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This course will cover the foundations of functional analysis in the context of normed linear spaces The Big Theorems (Hahn-Banach, Baire Category, Uniform Boundedness, Open Mapping and Closed Graph) will be presented and several applications will be analysed. The important notion of duality will be developed in Banach and Hilbert spaces and an introduction to spectral theory for compact operators will be given.
Course description
This course covers major theorems of Functional Analysis that have applications in Harmonic and Fourier Analysis, Ordinary and Partial Differential Equations. This course is a natural follow on of the course Linear Analysis; while the main focus of the Linear Analysis is on Hilbert spaces with its rich geometrical structures this course will work with normed linear spaces. Hilbert space is a special case of a normed linear space. Despite working in this more general framework many results encountered in Linear Algebra will be re-introduced in this course in more general form. For example the spectral theorem will be presented for all compact operators.
Review of linear spaces and their norms.
The Hahn-Banach, Baire Category, Uniform Boundedness Principle, Open Mapping and Closed Graph theorems.
Duality in Banach and Hilbert spaces.
Spectral theory for compact operators on Banach spaces. Fredholm alternative.
Weak topologies, Banach-Alaoglu and the Arzela-Ascoli theorem.
1. Facility with the main, big theorems of functional analysis.
2. Ability to use duality in various contexts and theoretical results from the course in concrete situations.
3. Capacity to work with families of applications appearing in the course, particularly specific calculations needed in the context of Baire Category.
4. Be able to produce examples and counterexamples illustrating the mathematical concepts presented in the course.
5. Understand the statements and proofs of important theorems and be able to explain the key steps in proofs, sometimes with variation. | 677.169 | 1 |
A summary of beginning algebra concepts is presented here, with example problems and solutions. Beginning Algebraic Concepts and Problems Addition and Subtraction EquationsIn kindergarten, children are exposed to linear equations for addition and subtraction. They also learn to add and subtract for numbers 0-5. In first grade, they begin doing more complex problems, using numbers up to 100.
Beginning Algebra includes printable full-colorillustrated notes, automatically graded algebra problems with worked-out answers, and aglossary of mathematical terms, which makes learning beginning algebra online easy.Beginning Algebra is a developmental math course at two-year colleges. The courseincludes factoring, equations, and functions in order to prepare the student for successin college mathematics. | 677.169 | 1 |
Mathematics Class X by R. D. Sharma is designed especially for a student of class 10 under the Central Board of Secondary Education. This book is highly reliable as it is designed according to the syllabus prescribed by the Central Board of Secondary Education and Continuous and Comprehensive Evaluation. This book is very useful to the learner as all the problems in the book are explained with detailed steps. The book also contains over 1400 solved questions that give the student the additional practice that he requires.
About Dhanpat Rai and Co.
This publishing house was first established in 1951 and has since then, being publishing books by various authors and on different subjects. Some of the other books published by this company include Essentials of Mathematics as per New Guidelines of CCE for class 9 by Mamta Batra and Essentials of Mathematics for class 10 by Mamta Batra.
This book is superb. Everyone knows that nothing is going to come from the reader and everything from outside. So this book has so many questions that you can keeep on solving it as much as you want. There is each and every type of question they can ask. They have explained things in a step by step manner which is more easy to understand. You know in guides like oswaal (which actually i have) they dont explain why does it happen. They will just write the solution. So in so many ways r.d shar...
Book is good. contains all contents of NCERT but in a very specialized way. all students of class 10th should must buy it. And a very special thanks to Flipkart. they have packed it very well. and I have got it within 4 days of placing the order. Overall excellent experience
This book is the best in class for mathematics ( CBSE) i have been refering this book since class 9 and it helped me a lot securing gud marks in class 9 and so.... If you are looking forward to buy this book dont stop just click it !!! | 677.169 | 1 |
INTERMEDIATE ALGEBRA Advice
Showing 1 to 3 of 7
I would recommend this class if you have a lot of time to study. The professor teaches well but does not teach every example and there is a lot to learn in each chapter. This math course is also a course where you should learn how to master the basics of math thoroughly because it will advance in college algebra (which is the next math course you would most likely take).
Course highlights:
My highlights of taking this course was understanding the materials taught and getting a good grade on assignments and tests. Learning how to communicate with my professor and classmates when needed to was something that I learned. Taking a math course is difficult to many students so don't be afraid to ask questions. Asking questions can be a key to passing the course.
Hours per week:
9-11 hours
Advice for students:
Study and take notes. Ask questions if you do not understand what she is implying. Take time to study out of class and do all the assignments given. Make sure to be precise with your notes. | 677.169 | 1 |
The purpose of A Guide to Real Variables is to provide an aid and conceptual support for the student studying for the qualifying exam in real variables. Beginning with the foundations of the subject, the text moves rapidly but thoroughly through basic topics like completeness, convergence, sequences, series, compactness, topology and the like. All the basic examples like the Cantor set, the Weierstrass nowhere differentiable function, the Weierstrass approximation theory, the Baire category theorem, and the Ascoli-Arzela theorem are treated.The book contains over 100 examples, and most of the basic proofs. It illustrates both the theory and the practice of this sophisticated subject. Graduate students studying for the qualifying exams will find this book to be a concise, focused and informative resource. Professional mathematicians who need a quick review of the subject, or need a place to look up a key fact, will find this book to be a useful resource too.
"synopsis" may belong to another edition of this title.
Book Description:
This concise guide is an aid and conceptual support for students taking an undergraduate real analysis course. It covers the core topics and focuses on concepts, results, examples and illustrative figures, rather than the details of proofs, in order to remain a concise guide for students to dip into.
About the Author:
Steven Krantz is well-known for his skill in expository writing. He is the author of more than 50 books, and more than 150 scholarly papers. The MAA has awarded him both the Beckenbach Book Prize and the Chauvenet Prize. | 677.169 | 1 |
Mathematics
Senior School At Dianella Secondary College, we offer a range of maths courses to prepare students for the future. We offer ATAR courses for potential university studies such as Methods and Specialist Courses. We also offer Mathematics Applications for students applying for University or TAFE courses where some maths is required. The Mathematics Applications course is recommended to students who are pursuing elite trades, such as Heavy Plant Mechanics, Plumbing and Electrician Apprenticeships. General Maths courses are offered for students planning to attend TAFE/ workforce and Foundation Mathematics for students who are challenged by mathematics. It is vital that all students have an understanding of mathematics principles to be prepared for the future.
Lower School Our lower school students are taught a range of maths concepts as per the WA and Australian Curriculums. These classes are designed to prepare students for NAPLAN and OLNA Testing, as well as Senior School Mathematics Courses
Dianella Secondary College offers students many opportunities to excel in Maths. Year 10 Students can complete a Certificate I in Financial Literacy through The Smith Family. This course educates students in money management and achieving financial goals. Year 7 & 8 students participate in the Reframing Mathematical Futures project, which allows them to participate in inquiry learning to develop the research and analytical skills necessary for future learning.
Our Mathematics team are devoted to helping all student succeed in their math studies and can often be found at the Homework Centre after school each day. | 677.169 | 1 |
Animated
Mathematics
Introduction
This document is based on a talk
at the SVG Open 2003 -
Vancouver. It contains graphics written in
SVG format and in
order to be fully accessible to the reader, it should be viewed by
a browser able to display SVG. As an example "Internet Exporer"
needs a plugin e.g. "Adobe SVG
Viewer" that can be downloaded for free.
The aim of this
document is to present to the
SVG-developers' community some application of SVG
graphics for science education. It
aims also the educators of science by showing them
applications of the recent SVG graphics technique that undoubtebly
could boost the teaching abilities.
About three years ago I decided to work on a teachware project of mathematics intendent for
freshmans of science. Beeing physicist myself with
teaching experience of more than 30 years, it looked to me very
attractive to develop a teaching tool
that can be open with a web-browser not only for
text and graphics, but also for showing animations
and interacting with the user. Animated applets
were new at that time, but their teaching potential was immediately
recognised and I intended to make an ample use of them.
A year ago I was introduced to SVG and
became immediately and unconditionally a fan of it. It has all
the necessary properties of what I could dream of for my project. I
am still a novice in the subject and the animations I am presenting
are lacking for instance interactivity, but even so, I've got so
far a very warm and encouraging response from my friends,
collegues and students.
The curve to be approximated as a chain of Bezier quadratic
curves (a "path" in SVG terms) should not have different points
with the same value of the derivative.
The user should supply the coordinates of the end points of the
curve and also the derivatives there (derivative with infinite
value is acceptable).
The user should supply the maximal allowed deviation (in "user
units" by SVG terms) of the Bezier "path" from the curve. This
value defines the necessary accuracy and is used by the program for
terminating the approximation procedure.
The user should supply a coded Java program ("method" in Java
terms) that calculates the point on the curve for a given value of
the derivative.
When the approximation is achieved, the program outputs the
"path" ready to be plugged in the SVG code.
Since for many people Java is not their cup of tea, but they use
a different program language, here is a detailed presentation of the
algorithm used, so they could apply it on a different platform.
Each link of the present section that follows leads to an SVG file
dispalyed in a separate window. It is recommended to expand the
window to a maximum.
This section contains examples intended to be used in the
teachware project. Each one includes animated graphics usind SVG.
As known "One picture is worth a thousand words". It is a well
known fact that a suitable illustration sometimes can make
understandable a very complicated and difficult descriptions. From
my experience I would dare say that "One animation is worth a
thousand pictures". I hope that the examples given here will
illustrate that point.
As in the previous section each link that follows leads to an
SVG file dispalyed in a separate window. It is recommended to
expand the window to a maximum. Each one of the links is related to
a different subject of simple calculus. One have to follow any
additional link that appears in a SVG file itself.
Inversion
of coordinates shows what kind of transformation is
necessary in order to invert a planar rectangular coordinate
system.
The first
animation shows that a simple rotation in two
dimensions is not enough.
The second
animation shows a three dimensional rotation around
a diagonal axis (of the plane) that performs the required inversion.
In order to achieve the visual effect, SVG uses two static
rotations and an animated scale transformation applied
simultaneously.
The third
animation shows a two-dimensional mirror
transformation that also solves the problem of inversion. The
effect is achieved in SVG by animated stroke-opacity. | 677.169 | 1 |
Geometrical mathematics involves many topics other
than traditional Euclidean geometry. This course explores topics that vary from
semester to semester and may include some, but not all of the following:
symmetry, groups, frieze and wallpaper patterns, graphs, surfaces, knots, and
higher dimensions. Prerequisite: eligibility for Q courses and a
willingness to explore new ideas and construct convincing arguments is a
necessity.
19328
MATH 110†† Precalculus Mathematics
Maria Belk
M . W . .
3:00
pm -4:20 pm
OLINLC
115
MATC
A
course for students who intend to take calculus and need to acquire the
necessary skills in algebra and trigonometry. The concept of function is
stressed, with particular attention given to linear, quadratic, general
polynomial, trigonometric, exponential, and logarithmic functions. Graphing in
the Cartesian plane and developing the trigonometric functions as circular
functions are included.† Prerequisites:
successful completion of Q exam.† ††
19330
MATH 141
A† Calculus I
Cliona Golden
M . W . .
9:00† -10:20 am
HEG
106
MATC
An
introduction to the basic ideas of differentiation and integration in one
variable. Topics include limits, techniques of differentiation, definite
integrals, the fundamental theorem of calculus, and applications.† Prerequisite: Precalculus or the
equivalent. ††
This class will introduce the mathematical ideas
underlying string theory, a theory of particle physics which supposes that the
fundamental constituents of matter and energy are not points, but rather tiny
strings or loops. No prior background in physics is required. We will read and
discuss several popular books on string theory as a means to motivate concepts
from the entire mathematical curriculum. These ideas include: complex numbers, quaternions,
and their generalizations; Taylor series and Fourier series; spaces of
dimensions 4 and higher; the geometry and topology of two dimensional surfaces;
non-commutative algebra; and supersymmetry. Prerequisites: Mathematics 141 or
the equivalent.
Cross-listed:
Cognitive Science†† This course will cover the basics of linear
algebra in n-dimensional Euclidean space, including vectors, matrices, systems
of linear equations, determinants, eigenvalues and eigenvectors, as well as
applications of these concepts to the natural, physical and social
sciences.† Equal time will be given to
computational, applied, and theoretical aspects of the course material.† Prerequisite: Math 141-142 or
permission of the instructor. ††
19077
MATH 242
B† Linear Algebra
With†
Applications
Jules Albertini
M . . . .†
†.
.W . .
3:00
pm -4:20 pm
4:30
pm - 5:50 pm
RKC
101
RKC
101
MATC
See
above.
19078
MATH 261
A† Proofs and Fundamentals
Samuel Hsiao
. T . Th .
10:30† -11:50 am
HEG
106
MATC
This
course introduces students to the methodology of mathematical proof. The logic
of compound and quantified statements, mathematical induction, and basic set
theory including functions and cardinality are covered. Topics from
foundational mathematics are developed to provide students with an opportunity
to apply proof techniques.† Prerequisite:
Mathematics 141 and 142, or permission of instructor.†† ††
19079
MATH 261
B† Proofs and Fundamentals
Lauren Rose
M . W . .
1:30
pm -2:50 pm
HEG
106
MATC
See
above.
19332
MATH / CMSC 303†† Computational Geometry
Mary Krembs
. T . . .
1:00
pm -2:20 pm
RKC
100
MATC
Cross listed: Computer Science†† This class will cover a variety of topics
from computational geometry. Focus will be given to computational complexity of
the algorithms presented as well as appropriate data structures. Topics may
include Voronoi
Diagrams, convex hull calculations, line segment intersections and more.
Pre-requisites: Math 212, Math 242 and some programming knowledge.
19333
MATH 319†† Probability and Statistics
Cliona Golden
. T . Th .
9:00† -10:20 am
ALBEE
106
MATC
Everyday we make decisions based on numerical data
in the face of uncertainty. We do so while reading the latest political polls,
playing a card game, interpreting a medical diagnosis, or analyzing a
scientific experiment. Probabilistic models and statistical methods help us to
think through such decisions in a precise mathematical fashion. This course
provides a calculus-based introduction to techniques and applications of
probability and statistics. Topics considered will include random variables and
their distributions, the Central Limit Theorem, hypothesis testing. Prerequisites:
Math 212. Some
knowledge of Linear Algebra is helpful. For students
concentrating in economics, Math 319 can substitute for Economics 229.
19331
MATH 321†† Partial Differential Equations
John Cullinan
. T . Th .
1:00
pm -2:20 pm
RKC
102
MATC
This course is an introduction to the theory of
partial differential equations. The primary focus is the derivation and
solutions of the main examples in the subject rather than on the existence and
uniqueness theorems and higher analysis. Topics include hyperbolic and
elliptic equations in several variables, Dirichlet problems, the Fourier and Laplace transform,
Green's functions.
19081
MATH 332†† Abstract Algebra
James Belk
. T . Th .
2:30
pm -3:50 pm
RKC
102Mathematics
261 or permission of the instructor.
19334
MATH 432†† Advanced Algebra:
Galois Theory
Lauren Rose
. T . Th .
10:30† -11:50 am
ALBEE
106
MATC
This
course is a continuation of Mathematics 332.†
The primary goal is to develop the Galois theory of fields.† Toward that end we study the theory of field
extensions including algebraic extensions, automorphisms of fields, splitting
fields, and separable extensions.† As
time permits we may develop some topics in advanced group theory such as series
of groups and the Sylow theorems. Prerequisites:†Mathematics 331 and 332, or permission of the
instructor.†
19335
MATH 454†† Knot Theory
Ethan Bloch
M . W . .
1:30
pm -2:50 pm
ALBEE
106
MATC
Knot
theory is an active branch of contemporary mathematics that, similarly to
number theory, involves many problems that are easy to state but
difficult to solve; unlike number theory, knot theory involves a lot of
visual reasoning. Knot theory is a branch of topology, but it also
has applications to aspects of biology, chemistry and physics (though for
lack of time these applications will not be discussed in class).
This course is an introduction to the theory of knots and links.
