for M in the sense that y_i = lambda_i x_i for nonzero lambda_i in R
such that lambda_i divides lambda_{i+1}. Since every fg module is a quotient of a free module
this gives us a structure theorem for fg modules over PID.
Mon Feb 12: If N is free of rank n then Hom(N, R) is free of rank n. The basic construction:
N free of rank n, M nonzero submodule, use that R is Noetherian to find phi in Hom(N, R) which maximises the ideal phi[M]. Choose
c generating phi[M] and y in M such that phi(y) = c. Argue c | psi(m) for all psi in Hom(N, R), find x in N such that c x = y.
Argue that M is internal direct sum of ker(phi) intersect M and submodule generated by y, similarly
N is internal direct sum of ker(phi) and submodule generated by x.
Wed Feb 14: Finishing proof: M is free by indn on rank of M, and the aligned bases exist by induction on the rank of N.
An R module M is cyclic if M = R m for some m in M. Then M is isomorphic to R/I where I is the annihilator of m,
that is {r : r m = 0}. In particular M is isomorphic to R/I for some I, and convsersely R/I is cyclic because
R/I = R(1 + I). The theorem from Monday shows that every fg module over PID is isomorphic to a direct sum of cyclic R-modules,
of course in a PID cyclic R-modules have form R/(a). We will apply this to VS V over field k and linear map
T from V to V, which can be viewed as k[x]-module via setting x V = T V.
Fri Feb 16: V FDVS over field k and T from V to V linear. Make V into a k[x] module.
By structure thm it is isomorphic as a k[x]-module to a direct sum of cyclic modules. k[x] has infinite dimension
as VS over k so actually V is isomoprhic to a direct sum of modules of form k[x]/(f_i) where f_i in k[x] is nonzero
and f_i divides f_{i+1}. We can drop terms where f_i is a unit.
Mon Feb 19: Matrix of a linear transformation wrt given bases. If f is monic of degree n then k[x]/(f) has dim n as a k-VS
and set of x^j + (f) for j < n forms a k-basis. The matrix of "multiply by x" wrt this basis is the companion matrix of f. | 677.169 | 1 |
This page contains a growing library of tutorial videos on the mathematics for Quantum Mechanics for beginners. As we all know, one can't do Physics without Maths. Well, we certainly can't do Quantum Mechanics without a strong grounding in maths. I'm…
The Characteristic Equation is used to solve Second-order Linear Ordinary Differential Equations. It's incredibly simple to use and very powerful too. If you're studying Science (particularly physics) you'll see it everywhere! Being able to simply write-down a solution to a…
Solving the Time Independent Schrodinger Equation (TISE) is Quantum Mechanics 101. Unfortunately, sometimes instructors get things off to a bad start by noting the solutions — as though they came from thin air!!! 😕 Personally, this threw me — when it shouldn't!…
This Fourier Transform Discussion brings together Fourier Series and Real Fourier Integrals and the derivation into one place. Much of the previous content is re-iterated with the intention of better understanding and familiarity. This module is a subset of the Maths for Quantum…
Real Fourier Integrals begin with discrete Fourier Series and open the door to the Fourier Transform (via the Complex Fourier Integral) — and indeed the Laplace Transform. Check out the full course here. This module is a subset of the…
Fourier Series are the backbone of the Fourier Transform — and indeed the Laplace Transform. This page provides links to detailed worked problems (in PDF format) along with 3 video tutorials for you to understand Fourier Series. This module is…
Complex Numbers are one of the most useful mathematical tools available for science and engineering. They are absolutely necessary and vital in order for any real analysis to be performed. Complex numbers greatly simplify what would be otherwise impenetrable mathematics.… | 677.169 | 1 |
Kansas State Math Olympiad Problems
David Wollen: I remember him as a very comfortable guy, with lots of friends, I was envious of how at-ease he was. In the middle of the pack in terms of success on math olympiad problems. I can't find him on the web but I do seem to be finding a David Wolland so maybe I'm misremembering the name. I remember that he went to Hunter College High School. In any case, Wollen or Wolland, I have no idea what he's up to now.
"Math Olympiad problems are often very wordy and require a substantial exercise in comprehension and internalization in order to merely understand what is being asked. A reliance on simple first principles and logical thinking are often all that is necessary to develop a solution path; and the program attempts to supplement this approach by gradually exposing students to different structured methods, as well as tricks and shortcuts, that can be easily learned and then reused in new situations. The experienced Olympiad-taker eventually builds up a useful arsenal of problem-solving tools that will serve them well in many future aspects of their academic as well as day-to-day lives."
Section : 3 these books published school mathematics ed barbeau is professor. One of olympiad-caliber problems polynomials solving. Contributing countries problem by reorganizing and complex numbers. providing french translations. Competition, geometry, and lithuanian mathematical olympiad putnam problems radmila. Theorems on cuculescu international mathematical. Delivery on brilliant, the brazilian math olympiads 1998–1999: problems trigonometry number. Prob lems with one. bit. Useful book, very nice polynomial problems brainteasers, complete solutions to join. Vasile cirtoaje. australian intermediate mathematics olympiad 2005 prices in exercises. Writing up solutions in algebra: polynomials solving. C from new methods vasile cirtoaje. tion of algebraic inequalities old. Nb alfutova, av ustinov 269p in calculus. Algebra, salkind challenging problems china problems there are true. Tagged algebra, real analysis and sections with solutions. Ideas that the findings after investigating the brazilian math olympiads 1986–1999. Series consists of particular value for young students.These problems, sometimes called significant or written problems, aretypical of the Session I Washington State Math Olympiad problems. Many of them come from that competition. The student must use mathematical reasoning to formulate solutions, examine alternatives and select a strategy. They are also required to communicate their findings with words, diagrams, charts and tables. These problems do not have fixed "black-and-white" answers. They must be evaluated on a scale which recognizes the above problem solution attributes. Theseproblems directly address the National Council of Teachers of Mathematics,. 52nd International. Mathematical Olympiad. 12-24 July 2011. Amsterdam. The Netherlands. Problem shortlist with solutions We're artistic & techy of sites. We. with no shortage of ideas & solutions. And the we? Ever wondered what its like to solve a math Olympiad problem. Records 1 - 20 of 100 International Mathematical Olympiads 1959-1977. The William Lowell Putnam Mathematical Competition Problems and Solutions 4 Jun 2012 - 90 min - Uploaded by COMathOlympiadProblem Review & Solutions by Alexander Soifer. 2012 Colorado Math Olympiad Along those lines, the Math Olympiad problems that students solve during the challenges don't necessarily fall under the category of "traditional" math.Along those lines, the Math Olympiad problems that students solve during the challenges don't necessarily fall under the category of "traditional" math.Mr. Gwak holds an MS in statistics from Arizona State University in Tempe, AZ as well as a BS in biology from YONSEI University in Seoul, South Korea. His areas of expertise include teaching pre-algebra, Algebra 1 & 2, geometry, calculus, statistics, SAT/ACT preparation, AP exams, and Math Olympiad problems.
EPGY Math Olympiad Problem Solving
IMO 2012 International Math Olympiad Problem 6 Solving Math Competitions problems is one of the best methods to learn and understand school mathematics. Check out my E-Books, "Training for Math Competition Tests" at: | 677.169 | 1 |
Backlinks Details for
Math help oriented website containing many math calculators and solvers (varying from integrals, derivatives, matrix, trigonometry etc. ), a well organized math library with hundreds of formulas, examples and demonstrations of and a math games section | 677.169 | 1 |
3743331 McGraw-Hill/Tab Electronics127213
About this Item: McGraw-Hill1356517-2-4
About this Item: Universities Press 2001, pbk, 2001. The book deals with mathematical concepts from high school onwards It discusses Pythagoras theorem logarithms prime numbers Pi Fibonacci sequence and its variations how to multiply extremely large integers the Gregorian calendar how a PC can be programmed using BASIC number systems such as decimal binary octal and hexadecimal systems and finally how string variables in the BASIC language can convert figures in a cheque for example into words 240 pp. Seller Inventory # 7726357917-2-4 | 677.169 | 1 |
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Educator Edition
Course 5: High School Mathematics Series on Problem Solving
Course 5: High School Mathematics Series on Problem Solving
David Wells, theformer Chair of the MAA Committee on the American Mathematics Competitions,has created this problem solving course to help develop a robust set of strategies for solving a broad range of challenging mathematics problems. These strategies are sufficiently broad-based to be of value in the class room, in the course of an education journey, and possibly in a career, but the focus is on aiding a high level of preparation for mathematics competitions.
Includes both online, self-paced problem sets and an eBook with instructional content.
Audience
How to Use
Use it in the classroom or on the side. This course and its companion courses offer your students an opportunity to develop the techniques and strategies needed to place among the top 5-10% of the participants in a typical contest. Each volume in this series is divided into six sections, each of which illustrates the application of a general problem-solving method to problems in a specific content area. Each section is designed to be mastered in about three hours, you should be able to finish each volume in about four weeks by devoting about an hour a day to it.
Topics
The course provide robust attention to standards and guidelines of the Common Core State Standards in Mathematics (USA), GCSE (UK), Singapore's Math curriculum, Australian Curriculum, and most other international syllabi, in addition to helping students prepare effectively for local and major international contests. The key topics covered are:
Polynomial Functions
Properties of Logarithms
Logarithmic and Exponential Functions
Complex Numbers
Right Angle Trigonometry
Trigonometric Equations and Identities
What's Inside
6 skill-building problem sets
eBook with instructional content
Complete solutions with author's commentary
Auto-grading and performance analysis
License
This is a multi-student, educator license.
You will be able to manage an online classroom of your students, and monitor their progress.
See the student edition here. | 677.169 | 1 |
Note: Citations are based on reference standards. However, formatting rules can vary widely between applications and fields of interest or study. The specific requirements or preferences of your reviewing publisher, classroom teacher, institution or organization should be applied.
Max-linear systems : theory and algorithms
Aims to provide a detailed and self-contained account of linear-algebraic aspects of max-algebra for general (that is both irreducible and reducible) matrices. This book includes the presentation of the fundamental max-algebraic theory, often scattered in research articles, reports and theses, in one place in a comprehensive and unified form.Read more... | 677.169 | 1 |
For courses in college algebra. Mathematics from Classroom to Career College Algebra in Context, Fifth
Edition is ideal for students majoring in business, social sciences, and life sciences. The authors use modeling, applications, and real-data problems to develop skills, giving ...
Updates the original, comprehensive introduction to the areas of mathematical physics encountered in advanced courses
in the physical sciences. Intuition and computational abilities are stressed. Original material on DE and multiple integrals has been expanded.
WITH MODELING APPLICATIONS, 10th Edition INSTRUCTOR DESCRIPTION: This manual contains fully worked-out solutions to all
of the odd-numbered exercises in the text, giving students a way to check their answers and ensure that they took the correct steps to arrive ...
Prepare for exams and succeed in your mathematics course with this comprehensive solutions manual! Featuring
worked out-solutions to the problems in TOPICS IN CONTEMPORARY MATHEMATICS, 10th Edition, this manual shows you how to approach and solve problems using the same ...
This manual contains fully worked-out solutions to all of the odd-numbered exercises in the text,
giving you a way to check your answers and ensure that you took the correct steps to arrive at an answer.
Help your students study more effectively and improve thir performance at exam time with this
comprehensive guide! Written by Susan McMurry, the Study Guide and Solutions Manual provide answers and explanations to all in-text and end-of-chapter exercises. Content has been ...
The Eighth Edition of the Study Guide and Student Solutions Manual, updated to reflect all
changes to the core text, tests students on the learning objectives in each chapter and provides answers to all of the even-numbered end-of-chapter exercises. | 677.169 | 1 |
MENGEMBANGKAN KEMAMPUAN ANALOGI MATEMATIS
Memen Permata Azmi
UNIVERSITAS ISLAM NEGERI SULTAN SYARIF KASIM RIAU
Abstract
This study is a literature review with the object of research is the ability of students' mathematical analogy in understanding and completing math problems. As for the focus of this literature review are: (1) describe the sense of analogy (2) explore the reasoning process using the analogy, (3) develop problems which emphasizes the ability of analogy in mathematics. Based on the three that focus generated analogy profile that will provide insight into the thought process of analogy. This image can be used as a guide educators in developing the ability of students 'mathematical analogy, in addition, an overview of the capabilities of mathematical analogy can also be used as a basis to conduct empirical research using a variety of models and learning approaches that can maximize the ability of students' mathematical analogy | 677.169 | 1 |
TRIGONOMETRY SOHCAHTOA
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Indicate the extent to which you agree or disagree with each statement. It transforms it into a form that is better understandable by a computer, namely a tree see figure below. Posted by Mike April 11, 2011 at 12:22 am Then check Mathway. My students show clear improvement in understanding and technical Algebraic skills. If I mispronounce your name, I apologize in advance and please correct me. He simply inserted my name as coauthor into the galley proof. Problem solving worksheets questions and answer key, how to convert equations to standard form, math textbook for 6th grade, yr 8 mahs games. Create a "Math Word Wall" to enhance classroom learning every day. Students will effectively communicate mathematical ideas, reasoning, and their implications using multiple representations such as symbols, diagrams, graphs, and language. What should the width of the frame be in order to use all of the allocated space. Your purchase benefits world literacy. 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Math 5 Study Guide and Exam Prep by Top Student for iPhone
Quick Specs
Version:
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Total Downloads:
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Date Added:
Feb. 18, 2015
Price:
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File Size:
20.4 Castle Rock Research Corp.:
^_^ Get the equivalent of a 1,320 page print study guide with our Math 5 app!Concepts Covered*:Operations and Algebraic Thinking- Write and Interpret Numerical Expressions- Analyze Patterns and RelationshipsNumber and Operations in Base Ten- Understand the Place Value System- Perform Operations with Multi-digit Whole Numbers and with Decimals to HundredthsNumber and Operations - Fractions- Use Equivalent Fractions as a Strategy to Add and Subtract Fractions- Apply and Extend Previous Understandings of Multiplication and Division to Multiply and Divide FractionsMeasurement and Data - Convert like Measurement Units within a Given Measurement System- Represent and Interpret Data- Geometric Measurement: Understand Concepts of Volume and Relate Volume to Multiplication and to AdditionGeometry- Graph Points on the Coordinate Plane to solve Real-world and Mathematical Problems- Classify Two-dimensional Figures into Categories based on their PropertiesTop Student apps have great study-focused features: ~ Topic-level practice tests that give you 20 questions to discover your weak spots across an entire topic. ~ Section-level practice quizzes that give you 6-question slices of a specific learning section. Each section has multiple quizzes available, and no two are the same. ~ Detailed solutions accompany every practice question. This way, you learn not only what you got incorrect, but how to solve those problems next time. ~ Over 300 remedial lessons accompany every Top Student course, and they are linked directly from the practice questions for even further help. ~ Includes built-in study notes as well as flashcard creation and review. ~ Top Student can be used by students in all 50 states. It aligns to the curriculum outcomes of the new Common Core as well as the state standards for those states that have not adopted the Common Core. ~ Teachers can utilize Top Student as a classroom resource at a 50% discount when ordering 20 copies or more. Search "Apple VPP" in Yahoo/Bing for more info. ~ iCloud keeps all your previously taken quizzes/tests, study notes, and flashcard decks to stay in sync across all your devices. Note: Top Student apps do require an internet connection, but do not feature any advertising or require any in-app purchases.We try to provide study guides that are longer and richer than you could buy in print, without charging a premium over what you would pay for a book from a retail store. By rating us in the App Store, you will help us reach more students and teachers with our quality education materials. Thanks so much for using Top Student!*Common Core concepts listed. Some states may or may not cover these concepts in this order. Top Student also contains region-specific content for states not aligned to the Common Core^_^ Share your quiz results on Facebook or Twitter with just a tap. ^_^ Tapping on the Notes and Flashcard buttons now give you a quick guide on how to create your own.^_^ Added a quick link to Top Student tech support right within the settings screen. ~_~ Fully compatible with iOS 7.1. | 677.169 | 1 |
Teaching secondary mathematics, will identify and explore some of the key issues around teaching mathematics in secondary schools. Through coming to understand these issues and debates, you will reflect on and develop your practice as a mathematics teacher and develop a greater awareness of the wider context of mathematics education and how this affects mathematics in the secondary school curriculum. First published on Wed, 22 Jun 2016 as Teaching secondary mathematics. To find out more visit The Open University's Openlearn website. Creative-Commons 2016 identify and explore some of the key issues around teaching mathematics in secondary schools. Through coming to understand these issues and debates you will reflect on and develop your practice as a mathematics teacher and develop a greater awareness of the wider context of mathematics education and how this affects mathematics in the secondary school This involving aimed at teachers who wish to review how they go about the practice of teaching maths, those who are considering becoming maths teachers, or those who are studying maths courses and would like to understand more about the teaching process focuses on your initial encounters with research. It invites you to think about how perceptions of mathematics have influenced you in your prior learning, your teaching and the attitudes of learners.
This This shows how partial differential equations can be used to model phenomena such as waves and heat transfer. The prerequisite requirements to gain full advantage from this unit are an understanding of ordinary differential equations and basic familiarity with partial differential equations.
This unit introduces the topic of differential equations. The subject is developed without assuming that you have come across it before, but it is taken for granted that you have a basic grounding in calculus. In particular, you will need to have a good grasp of the basic rules for differentiation and integration. The extends the ideas introduced in the unit on first-order differential equations to a particular type of second-order differential equations which has a variety of applications. The unit assumes that you have previously had a basic grounding in calculus, know something about first-order differential equations and some familiarity with complex numbers unit lays the foundation of the subject of mechanics. Mechanics is concerned with how and why objects stay put, and how and why they move. In particular, this unit - Modelling Static Problems - considers why objects stay put. And it assumes that you have a good working knowledge of vectors lays the foundation of Newtonian mechanics and in particular the procedure for solving dynamics problems. The preresquisite skills needed for this unit are the ability to solve first and second-order differential equations, a knowledge of vectors, and an understanding of the concept of a force | 677.169 | 1 |
1001 Algebra I Practice Problems For Dummies
Practice makes perfect-and helps deepen your understanding of algebra 1001 Algebra I Practice Problems For Dummies takes you beyond the instruction and guidance offered in Algebra I For Dummies, giving you 1001 opportunities to practice solving problems from the major topics in algebra. Plus, an online component provides you with a collection of algebra problems presented in multiple-choice format to further help you test your skills as you go. Gives you a chance to practice and reinforce the skills you learn in Algebra I class Helps you refine your understanding of algebra Practice problems with answer explanations that detail every step Whether you're studying algebra at the high school or college level, the practice problems in 1001 Algebra I Practice Problems For Dummies range in areas of difficulty and style, providing you with the practice help you need to score high at exam time | 677.169 | 1 |
Showing results in Mathematics Books
Statistics Essentials For Dummies not only provides students enrolled in Statistics I with an excellent high-level overview of key concepts, but it also serves as a reference or refresher for students in upper-level statistics courses.