Topics include methods of knot tabulation, knot diagrams, Reidemeister
moves, invariants of knots, knots and surfaces, and knot
polynomials. Prerequisites: Math 351 or Math 361, or
permission of instructor. | 677.169 | 1 |
In some courses, all it requires to pass an exam is note taking, memorization, and remember. However, exceeding within a math course usually takes a different sort of effort. You cannot simply just show up for any lecture and view your instructor "talk" about geometry and . You find out it by executing: paying attention in school, actively learning, and resolving math complications – regardless if your instructor has not assigned you any. In case you find yourself battling to accomplish perfectly within your math class, then stop by best website for fixing math issues to determine how you may become a far better math student.
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Math programs comply with a pure progression – each builds upon the expertise you've obtained and mastered from the past class. In case you are locating it difficult to abide by new concepts at school, pull out your outdated math notes and critique previous materials to refresh your self. Make certain that you meet the conditions just before signing up to get a class.
Critique Notes The Night Right before Class
Loathe every time a trainer phone calls on you and you have neglected how to address a particular dilemma? Avoid this moment by reviewing your math notes. This will likely assist you to ascertain which concepts or issues you'd love to go above in class the following working day.
The considered executing homework just about every night could appear irritating, but if you would like to reach , it can be important that you continually exercise and master the problem-solving procedures. Make use of your textbook or on the internet guides to work by way of top rated math troubles over a weekly foundation – even when you have no homework assigned.
Make use of the Supplements That come with Your Textbook
Textbook publishers have enriched present day publications with additional material (such as CD-ROMs or on the web modules) that could be accustomed to help students achieve more observe in . Many of these materials might also include an answer or explanation guidebook, that may enable you to with functioning as a result of math complications yourself.
Examine Ahead To remain In advance
If you need to lessen your in-class workload or perhaps the time you invest on research, use your spare time right after university or about the weekends to go through ahead into the chapters and ideas that may be coated the subsequent time that you are at school.
Overview Old Tests and Classroom Examples
The function you do in class, for homework, and on quizzes can provide clues to what your midterm or remaining exam will glance like. Make use of your aged assessments and classwork to create a individual review manual for the future exam. Glance within the way your trainer frames concerns – this can be possibly how they will look in your examination.
Figure out how to Function Because of the Clock
That is a well known research suggestion for folks getting timed examinations; primarily standardized tests. In the event you have only forty minutes for your 100-point check, then you can certainly optimally shell out 4 minutes on each individual 10-point dilemma. Get details regarding how extensive the test are going to be and which types of issues will be on it. Then approach to assault the easier thoughts very first, leaving you sufficient time for you to expend around the more demanding ones.
Improve your Methods to receive math homework assist
If you are obtaining a tough time knowing concepts in school, then you'll want to get aid outside of class. Talk to your buddies to make a examine group and visit your instructor's office environment hrs to go around tricky difficulties one-on-one. Show up at study and evaluate classes when your instructor announces them, or employ a private tutor if you need one particular.
Talk To Oneself
Once you are reviewing difficulties for an examination, attempt to clarify out loud what approach and solutions you accustomed to obtain your answers. These verbal declarations will occur in useful for the duration of a check once you need to remember the steps it is best to get to find a solution. Get extra apply by striving this tactic with a buddy.
Use Study Guides For More Exercise
Are your textbook or course notes not aiding you understand that which you must be learning at school? Use research guides for standardized exams, like the ACT, SAT, or DSST, to brush up on aged materials, or . Review guides generally arrive outfitted with complete explanations of the way to remedy a sample dilemma, , and you simply can often obtain in which could be the much better obtain mathcomplications. | 677.169 | 1 |
The books are PDF files and we have added bookmarks to aid navigation, and reader-extended them so that learners can use the comment, markup and drawing tools to type answers and complete some of the exercises on screen.
(We've not added answer boxes to these books because: there are few questions that can be answered with plain text answer boxes (the maths is more advanced); in many cases there isn't space on the page to insert the answer boxes; and we're still working on the earlier levels.)
These books are for learners who cannot read or access the paper copies, and we've had feedback that they are helpful for learners with visual impairment, physical disability, dyslexia and ASD. | 677.169 | 1 |
Professor John Stillwell writes, in the preface to his book Numbers and Geometry (New York: Springer-Verlag, 1998):
"What should every aspiring mathematician know? The answer for most of the 20th century has been: calculus. . . . Mathematics today is . . . much more than calculus; and the calculus now taught is, sadly, much less than it used to be. Little by little, calculus has been deprived of the algebra, geometry, and logic it needs to sustain it, until many institutions have had to put it on high-tech life-support systems. A subject struggling to survive is hardly a good introduction to the vigor of real mathematics.
". . . . In the current situation, we need to revive not only calculus, but also algebra, geometry, and the whole idea that mathematics is a rigorous, cumulative discipline in which each mathematician stands on the shoulders of giants.
"The best way to teach real mathematics, I believe, is to start deeper down, with the elementary ideas of number and space. Everyone concedes that these are fundamental, but they have been scandalously neglected, perhaps in the naive belief that anyone learning calculus has outgrown them. In fact, arithmetic, algebra, and geometry can never be outgrown, and the most rewarding path to higher mathematics sustains their development alongside the 'advanced' branches such as calculus. Also, by maintaining ties between these disciplines, it is possible to present a more unified view of mathematics, yet at the same time to include more spice and variety."
Stillwell demonstrates what he means about the interconnectedness and depth of "elementary" topics in the rest of his book, which is a delight to read and full of thought-provoking problems.
I would second that, and add a recommendation for "Chapter Zero" which is a book targetted at the high school/early college level which provides an introduction to those fundamentals that are often skipped in the rush towards calculus.
right? I have not read this particular book, but in general most students who desire to study math should take a look at a "transitions course" textbook or two, to fill in the gaps left by studying only in the fast lane to calculus.
I agree agree that probability and statistics are much more important in life than just calculus. That is why in college I am studying Artificial Intelligence and Machine Learning - these are all math and probabilities.
Yet, I think Arthur Benjamin is right but for the wrong reasons:
1. People should know statistics instead of Calculus.
To know probability well you need to have mastered calculus. All the distributions, all the formulas build on things like sequences, and integrals.
2. If everybody knew statistics we wouldn't be in the economic mess.
Plain speculation. The majority people who have important part in the management of banks know statistics.
3. from continuous mathematics to discrete mathematics...
Probability and statistics involves tons of continuous mathematics and Analysis. Is a Gaussian distribution discrete? Is the Central Limit Theorem discrete?
The reason probabilities and statistics is important is because it lets people better understand why stuff around them happens and lets them reason about uncertain processes. Life is behavior under uncertainty.
I believe it is important to remember that Arthur Benjamin is referring to High School Mathematics.
To know probability well you need to have mastered calculus.
I won't argue that point itself. However, given that the audience for this mathematics education is High School Students, we won't have to go that far. Regression lines, standard deviations, and Simpson's paradox can be understood without Calculus. Personally, more time should be focused on the analysis and application (again, at a High School Level).
I would go further and not only teaching probability and statistics, but also teach basic calculus with simple polynomials, programming, Monti Carlo simulations, sines and cosines, computer simulations, all starting around age 13.
Advance algebra, geometry, and full trigonometry are not required for any of that.
Why make students wait until senior year or college to experience the fun stuff?
An understanding of statistics wouldn't realistically change all of these things. In practice, people can always be swayed by a powerful rhetoric, emotions, and cultural habit. Statistics lend more weight to arguments, but only a tiny fraction of people will go back and verify a statistic for accuracy.
The rational reason to vote is not because your vote actually has an effect on the election's outcome. Rather, it is because if nearly no one voted, then politicians would have no incentive to take care of the needs of the people. The reason why representative democracy works (when it does work) is because the people have the power to remove politicians from office (or prevent their reelection).
Of course, it is unwise to limit your involvement in government to merely voting, but that is a separate topic.
You believe there is no rational reason for you to vote, yet you vote anyway? So you believe that acting irrationally is a good thing to do?
I can see how we might differ in opinion about what is the rational action in a given situation, but I have a hard time understanding how we can agree on the correct action to take, but disagree as to its rationality.
Rationally the effort of you, personally, going to vote only matters if it changes the outcome. However the odds of a single vote doing that are very, very low. The odds of it changing the reported statistics even by 0.1% are also low. At a national level the odds of doing either are effectively non-existent.
Therefore rationally there is no point in an individual voting.
I know this. But emotionally I feel better knowing that I tried to use my voice, even though logically I know that the act was meaningless. I long ago came to accept that my emotions do not respond to logic, and therefore I have come to let emotion drive my goals, and then use logic to achieve those goals.
Therefore I am willing to engage in a logically pointless activity in return for the emotional satisfaction I derive. Even though I am aware that the emotional satisfaction is illogical.
You're doing a lot of assuming you're right, and then concluding that anyone who disagrees with you is wrong. That's poor reasoning. In particular you say
If you find that rationality and logic indicate that an individual should not vote, then you haven't used enough of them.
Specifically, if everyone was rational according to the definition you're implying, then bad things would happen. That sounds to me like it's the wrong definition.
You have reasoned from the premise to an apparently absurd conclusion, and therefore conclude that the premise was wrong. But in fact what you should do is look farther to see whether the premise is, in fact, RIGHT! To that end I strongly recommend that you read The Logic of Collective Action by Mancur Olson. This sets out the classic theory of public goods which, among other things, concluded that very often bad things happen if everyone acts in their own self interest.
Now rather than seek a reason to reject the premise, analyze it. My claim is that if your reason for voting is X (for any particular X you want), then unless your act of voting has a chance of affecting X, you logically shouldn't spend energy voting. Why would that be? Well when you vote you have a cost (your effort) and a reward (something you care about becomes more likely). If your expended effort has essentially chance of resulting in a reward, then logically that effort was wasted.
This applies whether X is "get the election outcome you want" or "makes politicians care about the electorate" (which is the reason you gave for why people should vote) or anything else. If your vote isn't the deciding factor one way or another, then it is a waste of energy for you to vote. And that applies to both of the criteria I just listed.
In fact if you want to make politicians care it is far, far more effective to send an email, make a phone call, or send a piece of snail mail. Then you get to not just make them aware that someone is out there, but you actually get to tell them your specific concerns. Now odds are that you won't sway them. But the effort involved is on part with voting, and it is much more effective. So if you're willing to vote to make them care, you should send email about something every weekend!
When you look at things this way, my voting actually is logically defensible. After all the warm fuzzies I get from my emotional reaction to voting is a guaranteed return on effort that justifies the effort I expend. There is no question that the act of my voting makes the difference in my getting that feeling. So it makes sense for me to vote.
The guy's rhetoric is pretty divorced from the sad state of actual math education today. The way that the standard math curriculum today heads up to a point in a pyramid is a problem in itself since a lot of the topics are made dull in themselves ("This is just something you need to learn for calculus" is a terrible answer for "why should I learn this?" but substituting "Statistics" wouldn't change things much). It doesn't really matter what the point of the pyramid is when most people never get there.
Just as much, the latest economic meltdown was engineered and believed in by statistics experts. For every Mandlebrot debunking the events, there were ten Myron Scholes basking in the glory of validating Wall Street's delusions with some mathematical magic. Statistics doesn't protect from wishful thinking outside of controlled, experimental situations.
And statistics in daily life? One might use some basic probability but the only other use it would have would sorting the pseudo-statistical rhetoric used by the media. A simple course in mathematical literacy with an emphasis on fallacies would be best for sorting this stuff. BUT again, no course can protect from wishful thinking, can protect people from the fallacies that let them ignore possible later dangers for immediate apparent gain. Further, a non-calculus-based statistics or mathematically literacy course isn't a basis for further scientific study the way calculus is, and believe-it-or-not some students still become physicists, chemists and engineers where calculus is indeed the foundation.
I could narcisistically say that my favorite, evolutionary game theory, would make a much better "point" for the curriculum pyramid but really, what is needed is to make every math class interesting in and of itself. With TV-dazed kids and math-apathetic teachers, I don't know if any curriculum could change things BUT I would want to have the curriculum of every class interesting and mentally challenging - taught axiomatically, Algebra and Geometry ARE interesting in and of themselves and a student needs no background at all for them. Math should be rigorous, conceptually challenge and optional past the basics. It seems like we'd need a different world for this but small steps are being made.
Firstly, Art is actually a math professor, and dealing with the low standards of incoming students is a major concern. I don't think he is "divorced from the sad state of actual math education today."
But even more, you say:
> ... taught axiomatically, Algebra and Geometry
> ARE interesting in and of themselvesI think we all agree that classes in general should be stimulating and interesting, andshould be better tailored to suit the needs of the individuals, but that's the problem. For a given child we don't know what they'll need, and we don't know what they'll like, and every answer will be different.
The problem is "one class fits all" and that's not going to change simply by re-writing the curriculum.Uh, yeah I've dealt with those students. Notice the last part I add - optional. The thing that kills math interest utterly is those "required" classes which teach nothing to the uninterested.
Modern schooling drags the uninterested through a process of making motions towards understanding - we all know its a waste of time. It really would be better to give up until the students are interested. A motivated student can learn more in a day than the bored learn in the semesters of basic math. That might put you out of a job but those jobs just shouldn't exist. Sorry.
Won't put me out of a job - you've jumped to an incorrect conclusion. I'm not a teacher. I run two companies, and I go out to schools to give talks on why math is fun, interesting, useful, and occasionally exciting. Most of the students I deal with are motivated and interested, but even then, some don't like puzzles, and don't like starting from the ground up axiomatically.
This Saturday I'm talking about the Banach-Tarski theorem, and I'm starting from the result, then wroking backwards, deciding what we need to know as we peel it back. I've found that working backwards from a surprising result can create motivation to understand, but sometimes it causes the students to dismiss the whole thing as useless, pointless and irrelevant.
At the same time, it seems like the social attitude towards mathematics has reached the point where it would be useful for schools to ask students to put aside some of their initial attitude towards math.
The best teachers I've had often demanded more than I was initially capable of accomplishing. It's true that such teachers risked losing some of their audience. But if we don't have such teachers we risk even more.
Statistics is a very interesting subject, and it is a distinct subject from mathematics proper. Here (in what is becoming a FAQ post for HN) are two favorite recommendations for free Web-based resources on what statistics is as a discipline, both of which recommend good textbooks for follow-up study:
"Advice to Mathematics Teachers on Evaluating Introductory Statistics Textbooks" by Robert W. Hayden
I think this is directed mostly at the people who will never take another math class after they leave high school. Speaking from a canadian perspective, I had Grade 11 Math, Grade 12 Math, and Calculus classes. about half of the work in grade 12 was directly preparatory for the calc class. Students persuing a trade/vocational school or no post secondary education would only have taken 11 and 12 math. if the half of the math class that was 'wasted' calc prep was replaced with 'probability in the real world' type material, you'd still be in the basic precalc stats area, but possibly giving something more useful to the kind of people that are not well represented at a site like this.
True, but you don't need a lot of calculus to do a large amount of interesting statistics and probability. And the little you do need is probably better being taught as needed in response to actual problems showing up. Most people learn better when they see a clear reason for what they are being taught.
Start with discrete probability, no calculus needed. Then when you move to continuous case show how integrals show up naturally in place of sums, and hey presto a clear and obvious intro calculus which far more people will understand the use for.
Calculus is beautiful and it is absolutely necessary for all physical sciences and has serious applications for financial sectors, computer science, and many other fields as well.
However, for the average person who is not going into any technical field, probability will have a far greater impact on their day to day lives than calculus. Probability is useful for everyone in this world.
Anecdotally, I have a bachelor's in mathematics. It occurred to me several years later when I went back to start on my master's that I had virtually never used calculus after graduating and had to review a lot of my basic calculus notes.
At the high school level you don't really know what you'll be doing 15 years later? You should have a complete grounding, so that you can make those decisions and not have to play catch up later on. I am not saying probability and stats are less important (probability is as important and increasingly stats), but you need calculus as well, at least a good basic grounding.
Agreed, but that is not the question. I would love to see everyone holding a diploma walking out with some knowledge of both calculus and statistics.
The question is given limited time in school, which is more important and useful for the average person? I think the answer is statistics and probability. People confront probability and statistics in the news all the time and make practical decisions based on what they think is more likely. Most people can apply probabilities in their daily life, few people in nontechnical fields will use calculus.
I brought up my own experiences to point out that as a former military analyst and current DBA and programmer I have used basic statistical knowledge on a regular basis. I have used knowledge of Calculus so little in my daily life and job that I had to give myself a very thorough refresher when I returned to an academic study of mathematics.
As a counter point, I have a masters in math, but highschool calculus almost drove me away from math completely. It was very obtusely taught and by far the dullest course I took in highschool.
The amount of calculus you actually need for high school science is both a lot less than what is taught at high school and different calculus than is taught at high school. I agree that most of calculus should be left to university since they're going to have to re-teach most of it anyway to undo the damage done by a bad high school curriculum.
Hmm. Maybe what I really meant was: this has been submitted at least twice before, three and four months ago or so, and in neither case did it generate any discussion.
I hope it does this time, because it's been shown to be interesting enough to be "discovered" by more than one participant.
And I do. I've never understood the US schools emphasis on calculus, and building it up to be such a huge deal. I first did calculus aged 16 in Year 10, and it was just another part of the syllabus. One more step to understanding the way stuff works.
Replacing it by another "BIG IDEA" seems not necessarily to be a Good Thing(tm). Perhaps there should be more of a plain, and less of a pyramid.
I agree that more elementary stats done earlier would be a really Good Thing(tm), but replacing one pyramid with another does not seem to me to be so.
First there is the recognition that there is no pyramid. Since math is so highly interrelated, learning about one area almost always helps understanding in a different area. Granted some areas require a certain prerequisites, hence you will encounter peaks, but I agree aiming for only one peak does not make all that much sense since calculus is only useful in certain situations.
Maybe it's built in "pyramid" like this because:
1. Knowledge is hierarchical
2. Calculus has a longer list of skills that needs to be mastered before learning the subject.
3. Historically, calculus came around first (am I right?). This might not be a coincidence.
Understanding (the path to knowledge) might be hierarchical but knowledge in general isn't. Organizing knowledge in hierarchies is a conventional teaching technique, and that has some self-fulfilling qualities: if you teach people in hierarchies, they'll see the world that way. | 677.169 | 1 |
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Objective : Understand how Mathematica can be an especially powerful and useful tool to solve complicated scientific problems in a smart, efficient and quick way.
Program and content :
Teaching goals:
Mathematica is a general software designed for scientific and technical calculation in various fields such as Physics, Mathematics, Biology, Computer Sciences, Economics, Finance, etc. It makes use of the newly named "Wolfram Langage".
It is especially a high level symbolic language allowing to deal with a wide range of common programming styles in a very flexible way. The essential unifying principle of Mathematica is the concept of expression. Each mathematical object has the same underlying structure, allowing Mathematica to cover various fields with quite a few basic operations and making it very quick and easy for an engineer to solve complex problems.
The aim of this course is to learn the structure of the Wolfram Langage in order to apply it to various fields of physics, mathematics or computer sciences using different programming styles : iterative programming (classical but not very efficient), object-oriented programming, functional programming, pattern recognition programming, etc, each of those methods having specific advantages according to the nature of the problem to be solved.
We will also see numerous functions available to directly solve some problems such as numerical or symbolic calculation, graphics functions, functions for data analysis, monte-carol simulations, etc.
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Reading:
A single number in the reading column means to read that entire
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number, it means up to the first heading on that page. The same
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section.
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These are minimal recommended problems to prepare for the next day's
quiz on the reading. Be sure you can do them. In addition, we
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how you would do them. Note that R1.[5,9,15] means R1.5, R1.9, R1.15.
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These are the labs that you will work on that day. Unless otherwise
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This volume is intended to serve a dual purpose. The first ten chapters form the basis for a course in Group Theory, including exercises at the end of each chapter. The final ten chapters are designed as useful optional material in a course or as reference material. When used as a textbook, this book is intended for students who have had an introductory course in Modern Algebra (such as that taught from Birkhoff and MacLane's A Survey of Modern Algebra). This book was developed from lecture notes on a course of Group Theory delivered by the author at Ohio State University over a period of years, The first ten chapters (the core course) covers: 1. Algebraic Laws, Definitions for Groups; Subgroups, Cosets, etc. 2. Normal Subgroups and Homomorphisms 3. Elementary Theory of Abelian Groups 4. Sylow Theorems 5. Permutation Groups 6. Automorphisms 7. Free Groups 8. Lattices and Composition Series 9. A Theorem of Frobenius; Solvable Groups 10. Supersolvable and Nilpotent Groups The final ten chapters of reference material covers: 11. Basic Commutators 12. The Theory of p-Groups; Regular p-Groups 13. Further Theory of Abelian Groups 14. Monomial Representations and the Transfer 15. Group Extensions and Cohomology of Groups 16. Group Representation 17. Free and Amalgamated Products 18. The Burnside Problem 19. Lattices of Subgroups 20. Group Theory and Projective Planes Hardback in burgundy cloth, ppxiii, 434, including Bibliography, Index, and Index of Special Symbols.
"synopsis" may belong to another edition of this title.
Product Description:
Perhaps the first truly famous book devoted primarily to finite groups was Burnside's book. From the time of its second edition in 1911 until the appearance of Hall's book, there were few books of similar stature. Hall's's ""Theory of Groups"".From the preface to the second edition (1976): 'The's ""A Survey of Modern Algebra"". I have tried to make this book as self-contained as possible, but where background material is needed references have been given, chiefly to Birkhoff and Mac Lane'.
About the Author:
Marshal Hall, Jr., (1910–1990) worked in Naval Intelligence during World War II, including six months in 1944 at Bletchley Park in the UK, the famed center of British codebreaking. He taught at Ohio State from 1946 until 1959, when he joined the faculty at the California Institute of Technology. In 1971 he became the first IBM Professor at Caltech, the first named chair in math. He retired from Caltech in 1981 and later taught at Emory University. In addition to group theory, he made significant contributions to combinatorics and other areas. | 677.169 | 1 |
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Content ratings help you understand the type of content you might find in an app or game, so you can decide if they are suitable for you and your family. Press the down-arrow key and enter the right side of the equation to be solved in E2. Find the length of one side s of each square. HippoCampus is not a credit-granting organization, and does not monitor, grade, or give transcripts to anyone using the site. Test and quiz key -66842003. Until group work started in middle school, he liked math and considered himself good at it. Most of the other content requires a resolution of 600x800 or higher. Do you have any questions to ask us. Freeman and Company, solve wronskian calculator, inequality calculator, sumnation calculator, properties of exponent calculator, steps to write chemical equations, factor expression on ti-84. Creating Collaborative Classrooms Traveling Workshop SeriesJoin CPM for a day of free professional learning. Step by step insights will get you in motion. 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Share or assign lessons and chapters by clicking the "Teacher" tab on the lesson or chapter page you want to assign. Softonic uses the rating systems by PEGI and ESRB. Whether or not these differences occurred for all levels of students in the classes was also investigated. Lial, Callie J Daniels, David Then 10 - Help thanks wow study guide equals the number of pounds of the chocolate candy. Perry's Pre-Algebra 193 Chapter 13 Practice Workbook. From Site Map Page The Site Map Page for the site will contain a link for every pdf that is christmas homework pass printables for downloading. I really appreciate it. Sign in or create an account Search by title, author, isbn, etc. Our Math Coaches and Teacher Leaders have provided a multi-layered effect that encourages the math operations worksheets of change in the pedagogy of math instruction. So that can be what you mean by an American approach. 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Indeed a key element in curriculum design is to provide for continuous cor-rection and improvement. Textbook: Marsden and Tromba. The Textbook is similar to the one that I use for Algebra 1. Click here for our Terms of Use and our Privacy Policy. With Queri, you get the same help at your own time and pace, and for less money. Downloads paid by PayPal may take up to 24 hours to show up in your e-mail box. I'm so happy because it takes me forever to do my homework when I don't know 1 SINGLE problem. CORD set the standard by creating the first truly contextual-based Algebra 2 textbook in 2008. This will insure you'll always know what I've been up to and where you can find me. Decent nights in Washington and Oregon, you put those together, he could be sitting at 1016 conservatively by the end of the month. Follow 4 answers 4 Report Abuse Are you sure you want to delete this answer. Calculus is on its way. If you are even luckier, the answer provided will be correct and will have some good explanation to go with it. I've read articles that call you and Bob Frankston the "fathers basic questions to get to know someone the personal computer revolution. Attendees agree to these terms and conditions by registering for this workshop. He worked frantically on it until - just ten minutes short of the deadline - he found a method that worked, and daily planner template finished the problems definition of judicial review for kids as time was called. What is the length of the sides of the frame. Influenced upon public opinion Lakshmi lay with Kubera. If you can get your school to allow you to work independently during the CPM time-slot even better, a small group of like-minded studentsso much the better but if you cannot, compensate by supplementing on your own time. Lightner Fayetteville State University 46 Sales Management Training Program Network A 0 2 2 0 2 FinishStart D 2 4 2. 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Use trigonometry to calculate unknown angles in right-angled triangles.
List outcomes for multi-step chance experiments and assign probabilities for these experiments.
Calculate quartiles and inter-quartile ranges.
Advance:
During the course, if the student is identified as capable, he/she will receive extra-training to go above the current year level curriculum
Advance mathematical proof: proof by direct proof, by contradiction and by induction
Advance plane geometry
3D visualisation
Introduction to Calculus
Statistical Analysis
Should the student be willing and capable, he/she will be offered training for the following competitions:
Australian Mathematics Competition
Mathematics Challenge for Young Australians
Australian Intermediate Mathematics Olympiad
Exceptional students will receive:
Recommendation to UWA Academy for Young Mathematicians
Invitation to national and international competitions such as Tournament of Towns and Australian Mathematics Olympiad
A chance to join WA Maths Olympiad team
Maths Application: Students will be able to:
Understand the concepts and techniques, as well as applying reasoning skills and solve practical problems in consumer arithmetic, algebra and matrices, shape and measurement, univariate data analysis and the statistical process, linear equations and their graphs, and applications of trigonometryConstruct proofs of results in a variety of contexts, including algebraic and geometric
Interpret mathematical information and ascertain the reasonableness of their solutions to problems.
Maths Application: Students will be able to:
Understand the concepts and techniques, as well as applying reasoning skills and solve practical problems in bivariate data analysis, growth and decay in sequences, graphs and networks, time series analysis, loans, investments and annuities, and networks and decision mathematicsEvaluate the reasonableness of their solutions to problems and their answers to questions
Choose and use technology appropriately and efficiently.
Maths Methods: Students will be able to:
By the end of this unit, students:
Understand the concepts and techniques, apply reasoning skills and solve problems in calculus, probability and statistics.
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Low cost math gurus on line
Math classes observe a natural progression – each builds on the information you have received and mastered from your former training course. For those who are discovering it hard to adhere to new principles in school, pull out your old math notes and critique former content to refresh you. Be sure that you satisfy the prerequisites just before signing up for just a class.
Overview Notes The Night In advance of Course
Dislike any time a trainer phone calls on you and you have overlooked the way to address a selected difficulty? Keep away from this second by examining your math notes. This can enable you to determine which concepts or queries you'd want to go above in school another day.
The considered executing homework each individual night time could appear irritating, but when you would like to succeed in , it is important that you repeatedly follow and grasp the problem-solving methods. Make use of your textbook or on the web guides to operate through leading math issues on the weekly basis – regardless if you've no homework assigned.
Make use of the Health supplements That come with Your Textbook
Textbook publishers have enriched present day publications with more material (which include CD-ROMs or on the internet modules) that can be accustomed to assistance learners gain further exercise in . Many of these elements can also incorporate an answer or clarification guideline, which could help you with performing through math complications yourself.
Read Ahead To stay Ahead
If you prefer to minimize your in-class workload or the time you commit on homework, use your free time soon after university or around the weekends to read through ahead to the chapters and ideas that will be covered another time you are in class.
Overview Old Assessments and Classroom Examples
The get the job done you are doing at school, for research, and on quizzes can provide clues to what your midterm or ultimate examination will look like. Make use of your aged assessments and classwork to make a particular review guideline for the approaching test. Appear at the way your instructor frames thoughts – that is almost certainly how they'll show up in your examination.
Discover how to Do the job Because of the Clock
This can be a well known review idea for people today using timed tests; in particular standardized checks. In the event you have only 40 minutes for any 100-point exam, you'll be able to optimally commit 4 minutes on every single 10-point query. Get data about how long the exam are going to be and which kinds of thoughts will be on it. Then prepare to assault the easier issues to start with, leaving yourself ample the perfect time to expend to the extra complicated ones.
Maximize your Assets to have math homework assistance
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Talk To Oneself
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Use Review Guides For Additional Observe
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An understanding of the developments in classical analysis during the nineteenth century is vital to a full appreciation of the history of twentieth-century mathematical thought. It was during the nineteenth century that the diverse mathematical formulae of the eighteenth century were systematized and the properties of functions of real and complex variables clearly distinguished; and it was then that the calculus matured into the rigorous discipline of today, becoming in the process a dominant influence on mathematics and mathematical physics.
This Source Book, a sequel to D. J. Struik's Source Book in Mathematics, 1200–1800, draws together more than eighty selections from the writings of the most influential mathematicians of the period. Thirteen chapters, each with an introduction by the editor, highlight the major developments in mathematical thinking over the century. All material is in English, and great care has been taken to maintain a high standard of accuracy both in translation and in transcription. Of particular value to historians and philosophers of science, the Source Book should serve as a vital reference to anyone seeking to understand the roots of twentieth-century mathematical thought | 677.169 | 1 |
Education and Human Development Master's Theses
Technology is the technical means people use to improve their surroundings. People use technology to improve their ability to do work. Classrooms around the world have implemented many forms of technology to enhance student interest and achievement. One form of technology that is common to math classrooms is the graphing calculator. One eighth grade math class of nineteen students from an urban middle school was taught a unit on Solving Systems of Equations by Graphing. The unit was implemented with and without the use of the graphing calculator. Students were first introduced to the unit through the use of pencils ...
Faculty Work Comprehensive List
Algebra deals with more than computations such as addition or exponentiation; it also studies relations. Calculus touches on this a bit with locating extreme values and determining where functions increase and decrease; and in elementary algebra you occasionally "solve" inequalities involving the order relations of < or ≤ , but this almost seems like an intrusion foreign to the main focus, which is making algebraic calculations.
Relational ideas have become more important with the advent of computer science and the rise of discrete mathematics, however. Many contemporary mathematical applications involve binary or n-ary relations in addition to computations. We began discussing this topic in the last chapter when we introduced equivalence relations. In this chapter we will explore other kinds of ...
Honors Scholar Theses
Differential equations are equations that involve an unknown function and derivatives. Euler's method are efficient methods to yield fairly accurate approximations of the actual solutions. By manipulating such methods, one can find ways to provide good approximations compared to the exact solution of parabolic partial differential equations and nonlinear parabolic differential equationsTextbooks Collection
Grades 7-8 Mean, Median, And Mode, Rich Miller Iii
Math
This lesson is a math lesson for seventh and eighth grade students on mean, medium, and mode. Through this lesson students will be able to understand the measures of central tendency and their definitions, how to calculate them and what steps are involved, and how the theories can be applied on real life. In this lesson, students are tiered by ability and are able to pick a project based off of their interest and the math concept they are working on. Each activity has a tiered task card to guide the students.
Faculty Authored Books
Active Calculus 2.0, Matthew Boelkins, David Austin, Steven Schlicker
Open Textbooks
Active Calculus is different from most existing calculus texts in at least the following ways: the text is freely readable online in HTML format and is also available for in PDF; in the electronic format, graphics are in full color and there are live links to java applets; version 2.0 now contains WeBWorK exercises in each chapter, which are fully interactive in the HTML format and included in print in the PDF; the text is open source, and interested users can gain access to the original source files on GitHub; the style of the text requires students to be ...