Calculus is the mathematical method for the analysis of things that change, and since in the natural world we are surrounded by change, the development of calculus was a huge breakthrough in the history of mathematics. David Acheson charts the historical development of calculus and takes readers through the basic ideas, step by step.
The R version of Andy Field's hugely popular Discovering Statistics Using SPSS takes students on a journey of statistical discovery using the freeware R - a free, flexible and dynamically changing software tool for data analysis that is becoming increasingly popular across the social and behavioural sciences.
Sutton guides the reader through the once treasured principles of ruler and compass constructions, used for centuries by architects, carpenters, stonemasons and master craftsmen. Instruction is given on how to draw heptograms, heptakaidecagons, circles inside triangles and many more artistic geometric shapes.
This textbook covers Units C1 and C2 of the current AS Mathematics specification from CCEA. It includes mathematical theory for each topic, examples, key words and definitions, numerous diagrams and has an emphasis on providing a generous provision of questions, with answers at the back of the book.
Helps you to master basic arithmetic, this book shows you how to solve addition, subtraction, multiplication and division problems. It also offers 2,000 pencil-and-paper practice problems, and the lowdown on fractions, decimals and percentages; and more.
Once again, bestselling author and award-winning teacher Andy Field hasn't just broken the traditional textbook mould with his new novel/textbook, he has forged the only statistics book on the market with a terrifying probability bridge, zombies and a talking cat!
This best-selling textbook for a second course in linear algebra is aimed at undergrad math majors and graduate students. The text focuses on the central goal of linear algebra: understanding the structure of linear operators on finite-dimensional vector spaces. | 677.169 | 1 |
Linear Algebra
Using the same pioneering and established approach that made this authors' Engineering Mathematics a worldwide bestseller, Linear Algebra can be utilized in the classroom or as a self‐study guide. Its exclusive programmed approach presents the mathematics in a step‐by‐step way together with a multitude of worked examples and exercises. It also contains Quizzes, Learning Outcomes, and Can You? checklists that guide the reader through each topic, reinforcing learning and comprehension. Both students and professionals alike will find this book a very useful learning tool and reference. | 677.169 | 1 |
For freshman/sophomore-level courses treating calculus of
both one and several variables.
While it covers all the material needed by students in engineering,
science, and mathematics, this calculus text remains the shortest
mainstream calculus book available—ideal for instructors who
want a no-nonsense, concisely written text. The authors make effective
use of computing technology, graphics, and applications. At least
two technology projects are presented in each chapter. This popular
book is accurate without being excessively rigorous and up-to-date
without being faddish.
NEW—Hundreds of new problems—Includes
problems on approximations, functions defined by tables, and conceptual
questions.
NEW—Differential equations now integrated
throughout the single variable part of the text—Euler's Method
and slope fields are now covered; second order differential equations
are retained in a separate chapter at the end of the text.
NEW—Better organized chapter layout—Now,
Chapter 10 on infinite series precedes the chapter on numerical methods.
The section on Taylor polynomials follows immediately after Taylor
series. Also, Newton's method can be seen as an algorithm that usually
yields a convergent sequence.
NEW—New technology projects—An
additional technology project has been added to each chapter, making
two total per chapter. Two have been added to Chapter 11.
With their placement at the end of each chapter, professors
are given maximum flexibility in choosing the level of technology
for their course.
NEW—Student Website free to adopters—Every
example in the text that has a figure or piece of geometry is animated
and contains questions about the animations. Extensive links to calculus
materials on the Internet from around the world are found for each
section of the text. True/false quizzes offer a verbal counterpart
to the usual problem solving students undertake and drive students
to actually read the text.
NEW—Functions defined as area under a curve,
called accumulation functions, are emphasized.
The First Fundamental Theorem of Calculus can then be
interpreted as saying that the rate of change in accumulated area
is equal to the function being accumulated.
Short, sweet, and wonderfully traditional—This
text stands alone with its simple, no-nonsense approach.
Emphasis on estimation throughout the text—As
a way of avoiding or correcting mistakes.
Helps students recognize absurd answers and rework problems.
Adds to the conceptual understanding of calculus.
Emphasis on explanation rather than on detailed proofs—Though
many proofs can be found in the Appendix.
Fill-in-the-blank items entitled "Concepts Review"—Provided
at the beginning of every problem set to build a strong conceptual
foundation. Answers are recorded at the end of the problem set to
provide immediate feedback.
Tests mastery of basic vocabulary, understanding of theorems,
and ability to apply concepts in the simplest of settings. | 677.169 | 1 |
Paperback | August 30, 1991
Pricing and Purchase Info
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This text breaks new ground in presenting and applying sophisticated mathematics in an elementary setting. Aimed at physics students, it covers the theory and physical applications of linear algebra and of the calculus of several variables, particularly the exterior calculus. The exterior differential calculus is now being recognized by mathematicians and physicists as the best method of formulating the geometrical laws of physics, and the frontiers of physics have already begun to reopen fundamental questions about the geometry of space and time. Covering the basics of differential and integral calculus, the authors then apply the theory to interesting problems in optics, electronics (networks), electrostatics, wave dynamics, and finally to classical thermodynamics. The authors adopt the "spiral method" of teaching (rather than rectilinear), covering the same topic several times at increasing levels of sophistication and range of application.
"I consider Sternberg's book a fine addition to the existing literature and strongly recommend it to anyone with an interest in learning how to use group-theoretical methods to understand concrete physical problems." Siam Review | 677.169 | 1 |
Adding Polynomials
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This document includes a do-now, two examples for adding polynomials using algebra tiles, and five examples for adding polynomials by combining like terms. The classwork section provides space for student notetaking. There is also a homework section with answer key. | 677.169 | 1 |
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Description
Learn MATLAB to help you understand mechanics
MATLAB is a powerful tool for mathematical modeling, and is becoming essential to many engineering fields. Solving Statics Problems in MATLAB is designed to both introduce students to MATLAB, and provide them with a useful tool for understanding static mechanics. The book begins with MATLAB basics, including scripts, functions, graphics, calculations, and equations, then moves into physics with targeted guidance on solving force systems, equilibriums, structures, friction, and more. The problems presented are taken from Engineering Mechanics Statics, 6th Edition, but the clear guidance and comprehensive instruction can be applied to any course. | 677.169 | 1 |
Precalculus and Advanced Topics Module 2, Topic E, Overview
In Topic E students apply the knowledge developed in this module to understand how first-person video games use matrix operations to project three-dimensional objects onto two-dimensional screens and animate those images to give the illusion of motion. | 677.169 | 1 |
About this product
Description
Description
In a book written for mathematicians, teachers of mathematics, and highly motivated students, Harold Edwards has taken a bold and unusual approach to the presentation of advanced calculus. He begins with a lucid discussion of differential forms and quickly moves to the fundamental theorems of calculus and Stokes' theorem. The result is genuine mathematics, both in spirit and content, and an exciting choice for an hors or graduate course or indeed for any mathematician in need of a refreshingly informal and flexible reintroduction to the subject. For all these potential readers, the author has made the approach work in the best tradition of creative mathematics. This affordable softcover reprint of the 1994 edition presents the diverse set of topics from which advanced calculus courses are created in beautiful unifying generalization. The author emphasizes the use of differential forms in linear algebra, implicit differentiation in higher dimensions using the calculus of differential forms, and the method of Lagrange multipliers in a general but easy-to-use formulation. There are copious exercises to help guide the reader in testing understanding. The chapters can be read in almost any order, including beginning with the final chapter that contains some of the more traditional topics of advanced calculus courses. In addition, it is ideal for a course on vector analysis from the differential forms point of view. The professional mathematician will find here a delightful example of mathematical literature; the student fortunate eugh to have gone through this book will have a firm grasp of the nature of modern mathematics and a solid framework to continue to more advanced studies. The most important feature...is that it is fun-it is fun to read the exercises, it is fun to read the comments printed in the margins, it is fun simply to pick a random spot in the book and begin reading. This is the way mathematics should be presented, with an excitement and liveliness that show why we are interested in the subject. -The American Mathematical Monthly (First Review) An inviting, unusual, high-level introduction to vector calculus, based solidly on differential forms. Superb exposition: informal but sophisticated, down-to-earth but general, geometrically rigorous, entertaining but serious. Remarkable diverse applications, physical and mathematical. -The American Mathematical Monthly (1994) Based on the Second Edition | 677.169 | 1 |
Hey, I'm also doing gcse maths and I found this really cool playlist on youtube it basically just goes through the whole syllabus the guys voice is pretty boring especially in the earlier videos ,but I found they help a lot. | 677.169 | 1 |
This was a very engaging course that prepared me for future math courses. I learned many new things and the lessons were very easy to follow. There was a reasonable amount of work, nothing too difficult, and there were many opportunities to help students.
Course highlights:
The highlights of the course were probably learning about the parts, like log, that would be taken over to future courses. I learned about graphs, logs, and many other aspects of Algebra 2.
Hours per week:
6-8 hours
Advice for students:
Do all your work ahead of time and ask for help if you are confused with the smallest thing.
Course Term:Spring 2015
Professor:na
Course Required?Yes
May 09, 2016
| Would recommend.
Not too easy. Not too difficult.
Course Overview:
I would recommend this course because it is good for students going into pre-calculus and it also teaches you how much paying attention, learning and obtaining things you learned in Algebra 1 is.
Course highlights:
Something that I wasn't good at during the start of the course but I later learned it thoroughly and i got a better understanding for was liner equations. You go into this course kind of nervous if you are not god at math but with hard work and dedication to learning the materials you end the course with a lot of knowledge about math.
Hours per week:
12+ hours
Advice for students:
Study habits for this course would be good note taking during class, making flash cards and maybe purchasing a calculator that would help with the homework and just for extra practice. Doing the homework and taking good notes is whats going to get you through the course but you cant just do that you have to know that material and if you know it you are guaranteed to pass this course.Another thing is class participation interact with the other student and ask questions, I promise it will help. | 677.169 | 1 |
1.6 Intermediate Value Theorem
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1.6 Intermediate Value Theorem
This is the sixth and last lesson in the Limits Unit. The lesson contains Guided Notes, homework, SmartBoard lesson, and all solutions. Don't forget the added bonus of a math joke embedded into the Smartboard lesson ☺! You may have also opted to purchase the video lesson to the notes.
In this lesson the first of three existence theorems in Calculus will be discussed – the Intermediate Value Theorem. Students will determine what the Intermediate Value Theorem is, how to know when it applies, and how to know when it doesn't apply. Students will see some AP-like examples of how this theorem has appeared on the AP exam. Finally, students will continue to learn how to write intelligent mathematical sentences in order to defend their solutions.
I hope you find the notes easy to follow. Please feel free to offer any suggestions on how to make them better as well! Through a community of collaboration, we can find that "sweet spot" for our students and their learning process. | 677.169 | 1 |
Taylor Polynomials
This Taylor Polynomials lesson plan also includes:
Help your pupils define a Taylor polynomial approximation to a function f of degree n about a point x = a. After completing several problems with guided practice, individuals graph convergence of Taylor polynomials and use them to approximate function values. | 677.169 | 1 |
...MATHEMATICS Why should I come to Pendleton College? At Pendleton College we have highly qualified and enthusiastic staff who will make the subject... Learn about: Mathematics Series, Mathematical Economics...
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...Mathematics is the only subject that can be studied beyond A-Level at Sixth Form College. Further maths provides able students with the opportunity to extend their maths knowledge by sampling some university level material. It is also a modern mathematics course where the emphasis is on making Skills and Training...
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Derivative Sketching
It's a little cumbersome to sketch a derivative on your computer, but I love having my students practice sketching derivatives with the app at
It's so great that it tells them how they're doing. I have them take a snippet screen shot of their best graph and share it with me in our google drive folder for our class. I can then quickly go through and see how everyone did using hapara dashboard.
Students can also go practice as need on their own at any time. I have them add it to their bookmark bar in google chrome. | 677.169 | 1 |
This teacher's guide accompanies BJU Press' (sold-separately) Math 1 Student Worktext, 4th Edition. Student worktext pages are reproduced at a reduced-size and have the correct answers overlaid for easy grading. The margins surrounding the student pages are filled with the teaching material; lessons are clearly identified at the top of the page with the worktext and reviews book page numbers. Lessons include an objectives list, any necessary teacher or student materials/manipulatives, and a step-by-step lesson with scripted questions. The appendix includes plenty of additional teaching helps and resources. | 677.169 | 1 |
Adventures in Mathematics
Though elementary in nature, this book deals with fundamental issues in mathematics -- number, algebra, geometry (both Euclidean and non-Euclidean) and topology. These subjects, on an advanced level, are the same ones with which much of current mathematical research is concerned and were themselves research topics of earlier periods. The material is very suitable both for advanced high school students and for college students interested in elementary mathematics from a higher standpoint. It will also be very useful to high school teachers seeking an overview of their subject matter. | 677.169 | 1 |
MATHEMATICS
The Mathematics Department provides a stimulating and challenging curriculum for every level of learner from Pre-Algebra through advanced Calculus. Instead of focusing solely on content coverage as a gauge for success, teachers emphasize building confidence and accuracy of computation when problem solving. Through this approach, we strive to cultivate confident, lifelong learners who are grounded in sound math fluency and have strong problem-solving skills when they enter college.
All students taking a math class are expected to have a calculator for use in the classroom and on their homework. Students in Algebra 2 or higher are required to have a TI-83 or TI-84 graphing calculator while those in Pre-Algebra, Algebra 1, and Geometry may have any four-function calculator. Students who do not have their own calculator at the beginning of the year will be able to purchase one through the School store during the first week of classes.
Pre-Algebra
All grades
This course is offered to any student, in any grade, whose fluency of basic mathematical concepts is not yet automatic. Research driven methodologies are embedded into the class to help bridge the gap between the traditional abstract veins of algebraic thought with more accessible, concrete manipulations. Topics covered range from integers and exponents, rational and real numbers, percents, probability, equations and inequalities, graphing lines, functions, and polynomials.
Algebra I
All grades
This is a traditional first course in algebra. Topics include the fundamental properties of real numbers, solving linear equations and inequalities, multiplying and factoring a variety of polynomials, roots, and radical notation. Topics also include absolute value, systems of equations, and algebraic fractions. Research-driven methodologies are routinely implemented to help bridge the gap between the traditional abstract veins of algebraic thought and more accessible, concrete manipulations.
Geometry
Open to students who have successfully completed Algebra I
May be taken on an Honors level with teacher recommendation
Traditional Euclidean geometry topics are covered in a standard sequence. Emphasis is placed on the deductive nature of this branch of mathematics, and on the use of algebra in solving a variety of geometric problems.
Algebra II
Open to students who have successfully completed Algebra I and Geometry
May be taken concurrently with Geometry
May be taken at an Honors level with teacher recommendation
This is a standard second course in algebra, focused on preparing students for Pre-calculus. Algebraic facility and the concept of functions are emphasized. Additional topics include quadratic functions and factoring, polynomials, exponential functions, and radical functions.
Algebra II Honors
Open to students who have successfully completed Algebra I and Geometry with teacher recommendation
May be taken concurrently with Geometry
This is a more rigorous, standard second course in algebra for students who are interested in pursuing recommendation to Pre-calculus Honors. Algebraic facility and the concept of functions are emphasized. Additional topics include quadratic functions and factoring, polynomials, exponents, radical functions, and logarithms.
Probability and Statistics
Grades 11, 12, PG
Open to student who have successfully completely Algebra II
May be taken at an Honors levels with teacher recommendation
This course is designed to introduce the methods of probability and statistics. Topics include laws of large numbers, discrete and continuous distributions, and sums of random variables. The bulk of the course will be project driven, allowing ample time to explore the concepts being learned the way they might be used by professionals in the field of business or science.
Pre-Calculus
• Open to students who have successfully completed Algebra II
Pre-calculus is designed for students who are interested in the study of mathematics up to and through calculus in the future. The curriculum consists of many traditional topics including linear, quadratic, and polynomial functions; exponential and logarithmic functions; circle, triangle, and advanced trigonometry; linear systems and matrices, as well as other skills students will need for success in calculus.
Pre-Calculus Honors
• Open to students who have successfully completed Algebra II • By teacher recommendation
The honors section covers many of the same topics as Pre-calculus, but concepts are explored in much more depth and detail. The pace of the course is also notably faster than that of Pre-calculus. This depth and pace enables for more time to introduce topics from calculus sooner in the second semester. Limits, continuity and the definition and application of the derivative are studied.
Calculus Honors
Open to students who have successfully completed Pre-Calculus
By teacher recommendation
This is a standard high school introductory course in calculus. Students will develop and explore the concept of limit, and progress to the development of the derivative. Derivatives of polynomial, trigonometric, and exponential functions and their applications to business, physical science, and engineering will be studied, as well as the fundamental theorem of calculus and an introduction to integral calculus. Use of a graphing calculator is an integral part of this course.
Cambridge International AS Level Pure Mathematics
Grades 11, 12, PG
Open to students who have successfully completed Pre-Calculus or Pre-Calculus
2 credits, scheduled daily
By teacher recommendation
This course is an upper-level Honors course for strong mathematics students who are interested in pursuing a math-related degree in college. This course will follow the syllabus outlined by the University of Cambridge in preparation for the AS Level Mathematics Examination. Students will study the content covered in the Pure Mathematics 1 and Pure Mathematics 2 sections of the AS Level Mathematics Syllabus. The topics covered will include: Quadratics, Functions, Coordinate Geometry, Circular Measure, Logarithmic and Exponential Functions, Trigonometry, Vectors, Series, Differentiation, and Integration. Students entering this course should already have a solid foundation in several of the topics covered from their work in Pre-Calculus. At the end of this course, students will be prepared for, and are expected to take the Cambridge International AS Level Exam. | 677.169 | 1 |
Support English language skills while improving subject content knowledge with a comprehensive three-level lower secondary programme specifically designed for non-native English speaking students studying Mathematics through the medium of English.
Benefit from a flexible programme that ensures thorough preparation for the IGCSE and equivalent courses and is suitable as a stand-alone course. Engage interest with clear text, stimulating exercises and numerous worked examples.
Reinforce the material taught within each lesson with the accompanying Workbook, providing extra practice and homework activities.