Theses and Dissertations
To master material, students need to make it their own. As teachers, we should structure their interactions with mathematics in ways that are memorable, meaningful, and fun. One way to do this is to provide activities that stretch beyond the textbook and lead students to think and talk to one another about mathematics. This thesis contains a set of activities designed to enhance a precalculus course, along with solutions and feedback on each activity.
Calculating The Time Constant Of An Rc Circuit, Sean Dunford
Undergraduate Journal of Mathematical Modeling: One + Two
In this experiment, a capacitor was charged to its full capacitance then discharged through a resistor. By timing how long it took the capacitor to fully discharge through the resistor, we can determine the RC time constant using calculus.
All Articles in Mathematics
Three Environmental Fluid Dynamics Papers, Eden Furtak-Cole
All Graduate Theses and Dissertations
Three papers are presented, applying computational fluid dynamics methods to fluid flows in the geosciences. In the first paper, a numerical method is developed for single phase potential flow in the subsurface. For a class of monotonically advancing flows, the method provides a computational savings as compared to classical methods and can be applied to problems such as forced groundwater recharge. The second paper investigates the shear stress reducing action of an erosion control roughness array. Incompressible Naiver-Stokes simulations are performed for multiple wind angles to understand the changing aerodynamics of individual and grouped roughness elements. In the third paper ...
All Dissertations, Theses, and Capstone Projects
In this dissertation we prove new results on the existence of infinitely many solutions to nonlinear partial differential equations that are perturbed from symmetry. Our main theorems focus on polyharmonic Dirichlet problems with exponential nonlinearities, and are now published in Topol. Methods Nonlinear Anal. Vol. 50, No.1, (2017), 27-63. In chapter 1 we give an introduction to the problem, its history, and the perturbation argument itself. In chapter 2 we prove the variational principle of Bolle on the behavior of critical values under perturbation, and the variational principle of Tanaka on the existence of critical points of large augmented ...
Peter Martin
In patients with recurrent Hodgkin or non-Hodgkin's lymphoma, autologous stem cell transplantation (ASCT) can offer potential for cure or long-term remission. Because of potential toxicity, elderly patients are usually not considered candidates, but data regarding tolerability and efficacy in this group are lacking. The transplant database at Weill Cornell Medical College was reviewed to identify patients with lymphoma undergoing ASCT at age 69 or greater. Clinical data and comorbidities were correlated with outcome. Twenty-one patients were identified. Sixteen of 19 evaluable patients (76%) achieved complete remission following ASCT, while 2 patients died before response assessment. Median progression-free survival following ...
Ronald Greenberg
Abstract. This paper can be used in two ways. It can provide reference information for incorporating diagonal elements (for bracing or gear meshing) in educational robots built from standard LEGO kits. Alternatively, it can be used as the basis for an assignment for high school or college students to recreate this information; in the process, students will exercise skills in both computer programming and data analysis. Using the paper in the second way can be an excellent integrative experience to add to an existing course; for example, the Exploring Computer Science high school curriculum concludes with the units "Introduction to ...
Ronald Greenberg
Magic tricks based on computer science concepts help grab student attention and can motivate them to delve more deeply. Error detection ideas long used by computer scientists provide a rich basis for working magic; probably the most well known trick of this type is one included in the CS Unplugged activities. This paper shows that much more powerful variations of the trick can be performed, some in an unplugged environment and some with computer assistance. Some of the tricks also show off additional concepts in computer science and discrete mathematics.
An Investigation Of Montmort's "Probleme De Recontres" And Generalizations, Ronald I. Greenberg
Ronald Greenberg
I have investigated a problem which may be phrased in many ways, such as finding the probability of answering a given number of questions correctly on a randomly-completed matching test which may have a number of extra "dud" answers. I have determined such probabilities, the average number of correct answers, and other allied results. I have also investigated a related problem involving the number of ways of choosing a different element from each of a certain collection of sets.
Ashley D. Holland, Ph.D.
Penalized spline estimators have received considerable attention in recent years because of their good finite-sample performance, especially when many regressors are employed. In this paper, we propose a penalized B-spline estimator in the context of the partially linear model and study its asymptotic properties under a two-sequence asymptotics: both the number of knots and the penalty factor vary with the sample size. We establish asymptotic distributions of the estimators of both the parametric and nonparametric components in the model. In addition, as a previous step, we obtain the rate of convergence of the estimator of the regression function in a ...
On The Inverse Of A Class Of Weighted Graphs, Swarup Kumar Panda, Sukanta Pati
Electronic Journal of Linear Algebra
In this article, only connected bipartite graphs $G$ with a unique perfect matching $\c{M}$ are considered. Let $G_\w$ denote the weighted graph obtained from $G$ by giving weights to its edges using the positive weight function $\w:E(G)\ar (0,\ity)$ such that $\w(e)=1$ for each $e\in\c{M}$. An unweighted graph $G$ may be viewed as a weighted graph with the weight function $\w\equiv\1$ (all ones vector). A weighted graph $G_\w$ is nonsingular if its adjacency matrix $A(G_\w)$ is nonsingular. The {\em inverse} of a nonsingular weighted graph ...
On The Second Least Distance Eigenvalue Of A Graph, Xueyi Huang, Qiongxiang Huang, Lu Lu
Electronic Journal of Linear Algebra
Let $G$ be a connected graph on $n$ vertices, and let $D(G)$ be the distance matrix of $G$. Let $\partial_1(G)\ge\partial_2(G)\ge\cdots\ge\partial_n(G)$ denote the eigenvalues of $D(G)$. In this paper, the connected graphs with @n1(G) at least the smallest root of $x^3=3x^2-11x-6 = 0$ are determined. Additionally, some non-isomorphic distance cospectral graphs are given.
Traveling In Networks With Blinking Nodes, Braxton Carrigan, James Hammer
Theory and Applications of Graphs
We say that a blinking node system modulo $n$ is an ordered pair $(G,L)$ where $G$ is a graph and $L$ is an on-labelling which indicates when vertices can be visited. An On-Hamiltonian walk is a sequence of all the vertices of $G$ such that the position of each vertex modulo $n$ is an integer of the label of that vertex. This paper will primarily investigate finding the shortest On-Hamiltonian walks in a blinking node system on complete graphs and complete bipartite graphs but also establishes the terminology and initial observations for working with blinking node systems on other ...
Review Of Painting By Numbers By Jason Makansi, Thomas J. Pfaff
Numeracy
In Painting by Numbers Jason Makansi adds another book to the quantitative literacy bookshelf, with a book focusing on models. The book offers twelve commandments to aid the reader in assess quantitative models. The second section of the book offers examples to apply the models. Increasing quantitative literacy is crucial and generally, the more books the better. Unfortunately, this book is too superficial, often misses key ideas, and can easily lead a person to ...
A Few Reflections On A Numerate Life, John Allen Paulos
Numeracy
This piece briefly introduces and excerpts A Numerate Life: A Mathematician Explores the Vagaries of Life, His Own and Probably Yours, written by John Allen Paulos and published by Prometheus Books. The book shares observations on life—many biographical—from the perspective of a numerate mathematician. The excerpt uses basic statistical reasoning to explore why we should expect that being odd is a most normal experience.
Numeracy
This study was designed to determine if embedded remediation is significant in accelerating the pathway to completion of a college-level math course for students needing remediation. The project studied the impact on student success in a quantitative literacy course at a Massachusetts four-year state university with remedial material embedded. The course satisfies the university's general education math requirement for students with liberal arts majors who are not required to complete college algebra or calculus-based courses. The paper begins with a presentation of the issues with remedial mathematics and its impact on students' graduation and persistence. Next, the paper covers ...
Mathematics and Statistics Faculty Publications and Presentations
Images of the retina acquired using optical coherence tomography (OCT) often suffer from intensity inhomogeneity problems that degrade both the quality of the images and the performance of automated algorithms utilized to measure structural changes. This intensity variation has many causes, including off-axis acquisition, signal attenuation, multi-frame averaging, and vignetting, making it difficult to correct the data in a fundamental way. This paper presents a method for inhomogeneity correction by acting to reduce the variability of intensities within each layer. In particular, the N3 algorithm, which is popular in neuroimage analysis, is adapted to work for OCT data. N3 works ...
Fuzzy Analogues Of Sets And Functions Can Be Uniquely Determined From The Corresponding Ordered Category: A Theorem, Christian Servin, Gerardo Muela, Vladik Kreinovich
Departmental Technical Reports (CS)
In modern mathematics, many concepts and ideas are described in terms of category theory. From this viewpoint, it is desirable to analyze what can be determined if, instead of the basic category of sets, we consider a similar category of fuzzy sets. In this paper, we describe a natural fuzzy analog of the category of sets and functions, and we show that, in this category, fuzzy relations (a natural fuzzy analogue of functions) can be determined in category terms -- of course, modulo 1-1 mapping of the corresponding universe of discourse and 1-1 re-scaling of fuzzy degrees.
A Series Of Papers On Detecting Examinees Who Used A Flawed Answer Key, Marcus W. Scott
All Graduate Theses and Dissertations
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OCTAVE is the open-source equivalent of MATLAB and was developed at the University of Wisconsin starting
the late 1980s (Octave was the name of a chemical engineering professor, Octave Levenspiel; nothing to do
with music). They are constructed in different ways, but the basic OCTAVE commands are the same as those of
MATLAB and OCTAVE will run programs written for MATLAB. In my opinion OCTAVE is a better language for
students to learn because of the programming structure; whereas MATLAB ends loops, etc. with the same command
"end", OCTAVE introduces "for ... endfor", etc. (but it will accept "end").
The following manual is a sixty page introduction, especially written for Student Linux (available below),
to
using Octave for
solving linear and
polynomial equations, statistics, data analysis, an introduction to programming, graphing, "tossing coins on
a
computer" (simulation), etc. A special feature (section 01) is "A sample Octave session" which allows the
student to rapidly learning the essential features (diaries, variable ...) of using Octave. Suggested
excercises are included in each section and Octave sessions and programs are commented.
This booklet may be freely distributed for educational purposes.
I wrote this manual for students in modelling, linear algebra, probability etc. Various editions appeared
between 1994 and 2004. I am putting it on the web in the hope that it will prove useful to others. It may
be freely distributed for
educational purposes.
This manual takes the approach, "If you want to do this, these are the commands". All commands are
illustrated by examples and programs especially written for this text.
STUDENT LINUX is a pre-configured version of PCLINUXOS with the KDE desktop. It is meant for students of
mathematics, physics, computing and the naural sciences. It is "good to go" so that the student does not have
to figure out which programs to install, then customize then .... . It contains OCTAVE, \TEX, \LATEX and
various useful tools.
The following ISO files (2.6 GB) can be burned to a DVD and run either "live" (without installation) or
installed (alone or as
part of a dual-boot computer). A specially written shell files allows the user to create their own ISO file. | 677.169 | 1 |
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Buy New Textbook
Mathematical Models in Biology is an introductory book for readers interested in biological applications of mathematics and modeling in biology. Connections are made between diverse biological examples linked by common mathematical themes, exploring a variety of discrete and continuous ordinary and partial differential equation models. Although great advances have taken place in many of the topics covered, the simple lessons contained in Mathematical Models in Biology are still important and informative. Shortly after the first publication of Mathematical Models in Biology, the genomics revolution turned Mathematical Biology into a prominent area of interdisciplinary research. In this new millennium, biologists have discovered that mathematics is not only useful, but indispensable! As a result, there has been much resurgent interest in, and a huge expansion of, the fields collectively called mathematical biology. This book serves as a basic introduction to concepts in deterministic biological modeling.
Leah Edelstein-Keshet is a member of the Mathematics Department at the University of British Columbia and past president of the Society for Mathematical Biology
Preface to the Classics Edition
p. xv
Preface
p. xxiii
Acknowledgments
p. xxvii
Errata
p. xxxi
Discrete Process in Biology
p. 1
The Theory of Linear Difference Equations Applied to Population Growth
p. 3
Biological Models Using Difference Equations
p. 6
Cell Division
p. 6
An Insect Population
p. 7
Propagation of Annual Plants
p. 8
Statement of the Problem
p. 8
Definitions and Assumptions
p. 9
The Equations
p. 10
Condensing the Equations
p. 10
Check
p. 11
Systems of Linear Difference Equations
p. 12
A Linear Algebra Review
p. 13
Will Plants Be Successful?
p. 16
Qualitative Behavior of Solutions to Linear Difference Equations
p. 19
The Golden Mean Revisited
p. 22
Complex Eigenvalues in Solutions to Difference Equations
p. 22
Related Applications to Similar Problems
p. 25
Growth of Segmental Organisms
p. 26
A Schematic Model of Red Blood Cell Production
p. 27
Ventilation Volume and Blood CO[subscript 2] Levels
p. 27
For Further Study: Linear Difference Equations in Demography
p. 28
Problems
p. 29
References
p. 36
Nonlinear Difference Equations
p. 39
Recognizing a Nonlinear Difference Equation
p. 40
Steady States, Stability, and Critical Parameters
p. 40
The Logistic Difference Equation
p. 44
Beyond r = 3
p. 46
Graphical Methods for First-Order Equations
p. 49
A Word about the Computer
p. 55
Systems of Nonlinear Difference Equations
p. 55
Stability Criteria for Second-Order Equations
p. 57
Stability Criteria for Higher-Order Systems
p. 58
For Further Study: Physiological Applications
p. 60
Problems
p. 61
References
p. 67
Appendix to Chapter 2: Taylor Series
p. 68
Functions of One Variable
p. 68
Functions of Two Variables
p. 70
Applications of Nonlinear Difference Equations to Population Biology
p. 72
Density Dependence in Single-Species Populations
p. 74
Two-Species Interactions: Host-Parasitoid Systems
p. 78
The Nicholson-Bailey Model
p. 79
Modifications of the Nicholson-Bailey Model
p. 83
Density Dependence in the Host Population
p. 83
Other Stabilizing Factors
p. 86
A Model for Plant-Herbivore Interactions
p. 89
Outlining the Problem
p. 89
Rescaling the Equations
p. 91
Further Assumptions and Stability Calculations
p. 92
Deciphering the Conditions for Stability
p. 96
Comments and Extensions
p. 98
For Further Study: Population Genetics
p. 99
Problems
p. 102
Projects
p. 109
References
p. 110
Continuous Processes and Ordinary Differential Equations
p. 113
An Introduction to Continuous Models
p. 115
Warmup Examples: Growth of Microorganisms
p. 116
Bacterial Growth in a Chemostat
p. 121
Formulating a Model
First Attempt
p. 122
Corrected Version
p. 123
A Saturating Nutrient Consumption Rate
p. 125
Dimensional Analysis of the Equations
p. 126
Steady-State Solutions
p. 128
Stability and Linearization
p. 129
Linear Ordinary Differential Equations: A Brief Review
p. 130
First-Order ODEs
p. 132
Second-Order ODEs
p. 132
A System of Two First-Order Equations (Elimination Method)
p. 133
A System of Two First-Order Equations (Eigenvalue-Eigenvector Method)
p. 134
When Is a Steady State Stable?
p. 141
Stability of Steady States in the Chemostat
p. 143
Applications to Related Problems
p. 145
Delivery of Drugs by Continuous Infusion
p. 145
Modeling of Glucose-Insulin Kinetics
p. 147
Compartmental Analysis
p. 149
Problems
p. 152
References
p. 162
Phase-Plane Methods and Qualitative Solutions
p. 164
First-Order ODEs: A Geometric Meaning
p. 165
Systems of Two First-Order ODEs
p. 171
Curves in the Plane
p. 172
The Direction Field
p. 175
Nullclines: A More Systematic Approach
p. 178
Close to the Steady States
p. 181
Phase-Plane Diagrams of Linear Systems
p. 184
Real Eigenvalues
p. 185
Complex Eigenvalues
p. 186
Classifying Stability Characteristics
p. 186
Global Behavior from Local Information
p. 191
Constructing a Phase-Plane Diagram for the Chemostat
p. 193
The Nullclines
p. 194
Steady States
p. 196
Close to Steady States
p. 196
Interpreting the Solutions
p. 197
Higher-Order Equations
p. 199
Problems
p. 200
References
p. 209
Applications of Continuous Models to Population Dynamics
p. 210
Models for Single-Species Populations
p. 212
Malthus Model
p. 214
Logistic Growth
p. 214
Allee Effect
p. 215
Other Assumptions; Gompertz Growth in Tumors
p. 217
Predator-Prey Systems and the Lotka-Volterra Equations
p. 218
Populations in Competition
p. 224
Multiple-Species Communities and the Routh-Hurwitz Criteria
p. 231
Qualitative Stability
p. 236
The Population Biology of Infectious Diseases
p. 242
For Further Study: Vaccination Policies
p. 254
Eradicating a Disease
p. 254
Average Age of Acquiring a Disease
p. 256
Models for Molecular Events
p. 271
Michaelis-Menten Kinetics
p. 272
The Quasi-Steady-State Assumption
p. 275
A Quick, Easy Derivation of Sigmoidal Kinetics
p. 279
Cooperative Reactions and the Sigmoidal Response
p. 280
A Molecular Model for Threshold-Governed Cellular Development
p. 283
Species Competition in a Chemical Setting
p. 287
A Bimolecular Switch
p. 294
Stability of Activator-Inhibitor and Positive Feedback Systems
p. 295
The Activator-Inhibitor System
p. 296
Positive Feedback
p. 298
Some Extensions and Suggestions for Further Study
p. 299
Limit Cycles, Oscillations, and Excitable Systems
p. 311
Nerve Conduction, the Action Potential, and the Hodgkin-Huxley Equations | 677.169 | 1 |
Resources for this lesson:
You have now been introduced to a number of additional function families that may be used to model real-world data. You have also begun to analyze when each function family may be an appropriate choice for a data set. Before proceeding to the next lesson, complete the lesson reflection.
Algebra II Journal: Reflection 3
Respond to the following reflection questions in your Algebra II Journal and submit to your teacher.
Select one of the new function families to research in more depth:
Cubic Functions
Quartic Functions
Power Functions
Logarithmic Functions
Logistic Functions
Trigonometric Functions
For the function family you selected, use your textbook and online searches to develop a deeper understanding of the function family. Summarize your findings and submit to your teacher. Make sure to address the following:
Determine the key features of this function family. (end behavior, number of possible maximum and minimum values, increasing/decreasing trends, etc.)
Include sample graphs to represent the variety of functions within this function family.
Include any possible contextual examples that could be modeled with this function type | 677.169 | 1 |
Synopsis
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Mathematics - Algebra
[College Level] Abstract Algebra On Line
"This site contains many of the definitions and theorems
from the area of mathematics generally called abstract algebra. It is intended for undergraduate students taking an abstract algebra class at the junior/senior level, as well as for students taking their first graduate algebra course."
Maintained by John Beachy
Algebra Story and Word Problems
"Reliable problem solving in all subjects that use mathematics for problem solving. Algebra, Physics, Chemistry... from grade school to grad school and beyond."
Algebra.help
"We use some of the latest technology to help you learn and understand algebra. Our website features lessons to learn or refresh old skills, calculators that show you how to solve problems
step-by-step, and interactive worksheets to test your skills.
BrainTrax
"...
Sections include: Algebra ; Trigonometry ; Calculus I ; Calculus II.
- University of Missouri, Rolla
Elements of Abstract and Linear Algebra
"This is a foundational textbook on abstract algebra with emphasis on linear algebra. You may download parts of the book or the entire textbook."
By Edwin H. Connell
Symbolic Mathematical Computation Information Center
"The area of Symbolic and Algebraic Computation (SAC), also known as Computer Algebra (CA) in some circles, aims to automate mathematical computations of all sorts...This document is a starting point for discovering information about SAC."
Academic Info. All rights reserved.
Online Degree Information
Do you want to improve your earning potential and further your career? Learn about earning an online degree through an an accredited online college or campus-based university. Browse through hundreds of subjects to find your desired degree program or online course - or start by choosing your degree level (e.g. associate, bachelor, master or doctoral). | 677.169 | 1 |
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Achieve What You Want
Why should you learn cloud computing? Now-a-days Cloud computing or simply Cloud is the buzzing world in the technology industry. With the current challenging business environment all industry demands cost effective and reliable (i.e. always on) solutions. Cloud computing technology provides the answer. This makes it absolutely essential to have a basic knowledge on cloud…
Mathematics is everywhere!! And the base of mathematics is fundamental operations like Multiplication, Division, Addition and Subtraction. There are lot of people who have a math phobia or they just don't like mathematics, the root cause is not Mathematics rather the way they encountered it. I guarantee that after taking this course you will love mathematics and enjoy doing… | 677.169 | 1 |
completely rewritten and revamped for the new NESA 2 Unit advanced course. This course will prepare teachers for teaching the harder material in the 2 unit mathematics Year 12 component of the course. Difficult material from the course will be presented and taught to the attendees. Assessment task preparation will be discussed. Strategies to maximise HSC performance will be revealed. Teachers will receive a variety of resources which they can use to teach several of the more difficult topics from this course. As a result of attending this course teachers can tackle teaching 2 unit mathematics and the calculus components with much more confidence. This course would also suit schools and teachers who are seeking to improve their students' results in HSC Mathematics.
Preparing to Teach 2 Unit Mathematics HSC Course
About the team
Creator
Morris has previously occupied the position of Head of Mathematics and Mathematics Technology at Reddam House, Kincoppal Rose Bay and The Emanuel School in Sydney. Qualified with an M.A. in pure mathematics and a B. Ed. (maths), Morris has experience teaching in a wide variety of schools and has delivered many professional development courses for mathematics teachers both in Australia and overseas. Morris was recognised in 2006 with an Outstanding National Achievement for Excellence by a Teacher the National Awards for Quality Schooling. Morris has also been designated by Apple as a Distinguished Educator. | 677.169 | 1 |
Amarjit Girn
Amarjit Girn
is
a
Math professor
at
Dawson College
located in
Montreal, Quebec. When comparing
Amarjit Girn's ratings to other professors
in the province of Quebec,
Amarjit Girn's ratings are
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stars.
Additionally, the average professor rating at
Dawson College is
4.11
stars.
Mr Girn is a good teacher who really cares about his students. He only has one way of explaining things, though, so if you don't get it you might have some trouble, but the book should help you get over that.
if you have him for mechanical engineering, you are almost better off staying home and waiting for an other teacher to teach the class. this semester more than half the class failed!! he really knows his stuff but doesnt seem to be able to teach it. good luck if you are pre-registered in his class | 677.169 | 1 |
Mathex Scientific Calculator v1.4.3 Patch Apk
Direct algebraic logic: enter equations as they are written. History Playback: Recall any of the 10 last steps you have made. Expression (re)editing: change equationsand recalculate. Chain calculations: use answer in following equation. 2-Line display: check your equation and answer at the same | 677.169 | 1 |
The Vision of Mathematics Across the Curriculum
Dear Reader,
In 1994, Dartmouth College received a generous grant from the National Science Foundation to integrate mathematics throughout the undergraduate college curriculum in a five-year project, Mathematics Across the Curriculum (MATC). The project has involved over 40 faculty members from Dartmouth and various other colleges and universities representing departments of biology, chemistry, music, drama, English, art history, computer science, physics, earth science, economics, engineering, medicine, mathematics, and Spanish, producing lesson plans, short books, videotapes, and a Web site with images and texts. The series of volumes published by Key College Publishing represents some of the best of the MATC collection.
These materials will make it easier for students to become more quantitatively literate as they tackle complex, real-world problems that must be approached through the door of mathematics. We hope that you, the reader, will appreciate our efforts to place the mathematics in this book completely in the context of your field of interest. Our goal is to help you see that applied mathematics is a powerful form of inquiry, and ever so much richer than mere "word problems." We trust that you will like this approach and want to explore some of the other volumes in the series. | 677.169 | 1 |
In this lesson we will review what you have learned in previous classes about mathematical equations of
relationships and corresponding graphical representations and how these enable us to address a range of
mathematical applications. We will review key properties of mathematical relationships that will allow us to
solve a variety of problems. We will examine examples of how equations and graphs can be used to model
real-life situations. | 677.169 | 1 |
Definitely using this as a lesson opener for special right triangles. There's also a link here for intro to trig functionsQuadratic Functions: Vertex Form Lesson
Transformations of the quadratic function - graphic organizer. Students love having all of the transformations on one clear sheet that they can refer to often. Two fill-in versions included for different levels!
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CHAPTER 11 pinner says: Today's project in College Algebra was making the color coded definition patterns "cheat sheets." It worked like a charm! Almost the whole class was engaged and understood how to convert from one to the other! | 677.169 | 1 |
Mathematics homework help
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Hotmath explains math textbook homework problems with step-by-step math answers for algebra, geometry, and calculus.However, this school subject is an Achilles heel of many students, no matter where they study.LearnOk is a gathering of students and experts that yearn to help each other through their studying problems.Math is a subject, which is extremely useful and interesting, to some extent, as it teaches us to count quickly, develops our logic and analytical abilities.
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S.O.S. MATHematics is your free resource for math review material from Algebra to.StudyDaddy is the place where you can get easy online Math homework help.Affordable and authentic custom written assignments designed for international students. | 677.169 | 1 |
An introduction to circuit complexity and a guide to Ha èstad's proof An introduction to circuit complexity and a guide ... A Guide to Hastad's Proof ..... we understand how circuits relate to Turing machines, as discussed in the next ......
Appendix B: Introduction to the Experiment and Questionnaire Introduction to the. Experiment and. Questionnaire. The handout given to
subjects, before the test, explaining the procedure of the experiment is given in
Section ......
Introduction to Data, Text, and Web Mining for Business Analytics ... Introduction to Data, Text, and Web Mining for Business Analytics Minitrack.
Dursun Delen. Oklahoma State University dursun.delen@okstate.edu....
AN INTRODUCTION TO MATERIALS ENGINEERING AND SCIENCE An introduction to materials engineering and science: for chemical and materials
engineers. Brian S. Mitchell p. cm. Includes bibliographical references and ......
Introduction to Photonics. Optics and Lasers - UPC Introduction to Photonics. Optics and Lasers presents a general overview of the
world of. Photonics, introducing the fundamental aspects concerning light and its
......
Introduction to Groups, Rings and Fields Introduction to Groups, Rings and Fields. HT and TT 2011 ... GRF is an
ALGEBRA course, and specifically a course about algebraic structures. ...... We
next give an application of the Division Algorithm which will be important later on,
specif-.... | 677.169 | 1 |
Arithmetic and Geometric Sequence Practice
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This worksheet has both arithmetic and geometric sequences mixed in. It has the students find the recursive and explicit formulas for a geometric sequence when given the sequence. The students will be given formulas and sequences and will have to determine what type of sequence they are dealing with and then answer the questions. The students will also be given two real world scenarios where they will have to create a table , graph, write an equation, and then answer a question. | 677.169 | 1 |
GeoGebra Exam
GeoGebra Exam allows your students to use GeoGebra during exams without being able to access the Internet or other software installed on the computer. Leaving the GeoGebra window in any way triggers an alert, which can easily be spotted by the teacher and is documented in the Exam Log.
What is GeoGebra Exam?
[img] GeoGebra Exam allows you and your students to use the power of GeoGebra during exams on paper (i.e. like a graphing calculator or pocket calculator) while restricting their access to the Internet or other software that should not be used during the exam.[br][br][img] GeoGebra Exam...[br][list][*]... can easily be accessed at [url= runs in your browser, so no additional installations are required.[/*][*]... can be customized in case your students should not have access to the full power of GeoGebra (e.g. deactivate the GeoGebra CAS)[/*][*]... runs in full screen mode allowing no space for other information to be displayed on screen.[br][/*][*]... doesn't allow access to the Internet, the GeoGebra Materials platform, or files saved on the computer.[/*][/list]
GeoGebra Exam activated
GeoGebra Exam Alert
Leaving the [img] GeoGebra Exam window triggers a visual alert that is easily detectable and recorded in the Exam Log.
The GeoGebra Exam Tablet Apps
What are the GeoGebra Exam Tablet Apps?
While [img] GeoGebra Exam for laptops and desktop computers can be customized by the user, the GeoGebra Exam Apps for tablets provide a different preselected set of features each.[br][br]Currently, the following GeoGebra Exam Tablet apps are available:[br][table][tr][td][img] Exam CAS[/td][/tr][tr][td][img] Exam Graphing Calculator [/td][/tr][tr][td][img] Exam Simple Calculator[/td][/tr][/table][u][br]Hints[/u]: [br][list][*]If you are not sure which GeoGebra Exam Tablet app you are currently using, check the header of the Exam Log.[/*][*]Using the Exam Tablet apps you cannot exit [img] GeoGebra Exam, only restart it.[/*][*]Please note that the screen saver is switched off by default and the screen lock triggers the visual alert.[/*][/list]
What are the Differences between the GeoGebra Exam and the corresponding Tablet Apps?
[list=1][*]When launching the GeoGebra Exam Tablet apps, [img] GeoGebra Exam is directly activated, using the set of preselected features.[/*][*]After ending [img] GeoGebra Exam you can directly restart it if you are using one of the Exam Tablet apps.[/*][*]No customization of [img] GeoGebra Exam is necessary while using one of the GeoGebra Exam Tablet apps (i.e. deactivation of CAS or 3D Graphics). Just choose the one that best meets your needs.[/*][*]Depending on the Exam Tablet app you chose, commands and access to other GeoGebra Views might be restricted and the menu could be simplified.[br][/*][*]When working with the Exam Tablet apps, deactivated functionalities do not appear in the Toolbar and are not shown in the Exam Log either. Instead, the name of the Exam Tablet app used is shown in the Exam Log.[/*][*]You cannot change the language of the user interface. The GeoGebra Exam Tablet apps use the language setting of your tablet.[/*][/list] | 677.169 | 1 |
These Problem Sets have been designed to help you master all the required content for the IM3 course. It is not structured like most math courses you have previously taken, and you will see that it requires a different approach on your part.
In each Problem Set, you will be given a number of problems - usually between 7 and 8 - to prepare for the next lesson. They should take 80 - 100 minutes in total (inclusive of class time). You might not always be able to fully solve all problems, but we expect you to attempt as many as you can. In class, you will be expected to present your solutions and discuss solutions that others have shared. Each lesson will involve discussing the problems you have prepared for homework in preparation for the next lesson. Lessons are your principal opportunity to ask for help on material you couldn't do, so be prepared to ask other students how they solved problems or how they knew what approach to take. Discussion should take about 40 minutes in your lessons, and the remainder of the time will be spent looking at further problems from subsequent Problem Sets.
How you take notes is very much up to you, but we will indicate whenever we think there is a topic on which you are likely to want to take notes. If you are unsure what you are supposed to have understood from a question, ask your peers.