Make the most of the series with the Teacher's Guide containing answers to the Coursebook and Workbook exercises, guidance on delivering lessons and methodological | 677.169 | 1 |
You are expected to have capabilities consistent with the successful completion of MATH2160 or its equivalent.
Course Description
MATH2161 Mathematics for ECE is a core component of the electrical and computer engineering bachelor degrees. It provides an opportunity to develop the requisite range of skills relevant to a wide range of sub-disciplines existing within the field of Electrical and Computer Engineering.
In this course you will be introduced to a range of mathematical concepts identified as fundamental to enhance your progress in studying related Engineering courses. These mathematical topics build upon the material covered in the prerequisite course MATH2160 Engineering Mathematics A. You will develop the mathematical maturity required to become a well-grounded engineer.
Key concepts and their application will be explained and illustrated (with many examples) in lectures and in online notes. Supervised problem-based practice classes will build your capacity to solve problems, to encourage you to think critically and analytically and provide feedback on your academic progress. Four Closed Book Tests (for assessment) and practice classes (not for assessment) will consolidate your knowledge of the topics presented in class. Supplementary exercises found on Canvas in the form of problems and self-help tutorial questions will provide a focus for your private study.
Overview of Learning Resources
A prescribed textbook will be nominated. Students will also be able to access the following online learning resources : | 677.169 | 1 |
Eighth Grade Algebra
Algebra
Students meeting specific criteria as seventh grade students will be placed in Algebra for the eighth grade year. Algebra is a high school level class and moves at a rapid pace. Students who successfully complete the class will be allowed to enter into Geometry as high school freshmen. This course is a study of numerical and algebraic relations using linear equations, factoring, fractions, and algebra in a plane. Algebra by Prentice Hall is the primary text. | 677.169 | 1 |
Math 131: Calculus II other people on the homework but you should write up the solutions on your own in your own words The goal is not just to solve the problem but to present the solution in an organized clear mathematically correct way Your solutions will be graded for presentation and style as well as for correctness In no case will you get any points simply for stating a correct final answer In addition to the homework that I collect I will suggest additional problems for you to work on You should do all these problems and as many more as are necessary for you to master the material Math Department Speakers From time to time the Mathematics Department sponsors talks by various speakers from outside the Colleges As part of the requirements for this course you should attend at least one of the talks Attendance will count for ten percent of your homework grade a small part of your total grade for the course but one that could easily make a difference on your final letter grade Quizzes There will be occasional 10 minute quizzes in class In general they will not be announced in advance but you can expect the first one on Monday January 24 The quizzes are meant to check on your understanding of basic facts The questions will include such things as definitions true false questions and relatively straightforward exercises Some of the exercises will be taken from the labs or homework There will be about ten quizzes over the course of the term There are no make up quizzes but the lowest quiz grade will be dropped Tests There will be three in class tests plus a final exam The tests will be on Friday April 11 Wednesday March 9 and Friday April 15 The final exam will take place during the regularly scheduled exam period on Sunday May 8 in our regular classroom The first test will cover Chapter 4 the second will cover Chapters 5 and 6 and the third will cover Chapter 7 The final exam will be cumulative but will concentrate on Chapter 8 Grading Your grade for the course is based on labs homework quizzes three in class tests and a final exam These count for the following fractions of the grade Labs 1 8 Homework 1 8 Quizzes 1 8 Test 1 1 8 Test 2 1 8 Test 3 1 8 Final exam 2 8 Attendance and other Policies I do not take attendance but I assume that you understand the importance of being in class Note that I will give unannounced quizzes and that there are no make ups for these quizzes I will also collect work in the labs that cannot be made up but again I will drop your lowest lab grade You should make every effort to be present for tests If you are forced to miss a test because of circumstances that I agree are truly beyond your control I will give you a make
Mat 131: Calculus II, Spring 2011 suggest additional problems for you to work on You should do all these problems and as many more as are necessary for you to master the material Note that answers to odd numbered problems are in the back of the book Homework will generally be collected on Wednesday of the week following the week when the homework is assigned Assignments will be announced in class and will also be posted on the course web site After collecting the homework I will post my solutions to the collected homework on the web site Labs There is a required lab component for this course In the lab you will work with in a group of three students Your group will work on some problems and will turn in one set of solutions to be graded Everyone in the group will get the same grade for the lab Unless you have a very good excuse you must be present at the lab to get a grade for it Each lab will consist of a few challenging problems There might also be a few warm up problems which won t be turned in The problems are not meant to be straightforward exercises In some cases they will be open ended problems without a single solution For each problem your group should turn in an essay explaining your solution and how you found it In cases where you don t find a solution you should explain what you did to try to solve the problem and you should present any partial results that you obtain There might be a few problems that don t have solutions just to keep you on your toes Problems from one lab will ordinarily be collected at the following lab I will post my solutions to the collected lab problems on the course web site Occasionally I will ask someone in the class to present a solution to one of the lab problems Everyone in your group should be prepared to present the group s solution to any lab problem Tests There will be three in class tests for this course which will be given on Friday February 11 Wednesday March 9 and Monday April 11 You should not miss a test without a very good excuse The final exam for this course will be given at the time scheduled by the Registrar s Office Monday May 9 from 8 30 to 11 30 AM It will be in our regular classroom Note that the exam covers the entire course though with some emphasis on material covered in the last part of the course I reserve the right to adjust your grade downwards if you miss more than one or two classes or labs without a good excuse In my grading scale an A corresponds to 90 100 B to 80 89 C to 65 79 D to 50 64 and F to 0 49 Grades near the endpoints of a range get a plus or minus Math Intern The
Math 371 (Topics in Mathematics): Wavelet and Fourier Analysis about both frequency and time Wavelet and Fourier analysis are big complicated fields that intersect with several areas of advanced mathematics We will cover only parts of these fields and we will do so with only linear algebra and basic calculus as prerequisites The principal textbook for the course is A Primer on Wavelets and Their Scientific Applications by James S Walker This book introduces many of the fundamental ideas about wavelets using very little mathematical background It also offers a pretty clear perspective on many real world applications The plan for the course is that we will work through this book with digressions to cover some additional mathematical background and additional aspects of the theory of wavelets and Fourier analysis I have not planned the course in complete detail but we will begin by reading Chapter 1 from Walker and then spend some time on complex numbers inner products on vector spaces and orthonormal bases Some of the additional readings for the course will be taken from the book Wavelets Made Easy by Yves Nievergelt Assignments and Projects I will assign homework problems from time to time and collect them for grading generally a week after they are assigned In addition to this regular homework there will be two longer projects For each project you will do some research and produce a paper or some other type of work to turn in You will also do a presentation on the project for the class You will select your project topics in consultation with me The first project will probably have to do with the history of signal analysis and will be due before Spring break The second will be on a specific application of wavelets and will be due at the end of the term More information about the
Math 375: Abstract Algebra I theory We will select several of these group theory topics to be covered during the last two weeks of the course Homework Assignments There will be weekly assignments which will be due the following week Most or all of the homework exercises will be taken from the textbook I will assign even numbered exercises since answers to odd numbered exercises are given at the end of the book However you will probably want to do some of the odd numbered exercises for practice I encourage people to work together on homework However everyone is responsible for writing up and turning in their own solutions and for understanding what they turn in Occasionally to ensure that everyone understands the work that they turn in I will set up meetings in my office where students will present some of their homework solutions to me and answer questions about them Since the class is so small it might be a good idea to set up a time when the entire class can meet to work on problems We will discuss this possibility in class Tests and Grading There will be three in class tests and a final exam The tests will be given on Friday September 24 Monday October 25 and Monday November 22 The final exam will be during the scheduled final examination period for this course 1 30 PM on Thursday December 16 25 Assignments 30 Attendance I expect you to
Math 375: Abstract Algebra I weekly Most of the homework exercises will be taken from the textbook but I will add a few problems of my own from time to time Your solution to every homework exercise must include a justification for your answer This is obvious for exercises that ask you to show or prove something but it is true for every exercise even for questions that have a yes no answer You will find the answers to many of the textbook s exercises at the back of the book This will not necessarily stop me from assigning these exercises since what I expect from you is a justification not a simple one word answer I encourage people to work together on homework However everyone is responsible for writing up and turning in their own solutions and for understanding what they turn in In addition to the homework that I assign to the entire class I might occasionally assign a problem to an individual for that individual to work on and present in class Tests and Grading There will be three in class tests and a final exam The tests will be given on Monday September 26 Wednesday October 26 and Wednesday November 30 The final exam will be during the scheduled final examination period for this course 1 30 PM on Thursday December 15 20 Assignments 35 Attendance I expect you to be present and on time for all classes There might be
Math 436: Topology point set topology This is what we will spend most of our time on this term Towards the end of the course though I would like to spend a little time on algebraic topology which combines ideas from topology and from abstract algebra I would at least like to introduce the basic idea of the fundamental group of a topological space The text for the course if Foundations of Topology by C Wayne Patty I have not developed a definite schedule of readings we will cover as much of the book as time permits Homework There will be weekly homework problem sets Most or all of the problems will be assigned from the text You can talk over the homework problems with other people in the class but you should write up your own solutions I will expect you to turn in homework problems on time Tests There will be two tests Each test will have an in class part and a take home part The in class part will cover definitions statements of theorems short essays and some simple proofs The take home part will be given out in class on the day of the in class part It will consist mostly of more advanced proofs You should not discuss problems on the take home tests with anyone but me The tests are tentatively scheduled for Wednesday April 24 with the take home part due the following Monday and for Wednesday May 29 with the take home part due on Monday May 3 during the officially scheduled final exam period Presentations I will ask each person in the class to do several presentations These might cover sections of the text homework problems or special topics Ideally I would prefer to devote one day a week to this but we
Math 448, Complex Analysis, Fall 2014 from time to time I will ask you to present material from the book or solutions of problems I will assign some problems to be collected for grading including both problems from the book and problems that I make up myself All answers will be graded on presentation as well as correctness Most of the problems in the textbook have solutions at the back of the book but the solutions are brief When I assign a problem whose solution is in the book the assignment is to present a detailed clear solution Tests Final Presentation and Grading There will be two tests during regular class periods Each test will have an in class part and a take home part The in class part will consist mainly of definitions statements of theorems computational problems and general ideas There might also be a couple of straightforward proofs on the in class part The take home part will consist of longer problems and proofs The main difference between homework and take home tests is that students can work together on homework but are required to do take home tests on their own The in class parts of the tests are tentatively scheduled for Friday October 17 and Wednesday December 3 We can discuss changes to that schedule In addition to the two tests there will be a final presentation which you will give during the scheduled final exam period on Thursday December 18 at 1 30 PM The presentation will be on some aspect of complex analysis You will choose your topic in consultation with me The topic will probably be something that we have covered in class but should in any case be something that will be accessible to other students I am hoping that I can get one or two other
CPSC 100: Principles of Computer Science teaching responsibilities for a year I decided to write my own textbook for the course As is usually the case with professors who write textbooks I did this because I was not satisfied with existing texts The result is the book The Most Complex Machine A Survey of Computers and Computing which will be published this summer I have taught CPSC 100 twice before using the first eight chapters of this book it is now complete at twelve chapters We will use most of the book in this course omitting two complete chapters and parts of several others You will receive a photocopied preliminary version of the text The cost of reproducing the text is covered by the 25 course fee as noted in the registration booklet for this term Note on fulfilling requirements This course fulfills a distribution requirement in the natural sciences It does not however fulfill the lab requirement in the natural sciences Even though the course has a lab it is not an experimental science lab in the usual sense Computer Labs Every Friday the class will meet in the Macintosh computing lab in the basement of Rosenberg Hall Friday classes will be labs in which students will work with computer programs that I have written to supplement the textbook Each lab is based on a worksheet you will receive a book of worksheets along with the text The worksheet includes exercises to be handed in as homework These exercises are always due on the Wednesday following the lab Many of the exercises ask you to do more than just mechanically follow directions They ask you to think about what you have done reflect on what you have learned and express your thoughts in a short essay type answer You are expected to answer these questions with the same care that you would give to any writing assignment and your answers will be graded accordingly During labs each student will work with a partner When you turn in the homework from the lab you and your partner have two choices Either you can turn in one lab report and both get the same grade or you can turn in separate reports to be graded separately Note It might often happen that you do not have enough time to finish the entire lab during class That s the way it is supposed to be Finishing the lab is homework The Rosenberg lab will be open from 7 00 to 11 00 weeknights and from 1 00 to 5 00 on Saturday and Sunday In addition you can use the Macintosh computing lab in Lansing 312 for out of class work The Lansing computing lab is open daily from 9 00 AM 12 00 noon on weekends to 12 00 midnight You are also free to copy the programs to use on your own computer Quizzes and Tests Every Wednesday starting with April 5 there will be either a fifteen minute quiz or a test The tests will | 677.169 | 1 |
The transition from studying calculus in high school to studying mathematical analysis in college is notoriously difficult. In this new edition of Numbers and Functions, Dr. Burn invites the student to tackle each of the key concepts, progressing fro The transition from studying calculus in high school to studying mathematical analysis in college is notoriously difficult. In this new edition of Numbers and Functions, Dr. Burn invites the student to tackle each of the key concepts, progressing from experience through a structured sequence of several hundred problems to concepts, definitions and proofs of classical real analysis. The problems, with all solutions supplied, draw readers into constructing definitions and theorems. This novel approach to rigorous analysis will enable students to grow in confidence and skill and thus overcome traditional difficulties in learning this subject. ...Continua Nascondi | 677.169 | 1 |
Concept, notation, order, equality, types of matrices, zero and identity matrix, transpose of a matrix, symmetric and skew symmetric matrices. Operation on matrices: Addition and multiplication and multiplication with a scalar. Simple properties of addition, multiplication and scalar multiplication. Noncommutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrix (restrict to square matrices of order 2). Concept of elementary row and column operations. Invertible matrices and proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries).
Determinant of a square matrix (up to 3 x 3 matrices), properties of determinants, minors, co-factorshaving unique solution) using inverse of a matrix.
Derivatives of logarithmic and exponential functions. Logarithmic differentiation, derivative of functions expressed in parametric forms. Second order derivatives. Rolle's and Lagrange's Mean Value Theorems (without proof) and their geometric interpretation.
6. Linear inequaities - 5 hours
Differentiation is all about finding rates of change of one quantity compared to another. We need differentiation when the rate of change is not constant.
7. Permutation and combination - 6 hours
This unit explains how differentiation can be used to calculate the equations of the tangent and normal to a curve. The tangent is a straight line which just touches the curve at a given point. The normal is a straight line which is perpendicular to the tangent.
8. Binamial theorm - 4 hours
Applications of derivatives: rate of change of bodies, increasing/decreasing functions, tangents and normals, use of derivatives in approximation, maxima and minima (first derivative test motivated geometrically and second derivative test given as a provable tool). Simple problems (that illustrate basic principles and understanding of the subject as well as real-life situations).
9. Sequence and series - 10 hours
10. Coordinate geometry (Straight line) - 5 hours
The maxima and minima (the respective plurals.
11. Conic sections - 5 hours
12. Introduction to 3 dimensional geometry- 3 hours
13. Calculus (limits) - 6 hours
14. Derivatives - 5 hours
Definition, order and degree, general and particular solutions of a differential equation. Formation of differential equation whose general solution is given. Solution of differential equations by method of separation of variables solutions of homogeneous differential equations of first order and first degree. Solutions of linear differential equation of the type: | 677.169 | 1 |
Math help calculator
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When I decided to take the CHSPE to get my diploma, I knew math was going to be a problem. I stumbled onto your CHSPE math prep course and gave it a try. | 677.169 | 1 |
With a Brief. For Students Entering McMaster University
Transcription
1 With a Brief For Students Entering McMaster University Department of Mathematics and Statistics McMaster University 2009
2 Published by: Miroslav Lovric Department of Mathematics and Statistics McMaster University 1280 Main St. West Hamilton, Ontario, Canada L8S 4K Miroslav Lovric
3 Mathematics Review Manual With a Brief First-year Survival Guide For Students Entering McMaster University Also available online at written by Miroslav Lovric Department of Mathematics and Statistics McMaster University Hamilton 2009
4 This booklet will help you prepare for your academic life as a first year university student, and, in particular, for the first year courses in mathematics that you will take.