For Mr S's E BLOCK class
After Problem Set 4.2
Assigned on Wednesday, Jan 17
Due: Sunday, Jan 21
From Problem Set 4.2 have ALL QUESTIONS complete. Higher Level Qs are always OPTIONAL
After Problem Set 4.1
Assigned on Monday, Jan 15
Due: Wednesday, Jan 17
From Problem Set 4.1 have ALL QUESTIONS complete. Higher Level Qs are always OPTIONAL
After Problem Set 3.8
Assigned on Monday, Dec 4
Due: Wednesday, Dec 6
From Problem Set 3.8 have ALL QUESTIONS complete. Higher Level Qs are always OPTIONAL
After Problem Set 3.7
Assigned on Wednesday, Nov 29
Due: Monday, Dec 4
From Problem Set 3.7 have ALL QUESTIONS complete. Higher Level Qs are always OPTIONAL
After Problem Set 3.6
Assigned on Monday, Nov 27
Due: Wednesday, Nov 29
From Problem Set 3.6 have ALL QUESTIONS complete. Higher Level Qs are always OPTIONAL
After Problem Set 3.5
Assigned on Wednesday, Nov 22
Due: Monday, Nov 27
From Problem Set 3.5 have ALL QUESTIONS complete. Higher Level Qs are always OPTIONAL
After Problem Set 3.4
Assigned on Monday, Nov 20
Due: Wednesday, Nov 22
From Problem Set 3.4 have ALL QUESTIONS complete. Higher Level Qs are always OPTIONAL
After Problem Set 3.3
Assigned on Thursday, Nov 16
Due: Monday, Nov 20
From Problem Set 3.3 have ALL QUESTIONS complete. Higher Level Qs are always OPTIONAL
After Problem Set 3.2
Assigned on Tuesday, Nov 14
Due: Thursday, Nov 16
From Problem Set 3.2 have ALL QUESTIONS complete. Higher Level Qs are always OPTIONAL
From Problem Set 2.9 have ALL QUESTIONS complete. Higher Level Qs are always OPTIONAL
After Problem Set 2.8
Assigned on Tuesday, Oct 31
Due: Thursday, Nov 2
From Problem Set 2.8 have ALL QUESTIONS complete. Higher Level Qs are always OPTIONAL
After Problem Set 2.7
Assigned on Sunday, Oct 29
Due: Tuesday, Oct 31
From Problem Set 2.7 have ALL QUESTIONS complete. Higher Level Qs are always OPTIONAL
After Problem Set 2.6
Assigned on Wednesday, Oct 25
Due: Sunday, Oct 29
From Problem Set 2.6 have ALL QUESTIONS complete. Higher Level Qs are always OPTIONAL
After Problem Set 2.5
Assigned on Sunday, Oct 22
Due: Wednesday, Oct 25
From Problem Set 2.5 have ALL QUESTIONS complete. Higher Level Qs are always OPTIONAL
After Problem Set 2.4
Assigned on Wednesday, Oct 18
Due: Sunday, Oct 22
From Problem Set 2.4 have ALL QUESTIONS complete. Higher Level Qs are always OPTIONAL
After Problem Set 2.3
Assigned on Monday, Oct 16
Due: Wednesday, Oct 18
From Problem Set 2.3 have ALL QUESTIONS complete. Higher Level Qs are always OPTIONAL
After Problem Set 2.2
Assigned on Wednesday, Oct 4
Due: Monday, Oct 16
From Problem Set 2.2 have ALL QUESTIONS complete. Higher Level Qs are always OPTIONAL
After Problem Set 2.1
Assigned on Monday, Oct 2
Due: Wednesday, Oct 4
From Problem Set 2.1 have ALL QUESTIONS complete. Higher Level Qs are always OPTIONAL
After our REVIEW CLASS
Assigned on Tuesday, Sept 26
Due: Thursday, Sept 28
For studying for our UNIT TEST, you SHOULD also look at some of the RESOURCES and maybe start studying for Thursday's TEST. HELPFUL HINT: Have a study partner, so you can share answers or problems or answer each others questions
After Problem Set 1.11
Assigned on Sunday, Sept 24
Due: Tuesday, Sept 26
From Problem Set 1.11 ALL QUESTIONS (Q1 - Q6) complete. Higher Level Qs are always OPTIONAL. You SHOULD also look at some of the RESOURCES and maybe start studying for Thursday's TEST | 677.169 | 1 |
Written by a prominent mathematician, this text offers advanced undergraduate and graduate students a virtually self-contained treatment of the basics of Galois theory. This two-part approach begins with the elements of Galois theory, focusing on rel Written by a prominent mathematician, this text offers advanced undergraduate and graduate students a virtually self-contained treatment of the basics of Galois theory. This two-part approach begins with the elements of Galois theory, focusing on related concepts from field theory, and a consideration of relevant facts from group theory leads to a survey of Galois theory. The second part explores the solution of equations by radicals, returning to the general theory of groups for relevant facts, examining equations solvable by radicals and their construction, and concluding with the unsolvability by radicals of the general equation of degree n > 5. 1962 ed. ...Continua Nascondi | 677.169 | 1 |
What a Cambridge mathematics degree can do for you
Thinking about and understanding the skills or competencies you have developed from your Cambridge Maths Degree is a crucial aspect to career planning. At some point you will need to compare your competencies with those required by an employer, course provider or research group. A major part of any selection process will involve demonstrating through your application paperwork and through interviews and other selection tests that you can match or exceed the competencies required for a particular opportunity. It is therefore crucial to understand which boxes your degree will tick for you and which other competencies you will need to demonstrate beyond this.
From an academic perspective
Your Cambridge Degree will enable you to develop many of the so called "transferable skills" which employers require - The following statement is taken from the Higher Education Academy and gives a largely academic viewpoint of skills you will have developed.
"A graduate in Mathematics typically will have the ability to:
demonstrate knowledge of key mathematical concepts and topics
abstract the essentials of problems and formulate them mathematically and in symbolic form so as to facilitate their analysis and solution
present mathematical arguments and the conclusions from them with accuracy and clarity
have skills relating to rigorous argument and solving problems in general, and a facility to deal with abstraction including the logical development of formal theories
demonstrate appropriate transferable skills and the ability to work with relatively little guidance or support.
Mathematics is rooted in the systematic development of methods to solve practical problems in areas such as surveying, mechanical construction and commerce. Such methods have a wide range of application. Thus generalisation and abstraction became important features and mathematics became a science involving strict logical deduction with conclusions that follow with certainty and confidence from clear starting points. Mathematics is fundamental to almost all situations that require an analytical model-building approach. Statistics encompasses the science of collecting, analysing and interpreting data and has become much concerned with the design processes for observational and experimental studies."
(You will find further statements describing skills derived from a maths degree in the QAA Subject benchmark statement for Mathematics, statistics and operational research)
From an employer's perspective
Looking at transferable skills from an employer's perspective, and using their language, the skills you can be expected to have gained from your degree at Cambridge are:
Analytical Skills - A general analytical approach to problems. An understanding of data sets and the ability to derive meaning from data.
Problem solving skills / creativity - A logical approach to problem solving, working from the known to the unknown and coming up with new solutions by applying your knowledge to new problems and situations.
IT Skills - From your general IT knowledge and CATAM project work.
Planning / time management - Completing your work requirements on time during short intense terms, while also engaging in other activities at Cambridge.
Adaptability / Persistence and 'Stick-ability' - Continually learning and adapting new material and applying this to new and varied problems. Working in a pressured environment. The rigour of working complex maths problems through to a solution.
Skills you may not necessarily gain directly, or sufficiently, from your course alone
There are other important skills that employers frequently seek, which you will not necessarily pick up directly from your course, and some of those skills which you develop on your course can be further developed elsewhere. "Elsewhere" can be in relation to positions of responsibility or other extra-curricular activities at Cambridge or to real world employment during vacations or in a gap year. Some of these other important skills are: | 677.169 | 1 |
Tutoring Tip of the Week: Always seek the challenge of going faster, never settle for just knowing
College Algebra
This course's emphasis is the study of functions, and their graphs, inequalities, and linear, quadratic, piece-wise defined, rational, polynomial, exponential, and logarithmic functions with appropriate applications.
Subjects Include:
Imaginary Numbers.
Linear Inequalities in One Unknown.
Quadratic Equations in One Unknown.
Rectangular Coordinates and Graphs of First- and Second- Degree Equations. | 677.169 | 1 |
Product Description
This is a full curriculum book that covers all the math concepts for Algebra 1. It includes Numbers Review, Fractions, Real Numbers, Exponents, Ratios, Rates, Proportions, Dimensional Analysis, Variables, Expressions, Equations, Formula, Relations, Functions, Linear Equations, Linear Inequalities, Polynomials, Factoring, Quadratic Equations , Radical Expressions and Triangles. (We recommend purchasing the workbook for a comprehensive program.)We recommend getting a workbook (eBook or printed) to practice problem solving to reinforce each math concept. Workbook for each grade level includes worksheets for each lesson, exams for each chapter and answer keys. You may download each worksheet and exam free under the Free Stuff section of the website or you may purchase an eBook for one low price saving you your valuable time.
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A+ Interactive Math (by A+ TutorSoft Inc.)
(49 Reviews)
We make your homeschool journey with math EASY! With our Math Curriculum Online Program, you can RELAX! You don't have to teach or grade Math. This program DOES EVERYTHING for you including teaching, grading and tracking.
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Maximize your mathematics curriculum to challenge all students This collection of lessons from experienced teachers provides multifaceted examples of rigorous learning opportunities for mathematics students in Grades 6–12. The four sample units focus on fractions, linear programming, geometry, and quadratic relationships. The authors provideWritten by experienced examiners to completely cover the 20th century aspects of the Cambridge IGCSE in History, this comprehensive text covers all the relevant material AND provides focused skills development to ensure students achieve their best. With nearly 400 pages of practice, it will help learners excel. more... | 677.169 | 1 |
By completing the work in this course, you will develop the skills
above. These skills will allow you to make and defend quantitative
estimates with limited information. You will also be able to devise strategies to make
well-defined estimates to answer questions. Lastly, you will be able to
evaluate the quantitative claims of others in your professional,
personal, and civic lives.
Topic Learning Objectives
Estimations and Models
Able to form plausible quantitative estimates with very little
specific information given.
Communicate clearly the assumptions and method of an estimation
Recognize the use of models in estimation and calculations
Identify type of model being used in an estimation
Place Value
Use concepts of place value to correctly use scientific notation
Use concepts of place value to convert between different base systems of numbers
Convert between decimal numbers and scientific notation
Describe how much less information each successive significant figure provides
Units and Dimensions
Recognize that physical quantities require a magnitude, dimension, and unit
Able to convert quantities of the same dimension to different units
Able to use dimensions as an analytical tool
Use the factor-label method to convert units
Recognize unit-conversion factors as having a value of one
Linear and proportional models
Able to extrapolate from proportions
Conceptual understanding of y-intercept
Recognize physical systems with linear models
Able to articulate the meaning of a slope for specific applications
Areas and Volumes
Able to estimate areas and volumes of physical objects
Able to convert between different units for areas and volumes
Able to apply area and volume models to other quantities and estimations
Use an appropriate model to find an equivalent area or volume to an area or volume of interest
Exponential models
Define exponential growth in terms of uniform relative increase and doubling time
Recognize estimations that require exponential model
Infer growth rates from graphs
Predict future values from exponential graphs
Class Texts
There are no required texts for this course. Any readings will be
supplied online or in the course notes. The course notes are available
online and can be found
here.
Course Requirements
This course will have homework assignments, in-class activities,
quizzes, exams, as well as readings and essays. All of these
assignments are designed to develop your quantitative reasoning skills.
You are required to buy a one-semester subscription to a tool we will
use called SageMathCloud.
Classroom Work, Activities, and Quizzes
By participating in classroom work regularly, you will gain skills you
need to collaborate with others on problem solving. This classroom work
may take the form of writing exercises, group exercises, or quizzes. If
you have an unexcused absence on the day of work, you will not receive
credit for that day's assignment.
Quizzes will often be taken in groups, with the group turning in a
single quiz based on consensus and receiving the same grade. We will
grade the quizzes as you are taking them and give you multiple
opportunities to achieve the correct answer. You will get full credit
on your first try and a reduction in credit for each additional attempt.
Homework
By completing the homework regularly, you will develop skills necessary to take
a question, create a strategy, and get estimate for the answer. You will also
develop your ability to communicate and explain these estimates in writing.
Your problem sets will be graded on the clarity of communication as much as the
correctness of the result. The point of most quantitative work is not only to
arrive at an answer but to communicate the answer to others.
The work you produce in this class will be practice for the work you will do in
the professional world. Your homework assignments will often be typeset,
printed, and turned in. Your calculations should be performed using a program
where the details of the calculation are recorded. We will be using a program
called Jupyter to perform these assignments.
You are encouraged to work in teams and discuss the strategies and even
numerical answers you are getting. You are strongly discouraged from looking at
other students completed assignments. If you look at your classmates completed
work, you are denying yourself the opportunity to construct the solution on your
own and this will prevent you from developing your skills.
Questions:
You will often have questions on homework. Please post these to the
class news forum on Moodle so that everyone can see them. It is also
possible that your classmates can answer more quickly than I can.
Evaluation:
It is important that you be able to evaluate the estimations that others
create. To practice this skill, you will frequently read, evaluate, and
provide constructive feedback on the work of others in the class as part of the
grading process.
Grading:
Homework will be graded pass or fail. In order to earn a pass the work must
Be submitted on time
Demonstrate a good-faith effort to complete the assignment
Show evidence of meeting the learning objective of the assignment
Not substantially resemble another student's work
Additionally, you should strive to reach the following goals:
Be sufficiently clear that the reader can immediately understand your work.
Explain with prose enough of your approach for the reader to follow your methods and reasoning
Challenging Homeworks:
Some of the homeworks will be significantly more difficult in order to
challenge you, stretch your abilities, and demonstrate mastery of the
course material. These problems will be clearly marked as challenging.
Grading
The letter grade in the class will be assigned according to the following
criteria. Please keep an organized index and folder of all of your classwork,
exams, and quizzes in case of any grading discrepancies.Complete 2 challenging homework assignments
A
Quiz and exam average of 80% or above
Satisfactorily complete over 90% of homework assignments
Complete 5 challenging homework assignments
Late Work
You will get six passes which allow you to take a quiz alone despite your absence or turn in a homework up to one week late, or to redo an assignment that wasn't satisfactory.
Use them wisely. | 677.169 | 1 |
Motivating readers by making maths easier to learn, this work includes complete past exam papers and student-friendly worked solutions which build up to practice questions, for all round exam preparation. It also includes a Live Text CDROM which features fully worked solutions examined step-by-step, and animations for key learning points.
Synopsis:
Edexcel and A Level Modular Mathematics C2 features: *Student-friendly worked examples and solutions, leading up to a wealth of practice questions. *Sample exam papers for thorough exam preparation. *Regular review sections consolidate learning. *Opportunities for stretch and challenge presented throughout the course. *'Escalator section' to step up from GCSE. PLUS Free LiveText CD-ROM, containing Solutionbank and Exam Cafe to support, motivate and inspire students to reach their potential for exam success. *Solutionbank contains fully worked solutions with hints and tips for every question in the Student Books. *Exam Cafe includes a revision planner and checklist as well as a fully worked examination-style paper with examiner commentary | 677.169 | 1 |
Learn math online
With Alison's free online maths courses, learn about algebra, geometry, statistics, trigonometry and more. Start math lessons today with Alison. You can learn anything. Expert-created content and resources for every subject and level. Always free. Free, unlimited access to lessons. Don't ever be stuck watching another boring 10-minute video again — you learn best by doing, not watching.
Free math lessons and math homework help from basic math to algebra, geometry and beyond. Students, teachers, parents, and everyone can find solutions to their math. How to Learn Math is a free self-paced class for learners of all. Stanford University pursues the science of learning. Online learners are important participants. Whom is this course for? This course is for teachers of math (K-12) or for other helpers of students, such as parents. After the summer I will release a student. You can learn anything. Expert-created content and resources for every subject and level. Always free.
Whom is this course for? This course is for teachers of math (K-12) or for other helpers of students, such as parents. After the summer I will release a student. The Mathematics Online Interview provides teachers with powerful information about early numeracy skills to use when planning to meet student learning needs. Courses aligned to Australian Curriculum maths standards, Mathletics supports a teacher's unique blend of student-driven learning & teacher-led instruction.
IXL is the world's most popular subscription-based learning site. Used by over 6 million students, IXL provides unlimited practice in more than 4,500 maths and.
Mathplanet.com is an online resource where one can study math for free. Take our high school math courses in Pre-algebra, Algebra 1, Algebra 2 and Geometry. We have.
Do you need help with math like subtraction, multiplication, division, fractions, decimals, and percents? With an emphasis on images and interactives, our math. | 677.169 | 1 |
4EGR 102Lecture 017EGR 102 Lecture Format•Lecture homework:•Posted on Angel – print a copy•Complete and turn in at beginningof each lecture•Papers mustbe stapled with name and lab section #•Show all work; Be neat & clear; Identify answers by boxing them in or circling them; Use units where appropriate•You will lose points if you do not obey these rules•Lecture quizzes:•Most every week over previously covered material•Bring a matrix capable calculator•Numbering scheme:•Lecture HW 01 -> First week Lab HW 03B -> Second lab of third weekEGR 102Lecture 018EGR 102 Labs•Topic introduction & example by TA•Some pre-recorded videos•
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Linear Algebra: An Introduction Using Mathematica
Fred Szabo, 2000, Academic Press, 590 pages, hardbound.
Linear Algebra was written for a standard first course in linear algebra.
The book emphasizes development of analytical and computational
skills, and includes worked examples providing step-by-step methods for
solving basic problems using Mathematica. | 677.169 | 1 |
Best Ever Book Lists
Available in PDF Format | MARYLAND TEST PREP Common Core Quiz Book PARCC Mathematics Grade 3: Revision and Preparation for the PARCC Assessments.pdf | English
Test Master Press Maryland (Author)
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Matches the 2016-2017 State Standards and Prepares Students for the PARCC Assessments!
This extensive skill-building quiz book contains over 200 pages of quizzes targeting over 50 mathematics skills!
Each quiz focuses on one specific skill, with questions progressing from simple to more complex. Students will develop a thorough understanding of each skill, while also gaining experience with all the types of tasks found on the PARCC assessments.
Divided into Convenient Topics - Covers every skill listed in the Common Core State Standards - Includes sections for operations and algebraic thinking, number and operations, fractions, measurement, data, and geometry - Each section contains a focused quiz for each individual skill - Each quiz includes a range of question types and increasing rigor to develop a thorough understanding of the skill - Targeted format allows test preparation to be easily integrated into student learning
Prepares Students for the PARCC Assessments - Covers all the skills assessed on the PARCC mathematics tests - Provides practice for selected response, constructed response, and computer-based questions - Includes more advanced questions to reflect more rigorous PARCC tasks - Prepares students for questions that involve written explanations, showing work, and justifying answers - Guided tasks teach students what is expected in answers
Key Benefits - Develops a thorough understanding by focusing on one skill at a time - Reduces test anxiety by allowing ongoing test practice - Individual quizzes allow gaps in knowledge to be targeted - Ensures students are comfortable with a range of question formats - Prepares students for all the question types found on the PARCC tests - Provides revision and test practice as the student learns
2.5
(11901)
Pdf
PDF
*An electronic version of a printed book that can be read on a computer or handheld device designed specifically for this purpose. | 677.169 | 1 |
Slope
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Objective: Find the slope.
This algebra lesson was adapted for SmartBoard. It contains lots of problems and hidden answers. Most of my lessons contain step by step instructions and word/real life problems. The students love going up to the SmartBoard to solve the problems, then check the hidden answer to see if they were correct. There are lots of problems to pick and choose. Most of my lessons have enough examples for the "I do it, we do it, you do it" model.
Available on pdf upon request. | 677.169 | 1 |
list of c-book units
The musical plane II
Created on 24 October 2016
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Designed and produced by the Spanish CoI
This c-unit has been designed by a team of Secondary School teachers of Mathematics and Music, together with education researchers. The main mathematical content addressed is the study of the line and piecewise-defined linear functions, its elements and a variety of their representations. This content is related to music, representing points in a musical plane and analyzing the influence of the elements of a line on its musical representation. The c-unit Musical Plane is structured in three parts:
The main objective of part 1 is to get used to the musical plane and to find out its structure. There is an analogy between the Cartesian plane and the musical plane.
The second part focuses on the understanding of a line with multiple representations such as the ones offered by the musical plane, the Cartesian plane or its algebraic representation.
The third part introduces different patterns one can find in a melody and its mathematical representation. Different piecewise-defined functions are studied and listened | 677.169 | 1 |
Real and complex analysis, fractional calculus and its applications, integral equations and transforms, higher transcendental functions and their applications, q-Series and q-Polynomials, analytic number theory | 677.169 | 1 |
Pre-Algebra
Pre-Algebra is a course generally taught between the 5th-6th grades. Pre-algebra may include subjects from geometry, especially subjects that further understanding of algebra in applications to area and volume. The objective of pre-algebra is to prepare the student for the study of algebra.
Accendo will help students prepare for tests and quizzes and assist with homework assignments to help improve overall understanding.
Pre-algebra includes the following topics:
Review of natural number arithmetic
New types of numbers such as integers, fractions, decimals and negative numbers
Factorization of natural numbers
Properties of operations such as associativity and distributivity
Simple (integer) roots and powers
Rules of evaluation of expressions, such as operator precedence and use of parentheses
Basics of equations, including rules for invariant manipulation of equations
Understanding of variable manipulation
Manipulation and arithmetic with the standard 4-quadrant Cartesian coordinate plane | 677.169 | 1 |
Algebra: Is |x|< 1?
Algebra is by far the most fundamental question type appearing on GMAT, GRE, or SAT. This topic encompasses subtopics such as Algebraic Expressions, Linear Equations, Quadratic Equations, Exponents, Inequalities, Absolute Value, and Functions.
One would often find good chunk of word problems appearing from this topic. It also covers arguably the most dreaded combination on these exams – Inequality + Data Sufficiency.
Like Number Systems, Algebra forms the basis for many question types on the test and there are many smart tricks to be learnt. One should learn how to avoid pitfalls, and be careful in dealing certain question types. This topic must be tamed with supreme authority to do well on the Maths section. | 677.169 | 1 |
Way of Analysis gives a thorough account of real analysis in one or several variables, from the construction of the real number system to an introduction of the Lebesgue integral. The text provides proofs of all main results, as well as motivations, examples, applications, exercises, and formal chapter summaries. Additionally, there are three chapters on application of analysis, ordinary differential equations, Fourier series, and curves and surfaces to show how the techniques of analysis are used in concrete settings.
Synopsis
Flexible enough to be used in one- or two-term course with or without Lebesgue integral. Strong motivation with theorems and examples are introduced in a context that makes them seem natural. Extensive chapter summaries provide a outline for revi | 677.169 | 1 |
selection of D1 revision resources for the AQA A-Level Spec. These resources include revision sheets and posters with fill in the gaps to help student remember the information. These sheets cover the sorting algorithms, definitions for D1 and other algorithms.
A series of lesson sheets that take you through the whole of the Edexcel AS Further Decision Maths 1 course. They are intended to be used in the order they are numbered. When used in conjunction with exercises on the topics these deliver the entire content of the course.Full lesson on investigating graph theory and networks which is extremely derivative -- very largely based on the stupendous lesson and worksheet uploaded by @Owen134866. I have added some more scaffolding in terms of discussing vocabulary and created a support sheet so that this topic can be accessed at KS3 and above.
I have delivered this lesson successfully to mixed ability Year 7s and high ability Year 9s to date, and always really enjoy it. It's generally something I pull out towards the end of term as a treat with a view to improving students' problem-solving skills.
Extension worksheet is adapted from the Konigsberg problem entry on Wikipedia although I have not yet used it -- it might prove to be a good extension to the main lesson for A Level students.
Please do rate and review this resource -- I appreciate feedback! | 677.169 | 1 |
the many topics featured in this vital guide from a veteran college mathematics professor are: Improving problem solving skills, Satisfying prerequisites, Reading the textbook, Learning symbolic form, Writing mathematics, Managing assignments, Getting the most out of class, | 677.169 | 1 |
Through this site isn`t the same as a simple solution manual you buy in an at the book store or down load from the web Our Over 40000 guides and Ebooks is why customers keep returning. If a Praxis II Mathematics: Content Knowledge (5161) Exam Secrets Study Guide: Praxis II Test Review for the Praxis II: Subject Assessments is needed by you, you can download them in pdf format from our website. Basic extendable that may be downloaded and continue reading numerous devices. You are able to revise this making use of your PC, MAC, tablet, eBook smartphone or reader.
Get the test prep help you need to be successful on the Praxis II Mathematics: Content Knowledge test. The Praxis II Mathematics: Content Knowledge (5161) Exam is extremely challenging and thorough test preparation is essential for success. Praxis II Mathematics: Content Knowledge Exam Study Guide is the ideal prep solution for anyone who wants to pass the Praxis II Math: Content Knowledge Exam. Not only does it provide a comprehensive guide to the Praxis II Mathematics: Content Knowledge Exam as a whole, it also provides practice test questions as well as detailed explanations of each answer.
Praxis II Mathematics: Content Knowledge Exam Study Guide includes:
A thorough and detailed overview of mathematics content knowledge skills for teachers
A review of algebra and number theory
A guide to measurement
An in-depth look at geometry
A review of trigonometry
A guide to functions
An in-depth look at calculus
An analysis of data analysis and statistics
An in-depth guide to probability
It's filled with the critical information you'll need in order to do well on the test: the concepts, procedures, principles, and vocabulary that the Educational Testing Service (ETS) expects you to have mastered before sitting for the exam.
The Praxis II Math Numbers and Quantity section covers:
Numbers and their Classifications
Operations
Factors and Multiples
Fractions, Percentages, and Related Concepts
The Praxis II Math Functions section covers:
Manipulation of Functions
Classification of Functions
Applying the Basic Operations to Functions
The Praxis II Math Geometry section covers:
Perpendicular and angle bisectors
Quadrilaterals, parallelograms, and trapezoids
Types of angles
Acute, right, and obtuse triangles
The Praxis II Math Calculus section covers:
Limits
Derivatives
Fundamental Theorems of Calculus
The Praxis II Math Probability and Statistics section covers:
Probability
Expected value
Data Analysis
The Praxis II Math Discrete Mathematics section covers:
Factorials
Permutations and Combinations
Sequences
Cartesian Products/Relations
If you want to spend your Praxis II Mathematics prep time on the information most likely to help you perform well on the exam, you've made the best decision using our Praxis II Mathematics study guide.
Praxis II Mathematics review book that will help you avoid the pitfalls of Praxis II Mathematics test anxiety.
Praxis II Math practice test questions and much more...
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Book's Overview
An introduction to geometry in the plane, both Euclidean and hyperbolic, this book is designed for an undergraduate course in geometry. With its patient approach, and plentiful illustrations, it will also be a stimulating read for anyone comfortable with the language of mathematical proof. While the material within is classical, it brings together topics that are not generally found together in books at this level, such as: parametric equations for the pseudosphere and its geodesics; trilinear and barycentric coordinates; Euclidean and hyperbolic tilings; and theorems proved using inversion. The book is divided into four parts, and begins by developing neutral geometry in the spirit of Hilbert, leading to the Saccheri–Legendre Theorem. Subsequent sections explore classical Euclidean geometry, with an emphasis on concurrence results, followed by transformations in the Euclidean plane, and the geometry of the Poincaré disk model.
General information about Geometry Illuminated: An Illustrated Introduction to Euclidean and Hyperbolic Plane Geometry (Mathematical Association of America Textbooks)
The author associated with Geometry Illuminated: An Illustrated Introduction to Euclidean and Hyperbolic Plane Geometry (Mathematical Association of America Textbooks) is Matthew Harvey.
The EAN for Geometry Illuminated: An Illustrated Introduction to Euclidean and Hyperbolic Plane Geometry (Mathematical Association of America Textbooks) is 9781939512116.
The edition for Geometry Illuminated: An Illustrated Introduction to Euclidean and Hyperbolic Plane Geometry (Mathematical Association of America Textbooks) is Ill.
The format for Geometry Illuminated: An Illustrated Introduction to Euclidean and Hyperbolic Plane Geometry (Mathematical Association of America Textbooks) is Import.
The ISBN for Geometry Illuminated: An Illustrated Introduction to Euclidean and Hyperbolic Plane Geometry (Mathematical Association of America Textbooks) is 1939512115.
The height for Geometry Illuminated: An Illustrated Introduction to Euclidean and Hyperbolic Plane Geometry (Mathematical Association of America Textbooks) is 1000 mm.
The length for Geometry Illuminated: An Illustrated Introduction to Euclidean and Hyperbolic Plane Geometry (Mathematical Association of America Textbooks) is 700 mm.
The width for Geometry Illuminated: An Illustrated Introduction to Euclidean and Hyperbolic Plane Geometry (Mathematical Association of America Textbooks) is 125 mm.
The language for Geometry Illuminated: An Illustrated Introduction to Euclidean and Hyperbolic Plane Geometry (Mathematical Association of America Textbooks) is English.
The MPN (Manufacturer's part number) for Geometry Illuminated: An Illustrated Introduction to Euclidean and Hyperbolic Plane Geometry (Mathematical Association of America Textbooks) is illustrations.
The binding of Geometry Illuminated: An Illustrated Introduction to Euclidean and Hyperbolic Plane Geometry (Mathematical Association of America Textbooks) is Hardcover.
The number of pages for Geometry Illuminated: An Illustrated Introduction to Euclidean and Hyperbolic Plane Geometry (Mathematical Association of America Textbooks) are 558.
The part number for Geometry Illuminated: An Illustrated Introduction to Euclidean and Hyperbolic Plane Geometry (Mathematical Association of America Textbooks) is illustrations.
Geometry Illuminated: An Illustrated Introduction to Euclidean and Hyperbolic Plane Geometry (Mathematical Association of America Textbooks) is grouped in Book group of products.
The publication date for Geometry Illuminated: An Illustrated Introduction to Euclidean and Hyperbolic Plane Geometry (Mathematical Association of America Textbooks) is 2015-09-30.
The publisher for Geometry Illuminated: An Illustrated Introduction to Euclidean and Hyperbolic Plane Geometry (Mathematical Association of America Textbooks) is The Mathematical Association of America.
The producer for Geometry Illuminated: An Illustrated Introduction to Euclidean and Hyperbolic Plane Geometry (Mathematical Association of America Textbooks) is The Mathematical Association of America.
The sales rank for Geometry Illuminated: An Illustrated Introduction to Euclidean and Hyperbolic Plane Geometry (Mathematical Association of America Textbooks) is 615828. | 677.169 | 1 |
Calculus: Differentiability and Continuity
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This is the fifth lesson in a thirteen-lesson unit on Differentiation quiz or exit ticket
✎ Teachers also have the benefit of a fully-editable SMART Board® Lesson for presentation and discussion.
Lesson Objective:
* Estimate instantaneous rates of change graphically and numerically
*Use derivatives to provide information about function behavior including increase, decrease, extrema, and rates of change.
*Use the derivative at a point to write and use the equation of a tangent line to a curve at a point
*Use the tangent line to investigate function behavior and function values in a small neighborhood. | 677.169 | 1 |
Matrices And Determinants
Determinants and matrices of order two and three- properties of determinants, evaluation of determinants, addition and multiplication of matrices, adjoint and inverse of a matrix. Solution of simultaneous linear equations using determinants.
Quadratic Equations
Quadratic equations and their solutions, relation between roots and coefficients, nature of roots, formation of quadratic equations with given roots.
Permutations And Combinations
Fundamental principle of counting; permutation as an arrangement and combination as a selection, meaning of P(n, r) and C(n, r), simple applications.
Vector Algebra
Vectors and scalars, addition of two vectors, components of a vector in two and three dimensional space, scalar and vector products, scalar and vector triple products. Application of vectors to plane geometry.
Trigonometry
Trigonometrical identities and equations. Inverse trigonometric functions and their properties. Properties of triangles including centroid, incentre, circumcentre and orthocentre. Solution of triangles. Heights and distances.
Measures Of Central Tendency And Dispersion
Calculation of mean, median and mode, standard deviation, variance and mean deviation for grouped and ungrouped data.
Probability
Probability of an event, addition and multiplication theorems of probability and their applications. Conditional probability; Bayes' theorem. Probability distribution of a random variate- Binomial and Poisson distributions and their properties.
Differential Calculus
Polynomial, rational, trigonometric, logarithmic and exponential functions.
Graphs of simple functions. Limits, continuity and differentiation of the sum, difference, product and quotient of two functions. Differentiation of trigonometric, inverse trigonometric, logarithmic, exponential, composite and implicit functions; derivatives of order up to two. Applications of derivatives-maxima and minima of functions of one variable, tangents and normals, Rolle's and Lagrange's mean value theorems.
Integral Calculus
Integral as an anti derivative, fundamental integrals involving algebraic, trigonometric, exponential and logarithmic functions. Integration by substitution, by parts and by partial fractions. Integration using trigonometric identities. Integral as a limit of sum. Properties of definite integrals. Evaluation of definite integral, determining areas of the regions bounded by simple curves.