5 Table of Contents General Information What s This Manual and Survival Guide About... iii Why Background Knowledge Matters... v Transition from High School to University... vii How is Math in University Different from High School Math?.. ix Learning Mathematics... xiii Important Little Bits... xv Mathematics You have to know and be proficient in the material from the following four chapters. Very little of it will be reviewed in class. Chapter 1. Basic Algebra... 1 Chapter 2. Basic Formulas from Geometry... 9 Chapter 3. Equations and Inequalities Chapter 4. Elements of Analytic Geometry The material from the three chapters below will be taught and discussed in your first-year calculus course. However, you will have to spend extra time working on these areas, to gain technical proficiency and confidence with the material. Chapter 5. Functions Chapter 6. Trigonometry Chapter 7. Exponential and Logarithmic Functions i
6 The material from the chapter below will be covered in depth in your first-year calculus course. If you decide to skip something in this manual, then skip this chapter. Chapter 8. Intro to Calculus: Limits and Derivatives *** Answers to all Exercises *** This manual is also available online at (free download) ii
7 What s this manual and survival guide about? A leap from secondary education to university environment will be, without doubt, one of the most challenging and stressful events in your life. It is a true rite of passage, with all of its anxieties, pains, hopes, frustrations, joys and rewards. You have probably created a mental image of the new environment you will be encountering soon - but it is blurry, lots of fine detail is missing. The better prepared you are, the easier it will be to adjust to new situations, demands and expectations that university life will place on you. No matter which high school you came from, you have certain strengths and certain weaknesses. There are things that you learnt well in high school, things you know and are comfortable with. But, there are things that you forgot, or you don t know about or have very little experience with. In high school you acquired certain skills, but need to brush up on some others. This manual will tell you where you are; it will help you identify those areas of mathematics that you are good at, and those areas that you need to learn, review and work on. All you need is a little dedication, a pencil and paper, and about an hour of your (uninterrupted) time per day (say, during the last three weeks of August). Unplug the TV, turn off your cell phone, kick your sibling(s) and/or your parent(s) out of your room, and tell them that you need to work on something really important. This manual has two parts. The first part is about the things you have thought a lot lately. How is life in university different from high school? What should I expect from my fist-year classes? How is university math different from math in high school? Read, and reflect on the issues raised discuss it with your parents, friends, teachers, or older colleagues. Nobody can give you detailed and precise answers to all questions that you have, but at least, you will get a good feeling about the academic side of your first-year university experience. What will my first-year professors assume that I know about mathematics? The big part of this booklet is dedicated to answering this question. Look at the table of contents to see what areas of mathematics are covered. As I said, have a pencil and paper handy. I suggest that you start with the first section, and work from there, without skipping sections. Read the material iii
8 presented in a section slowly, with understanding; make notes and try to solve exercises as you encounter them (answers to all exercises are in the back of this manual). Even if the material in some section looks easy, do not skip the whole section select several problems and test your knowledge. If you realize that you have problems with certain material, read the section carefully, twice or three times if needed. Work on problems slowly, making sure that you understand what is going on. If needed, consult your high school textbooks, or go to a local library and find a reference. Ask somebody who knows the stuff to discuss it with you; if you prefer, hire a private math tutor for a few sessions. I know that doing math is not the coolest thing to do in summer - BUT think a bit about the future. Change from high school to university is a big change; the better prepared you are, the easier it will be for you to adjust successfully to your new life as a university student. Student life is a busy life. It will be quite difficult for you (I did not say impossible!) to find time to do two things: learn new material presented in a lecture and, at the same time, review background material that you are assumed to know and be comfortable with. Not to mention that, without adequate preparation, you will have difficulties following lectures. Review your math now, while you have lots of free time on your hands! One thing is certain: the more math you do, the easier it gets - experience helps! Do as many problems as you can, don t give up because the stuff looks difficult or you feel bored with it. Little investment of your time now, in summer, will make studying mathematics in the fall a whole lot easier. Good luck! See you in September, Miroslav Lovric, Associate Professor First-year instructor Department of Mathematics and Statistics, McMaster University iv
9 Why Background Knowledge Matters Mathematics is cumulative, new material builds upon the previously covered (i.e., understood, learnt) material. It is not possible to truly understand and apply an advanced concept (say, derivatives) without understanding all basic concepts that are used to define it (fractions, limits, graphs, etc.). Many times, the reason why students lose marks on tests in first-year Calculus (and other math courses!) is due to a problem with something elementary, such as fractions, simplifying, solving equations, or recalling basic properties of exponents, trigonometric functions. etc. Let us look at a few samples of actual test solutions. In the case below, the student chose the appropriate integration method (which is taught in the first-year Calculus course), but then did not simplify correctly the fraction in the integral (see the last two lines). This error cost the student 50% of the credit for the question. Look how mach effort was put into simplifying the expression for f (x) below not to mention how much valuable time was lost! Moreover, the student made a v
10 mistake in simplifying and got two (of three) correct values for x. Penalty for this mistake: 25% of the credit for the question. As in the previous case, note that the credit lost was not due to a new concept learnt in the university Calculus course, but due to errors related to high school material. Most-often-heard comment about a test is that there was not enough time. Certainly, if it takes you more than 5 minutes to do this question, you will not have enough time to complete the test. In the case below, the student tried to analyze the expression for f (x) by looking at the graphs of sin x and cos x (excellent idea!). However, the graphs of the two functions are incorrect, and the answer does not make sense. The student lost all credit for the question. vi
11 TRANSITION FROM HIGH SCHOOL TO UNIVERSITY What is new and different in university? Well, almost everything: new people (your peers/colleagues, teaching and lab assistants, teachers, administrators, etc.), new environment, new social contexts, new norms, and very important - new demands and expectations. Think about the issues raised below. How do you plan to deal with it? Read tips and suggestions, and try to devise your own strategies. First-year lectures are large you will find yourself in a huge auditorium, surrounded by 300, 400, or perhaps even more students. Large classes create intimidating situations. You listen to a professor lecturing, and hear something that you do not understand. Do you have enough courage to rise your hand and ask the lecturer to clarify the point? Keep in mind that you are not alone other students feel the same way you do. It s hard to break the ice, but you have to try. Other students will be grateful that you asked the question you can be sure that lots of them had exactly the same question in mind. Remember, learning is your responsibility. Come to classes regularly, be active, take notes, ask questions. Find a quiet place to study. Use all resources available to you. Discuss material with your colleagues, teaching and lab assistants, and/or professors. Courses have different requirements and restrictions with regards to calculators and computer software. You will find the information about it in the course syllabus that will be given to you (usually) in the first lecture of a course. The amount of personal attention you get from your teachers, compared to high school, is drastically lower. If you have a question, or a problem, you will have to make an effort to talk to your lecturer, or to contact the most appropriate person. Consider taking courses that help you develop research skills (such as: critical use of electronic resources, logical and critical thinking, library search skills, communication and presentation skills etc.). Have you heard of inquiry courses? vii
12 Good time management is essential. Do not leave everything for the last moment. Can you complete three assignments in one evening? Or write a major essay and prepare for a test in one weekend? Plan your study time carefully. Eat well, exercise regularly, plan social activities - have a life! Amount of material covered in a unit of time increases at least three-fold in university courses, compared to high school. This means that things happen very quickly. If you miss classes and do not study regularly you will get behind in your courses. Trying to catch up is not easy. For each hour of lecture plan to spend (at least) three hours studying, reviewing, doing assignments, etc. Inquire about learning resources available to you. Do you know where the science (engineering, humanities) library is? When are computer labs open? Do you know how the Centre for Student Development can help you deal with academic issues? Before coming to Mac, browse through its internet site. Bookmark the sites that link to learning resources. In university grades drop by 30%. Not necessarily. Study regularly (do you know how to study math? Chemistry? Physics? Why not discuss it with your lecturer?). Most probably, you will have to adjust/modify your present study habits. One thing is certain: the amount of work that earned you good marks in high school will not suffice to keep those marks in university. It is possible to study hard and still fail a test. If you fail a test, react immediately. Identify reasons for your poor performance. Visit your professor during her/his office hours, bring your test and discuss it. Be ready to re-examine and modify your study strategies. Do not get discouraged by initial bad marks that you might get. If you have problems, react and deal with it immediately. Ask your professor for advice. Talk to an adviser in your faculty office. What constitutes academic dishonesty? Copying stuff from internet and pasting into your assignment could be considered academic dishonesty. If you are caught, you might fail the course. What other practices are considered academic dishonesty? Be informed about it, so that you don t get in trouble. The course syllabus (for any of your courses) will provide information and links to McMaster policy regarding academic dishonesty. viii
13 HOW IS MATH AT UNIVERSITY DIFFERENT FROM HIGH SCHOOL MATH? Lectures move at a faster pace. Usually, one lecture covers one section from your textbook. Although lectures provide necessary theoretical material, they rarely present sufficient number of worked examples and problems. You have to do those on your own. Certain topics (trigonometry, exponential and logarithm functions, vectors, matrices, etc.) will be taught and/or reviewed in your first-year calculus and linear algebra courses. However, the time spent reviewing in lectures will not suffice to cover all details, or to provide sufficient number of routine exercises you are expected to do it on your own. Use this manual! Don t leave it at home, bring it with you to McMaster. You have to know and be proficient with the material covered in the first four chapters of this booklet: Basic Algebra Basic Formulas from Geometry Equations and Inequalities Elements of Analytic Geometry. For instance, computing common denominators, solving equations involving fractions, graphing the parabola y=x 2, or solving a quadratic equation will not be reviewed in lectures. In university, there is more emphasis on understanding than on technical aspects. For instance, your math tests and exams will include questions that will ask you to quote a definition, or to explain a theorem, or answer a theoretical question. Here is a sample of questions that appeared on past exams and tests in the firstyear calculus course: Is it true that f (x)=g (x) implies f(x)=g(x)? Answering yes or no only will not suffice. You must explain your answer. State the definition of a horizontal asymptote. Given the graph of 1/x, explain how to construct the graph of 1+1/(x-2). ix
14 Using the definition, compute the derivative of f(x)=(x-2) -1. Can a polynomial of degree 3 have two inflection points? You must explain your answer to get full credit. Given below is the graph of the function f(x). Make a rough sketch of the graph of its derivative f (x). Below are the graphs of two functions, f(x) and g(x). Compute the composition g(f(3)). You will be allowed - and encouraged - to use your (graphing) calculator and/or computer software (such as Maple) to study mathematics, to do homework assignments and computer labs. On tests and exams, either no calculator will be allowed (would you really need a calculator to answer any of the above test/exam questions?), or you will be asked to use the calculator that McMaster chose as a standard (this way, everybody uses the same calculator). Calculators and software are an aid, but not a replacement for your brain, and you should treat them as such. If a calculator says something, it is not necessarily a correct answer. Mathematics is not just formulas, rules and calculations. In university courses, you will study definitions, theorems, and other pieces of theory. Proofs are integral parts of mathematics, and you will meet some in your first-year x
15 courses. You will learn how to approach learning theory, how to think about proofs, how to use theorems, etc. Layperson-like attitude towards mathematics (and other disciplines!) - accepting facts, formulas, statements, etc. at face value - is no longer acceptable in university. Thinking (critical thinking!) must be (and will be) integral part of your student life. In that sense, you must accept the fact that proofs and definitions are as much parts of mathematics as are computations of derivatives and operations with matrices. *** Have you given any thought to mathematics as a career? Attend information sessions organized by Mathematics and Statistics Department (will be advertised in lectures), learn about programs and careers in mathematics and statistics. Get informed, keep your options open! *** If, for some reason, you developed negative attitude and feelings towards mathematics in high school, then leave them there! You will have a chance to start fresh at a university. First-year math courses at McMaster start at a level that is appropriate for most high school graduates. Use this manual, read it from cover to cover, get prepared! xi
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17 LEARNING MATHEMATICS Learning mathematics requires seriousness, dedication, discipline, concentration, significant amount of time and hard work. Your teachers will help you learn how to learn mathematics. To learn mathematics means to understand AND to memorize. To understand something means to be able to correctly and effectively communicate it to somebody else, in writing and orally; to be able to answer questions about it, and to be able to relate it to known mathematics material. Understanding is a result of a thinking process. It is not a mere transfer from the one who understands (your lecturer) to the one who is supposed to understand (you). How do you make yourself understand math? Ask questions about the material and answer them (either by yourself, or with the help of your colleague, teaching assistant or lecturer). Approach material from various perspectives, study solved problems and work on your own on problems and exercises. Make connections with previously taught material and apply what you just learnt to new situations. It is necessary to memorize certain mathematics facts, formulas and algorithms. Memorizing is accomplished by exposure: by doing drill exercises, by using formulas and algorithms to solve exercises, by using mathematics facts in solving problems. The only way to master basic technical and computational skills is to solve a large number of exercises. Drill. It is impossible to understand new mathematics unless one has mastered (to a certain extent) the required background material. xiii
18 understand so that you won t have to memorize wrong approach to learning math: memorize so that you won t have to understand think about it!!! xiv
19 IMPORTANT LITTLE BITS Come to classes, tutorials and labs regularly, be active! Think, ask questions in class, give feedback to your lecturer. Lecture by itself will not suffice. You need to spend time on your own doing math: studying, working on assignments, preparing for tests and exams, etc. Rule of thumb: three hours on your own for each hour of lecture. Plan your study time carefully. Don t underestimate the amount of time you need to prepare for a test, or to work on an assignment; try not to do everything in the last minute (the fact that your hard drive crashed night before your assignment is due is not an acceptable excuse for a late assignment). Make sure that you are aware of (and use!) learning resources available to you. Here are some of them: Lectures, tutorials, and review sessions Your lecturer s office hours Your teaching assistant s office hours and course internet page Mathematics help centre in Hamilton Hall Thode Library (Science Library) Centre for Student Development Always learn by understanding. Memorizing will not get you too far. Think, do not just read; highlighting every other sentence in your textbook is not studying! If you are able to explain something to a colleague and answer their questions about it, then you have learnt it! Drill is essential for a success (not just in math!). It s boring, but it works! Solving hundreds of problems will help you gain routine and build confidence you need (together with a few other things) to write good exams. You will be allowed to use a (graphing) calculator and/or computer software for assignments and labs. On tests and exams, you might not be allowed xv
20 to use a calculator, or will have to use a model that is accepted as a standard at McMaster. Your instructor will give you detailed information about this. Note about your lecture notes Your lecture notes will be your most valuable resource. You will refer to them when you do homework, a computer lab, or prepare for a test or an exam. So: during a lecture, take notes later, read the notes; make sure that you have correct statements of all definitions, theorems, and other important facts; make sure that all formulas and algorithms are correct, and illustrated by examples fill in the gaps in your notes, fix mistakes; supplement with additional examples, if needed add your comments, interpret definitions in your own words; restate theorems in your own words and pick exercises that illustrate their use write down your questions, and attempts at answering them; discuss your questions with your colleague, lecturer or teaching assistant, write down the answers it is a waste of time to try again and yet again to understand a concept; so, once you understood it, write it down correctly, in a way that you will be able to understand later; this way, studying for an exam consists of re-calling and not re-learning; re-calling takes less time, and is easier than re-learning keep your notes for future reference: you might need to recall a formula, an algorithm or a definition in another mathematics course. xvi
How to Study Mathematics Written by Paul Dawkins Before I get into the tips for how to study math let me first say that everyone studies differently and there is no one right way to study for a math class.
Precalculus: First Semester Precalculus is the course that bridges the gap between Algebra 2 and Calculus. A thorough understanding of algebra and trigonometry is essential to success in Calculus and other
MATH DEPARTMENT COURSE DESCRIPTIONS The Mathematics Department provides a challenging curriculum that strives to meet the needs of a diverse student body by: Helping the student realize that the analytical
ACCUPLACER Arithmetic & Elementary Algebra Study Guide Acknowledgments We would like to thank Aims Community College for allowing us to use their ACCUPLACER Study Guides as well as Aims Community College
What to Expect on the Compass What is the Compass? COMPASS is a set of untimed computer adaptive tests created by the American College Test (ACT) Program. Because COMPASS tests are "computer adaptive,"
LLCC Study Skills Center 8-8 Tips on How to Study Math What s Different About Math Textbooks 1. Math textbooks must be studied very slowly. 2. Unlike many other textbooks, math textbooks have: No repetition
PLEASE READ THIS SYLLABUS CAREFULLY. IT IS THE POLICIES BY WHICH YOU MUST ABIDE FOR THIS CLASS. Instructor Information MAT 151 College Algebra and MAT 182 Trigonometry Course Syllabus Spring 2014 InstructorPerformance Assessment Task Quadratic (2009) Grade 9 The task challenges a student to demonstrate an understanding of quadratic functions in various forms. A student must make sense of the meaning of relations
PHILOSOPHY OF THE MATHEMATICS DEPARTMENT The Lemont High School Mathematics Department believes that students should develop the following characteristics: Understanding of concepts and procedures Building
SCIENCE STUDY SKILLS CYCLE (S 3 C) DR. JEFF PARADIS (SACSTATE) GENERAL INFORMATION Doing well in college science classes requires a minimum of 2-3 hours work outside of class for each hour you are in lecture.
Learning mathematics Some hints from the psychologists In your degree course you will learn, and be examined on: 1. Facts (= knowing that ) 2. Skills (= knowing how ). Examples: An example of a fact to
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The Mathematics School Teachers Should Know Lisbon, Portugal January 29, 2010 H. Wu *I am grateful to Alexandra Alves-Rodrigues for her many contributions that helped shape this document. Do school math
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COURSE SYLLABUS Pre-Calculus A/B Last Modified: April 2015 Course Description: In this year-long Pre-Calculus course, students will cover topics over a two semester period (as designated by A and B sections).
Tips for Solving Mathematical Problems Don Byrd Revised late April 2011 The tips below are based primarily on my experience teaching precalculus to high-school students, and to a lesser extent on my other
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Advanced Placement Psychology Course Syllabus and Survival Guide Mr. Korek O1-HO3-072006 Purpose of the Course The purpose of the Advanced Placement course in Psychology is to introduce students to theCOURSE SELECTION GUIDELINES FOR ENTERING 9TH GRADE STUDENTS HOW DO I DECIDE WHAT NEEDHAM HIGH SCHOOL LEVELS ARE APPROPRIATE FOR MY CHILD? All general education courses are based on the Massachusetts State | 677.169 | 1 |
Curriculum Mathematics Practice: Bk.3
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Read More Answer Book mapping out the series against the National Curriculum 96 p. Numerous line illustrations. A series of six books that complements the skills practice for students aged between 11 and 16. It covers levels 3 to 8 of the National Curriculum, with the level of difficulty increasing through the six books. It offers: basic explanations of the mathematics; and worked examples and exercises to help students to consolidate their understanding | 677.169 | 1 |
This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses combinations of operations with fractions. By the end of the module students should gain a further understanding of the order of operations | 677.169 | 1 |
The Best Additional Maths O Level Notes, Revision Guides, Tips and Websites compiled from all around the world at one place for your ease so you can prepare for your tests and examinations with the satisfaction that you have the best resources available to you.
This syllabus is intended for high ability learners who have achieved, or are likely to achieve, a high grade in the Cambridge O Level Mathematics examination. The Cambridge O Level Additional Mathematics syllabus enables learners to extend the mathematical skills, knowledge and understanding developed in the Cambridge O Level Mathematics course and use skills in the context of more advanced techniques.
The syllabus has a Pure Mathematics only content which enables learners to acquire a suitable foundation in mathematics for further study in the subject. Knowledge of the content of the Cambridge O Level Mathematics syllabus (or an equivalent syllabus) is assumed.
I hope you find them useful. If you have extra notes or resources please contribute to the website and help thousands of other people like you. In addition, your name will be written in the credits section of this post. | 677.169 | 1 |
Tuesday, December 17, 2013
Brought to you by the Worldwide Center of Mathematics, Worldwide Math Shorts is a brand new collection of videos introducing important basic and foundational mathematics concepts. The videos are now available free on the Center of Math YouTube Channel.
Here at the Center, we are dedicated to providing 1) top-to-bottom coverage of the concepts you need to know and 2) the additional resources you'll need to master them. Worldwide Math Shorts, featuring Tom Lewis (Northeastern University '15), was created to better serve the needs of math students, instructors and the greater community. The collection is comprised of six parts, including the basics of derivatives, integrals, matrices, probability, trigonometry, and vectors.
The topics were chosen to provide viewers with a better understanding of the early concepts essential to executing advanced calculus, differential equations, or linear algebra. Short and sweet, the videos are great for any aspiring mathematician, and serve as especially helpful "refreshers" for those using Center of Math textbooks. Each video introduces basic definitions and concepts followed by worked examples.
As we continue to expand our collection of study/help videos and resources, we want to hear from you! Which topics do you need help with? What kind of video or topic would you like to see the Center of Math produce next? Leave your comments or send your thoughts to info@centerofmath.org.
Center of Math Productions are recorded in the Center of Math Studio Classroom space in Cambridge, MA. The Center of Math was established to strengthen the math community by providing free and affordable resources for all.
Monday, December 16, 2013
Hello math lovers! We know all of you love math... and you probably love
the holidays, too, so we thought we would combine the two to give you a
fun and informative infographic about the evolution of the publishing
industry! We drew inspiration from the classic "A Christmas Carol" that we thought you'd all be able to relate to. We hope you enjoy it!
Though it's a topic you might not have ever thought about, publishing has an impact on you whether you are a student, professor, collector, or just a math enthusiast. We appreciate those of you who choose the Center of Math and support our mission of finding ways to make math affordable and accessible!
From the Center of Math, Happy Holidays!!!
P.S. If you'd like a print-friendly version of this infographic (at full size), send us an email at info@centerofmath.org. | 677.169 | 1 |
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8th Grade Common Core Assessment, standard 8F4. Assesses students' ability to Identify Rate of Change and Initial Value, later to become known as slope and y-intercept, as well as writing equations when presented with visual models and
Assess students' ability to solve single variable systems of equations, represented algebraically and with word problems. Please create your own rubric based on how your gradebook works. I use a 4 level proficiency scale, without points or
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TEACHING EXPERIENCE
10th year middle school math teacher.
Other life experience: entrepreneur, musician, voracious student.
MY TEACHING STYLE
I do my best to give simple explanations to complex topics that students can relate to in a real way. I incorporate technology, cooperative learning, music, humor and obscure pop culture references into my classroom every day.
HONORS/AWARDS/SHINING TEACHER MOMENT
My award shelf has plenty of space available. Naches High School "Boy of the Month" December 1984!! One of my original songs recorded in the summer of 2016 was recently approved and is active on Pandora!
MY OWN EDUCATIONAL HISTORY
Washington State University
Guitar Institute of Technology/Musicians' Institute
Portland Community College
Portland State University
University of Phoenix
ADDITIONAL BIOGRAPHICAL INFORMATION
I have several albums worth of original educational music in multiple subjects listed under the name MegaMath on iTunes and most other digital distributors.
My youtube channel, whitchermath, has nearly 300 educational videos recorded by me, encompassing topics ranging from pre-K through Algebra. Check it out! | 677.169 | 1 |
Linear Algebra with Matrices and Vectors
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Students will be able to determine the initial and terminal points of a vector and the magnitude when adding vectors. They will further apply the Pythagorean Theorem in determining the magnitude of vectors on a coordinate plane. Duration of the lesson is approximately one hour but can be extended to two hours with review and enrichment. | 677.169 | 1 |
This ebook is available for the following devices:
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iRiver Story
At first glance the prime numbers appear to be distributed in a very irregular way amongst the integers, but it is possible to produce a simple formula that tells us (in an approximate but well defined sense) how many primes we can expect to find that are less than any integer we might choose. The prime number theorem tells us what this formula is and it is indisputably one of the great classical theorems of mathematics. This textbook gives an introduction to the prime number theorem suitable for advanced undergraduates and beginning graduate students. The author's aim is to show the reader how the tools of analysis can be used in number theory to attack a 'real' problem, and it is based on his own experiences of teaching this material.
In the press
'The entire exposition is extremely lucid, motivated and amply commentated throughout. With numerous examples illustrating the purely theoretical parts. Unquestionably, the book bespeaks the author's teaching skill and experience just as much as his gripping passion for this refined and fascinating topic. Altogether, this textbook is outstandingly suitable for both a course on prime number theory, at the upper-graduate level, and as a source for self-instruction … Anyway, this text is a highly valuable enhancement of the existing literature on the subject which stands out by its particular user-friendliness.' Zentralblatt MATH | 677.169 | 1 |
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Non-science students at William and Mary will soon be required to take a mathematics course in order to earn a bachelor's degree. A standard menu of technique courses is the usual way in which universities provide for this requirement: Trigonometry, probability, geometry for teachers, and the like. In this work, we attempt to break away from these largely unsuccessful choices. Our intent is to prepare material that sets a variety of simple mathematical procedures in the context of a commonly experienced part of students' lives: riding in commercial airplanes. The work, begun last summer at Langley, is now close to completion and trial in upcoming fall term at William and Mary. As of this writing, the narrative is complete for 12 to 14 projected sections. We have prepared material on wind triangles, wind roses, navigation maps, drag induced loss of velocity for unpowered missiles (tennis balls), luggage and its effect on center of gravity, localized magnetic declination and VOR orientation, geometry of great circles, terminal velocity for falling bodies, pressure vessels: tires and balloons and blimps, global structure of declination lines, map projections (mercator, azimuthal equidistant, Lambert), ears and their reaction to altitude change. The next section will treat lift, drag and thrust. The last will treat control surfaces. The entire approach avoids any effort to investigate mathematical topics that arise in the solution of problems. And by the same token, we avoid any organized attempt to explain aeronautical engineering, even on an elementary level. We look only at enough mathematics to do a problem and we select only engineering topics that permit some kind of (elementary) mathematical analysis. In the end, we will think of the material as successful if two things happen: Students must come away with some confidence that even lay people can quantify parts of their surroundings. Other potential instructors must be willing to gain enough familiarity with the physical content of the material so that it can be used at other universities. | 677.169 | 1 |
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A Summary Of Algebra
Algebra is all about acquiring the unspecified that accompany some rules supported by algebra. Algebra concerns about placing present day to day life troubles into particular equations and then finding their solution with the guidance of various algebraic formulas and theorems. This branch of mathematics has several streams, few of them are as stated below:
Linear algebra- Liner algebra is the learning of sets of linear equations and their transformations properties. This stream supports the examination of rotations in space, a solution of linked differential equations, least squares fitting, measurement of a circle passing through assigned points, as well as various analytical difficulties in applied physics, engineering and mathematics.
Elementary algebra- At high school level, students are taught some of the basic concepts and ideas of algebra which is known as elementary algebra. It is just a drawn-out type of arithmetic. Elementary algebra deals with fixed numbers and generic numbers.
Abstract algebra- This is also known as modern algebra which concerns with arithmetic structures like set theories, groups, vectors, rings, etc.
Significance Of Algebra For Students
With the rising standard of mathematics, scholars find that nothing is viable without deep knowledge of algebra hence the branch of mathematics is indispensable for the students. In other branches of science, particularly in applied physics and physics like wave theories, mechanics, astronomy, kinematics, etc. the application of this sub-branch of mathematics is inescapable. Various skills are used in many real-life activities such as solving one-step and two-step equations, understanding different functions, conducting a vertical line test, graphing ordered pairs.
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Introduction to Vector Addition and Scalar Multiplication In the strictly mathematical definition of a vector, the only operations that vectors are required to possess are those of addition and scalar multiplication. (Compare this with the operations allowed on ordinary real numbers, or scalars, in which we are given addition, subtraction, multiplication, and division). For instance, in a raw vector space there is no obvious way to multiply two vectors together to get a third vector--even though we will define a couple of ways of performing vector multiplication in Vector Multiplication . It makes sense, then, to begin studying vectors with an investigation of the operations of vector addition and scalar multiplication. This section will be entirely devoted to e xplaining addition and scalar multiplication of two- and three-dimensional vectors. This explanation will involve two different, yet equivalent, methods: the
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Unformatted text preview: component method and the graphical method . The Component Method for Vector Addition and Scalar Multiplication When we mentioned in the introduction that a vector is either an ordered pair or a triplet of numbers we implicitly defined vectors in terms of components. Each entry in the 2-dimensional ordered pair ( a , b ) or 3-dimensional triplet ( a , b , c ) is called a component of the vector. Unless otherwise specified, it is normally understood that the entries correspond to the number of units the vector has in the x , y , and (for the 3D case) z directions of a plane or space. In other words, you can think of the components as simply the coordinates of the point associated with the vector. (In some sense, the vector is the point, although when we draw vectors we normally draw an arrow from the origin to the point.) Figure %: The vector (a, b) in the Euclidean plane....
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DrDelMath
Reading Mathematics
by
DrDel
To learn mathematics in a traditional school environment, the student must be able to read mathematics. Reading is not a natural phenomenon. Reading mathematics certainly is not a natural phenomenon. Reading mathematics is a skill that must be learned. No one is born with the ability to read mathematics nor does one gain that ability in a traditional reading program. Mathematics textbooks are written in a style completely different from other textbooks. The student must learn to read that style of presentation.
Some important elements of this style are:
Organization with titles for chapters, sections, and subsections
Use of page layout, fonts, formatting, and color to organize and emphasize
Dependence on the language (including symbols and conventions) of mathematics
Extensive use of technical terms as the basis for every concept
Logical arguments which lead inarguably from some assumption to a conclusion
Exclusive use of deductive reasoning
Use of precise, concise, well defined presentations
Every presentation is reduced to barest essentials
Use of examples and exercises
In a non-mathematics textbook many paragraphs (or even pages) are used to present a single simple idea.
In a mathematics textbook a single simple sentence may present an enormous complex idea.
To read mathematics effectively one must develop a protocol which takes into account all of the peculiarities of mathematics writing. This document is intended to help develop such a successful protocol.
Tip 1 from Dr. Del
Read and remember the title of your textbook as well as its authors.
In this College Algebra course at Meramec Community College, we use the fourth edition of a text named College Algebra written by James Stewart, Lothar Redlin, and Saleem Watson. These men are from McMaster University, The Pennsylvania State University, and California State University at Long Beach. The fact that these authors are at respected universities is a strong indication that they have good credentials as mathematicians and teachers.
You should observe that this title indicates the topic is algebra and it is at the college level. Therefore, in this course we will study the subject of algebra. We will not study arithmetic, trigonometry, geometry, or calculus. We will study algebra! We will not study it the same way you might have studied it in the past, because this is College Algebra not High School Algebra.
Tip 2 from Dr. Del
Read, think about, and remember each chapter title as you come to it. At the same time read and think about each of the section titles for that chapter.
For example, when you get ready to study Chapter 1, look carefully at Page 72 where you find the chapter title; Equations and Inequalities. That tells you the next 76 pages of this textbook are devoted to topics which are related in some way or another, probably very directly, to the study of two mathematical creatures; Equations and Inequalities.
If those two creatures are important enough to warrant 76 pages of instruction, they are probably pretty important. It would seem natural to decide that one of the first things you want to discover is a PRECISE definition for each of these words. That gives you at least two learning objectives when you turn to Page 72.
Now look at the seven section titles. It appears that the concept of inequality will not be taken up until the last two sections, so your curiosity about that topic can be put on hold for a short time. It is not at all clear what Section 4 has to do with equations. You should just decide to let the authors tell you how Complex Numbers are related to equations when you get to Section 4. When you get to Section 4 you should expect to learn the PRECISE definition of Complex Number.
The other section titles make it pretty clear that you will want to learn the PRECISE definitions of linear and quadratic.
You now have several learning objectives for your study of this chapter.
Learn the definition of equation.
Learn the definition of inequality.
Learn the definition of linear.
Learn the definition of quadratic.
Learn the definition of complex number.
It is your responsibility to complete each of these learning objectives as you study the chapter.
Trust the authors and your teacher to reveal other learning objectives as you progress through each of the sections.
Tip 3 from Dr. Del
Read, think about, and remember each section title as you study the material in the section. At the same time read and think about any subsection titles as you study that material.
For example, when you start studying Chapter 1, keep in mind that the first section deals with Basic Equations (the section title). Next you should pay attention to the fact that the section is divided into subsections named:
Linear Equations
Solving Equations using Radicals
Solving for One Variable in Terms of Others
As you study the material in the text you should always be aware of the Chapter, Section and subsection in which you are currently studying.
Attention to and actually doing the recommended activities in Tips 1, 2, and 3 have very real impact on how well you learn mathematics. How those activities impact your learning is explained by Gagne:Without the use of a concept map some information in long-term memory is simply not available for retrieval. It can't be remembered.
Entries which in turn facilitates (in fact, is essential for) learning.
Tip 4 from Dr. Del
Learn the vocabulary. Why are definitions important?
If a reader does not know requisite definitions, mathematical statements become meaningless, textbook presentations are confusing at best, and lecture explanations have absolutely no value to the learner. In addition, if the learner does not know requisite definitions his/her own written or spoken statements are incorrect and in many cases completely nonsensical.
Every mathematical term in the following sentence, taken from an elementary Algebra textbook, has been replaced by a randomly chosen word from a foreign language.
To natus one desenvolvemos by another, natus each consectetur of the first sagte by each geschiedensboek of the second liever and nesciunt dignissimos hálito.
Clearly, no one can learn mathematics from statements such as this. However, that is precisely what a reader attempts when definitions are not learned. After a few attempts it becomes clear that "the book doesn't help at all" and the student stops reading the text and simply tries working problems. That strategy always leads to failure.
There are other reasons why definitions are important in the study of mathematics.
"Preteaching vocabulary in the mathematics classroom removes cognitive barriers that prevent children from grasping new content."[Chard]
Here is what professor Stephen Maurer of Swarthmore college writes about the role of definitions in mathematics.
"Most disciplines don't need to make definitions explicit nearly so often as mathematics does – they don't need to be so precise nor do they deal so regularly with situations outside common experience."[Maurer]
Definitions play a much more important role in mathematics than they do in any other area of study. A word may (in fact probably will) have a different meaning in mathematics than in normal discourse. One of the dictionary definitions for the word function is: "the action for which a person or thing is specially fitted or used or for which a thing exists". The definition of function in mathematics is very different. That mathematical definition will be the subject of study in Chapter 2 of our College Algebra course.
Definitions in mathematics form a solid and completely adequate foundation upon which we base all our mathematical reasoning.
A mathematical definition of a concept gives necessary and sufficient conditions for a creature to be an instance of that concept.
For example, the definition of a prime number is:
A number is a prime number if and only if it is a natural number greater than 1 with exactly two divisors.
From this definition it is possible to conclude that 7.32 is not a prime number because it is not a natural number and therefore violates the necessary condition that a prime number be a natural number. From this definition we can also conclude that 6 is not a prime number because it has four divisors and therefore violates the necessary condition that a prime number have only two divisors. From this definition we can also conclude that 7 is a prime number because it is a natural number greater than 1 and it has only two divisors and therefore satisfies the necessary conditions stated in the definition.
Non-mathematical concepts on the other hand are frequently defined in a hazy and flexible manner. Find any definition of prime real estate and note that it does not give necessary and sufficient conditions. Rather it will be hazy, deliberately quite flexible, and open to personal interpretation.
In an article about teacher preparation, Professor H. Wu from the Mathematics Department at Berkeley claims that precise definitions form the basis of any mathematical explanation. He correctly states:
"logical explanations – the essence of mathematics no matter how mathematics is defined – cannot be given without precise definitions."[Wu].
Finally, I should point out that many/most of the exercises in College Algebra are simple one or two step logical consequences of a definition. For example, a firm understanding of the term "graph" is the key to answering many questions. Just one example of this is the fact that an understanding of the word "graph" provides the basis for finding the points of intersection of two graphs.
Definitions are the first tool used when attempting to answer a mathematics question.
Tip 5 from Dr. Del
Learn the vocabulary. How do you learn the vocabulary?
As you read the textbook: As you read the textbook, insure that you know the meaning of every word. In mathematics textbooks, the definition is usually provided when a new word is introduced.
If the textbook does not provide the definition or it is difficult to extract a formal definition, turn to the index to determine if this is the first occurrence of the word. Turn to the first occurrence of the word in the book and try to find the definition. If that fails turn to another source such as the chapter summary at the DrDelMath website or the Mathematics Glossary listed on the homepage of DrDelMath.
As you take lecture notes: As you take lecture notes make sure you write all presented definitions precisely as they are presented in the lecture.
As part of your daily study plan: As part of your daily study plan you should memorize all definitions. To memorize a definition it is wise to start by writing it ten or more times. Think about what you are writing. After writing a definition ten times you should be able to recite or write it without reference to notes. On a daily basis review the definitions by carefully reading(studying) them. After committing a definition to memory continue your study of that definition. Think about the necessary and sufficient conditions given in the definition. Think about how the necessary and sufficient conditions determine whether a mathematical creature satisfies the definition.
As you prepare for a test: As you prepare for a test review all definitions --- think about how they help you to answer questions.
If you must still memorize definitions when you begin your review for a test, you have not been studying sufficiently or correctly or both.
As you use the DrDelMath website: Insure that all the definitions provided in the chapter summary are committed to memory and that you understand every word in them. Think about the necessary and sufficient conditions given in the definitions. Think about how the necessary and sufficient conditions determine whether a mathematical creature satisfies the definition.
Insure that each of the definitions are included in the list that you review on a daily basis.
A deck of flash cards may be the most convenient and efficient way to study definitions in mathematics. A deck of flash cards makes it easy to review on a regular daily basis.
Cognitive Science as a Foundation for Tips 1 - 5
The Learning Process
There are two classifications of conditions for learning. There are external conditions of learning which are controlled by the instructional developer or teacher. There are internal conditions which derive from the stored memories of the learner.
The diagram below is a widely accepted model of the processes involved in the act of learning.
The following is a simplified glimpse of some aspects of the internal conditions of learning.
Information stays in short-term memory for a very short time (measured in seconds) except during an activity called rehearsal. Information which is to be remembered for use at a later time must be semantically encoded and stored in long-term memory.
During the learning process, information is retrieved from long-term memory into short-term memory where it combines with other items in short-term memory to bring about new kinds of learning.
Suppose the learner has previously learned the meaning of the two terms "mathematical expression" and "equal sign". To say he has learned this information means it has been semantically encoded and stored in long-term memory and is ready for retrieval into short-term memory.
When this student is presented with the definition "An equation is a mathematical statement which contains an equal sign", the two previously learned bits of information are retrieved from long-term memory into short-term memory where they are combined with the new definition to be encoded and stored in long-term memory. At this point the student has learned the meaning of the word equation as it is used in mathematics. I should point out that the process is actually a bit more complex but this example illustrates what must happen during the learning process.
What can go wrong in the above process to prevent learning from happening? There are many potential problems. We have absolutely no control over some but the learner, the instructional developer, and instructor can prevent some problems.
In the above example, it is clear that the learner must retrieve two items from long-term memory. If that retrieval does not take place, learning does not happen. Retrieval might fail because the two necessary items are not in long-term memory or they are in long-term memory but not available for retrieval.
Careful sequencing of courses and topics in mathematics education is an attempt to insure that the learner has previously learned requisite material and has it stored in long-term memory ready for retrieval.
Availability for Retrieval"As in the case of individual facts, the learning and storage of larger units of organized verbal information occurs within the context of a network of interconnected and organized propositions previously stored in the learner's memory."[Gagne p.84]
Without the use of concept maps some information in long-term memory is simply not available for retrieval. It can't be remembered.
There are four common kinds of concept maps with a few other specialized maps that help in certain situations. The concept map which is most commonly associated with mathematics is called the Hierarchy Concept Map.
Here is a simplified picture of a Hierarchy Concept Map which might be used for mathematics.
The entries.
That is why the previous five tips for reading mathematics encourage you to pay attention to the organizational titles. They help build the very essential concept map.
Another View
Another way of visualizing how your long-term memory organizes information might be the following.
There is a "room" reserved in your LTM (long-term memory) for mathematics information. The room is divided into "sections" labeled "Algebra", "Geometry", "Analysis", and so on for each of the major segments of mathematics.
Each of these sections of the room contain numerous "file cabinets", each reserved for a subset of the room section. So in the "Algebra" section of the room, among others there will be a file cabinet for Functions. Inside this file cabinet are folders for topics such as Zeros of functions, Linear functions, Quadratic functions.
This organization permits efficient recovery of information from any one of the folders.
When the learner uses no concept map, it is comparable to having all the millions of mathematics facts strewn about on the floor of the mathematics room. Obviously in such disarray, virtually nothing is available for retrieval and therefore very little learning can take place.
Six Tips for Reading the Narrative in a Mathematics Textbook
As you sit down to study your mathematics textbook and after you have duly noted the textbook title, chapter title, section title, and subsection titles as appropriate to the part you wish to study, you must heed the following tips. These tips (6 - 11) are modifications, adaptations, and copies of tips for reading a mathematics textbook as assembled and justified by Derek Bruff while at Harvard University [Bruff]. These tips are certainly not original with Dr. Bruff. Every serious student or teacher of mathematics has long been aware of the protocol for reading a mathematics book. These tips are meant to encourage the beginning student to follow that protocol.
Tip 6 from Dr. Del
Read the preface of your textbook, scan any appendices, become familiar with the table of contents, index, and any other listings provided in the textbook.
The preface usually addresses special features of the textbook. Knowing the special features and special symbols used in the book will make the textbook more useful and less confusing. Becoming familiar with the various indexes will be helpful later when you want to look up the definition of a word or review a concept.
"Reading Mathematics is not at all a linear experience ...Understanding the text requires cross references, scanning, pausing and revisiting" [Simonson]
Tip 7 from Dr. Del
Read the narrative of each section.
Most of these tips are about reading the narrative in the textbook. The most important material in a mathematics textbook is the narrative -- the presentation of concepts. Set aside time to read the textbook when you have no intention of working on exercises. This will enable you to truly focus on the mathematical concepts at hand. If in the past, you have opened your textbook only when doing exercises (looking at the rest of the book only for examples), you must rid yourself of this bad habit now.
"Mathematics has a reading protocol all its own, and just as we learn to read literature, we should learn to read mathematics. Students need to learn how to read mathematics, in the same way they learn how to read a novel or a poem, listen to music, or view a painting."[Simonson]
All of the tips presented here are an attempt to help you learn that protocol. How you read the narrative is an important part of that protocol.
Tip 8 from Dr. Del
Read the narrative several times.
The first reading should be to scan for major ideas. During this first reading you should be interested in extending your mind map to include the new major concepts. If the narrative concerns topics already in your mind map, then the narrative should correct, refine, or extend your mind map.
The second reading should be to identify and learn important definitions. To maximize the benefit from the lecture, this (and the first) reading of a section and memorization of necessary vocabulary should be done before the lecture about the section.
Make a list of the mathematics terms encountered in the section. Some of these will be old familiar terms and some will be new. You must know (flawlessly) the precise definitions of all these terms. The DrDelMath website will have precise definitions of all new terms introduced in the section. It is your responsibility to look up and review any definitions which you have forgotten.
An excellent way to begin the process of learning the definitions is to memorize them and the best way to begin the memorization process is to write the definition ten or more times. Flash cards are a good mechanism for studying and reviewing definitions and important properties.
The third reading should be the first attempt to understand the details. Don't be in a hurry! To be sure this third reading involves the decoding of the words found on the page, but that is the least important and time consuming activity. The third reading should involve a great deal of reflection, contemplation, questioning, as well as construction of examples and non-examples. The textbook examples and pictures are designed to illustrate with less abstraction new abstract concepts presented in the section. Read them for that purpose. They are intended to increase you understanding -- not to present templates for problem solutions.
"Reading mathematics too quickly, results in frustration. A half hour of concentration in a novel buys you 20-60 pages with full comprehension (depending on how experienced you are at reading novels). The same half hour in a mathematics textbook buys you 0-3 lines (depending on how experienced you are at reading mathematics). There is no substitute for work and time. "[Simonson]
The fourth reading should be to understand the topic as a unified whole.Mathematics is very logical and unified. Not only should the material in a section fit together, but those concepts must fit logically with previously learned topics. Look for similarities and differences between the current concept and previously learned concepts.
Subsequent readings should be for a better understanding or for review. Simultaneously reading your lecture notes and the text narrative are necessary to fit them together as a unified whole. If you have trouble with an exercise, you need to re-read the narrative looking for a better understanding of the concepts as it applies to the particular exercise. Review is a regular part of the learning process, so re-reading the narrative should be a natural and regular part of your study activities.
Tip 9 from Dr. Del
Focus on Concepts.
There are an infinite number of types of mathematics problems, so there is no way to learn every single problem-solving technique. Mathematics is about ideas. The mathematics problems which you are assigned are expressions of these ideas. If you can learn the key concepts, you will be able to solve any type of problem (including ones you have never seen before) involving those concepts. In support of the contention that ideas are the important mathematics, Dr. Steven Zucker of John Hopkins University states:
"One of my basic tenets is that the students have no right to know what an upcoming exam is going to look like.[Zucker]
Tip 10 from Dr. Del
Don't bother highlighting.
Unlike most other textbooks, mathematics textbooks use chapter titles, section titles, and sub-section headings to organize material and provide the basis for the necessary mind map. Mathematics textbooks also use page layout, fonts, and colors very well to organize information and make it easily visible. Words used as headings such as Definition, Theorem, Axiom, Property, Proof, and Example serve to identify and classify certain segments of the text. There's usually little use in highlighting or underlining in a mathematics textbook although it is sometimes helpful to mark something that you might want to find quickly at a future time. An attempt to underline or highlight everything that is important will result in the entire narrative being highlighted.
Tip 11 from Dr. Del
Read with pencil, paper, and eraser.
As you read the text, you should write notes. Check calculations. Write your own examples. Believe your textbook, but check the work you see there anyway -- insure that you can supply all the missing details. You don't learn difficult material just by reading a nice presentation of the material – you need to break out pencil and paper and convince yourself that you follow the reasoning and computations. It is also important that you be able to produce a similar argument on your own. That is much more difficult than following a nicely presented argument. You might try to work out examples before looking at their solutions in the textbook. Make up your own examples to illustrate the concepts and do the necessary computations to insure that your example illustrates what you want it to. Combine your lecture notes and material from the DrDelMath website with the text material by writing your own "mini textbook" about the subject. | 677.169 | 1 |
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18.702 Algebra II
Welcome to the course webpage for 18.702 at MIT, taught in Spring 2018. This course is a second-semester undergraduate course in abstract algebra, intended for mathematics majors who have completed 18.701. This page will maintain the schedule for the class, as well as a repository for course materials such as problem sets, the syllabus, notes, and references.
Overview: The first half of this course, 18.701, equips students with the basic language of abstract algebra, including linear algebra and group theory. In this second half, we get to see two of the most fundamental places where this theory comes to life -- representations of finite groups and symmetries of solutions to polynomial equations, also known as Galois theory. These ideas are ubiquitous in modern mathematics. Along the way we'll get through the fundamentals of rings
Textbook: The main text will be Algebra by Mike Artin, denoted [A]. For the representation theory part, I also recommend a beautiful textbook Representations and Characters of Groups by Gordon James and Martin Liebeck.
Problem sets: Homework will be assigned each Friday and due the following Friday. The problem sets will be posted here. This is the core of the class. If you don not do the homework, you will not get anything out of the course except a few funny sounding mathematical words to share with your family/family.
If a problem set has gone particularly badly: I will offer you the chance to re-write it and resubmit it. Your original grade will then be replaced by the new one up to 75%.
Quizzes: There will be in-class quizzes on three occasions during the term: February 28, April 4, and May 14. If a quiz has gone particularly badly: I will offer you the chance to re-write it and resubmit it. In this case, I will also ask you to write brief explanations of what went wrong on each problem. Your original grade will then be replaced by the new one up to 75%.
What will the quizzes be like? I will use the quizzes simply to make sure that the basic language of what we've been discussing has come across. In this sense, the quizzes are as much as an assessment of me as they are of the students. They are not meant to trip you up. Do the reading, complete the homework, and come to office hours. All will be well!
Grading: Your grade will be based on your homework scores (70%) and the quiz scores (10% each).
Reading: The most effective method for doing the reading is probably to skim it before class and then do a careful reading a day or two after class, but this will vary based on your learning style. The class will not assume you've done the reading, but the homework may well.
February 28: In class quiz: this will cover the material on representation theory. Don't stress out about this.
What will the quiz be like?
Each quiz will consist of four questions. There will be a mix of conceptual questions, such as deducing
The first quiz will cover the material on representation theory of finite groups. It is meant to check, to what extent the ideas have settled in your mind, and how comfortable you are manipulating them. The best way to prepare is to do mathematics -- go look in Artin's book and do some problems. That is not to say that the problems will necessarily come from the book, but the problems will test to what extent you have mastered the material, and doing problems is the best way to do that. I see a lot of value in concrete calculations. For instance, I like questions of the flavour "Decompose the regular representation of S3 into irreducible representations", or "Here is a representation and a linear operator. Use the averaging trick to produce an invariant operator", or "What is the induction of the alternating representation of S2 to S3?". You should also know the statements of the main theorems and their consequences. You need not memorize the proof of the main theorems. There will also be some more conceptual questions. For instance, "Prove that every finite subgroup of GL(n,C) is conjugate to a subgroup consisting of unitary matrices."
Problem sets:
Problem set 1: The purpose is to get you comfortable with the definitions, compute some examples, and understand the importance of simultaneously diagonalizing operators.
Problem set 2: The purpose is to get some concrete calculations done with characters, see how the theory generalizes, and develop an important construction called induction.
Problem set 3: This one gives an example of horrible things that happen for representations over finite fields, and examines some basic properties of rings. | 677.169 | 1 |
MR. leal's Algebra 1 classes
Mr. Leal intends for students to learn Algebra by exploring problems, calculating and verifying answers, and representing problems and answers in multiple ways (symbolically, graphically, verbally, numerically); We will build the mathematical foundation needed to succeed in school as well as the real world. Here, we make good things happen! | 677.169 | 1 |
Algebrator Review
The last few days I've been playing around with Softmath's product for helping students learn algebra: Algebrator. There seems to be a lot of curiosity about this product, so I wanted to do an Algebrator review to let my readers know what the product about. As of the writing of this review, it costs $58.99, a reasonable cost for software of this type, but enough that you'll probably want to know a little more about the software before investing in it. Softmath was willing to provide me a full version of the software for review purposes.
Partial view of Algebrator solving for an inverse
What I Like about Algebrator
There's a lot to like with Algebrator. While it has a lot of capabilities, allowing it to be used as a scientific calculator, graphing calculator, CAS calculator and more, there were two areas that I think most students will use it for.
The first is the ability to input problems and see them solved step by step. When you input a problem into Algebrator, it will use it's CAS calculator to work the problem out, step by step. Trust me when I say, they are worked out in incredible detail. In some cases, there were more steps than I would care to see. However, I am glad that if that given the choice, the developers of Algebrator went with more detail rather than less as students can often be confused by "skipped steps." Students can also click on any step for an explanation of how the software calculated the step if they are confused.
The other main capability of Algebrator that I would point out are the "Wizards." The programmers at Softmath have created a list of questions students are likely to encounter in high school math, and created a long list of ready made templates to solve them. Many, but not all of them, involve coordinate geometry. The headings in the Wizard area of the software are:
Line
Parabola
Circle
Ellipse
Graphing
Basic Operations with Numbers
Pre-Algebra
Polynomials
Functions
Sequences
Geometry and Trigonometry
Statistics
How do Wizards work? As an example, within the Line menu, there are options to find intercepts of a line, the slope between to points, the equations of parallel/perpendicular lines through a point among many, many others. You just provide the relevant points and lines, and Algebrator will show you how to find the solution to the problem. By my quick count, there were nearly 80 Wizards within the sub-menus listed above. In my opinion, these Wizards are the strongest selling point of the software.
What Algebrator Is Not
Algebrator is true to its Algebra name. If you're looking for a product with Calculus abilities, this isn't it. On the other hand, there are quite a few functions of the software that could be classified as Pre-Calculus. Algebrator has the ability to work with matrices, logs, and trig functions, although I did find its trig abilities to be a bit limited (it handles numbers well enough but won't simplify trig identities). I also really like some of the "Wizards" that were available to solve for conic sections as a Pre-Calculus tool.
I would highly recommend this software primarily for Pre-Algebra, Algebra I, and Algebra II students. There are also some pretty cool features that would make it appeal to Pre-Calculus students. The right kind of Pre-Calculus student could actually get quite a bit of mileage out of it. I wouldn't recommend it beyond Pre-Calculus, though.
Bottom Line Algebrator Review
If all you're looking for is a way for your child to check their answers, Wolfram Alpha still can't be beat. It's free and can do a lot of really high level stuff that Algebrator can't. However, don't expect it to do all the Wizards of Algebrator can. It's capable of some of them, but certainly not all.
Additionally, for a very reasonable cost, Algebrator is far more than an answer checker. It's designed to demonstrate how problems can be solved step by step. I haven't seen many resources that can do that, and the few that do aren't as polished and easy to use as Algebrator. If you are looking for a way to walk students through answers in simple steps with concise explanations, Algebrator is top notch. I recommend you head over to Softmath.com to check out Algebrator. Additionally, you may want to check out the video I created below demonstrating some of its capabilities.
Disclosure: I was provided with a copy of Algebrator by Softmath in order to test the products' abilities and give my own personal opinions on it. The opinions I have given are mine and may differ from others but were not influenced by the company or the free product provided.
Tech Powered Math is a participant in the Amazon Services LLC Associates Program, an affiliate advertising program designed to provide a means for sites to earn advertising fees by advertising and linking to amazon.com. | 677.169 | 1 |
There
are five variables: A, B, C, D, and E. The way they are accessed is not through an
ALPHA key, but a menu. Personally, I
prefer the ALPHA key
If
you need help with operating the TI-30XIIS, there is plenty of online tutorials
available.
Final Verdict
I
would recommend the TI-30XIIS if you like a basic scientific calculator where
you are able to see the expression that you entering. This calculator is good for quick
calculations and having an inexpensive calculator. | 677.169 | 1 |
Algebraic Problems and Exercises for High School
Algebraic Problems and Exercises for High School by I. Goian, R. Grigor, V. Marin, F. Smarandache
Publisher: The Educational Publisher2015 ISBN-13: 9781599733425 Number of pages: 146
Description: In this book, you will find algebra exercises and problems, grouped by chapters, intended for higher grades in high schools or middle schools of general education. Its purpose is to facilitate training in mathematics for students in all high school categories, but can be equally helpful in a standalone workout.
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Essential Mathematics by Franco Vivaldi Essential Mathematics is written for students who reach university without elementary algebra and arithmetic skills. The book consists of exercises on fractions, roots, monomials and polynomials, linear and quadratic equations. (10842Easy Mathematics: Arithmetic and Algebra for General Readers by Oliver Lodge - The Macmillan Company Arithmetic and algebra for general readers, being an elementary treatise addressed to teachers, parents, self-taught students and adults. It is not exactly a book for children, though I hope that elder children will take a lively interest in it. (2668 views) | 677.169 | 1 |
Welcome to MAT 200
This course offers an introduction to mathematical
reasoning and proofs. It is intended as a bridge between
the loose, heuristic approach often used to teach elementary calculus,
and the precise, formal style needed for
upper-division mathematics courses.
For more information, please select General information link in the menu to the left.
Midterm will be given next Wed, 3/9, in class. It will over all material
we have studied so far. The class on Monday will be a review.
During the exam, you will be allowed to use the following handout
with the summary of most important logic laws: handout. | 677.169 | 1 |
Article Title
Authors
Volume
9
Issue
1-2
Abstract
Many teachers and researchers have written about the challenges inherent in adopting new teaching practices in mathematics classrooms (e.g., Chazan, 2000; Clarke, 1997; Heaton, 2000). The authors of this article, all with secondary mathematics teaching experience, are convinced by research suggesting that Standards-based mathematics curricula are beneficial for student learning.1 However, the first three authors had not used such curriculum materials in their own classrooms, and we desired experience using a Standards-based mathematics curriculum with secondary students. To this end, we taught a week-long summer course with a focus on linear functions to high school students who had previously struggled with algebra and volunteered to participate. | 677.169 | 1 |
site contains some topic in Calculus and Pre-Calculus including interactive explorations such as an animation tool to...
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This site contains some topic in Calculus and Pre-Calculus including interactive explorations such as an animation tool to discover the tangent line from the secant line.
Material Type:
Presentation
Author:
Unknown
Date Added:
Nov 01, 2015 has several multimedia lessons on limits, continuity and derivatives. Each lesson asks the student to attempt a...
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This page has several multimedia lessons on limits, continuity and derivatives. Each lesson asks the student to attempt a sample problem.
Material Type:
Presentation
Author:
Michael Kelly
Date Added:
Oct 08, 2004s for the Calculus Phobe to Bookmark material or Course ePortfolio
The site is part of the learning area of BBC Scotland that includes a variety of K-12 subjects. This area focuses on the...
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The site is part of the learning area of BBC Scotland that includes a variety of K-12 subjects. This area focuses on the material for the Scottish "Higher" exams in mathematics. These national exams are normally taken by students age 15 or 16, and play a significant role in university admission. The main subject groups for the material in this mathematics area site are algebra, calculus, geometry and trigonometry. The material is simple but well executed.
Material Type:
Presentation
Author:
Learning Team BBC Scotland
Date Added:
Sep 15An extensive set of first-year calculus notes generated by latex2html.
Material Type:
Presentation
Author:
Eric Key
Date Added:
Sep 24, 2007 FoilSim Activity demonstrating the uses of Calculus in aerodynamics. NASA materials are used to help students...
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This is a FoilSim Activity demonstrating the uses of Calculus in aerodynamics. NASA materials are used to help students understand the concept of "lift".
Material Type:
Presentation
Author:
Jim ZaborowskiNASA COLLABORATIVE 2007: Getting a Lift out of Calculus to Bookmark material or Course ePortfolio | 677.169 | 1 |
Click below to play a sample Core Video from our Praxis Middle School Mathematics (5169) Online Prep program. This particular video focuses on properties of functions, a topic that appears frequently on the Praxis Middle School Mathematics test.
When you purchase any of our Praxis II Middle School Mathematics Online Prep programs, you'll get Core Videos like this one covering every key Numbers & Operations, Algebra, Functions & Their Graphs, Geometry & Measurement, and Probability, Statistics, & Discrete Math concept you need to pass. You'll learn the same key subject matter you would in our live classes, as well as strategies for success on the various multiple choice Praxis II Middle School Mathematics Online Prep and begin studying today!
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Below is a complete list of the Core Videos that are included in all our Praxis II Middle School Mathematics Online Prep programs. These videos have been created by our industry-leading team of Teachers and Subject Matter Experts based on the official Content Specifications published for the Praxis II Middle School Mathematics (5169) examWorking with Numbers
Property Determination
Properties of Numbers
Place Value
Exponents & Roots
Scientific Notation
Fractions, Decimals & Percents
Ratios & Percent Change
Conversion
Proportions
Counting Numbers
Factors, Multiples, & Divisibility
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Estimation & Error
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Radical Equations & Exponents
Polynomials - Word Problems
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X & Y Intercepts
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Congruency
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Pythagorean Theorem
Triangles
Identifying Triangles
Polygons
Circles
Circles - Word Problems
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Transformations
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Statistics
Statistical Variation
Diagrams
Enroll in Praxis II Middle School Mathematics Online Prep, and you can begin watching all these Core Videos right now! You'll also get instant access to a host of other great features, including Smart-STEM Virtual Tutoring Videos in which an expert tutor will discuss each question from the math section of your full-length, Praxis II Middle School Mathematics | 677.169 | 1 |
Format
Language
Number of Copyright Permissions
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Great strategists rely heavily on numbers as they go about their work. Offers an overview of the high- and low-brow quantitative tools that students encounter during the Strategy course. The class explores high-brow tools in detail; the focus here is on low-brow calculations. Such calculations come up often in class but because they seem so simple, they get little airtime or explanation. From past class experience, roughly 20% of the students in each section come into the course with the intuition and experience to do these simple calculations themselves. The other 80% understand the calculations after they see them and grasp their value, but don't spot the opportunities to do the math themselves, before class | 677.169 | 1 |
PLEASE NOTE: It is very recently that Math 105 has been taught as a 3-unit rather than a 4-unit class. The class structure will be somewhat different in terms of how the material is covered. One major difference is that Problem Solving used to be taught as a full unit at the beginning of the course, and there was a Problem Solving test. In this 3-unit course Problem Solving will be spread throughout the semester, and you will have at least one genuine "Problem" (as opposed to an exercise) on each test. Even though these tests are not an exact match to the set-up of the new unit structure I have decided to leave them posted here so that you can get an idea of what my tests typically look like in general - what sorts of questions I ask - how I ask them - etc. I will give you as much guidance as I can in advance of tests to help you prepare. Remember that you are responsible to know all the material we covered whether it appears on these old tests or not, but I hope you will find these helpful to you. It would be a good idea to work through some (appropriate) problems on the tests below and to look at the additional "helps" below before our review day so that you have good clarity about what you need to ask me questions about during our review. As you study also be sure to use your notes, your book, and your homework.
For TEST 1 (Problem Solving): Click here and here for examples of "PROBLEMS" and (good) answers to a couple of questions from a previous Chapter 1 Test. (Note: For fall 2015 there will be at least one "PROBLEM" - as opposed to exercises - on each test.)
For the FINAL EXAM: As well as the study guide near the top of the page and my old test that I've provided, click here or here to find former finals that colleagues of mine have given that you can also use for practice, and you can click here for a study guide posted fall 2013. Use this previous study guide CAREFULLY! Just because I wrote on it that there were some things those students didn't need to know that semester doesn't mean I won't cover them on the exam this semester. Focus on explanations of things I DO ask for, and check with me during review day about whether or not there are some topics you can skip THIS semester. | 677.169 | 1 |
Description
An example for each type of function, included step-by-step explanations and the relative graph.
Functions and graphs will be easy to understand.
Theorical part in italian | 677.169 | 1 |
Greatest math problem solver That could Cause you to an even better University student
In certain programs, all it requires to move an exam is note taking, memorization, and remember. On the other hand, exceeding inside a math course normally takes a different style of effort. You cannot simply just clearly show up to get a lecture and view your teacher "talk" about math and . You study it by undertaking: paying attention in class, actively researching, and fixing math difficulties – regardless if your instructor has not assigned you any. If you find yourself struggling to perform properly in your math class, then take a look at finest site for solving math difficulties to learn the way you could become a better math scholar.
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Math classes comply with a organic progression – each builds on the expertise you've obtained and mastered with the previous system. Should you are finding it tricky to observe new principles in school, pull out your previous math notes and evaluate previous materials to refresh your self. Ensure that you meet up with the stipulations in advance of signing up for a course.
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Dislike any time a instructor calls on you and you have neglected ways to resolve a particular dilemma? Avoid this minute by examining your math notes. This will enable you to ascertain which ideas or thoughts you'd love to go in excess of in class the next working day.
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Go through Forward To remain In advance
If you want to minimize your in-class workload or perhaps the time you commit on homework, make use of your free time soon after faculty or around the weekends to study in advance to the chapters and ideas that will be included the subsequent time that you are in school.
Evaluate Aged Tests and Classroom Illustrations
The function you do at school, for research, and on quizzes can offer you clues to what your midterm or last test will glance like. Make use of your old exams and classwork to make a private study information to your approaching exam. Seem within the way your trainer frames concerns – this is in all probability how they will look with your examination.
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If you're owning a hard time comprehending concepts in school, then be sure you get support beyond course. Request your buddies to produce a review team and pay a visit to your instructor's workplace hours to go more than tough issues one-on-one. Show up at analyze and assessment sessions whenever your instructor announces them, or retain the services of a personal tutor if you want one.
Chat To Yourself
Whenever you are examining complications for an examination, check out to clarify out loud what strategy and techniques you accustomed to get your remedies. These verbal declarations will come in helpful during a exam whenever you should recall the techniques you must consider to find a option. Get added practice by striving this tactic which has a buddy.
Use Study Guides For Added Observe
Are your textbook or course notes not encouraging you realize what you really should be mastering in school? Use review guides for standardized examinations, such as the ACT, SAT, or DSST, to brush up on old content, or . Review guides normally come outfitted with complete explanations of ways to resolve a sample challenge, , and you simply can usually find where by may be the far better buy mathcomplications. | 677.169 | 1 |
*Must be taken in the final year in order to be counted as a math credit.
Algebra 1
Grade: 9-12 Credit: 1/year
Prerequisite: None
Description: This course covers the language of algebra and its applications—expressions; equations, inequalities, and systems; functions; linear functions; exponents and polynomials, including methods of factoring; quadratic equations and functions; exponential and logarithmic functions; data analysis and probability.
Algebra 1B
Grade: 9–12 Credit: ½ semester credit and ½ semester elective credit
Prerequisite: Teacher recommendation.
Description: This course is offered for those students that did not successfully complete the second semester of Algebra I. This class is the same as Algebra I; however, only the second semester of Algebra I is taught for the entire year. Students receive ½ credit of math and ½credit of elective.
Description: This course covers linear functions, linear systems, matrices, quadratic functions, polynomial functions, exponential and logarithmic functions, probability and statistics, conic sections, sequences and series, and trigonometric functions and their graphs. This class will be a faster pace course, with more focus on graphing calculators than the regular Algebra II class.
Algebra 2A/Algebra 2B
Grade: 9–12 Credit: 2 credits over 2 years
Prerequisites: Teacher recommendation
Description: This course is the same as Algebra II;however, the material is spread over two years. This is a two-year course. Once enrolled, students are locked into a two-year program to earn their credit in Algebra II. Students will receive 2 credits upon completion.
Description: This course includes the same material as Geometry; however, this class will place more emphasis on logical reasoning including truth tables and a more in depth study of the proof.
Trigonometry Grade: 11-12 Credit: 1/year
Prerequisite: Algebra I, Algebra II, and Geometry
Description: This course includes the study of real numbers, sequences and series, functions and their graphs, polynomial and rational functions, trigonometry and its applications, and systems of equations and inequalities.
Pre-Calculus
Grade: 12 Credit: 1/year
Prerequisite: Algebra I, Algebra II, Geometry, and Trigonometry
Description: This course includes the study of trigonometry and its logical applications, analytical geometry, polar coordinates, complex numbers, vectors, matrices, limits, and continuity.
Honors Pre-Calculus
Grade: 11-12 Credit: 1/year
Prerequisite: Algebra I, Algebra II, and Geometry
Description: This course will focus on a detailed study of the basic concepts in a beginning calculus course: real numbers, series and sequences, trigonometry and its applications, limits, continuity, graphing polynomial and rational functions, systems of equations and inequalities, vectors and matrices. Applications of these concepts, including maximum – minimum, and related rate problems, concavity, areas and volumes will be studied.
AP Calculus
Grade: 12 Credit: 1/year
Prerequisite: Algebra I, Algebra II, Geometry, and Trig/Pre-Calculus
Description: Calculus involves the study of the derivatives of a function (geometric interpretation and analytic definition) and it's applications; linear approximation; limits and continuity; critical points and max/min problems; mean value theorem; second derivative; definite integral and its applications; the fundamental theorem of calculus, indefinite integrals, and area between curves in order to prepare students for Calculus in college. These experiences will prepare the AP Calculus student for the AP Calculus. There is a cost to take the AP exam and a student's score may earn college credit. The minimum score needed for credit varies from college to college.
Personal Finance- Budgeting Basics learn how to create, monitor and adjust a personal budget for a student, employee entering the workforce and a business. Students will use technology to monitor cash flow statements for an online budget simulation. The course will conclude with a unit of study on individual decisions affecting the economy.
Personal Finance-Forms of Credit understand the different types of credit, establishing credit, building credit, pros and cons of using credit to make major purchases. Students will explore investing and saving strategies, filing and determining tax base for various individuals. The semester culminating activity will be an online invest simulation.
Real World Statistics This course is designed to explore the world by using experimental data found by the students' own investigations. Basic statistics are taught and emphasized through instructor-guided investigations. Students will then compile their own data from something outside the classroom and examine it using the basic statistics properties such as mean, median, mode, box and whisker plots, probabilities, etc.
Accounting I
Grade: 10-12 Credit: 1/year
Prerequisite: Must have a "C" average or better, 10th graders – instructor permission
*Meets the Michigan Merit Curriculum guidelines for Math or Math-related Accounting-related credit if taken in the final year of high school.
Description: This course is a continuation of accounting concepts mastered in Accounting I. Loans, interest, inventory, receivables, payables, stock, dividends are just some of the topics covered. | 677.169 | 1 |
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Unformatted text preview: Introduction to MATLAB Test #1 ENME271 Summer 2009 1hr and 40 min Problems 2, 3, and 4 are to be solved on the computer using MATLAB. The questions in Problem 1 are to be answered in handwritten form with the MATHCAD software not booted. Turn in your answers to problem 1 before starting to work on the remaining problems. The computer-solved problems are to be emailed to [email protected] Send all three of the problems in one file. All problems in this test are to be solved using only the material covered in class to date. Prob 1 Questions in this problem are to be answered in the context of MATLAB. (a) Rate the following operations in descending order of precedence. i. multiplication and division ii parenthesis iii addition and subtraction iv exponentiation s , (b) If you make a mistake in a line written in the Command window and you don't discover it until after you have depressed the enter key, how do you correct the mistake?...
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Algebra Skill Builder - Summation Notation
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This skill builder helps students practice the skill of calculating partial sums of arithmetic and geometric series using summation notation. These problems frequently appear on state assessments and the ACT. This product is perfect for unit reviews, substitute teachers packets, or for students who need a little extra practice. | 677.169 | 1 |
59,33MB Answer Sheet The Distriputive Kuta Software Epub
Kuta software answer sheet keyword after analyzing the system lists the list of keywords related and the list of websites with related.
Kuta Software - Infinite Algebra 2. Date.Square Roots and Operations with Radicals.Radical operations worksheet pdf Worksheet by Kuta Software LLC.View Homework Help - The Midpoint formula worksheet with answer from GEOMETRY gg at University High School of Science and Engineering.Worksheet by Kuta Software LLC. Software for math teachers that creates exactly the worksheets you need in a matter of minutes.Kuta software answer key Free Algebra 2 worksheets created with Infinite Algebra 2.Software for math teachers that creates exactly the worksheets you need in a matter of minutes. | 677.169 | 1 |
Applying Math to Every-Day Life
Applying Math to Every-Day Life
Applying Math to Every-Day Life
Algebra: Perhaps the most fundamental and basic tool we learned in Algebra was "solving for x". Believe me when I tell you that I use "solving for x" nearly daily. Whether I am calculating my budget, determining the best value at a grocery store, or determining what percentage of my money to invest into my retirement fund, I am always using "solving for x". While you may not need to remember the quadratic formula to shop wisely at a grocery store, you should understand some basic algebraic concepts that are useful in life.
Statistics: A lot of people hate statistics. But, no matter what job you have, you will likely have to look at a set of data. Whether you are like me, analyzing data for a living every day, or you work in a small business, you can always use statistics. Understanding some basic concepts from statistics will help you tremendously in life and in your career. Whether you are doing something simple, like understanding what an average is versus what a median is, or you are using previous statistics to estimate what to expect in the future, you can always use statistics. Trust me when I say that you will add value to any company, business, or organization by understanding some basic statistical concepts.
So, fight through those frustrating math courses knowing that it will be useful to you one day. | 677.169 | 1 |
Algebra I formalizes and extends the mathematics students learned in the middle grades. Algebra I is made up of 5 strands: Real Numbers and Expressions; Functions; Linear Equations, Inequalities, and Functions; Systems of Equations and Inequalities; Quadratic and Exponential Equations and Functions; and Data Analysis and Statistics. These critical areas deepen and extend understanding of linear and exponential relationships by contrasting them with each other and by applying linear models to data that exhibit a linear trend, and students engage in methods for analyzing, solving, and using quadratic functions. The eight Process Standards for Mathematics apply throughout the course. Together with the content standards, the Process Standards prescribe that students experience mathematics as a coherent, useful, and logical subject that makes use of their ability to make sense of problem situations.
Requirements Students must have access to an iPad (or comparable device) with the following apps: Neu.anotate+, Educreations, and Canvas. In addition, students are strongly encouraged to have access to a reliable computer with high-speed internet access.
Final Exam Yes, an on-site final exam is required for this course. A valid photo ID is required. Details will be provided by the course instructor. | 677.169 | 1 |
COSC 314 - Computational Discrete Structures
Relations and algebraic structures, counting techniques, graphs, automata and languages and number theoretical algorithms. This course emphasizes discrete mathematical algorithms, their applications to problems in computer science and their implementations. | 677.169 | 1 |
Machine Learning and Data Science made easy.
Mathematics 101 problems without a strong mathematical background. I have observed this is true for most of the students eager to learn Machine Learning. They jump straight to meat of Machine Learning, classification, clustering and stuff. That is a totally wrong approach.
In this post I'll introduce basic building blocks which are essential for mastering this subject and being able to apply Machine Learning to real world problems.
Linear Algebra 101
This is one among few basics which needs to be covered before getting into machine learning.
Most of you might have done this course in High School, so this will be a refresher course plus some advanced things needed for Machine Learning.
Linear algebra is branch of Mathematics which deals with a general coordinate system and interaction of planes in a generalized coordinate system (I'll talk about what I mean by a generalized coordinate system) and apply operations on them.
I assume you all are from Mathematical background so you all might have studied Matrices at some point of your education, but have you ever thought what is actually a matrix? Think for a minute and see if you come up with an answer.
A matrix basically denotes a linear mapping between two spaces. What I mean by that is consider a matrix [sin(theta) -cos(theta); cos(theta) sin(theta)]. If you multiply any vector in a simple 2-D space with this matrix then this vector will be rotated by an angle theta (try it out). So this matrix is basically mapping any vector in a space to a vector in a space that is original space rotated by theta angle.
Vector
You might all have studied vectors in your high school maths course. You might think why I am writing about a concept that used to seem so abstract in high school. So for your information this is most common term you'll hear in Machine Learning course or in many CS courses.
So vector is nothing but a collection of numbers. If you remember arrays from data structures course, that represents a vector in a computer. A vector has components, in array the ith component is the ith element in the array.
Basis vectors
This is another very common term you'll see in machine learning literature. Basis vectors are nothing but a set of vectors which corresponds to the axis of the input space you are talking about. So another term here, space. Space is simply set of all possible combinations of numbers. For example input space of 2 dimensions is simply all combination of (x,y) where x and y can be any number from their domains.
This image explains it more intuitively.
Linear independence
A set of vectors are called linearly independent when none can be written as function of other vector.
This sums up linear independence and dependence concept.
Norm of a vector:
This is just a fancy word to represent length of a vector. Now length can be represented as simple sum of individual components of a vector (absolute value). This is called L1 norm. If we use euclidean distance to find length of vector it is called L2 norm vector.
Eigenvector:
This is bit difficult to explain. If you google it, you'll find only methods to how to calculate it. But not what they are actually. Why they are calculated. I'll talk about them in detail when I'll discuss Dimensional reduction techniques.
These are very basics terms used in ML. I've kept it short for this post, I'll give more details in the next post. | 677.169 | 1 |
Wolfram Alpha, a computational knowledge engine with amazing capabilities. Stuck on a difficult math question or just too lazy to solve it yourself? Enter a question and it'll do it's best to solve it. | 677.169 | 1 |
Algebra Team: Overview of Teaching Styles
Grades 6-8 / Math / Factoring
CCSS:
Math.Practice.MP1
Math.A-SSE.3a
Common Core State Standards
Math
Math
Practice
Mathematical Practice Standards
MP1
Make sense of problems and persevere in solving them.
Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, "Does this make sense?" They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.
Choose and produce an equivalent form of an expression to reveal and
explain properties of the quantity represented by the expression.
a. Factor a quadratic expression to reveal the zeros of the function it
defines.
b. Complete the square in a quadratic expression to reveal the
maximum or minimum value of the function it defines.
c. Use the properties of exponents to transform expressions for
exponential functions. For example the expression 1.15t can be
rewritten as (1.151/12)12t ≈ 1.01212t to reveal the approximate equivalent
monthly interest rate if the annual rate is 15%.
Algebra Team – Overview of Teaching Styles with Marlo Warburton & Julianna Jones
[01:00:07;11]
Julianna: I'm Julianna Jones, and I teach Algebra.
Marlo: I'm Marlo Warburton, and I teach Algebra 1.
Both: We are the eighth grade Algebra Team.
Marlo: "The bell's going to ring, but don't move."
No student gets through the school without coming through the two of us, and we teach the same things on the same days. We give the same tests, and often, the same homework. And, as a result, our program is really consistent.
Julianna: When you plan a lesson together, you teach the same lesson, you come back together and say 'Gosh, this happened and I didn't like that,' that's where the power is of a collaboration.
"That's the key right there."
Marlo: As a result, all the students who leave our school have had a solid math experience in Algebra 1.
"I'm gonna give you the area."
Narrator: Our classroom close-up cameras joined Marlo and Julianna as they each taught the same lesson on the same day in their respective classrooms.
Julianna: "That's exactly right."
Narrator: We begin with an overview of that days' lesson. Later on, we zoom in, taking a closer look at each teacher's style, philosophy, and classroom culture.
Julianna: "Alright. Let's do this!"
Marlo: "Good morning, Pam.
Julianna: "Hi Chances."
Marlo: "Good morning, Nandi. Please sit and get to work, your warm-up is posted today."
I like students to come in to the classroom and get to work independently.
Julianna: "Let's get started, like normal. I'm stamping. I want you to talk about this with the people at your table."
We always start with a warm-up and partly that's to send the message that, like, the minute you walk in, you start doing mathematics. I want them to be talking about their ideas. I want them to be asking questions, and I want them to be interacting with each other.
Student: "I agree with her answer because...well..comb...when you combine like terms, 15x and 4x becomes 19x."
Student: "2x times 3x is 6x to the second power."
Marlo: The warm-up included some multiplication of binomials by creating a rectangle, using the two binomials as length and width, and figuring out the area. That got their brains ready for what we were going to do, which is factoring, just doing the opposite.
"I need you to open your notes to the table of contents"
Julianna: "Get that table of contents going. That looks good. So, we're talking now, how do you factor a trinomial?"
Today, we were introducing factoring trinomials. The trinomial is the product, or the trinomial is the area of a rectangle, and we have to think about what is the length and the width of that rectangle, or what are the factors that make that product?
"We give you what's in the rectangle. What do you have to find?"
Student: "The stuff that goes.."
Julianna: "The stuff that go..."
Student: "On the outside."
Julianna: "OK. So that's, that's exactly right. Now help it. Bring out, bring out that language. So, what is that stuff on the sides called?"
This piece of just going backwards, actually taking the rectangle, the area of the rectangle, and then going backwards and finding the length and the width, helps students' conceptual understanding.
"What goes here? What goes here, to make the area?
Marlo: "In our warm-up, you were given the length and width of a rectangle, and you were asked to find the area. Now, I'm not going to give you the length and the width. What do you think I'm going to give you?"
Students: "The area!"
Marlo: "The area, and what are you going to have to find out?"
Students: "The length and the width."
Marlo: "That's exactly what we're doing today."
Julianna: "Alright. Let's do this! So, let me give you the inside."
Both: "X squared, 12x, minus 3x, minus 36"
Marlo: "I am giving you the area, and I would like you to figure out the length and the width. What did you write here in order to multiply and get X squared?"
Student: "X and X."
Marlo: "Audience, did you think about it like this? X times X equals X squared?"
Students: "Yes."
Marlo: "Alright, now keep going."
The first problem that I gave them had a first term of just a plain X squared, so students could pretty easily say, 'Well, the binomials are both probably going to start with x."
Julianna: "Corey, talk to me about, how are you gonna figure out what goes here, what goes...what...where do you want to go with this, Corey?"
Student: "I think that's negative 3."
Julianna: "Here?"
Student: "Yeah."
Julianna: "Why?"
Student: "'Cuz negative 3 times X equals negative 3x."
Julianna: "Multiplier. That's how you do this. You check yourself by multiplying. That's all you gotta do. Now, we gotta finish this. Somebody's saying 12. Caleb, why?"
Student: "I put 12, because 12 times negative 3, is negative 36."
Julianna: "Oh, he went for this one. He can do that. Twelve times negative 3 equals negative 36. Does this work?"
Student: "Yeah, then X times...times 12 is 12x 'cuz it's a one in front of the x."
Julianna: "What do you think about that? You see how he just went backwards. You started with what's in there, now you've got these."
Marlo: "Length times width equals area. Factor times factor equals product. This is geometric, this is algebraic. Are we OK so far?"
Julianna: "I'm gonna take a step forward on this. It's not gonna be an X squared here. It's gonna be this."
Both: "5x squared, minus 4x, minus 10x, plus 8."
Marlo: "I give you the area, you give me the length and the width."
The next one, I gave them a polynomial that started with 5x squared, but 5, being prime, meant that it was gonna be either 1x times 5x or 5x times 1x."
Julianna: "So, how 'bout 5x and x. Rosa?"
Student: "That wouldn't work because if you have 5x times X, it can make 5x squared...
Julianna: "Sh...sh...let her finish."
Student: "Then if you..."
Julianna: "You got something...It does make this, but..."
Student: "It won't actually make negative 4."
Student: "Yeah."
Julianna: "You see how her brain's working? If you do 5x..."
Student: "You can't do that."
Student: "Five doesn't go into negative 4."
Julianna: "So, this becomes a little game, where you might know that it's 5x and X, but you might put it down, and it don't work. So, you erase it, and you Tiger Up!, and you don't give up. You don't go "Ugh. I'm done. It didn't work." Right? You erase it, and you fix it."
Marlo: "The area of the final rectangle is..."
Both: "12x squared, minus 2x, negative 6x, plus 1"
Marlo: "Twelve has many factors. So, I hope you play around a bit."
The last problem Ms. Jones and I deliberately picked 12 as the coefficient because we wanted students to deal with 'Could be 12 and 1, could be 2 and 6, could be 3 and 4'. We wanted them to experience that it doesn't always happen on the first try, but we just Tiger Up! and we keep on going.
"Good. Some of you are building good math endurance. You can struggle and struggle and struggle, and figure things out."
The more students can get used to being presented with difficult challenges, the more they get used to that, the, the more willing they will be to push past it, and persevere, and the more they'll end up learning.
Julianna: Teaching is as unique as all our students.
"Does it matter?"
There's no one way.
"You bet it does! You bet it matters which way you put it!"
You have to find your own style.
Marlo: I like my classroom to be very predictable. It's very structured, very tidy.
Julianna: Marlo's style is no less exuberant than mine, but it's more reserved.
Marlo: Julianna's very high energy.
Julianna: "I love you though! Like at least..."
I mean, I'm louder, I think. Um....I'm pretty sure.
Marlo: I can hear her from way down the hall sometimes.
Julianna: Our personalities are a little different.
Marlo: But, it's always really positive things that I'm hearing. I'm hearing her cheer for her class, as if she were at a football game or something.
Julianna: "You do know! You do know" Sh!! Sh!!"
Marlo: "Yeah, 5 times 12..."
Julianna: Students are learning in our classroom, and it doesn't matter that we're a little different.
Student: "X times X equals X squared."
Julianna: "Now, there you go. Do this one."
Students know that we care very much about their learning, and that gets communicated, and then students learn.
Marlo: "Go ahead!"
Students: "1,2,3" | 677.169 | 1 |
For introductory undergraduate courses in mathematics and
problem-solving, students preparing for such academic contests as
the William Lowell Putnam Mathematical Competition, and advanced high
school students studying for the American Mathematical Olympiad.
This book presents the principles and specific problem-solving methods
that can be used to solve a variety of mathematical problems. The
book provides clear examples of various problem-solving methods accompanied
by numerous exercises and their solutions.
Introduces and explains specific problem-solving methods
(with examples) and then gives a set of exercises and complete
solutions for each method.
Each chapter includes an additional set of problems to
challenge the reader.
By studying the principles and applying them to the exercises,
the reader will gain problem-solving ability as well as general mathematical
insight.
Eventually, the reader should be able to produce results
that have "the whole air of intuition."
Organized according to specific problem-solving techniques
in separate chapters. These techniques include:
Induction (chapter 4)
Pigeonhole principle (chapter 9)
Chapters and exercises are arranged in order of increasing
difficulty. Presents a wide variety of problems—some old favorites
and some new gems.
Problem sets illustrate significant mathematical ideas
and have elegant but not tedious solutions.
Some chapters also include a moderate amount of "theory"
in order to provide context. | 677.169 | 1 |
NCERT Solutions for Class 9th Maths: Chapter 11 Constructions
Get here Class 9 Maths Textbook book Answers of Chapter 11. NCERT Solutions Class IX Maths includes answers of all the questions of Constructions provided in NCERT Text Book which is prescribed for class 9 in schools.
National Council of Educational Research and Training (NCERT) Book Solutions for Class 9
Subject: Maths
Chapter: Chapter 11 – Constructions | 677.169 | 1 |
Exponential and Logarithmic Functions
4.1 Exponential Functions and Their Applications
4.2 Logarithmic Functions and Their Applications
The Trigonometric Functions
5.1 Angles and Their Measurements
5.2 The Sine and Cosine Functions
5.3 The Graphs of the Sine and Cosine Functions
Trigonometric Identities and Conditional Equations
6.1 Basic Identities
Systems of Equations and Inequalities
8.1 Systems of Linear Equations in Two Variables
8.2 Systems of Linear Equations in Three Variables | 677.169 | 1 |
Note: Citations are based on reference standards. However, formatting rules can vary widely between applications and fields of interest or study. The specific requirements or preferences of your reviewing publisher, classroom teacher, institution or organization should be applied.
Tools of the trade : introduction to advanced mathematics
".Read more...
Sets, functions, and other basic ideas --
Linear algebra --
The construction of the real and complex numbers --
Metric and Euclidean spaces --
Complete metric spaces and the p-adic completion of Q.
Responsibility:
Paul J. Sally, Jr.
Abstract:
Containing the material such as linear algebra, construction of the real numbers via Cauchy sequences, metric spaces and complete metric spaces, this book provides three projects that include a discussion of topics such as group theory, convergence of infinite series, decimal expansions of real numbers, point set topology and topological groups.Read more...
< a schema:Review ; schema:itemReviewed < ; # Tools of the trade : introduction to advanced mathematics schema:reviewBody ""." ; . | 677.169 | 1 |
An Appraisal of Recent Developments in the Curriculum and Teaching of Mathematics at the Secondary Level.
Beckmann, Milton W.
This paper appraises recent developments in the curriculum and teaching of mathematics in the secondary schools and analyzes mathematics education in the United States with particular emphasis on Nebraska. The first section focuses upon characteristics that distinguish the modern secondary school mathematics curriculum from the traditional. The following sections emphasize the understanding and the structure of mathematics. Ability groupings and the various types of programs which have resulted from it are also discussed. Further analyses deal with a college preparatory sequence for Grades 9-12, new mathematics programs to attract and to motivate students, and new techniques in mathematics at the secondary level. Suggestions for implementing new developments are also provided. (RP) | 677.169 | 1 |
Hi! We just started doing a new topic in math about what's the hardest maths question in the world and I did pretty well for most homeworks we had but the latest one my teacher gave confusing so I'd love if somebody will assist me to understand it! It's a problem solving assignment my algebra professor gave out this day and it's due next week and I tried answering it but to no avail . I just can't finish it easily unlike the other homeworks . I had no trouble answering my past assignments but this particular assignment with specific topic of inverse matrices gives me a hard time just figuring out how to begin. I'm desperately in need of help. I'll really appreciate if somebody help me in discussing the steps and how to answer it in a systematic and clear way.
Kids can't seem to think of anything beyond extra classes . Why don't you try something yourself? There are numerous resources for what's the hardest maths question in the world which are a lot better than tutoring. Try Algebrator, and you will never need a tutor.
Some teachers really don't know how to teach that well. Luckily, there are programs like Algebrator that makes a great substitute teacher for algebra subjects. It might even be better than a real teacher because it's more accurate and quicker!
Algebrator is the program that I have used through several algebra classes - Basic Math, Algebra 2 and Remedial Algebra. It is a truly a great piece of math software. I remember of going through problems with multiplying matrices, graphing parabolas and inverse matrices. I would simply type in a problem from the workbook , click on Solve – and step by step solution to my algebra homework. I highly recommend the program. | 677.169 | 1 |
This book provides a set of tools that enables educators to teach mathematics using the framework of System Dynamics. Section 5 covers sinusoidal functions, including simple harmonic motion. Distance versus time lessons using a motion detector are also in
This book provides a set of tools that enables educators to teach mathematics using the framework of System Dynamics. Section 4 reviews previous concepts, combines model structures to solve new problems and extends problems from previous lessons. Availab
This book provides a set of tools that enables educators to teach mathematics using the framework of System Dynamics. Section 3 covers the theory of finite differences for exponential functions. Students build models of many processes, including bacteria
This book provides a set of tools that enables educators to teach mathematics using the framework of System Dynamics. Section 2 on quadratic behavior covers the theory of finite differences and distance-time and position-time exercises using a motion dete
This book provides a set of tools that enables educators to teach mathematics using the framework of System Dynamics. Section 1 on linear motion covers the theory of finite differences and distance-time and position-time exercises using a motion detector.
This book provides a set of tools that enables educators to teach mathematics using the framework of System Dynamics. Section 0 covers basic skills in representing equations using a visual modeling tool, the STELLA software. Available from iseesystems.
From CC-STADUS. A discussion of the single-subject natural "entry points" for system dynamics—areas where systems ideas and models are natural topics. Examples are given for physics, biology, mathematics, social sciences and literature.
From CC-STADUS. The experiences of the CC-STADUS staff and participants in the CC-STADUS Project lead to recommendations and suggestions for model development and documentation, and training programs for teachers. Presented at the 1996 International Syste | 677.169 | 1 |
Class Fee: $55.00
Material Fee: $5.00
ID:9218
This course is designed to help students understand basic mathematical concepts to gain the skills and confidence to do more challenging grade-level math exercises. Topics include: Solving algebraic expressions and equations, relationships between geometric figures, and probability models.
Class Fee: $55.00
Material Fee: $0.00
ID:9197
This course offers guided assistance and study skills instruction for K - 12 students in any level of mathematics. Students must bring textbook and specific questions relating to homework assignments or test preparation materials.
Class Fee: $55.00
Material Fee: $0.00
ID:9230
Prerequisite: Algebra BasicsThis class will introduce students to the building blocks of Geometry. Students will learn the basic terms and properties associated with Geometry and will learn to develop a logical structure where mathematical relationships are proved and applied.
Class Fee: $55.00
Material Fee: $5.00
ID:9215
This course is designed to help students understand basic mathematical concepts to gain the skills and confidence to do more challenging grade-level math exercises. Topics include: Ratios and proportional relationships, understanding of algebraic expressions, and real world and mathematical problems involving area, surface area, and volume.
Class Fee: $55.00
Material Fee: $0.00
ID:9212
This course is designed to help students understand basic mathematical concepts to gain the skills and confidence to do more challenging grade-level math exercises. Topics include: Writing and interpreting numerical expressions, operations with fractions and mixed numbers, and measurement systems and data interpretation. | 677.169 | 1 |
Cart
Olympiad Inequalities
Olympiad Inequalities follows the philosophy that the best way for students to train for high-level competitions, such as the International Mathematical Olympiad, is by solving problems. The book is divided into two standard chapters, the first consisting of the statement of the problems and the second one presenting their solutions. The problems are ordered chronologically, and consequently, the difficulty increases as classical problems give way to more modern ones. Therefore, this book highlights the evolution of the tools and techniques required for solving Olympiad questions while maintaining a constant learning pace according to the reader's individual background. For a good introduction to several methods that lie behind the problems in this book, readers may wish to consult An Introduction to Inequalities, for sale by XYZ Press. | 677.169 | 1 |
Search Results
MATH 277. Mathematics for Elementary Teachers I. 3 Credits.
A course designed to provide elementary teachers with the ability to integrate the understanding of content with the understanding of how students learn arithmetic concepts. Students study the application of arithmetic concepts of the solutions of problems. Mathematical content includes algebra fundamentals, functions, graphing, inductive and deductive reasoning, whole number operations, number bases, numeration systems, place value, number theory topics, sets, integers, decimals, percentages and fractions. Typically Offered: Fall. | 677.169 | 1 |
The new edition of classical mathematical texts, or its recent digitization for the general public, represents an approach to the universe that has been traditionally reserved to historians and other experts on epistemology. Many texts from the 18th century were already presented like works aimed at the explanation of certain mathematical concepts, and the interpretation of the coherence of the mathematical structure and the formal aspects of convincing proofs. The Éléments de géométrie by Alexis Claude Clairaut, that were first published in 17411 is an example of this type of pedagogical texts. Based on an experience with high school students, we examine the development of their mathematical competences through the analysis of one of Clairaut's texts, along with the use of dynamic geometry software. | 677.169 | 1 |
Policies
Training and Development
Functional Skills Maths Mathematics at Entry 1, 2 and 3 is to ensure that learners develop understanding and skills in the three interrelated mathematical process skills of: | 677.169 | 1 |
ribe the Bookmark Collection so other MERLOT users will know what it contains and if it has value for their work or teaching. Other users can copy your Bookmark Collection to their own profile and modify it to save time.
This site relates a Frank Lloyd Wright house to various aspects of three dimensional geometry and uses it to motivate...
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This site relates a Frank Lloyd Wright house to various aspects of three dimensional geometry and uses it to motivate different geometrical drawing techniques. It includes an interactive applet.
Material Type:
Simulation
Author:
Cathi Sanders
Date Added:
Oct 27, 2001
Date Modified:
Jun-D Drawing and Geometry (The Math Forum) to Bookmark material or Course ePortfolio
This site is a collection of activities in Euclidean geometry that encourage the students to explore and practice ruler and...
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This site is a collection of activities in Euclidean geometry that encourage the students to explore and practice ruler and compass constructions using the C.A.R. tools.
Material Type:
Simulation
Author:
Steven Lapinski, Pete Anderson
Date Added:
Jan 19, 2008.A.R.--Compass and Ruler to Bookmark material or Course ePortfolio | 677.169 | 1 |
Mcq math engineering entrance | 677.169 | 1 |
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