Differential Equations
Formation of differential equations. Solutions of first order differential equations- the method of separation of variables, homogeneous and linear differential equations.
Two Dimensional Geometry
Review of cartesian system of rectangular co-ordinates in a plane, distance formula, area of a triangle, condition for the collinearity of three points, slope of a line, parallel and perpendicular lines, intercepts of a line on the coordinate axes.
The Straight Line And Pair Of Straight Lines
Various forms of equations of a line, intersection of lines, angles between two lines, conditions for concurrence of three lines, distance of a point from a line. Equations of internal and external bisectors of angles between two lines, equation of a family of lines passing through the point of intersection of two lines, point of intersections and angles between two lines. Pair of straight lines- condition for the general second degree equation to represent a pair of lines, point of intersection and angle between pair of lines through the origin, combined equation of the bisectors of the angles between a pair of lines.
Circles And Family Of Circles
Equation of a circle- standard form, general form, parametric form, equation of a circle when the end points of a diameter are given. Radius and centre of a circle, points of intersection of a line and a circle. Condition for a line to be tangent, equation of a family of circles through the intersection of two circles, condition for two intersecting circles to be orthogonal.
Conic Sections
Sections of cones, equations of conic sections (parabola, ellipse and hyperbola) in standard forms, conditions for a line to be a tangent and point(s) of tangency.
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Units And Dimensions
Units for measurement, system of units, SI, fundamental and derived units, dimensions and their
Applications.
Mechanics
Motion in straight line, uniform and non-uniform motion, uniformly accelerated motion and its applications. Scalars and Vectors, and their properties; resolution of vectors, scalar and vector products; uniform circular motion and its applications, projectile motion Newton's Laws of motion; conservation of linear momentum and its applications, laws of friction, Concept of work, energy and power; energy-kinetic and potential; conservation of energy; different forms of energy. Elastic collisions in one and two dimensions. Center of mass of a many particle system; center of mass of a rigid body, rotational motion and torque. Angular momentum and its conservation. Moments of inertia, parallel and perpendicular axes theorem, moment of inertia for a thin rod, ring, disc and sphere. Gravitation: Acceleration due to gravity and its properties. One and two dimensional motion under gravity. Universal law of gravitation, planetary motion, Kepler's laws, artificial satellite-geostationary satellite, gravitational potential energy near the surface of earth, gravitational potential and escape velocity.
Heat And Thermodynamics
Thermal expansion of solids, liquids and gases and their specific heats, relationship between Cp and Cv for gases, first and second laws of thermodynamics , Carnot cycle, efficiency of heat engines. Transference of heat; thermal conductivity; black body radiations, Kirchoff's law, Wein's Law, Stefan's law of radiation and Newton's law of cooling.
Electrostatics,Current Electricity And Magnetostatics
Coloumb's law, dielectric constant, electric field, lines of force, field due to dipole , electric flux, Gauss's theorem and its applications; electric potential, potential due to a point charge; conductors and insulators, distribution of charge on conductors; capacitance, parallel plate capacitor, combination of capacitors, energy stored in a capacitor Electric current : Cells -primary and secondary, grouping of cells; resistance and specific resistivity and its temperature dependence. Ohm's law, Kirchoff's Law. Series and parallel circuits; Wheatstone's Bridge and potentiometer with their applications. Heating effects of current, electric power, concept of thermoelectricity-Seebeck effect and thermocouple; chemical effect of current- Faraday's laws of electrolysis. Magnetic effects: Oersted's experiment, Biot Savert's law, magnetic field due to straight wire, circular loop and solenoid, force on a moving charge in a uniform magnetic field(Lorentz force),forces and torques on a current carrying conductor in a magnetic field, force between current carrying wires, moving coil galvanometer and conversion to ammeter and voltmeter Magnetostatics: Bar magnet, magnetic field, lines of force, torque on a bar magnet in a magnetic field, earth's magnetic field; para, dia and ferro magnetism, magnetic induction, magnetic susceptibility. | 677.169 | 1 |
Coursework maths
Each course consists of 4 modules. Each module is designed to take hours to complete. This includes about 20 minutes to watch the video, and the remaining time for online activities.
The activities are a mix of traditional mathematical problem solving, and online interaction. For example, in Archimedes and the Law of the Lever you will use mathematical concepts to balance a lever. On the more social side of things, you will brainstorm and post pictures of levers from your daily life (and you get to see what everyone else posted). | 677.169 | 1 |
Foundation for college mathematics 11 paper near me
Except where otherwise noted, Math Bridge Course by the Washington Office of Superintendent of the middle-grades level to provide a strong foundation. .. Find the individual in your class who is closest to having the "perfect" human face. .. Goals: To select a card and enlarge it to best fit an 8 ½ " x 11 " sheet of paper.
College Algebra Near the end of most pages is a "Your Turn" section do these! And don't guess the answer: use pen and paper and try your best before seeing the But from that simple foundation many useful things can be built.
Going to college gives you the paper, which is essential to landing jobs, . dan_waterworth Jan 6 ' 11 at But the fact remains that the information is available without me being anywhere near a university CS or maths department.
Floor and Ceiling Function. So let us learn about in equalities. Log out click here. Lambton Kent DSB Roland W. You can also sum up a series, where Sigma Notation is very useful. Graphs can save you!
Foundation for college mathematics 11 paper near me - Ask
None Yellow Red Green Blue Search This site The web PowerSearch Getting Started with T.... Student Text Student Workbook Task Exemplars Teacher's Resource Technology Masters Web Tasks Getting Started with T.... And together they can be very powerful. Please change your browser preferences to enable javascript, and reload this page. Maybe you only know that something is less than, or greater than. Lambton Kent DSB Roland W. | 677.169 | 1 |
Videos
Our Features
Solved Examples
Solved examples are provided to help students understand and solve mathematical questions with ease.
Tutorial Videos
Questions are supported with thousands of short videos that provide step-by-step explanations on how to solve various types of questions.
Progress Reports
Our responsive intelligent system tracks the students' progress and their answer patterns to provide them with questions that fit their level and learning pace. Detailed reports of their progress are also provided and can be viewed by teachers and parents alike.
Assessments And Worksheets
Students can easily access the assessments and worksheets sent to their accounts. Additionally, the assessments and worksheets are autocorrected for you | 677.169 | 1 |
An innovative and appealing way for the layperson to develop math skills--while actually enjoying it Most people agree that math is important, but few would say it's fun. This book will show you that the subject you learned to hate in high school can be as entertaining as a witty remark, as engrossing as the mystery novel you can't put down--in... more...
Handy compilation of 100 practice problems, hints and solutions indispensable for students preparing for the William Lowell Putnam and other mathematical competitions. Preface to the First Edition. Sources. 1988 edition. more...
Critically acclaimed and commercially successful, this resource is packed with useful information and instruction. Features proven teaching techniques, games, and more. Suitable for parents of children from preschool to age 10. 2006 edition. more...
Over 300 challenging problems in algebra, arithmetic, elementary number theory and trigonometry, selected from Mathematical Olympiads held at Moscow University. Only high school math needed. Includes complete solutions. Features 27 black-and-white illustrations. 1962 edition. more...
Students and others wishing to know more about the practical side of mathematics will find this volume a highly informative resource. Accessible explanations of important concepts feature worked examples and diagrams. 1963 edition. more...
This original volume offers a concise, highly focused review of what high school and beginning college students need to know in order to solve problems in logarithms and exponential functions. Numerous rigorously tested examples and coherent to-the-point explanations, presented in an easy-to-follow format, provide valuable tools for conquering this... more...
"Fun and highly formidable math problems and puzzles from noted puzzle creator Terry Stickels." — Window on Resources Two friends wish to meet for breakfast twice a month throughout the year. In how many ways can they choose those two days so that they never meet on consecutive days? You want to measure 30 seconds and you have two pieces of string,... more... | 677.169 | 1 |
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Friday, March 19, 2010
The Excel Math Curricula
Math must be part of a critical core curriculum. It is one of the few subjects (along with reading and writing) worth "forcing" students to know. No one should enter the productive world, nor can they make good life decisions, without a deep and comfortable experience with math.
Given that, what math should be taught? Most math programs have been hopelessly tangled up in the same quagmire of precedent and capriciousness that has sunk the rest of formal schools' curricula.
Thus areas like algebra, geometry, and calculus are greatly overemphasized, while areas like discrete math, logic, programming, permutations, probabilities, and combinatorics are hugely deemphasized (the terms are complicated but the areas are not). For most students, calculus should be covered in history classes as a great invention in the same matter as pottery or the loom, if at all. Obviously for those passionate about math, and who go on to be pure or applied math or engineering majors, calculus should subsequently be required.
However, there remains a perfect tool and context for math, which many people already have. And that is a good spreadsheet such as Excel.
The built in math functions of a good spreadsheet have accurately captured a range of abilities necessary to use by planners, decision makers, and scientists.
Further, the program still requires rigorous, high level planning and programming. A spreadsheet does a lot of the rote work, but still requires and develops rock solid conceptualization and understanding of the material.
Students can solve the same problem in different ways, which is a plus for reactance inflicted teenagers (although bad for traditional teacher).
Finally, spreadsheets allow accessing information through symbols as well as more graphs. Most math is more visual anyway. (Will Wright, the brilliant creator of SimCity and The Sims, mused in a conversation we had if one should teach math without any numbers at all.)
Using a spreadsheet well, and being able to use as much of the built in equations as possible in the appropriate situation and to the right end, is a better framework than the textbooks and worksheets and obscure topic areas of yesteryear.
5 comments:
Children do not need to be forced to learn reading, writing, or math. Sure way to create the epidemic of math anxiety we have here in the United States. How about, instead, enticing and supporting them in their learning?
I loved the rest of what you had to say abut which aspects of math should be emphasized. I object to the idea of forcing learning. In fact, I'd go so far as to say that forced learning is a near-oxymoron...what is learned under coercion is so very often not what is being taught.
I currently teach a course (inside of course) that uses projects and excel spreadsheets with students that are not particularly strong in math. It is a wonderful tool, and more math teachers should use and teach excel. It is sad to think about all the students that have a strong quantitative background that don't know how to do the first thing with excel. I am enjoying the posts. Keep'em coming.
From the entry on leadership styles: <<<< * from the "talking-head" lecture (Level 1) * to environments that use sims and labs (Level 2) * to environments where students decide their own curricula, grading, and processes, and interact with complicated and real environments ( Level 3).>>>>
What about environments where a "curriculum" doesn't exist at all and where there is no grading? That is real unschooling. The adults in the unschooled child's life are facilitators and supporters - more like really great "docents of the world" than teachers. | 677.169 | 1 |
Modular Arithmetic and Elementary Algebra Lecturer : Michel Goemans
Abstract
These notes cover basic notions in algebra which will be needed for discussing several topics of this course. In particular, we will need them to describe the RSA cryptosystem, the primality testing algorithms, and for the material on error-correcting codes that we will be covering later in this course. Euclid's algorithm (or the Euclidean algorithm) is a… (More) | 677.169 | 1 |
Ncert 9th Class Guide Of Mathematics
Ncert 9th Class Guide Of Mathematics
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S.2.GLE.2.RA.1: The understanding and use of equations, inequalities, and systems of equations allows for situational analysis and decision-making. For example, it helps people choose cell phone plans, calculate credit card interest and payments, and determine health insurance costs.
S.2.GLE.2.RA.2: Recognition of the significance of the point of intersection for two linear equations helps to solve problems involving two linear rates such as determining when two vehicles traveling at constant speeds will be in the same place, when two calling plans cost the same, or the point when profits begin to exceed costs.
S.2.GLE.3.RA.1: Recognition that non-linear situations is a clue to non-constant growth over time helps to understand such concepts as compound interest rates, population growth, appreciations, and depreciation.
S.3.GLE.1.RA.1: The ability to analyze and interpret data helps to distinguish between false relationships such as developing superstitions from seeing two events happen in close succession versus identifying a credible correlation.
S.3.GLE.1.RA.2: Data analysis provides the tools to use data to model relationships, make predictions, and determine the reasonableness and limitations of those predictions. For example, predicting whether staying up late affects grades, or the relationships between education and income, between income and energy consumption, or between the unemployment rate and GDP.
S.4.GLE.2.RA.2: Knowledge of how to use right triangles and the Pythagorean Theorem enables design and construction of such structures as a properly pitched roof, handicap ramps to meet code, structurally stable bridges, and roads. | 677.169 | 1 |
Synopsis
Mathematical Explorations follows on from the author's previous book, Creative Mathematics, in the same series, and gives the reader experience in working on problems requiring a little more mathematical maturity. The author's main aim is to show that problems are often solved by using mathematics that is not obviously connected to the problem, and readers are encouraged to consider as wide a variety of mathematical ideas as possible. In each case, the emphasis is placed on the important underlying ideas rather than on the solutions for their own sake. To enhance understanding of how mathematical research is conducted, each problem has been chosen not for its mathematical importance, but because it provides a good illustration of how arguments can be developed. While the reader does not require a deep mathematical background to tackle these problems, they will find their mathematical understanding is enriched by attempting to solve them.
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JUMP TO...
Waves and wave propagation are ubiquitous in nature
and lead to many puzzling questions. For instance, what produces
mirages in the desert? Why is it that a storm over the ocean sets off
a steady swell of small-amplitude waves, but an earthquake at the sea
floor can release an enormous flood wave? Can you hear the shape of a
drum? In response to these questions, a great deal of mathematics has
been developed to understand and predict the dynamics of light or
sound waves, the propagation of quantum (matter) waves, the vibration
patterns of elastic bodies, or the peculiar nature of water waves.
This course will give a guided tour of mathematical wave theory
together with physical applications, including normal mode theory, the
linear wave equation, superposition, interference and diffraction,
short-wavelength asymptotics and ray theory, dispersion, and nonlinear
waves and solitons. By the last few weeks of the course, each student
will have chosen a topic for more intensive study, and will work
towards a final oral presentation and written report. Typically this
will involve numerical investigation on a computer (in which case
programming experience is helpful), but a theoretical topic is also
possible.
This new course is part of the
Courant's VIGRE program,
and uses the `undergraduate mathematics laboratory' concept of bringing advanced
undergraduates together with postdocs and professors to work on current
pure or applied research topics, usually with computer experiments. | 677.169 | 1 |
Overview
The main aim of this module is to provide you with a basic understanding of mathematics suitable for the Stages 2 and 3 degree programmes in Economics, Business, and Accounting. The mathematics material is developed in a clear, contextual framework, and is linked to a Stage 1 module in Economics. You develop your understanding with suitable problem sets combining mathematical concepts and economic methods.
Learning outcomes
By the end of the module you should be able to:
appreciate why economists use mathematics
use basic algebra, and understand linear, quadratic and simultaneous equations
understand how functions and equations are used in economics
calculate elasticities and work out equilibrium outcomes
differentiate simple functions and economic relationships
sketch curves and understand optimising behaviour in the context of marginal relationships
differentiate multivariable functions and calculate partial elasticities
set up and solve constrained optimisation problems
understand the basic concepts of matrices and matrix algebra
University of Kent makes every effort to ensure that module information is accurate for the relevant academic session and to provide educational services as described. However, courses, services and other matters may be subject to change. Please read our full disclaimer. | 677.169 | 1 |
Intro
Introductory Mathematics provides students a survey of preparatory topics for high school mathematics, including the foundations for high school algebra and geometry. Appropriate technology, from manipulatives to calculators, will be used regularly for instruction and assessment. It is designed to prepare students for success in Math I. The elective credit course includes studies of functions, equations and inequalities, statistics and much more. This course has a teacher-made final exam. We will be following the standard course of study found at For each session of classroom instruction, the student is expected to spend thirty minutes outside of class on assignments, review, and preparation. | 677.169 | 1 |
Unit 5
Exponential Functions
Unit Overview
Exponential functions develops student ability to recognize and represent exponential growth and decay patterns, to express those patterns in symbolic forms, to solve problems that involve exponential change, and to use properties of exponents to write expressions in equivalent forms. This unit is organized into two main components. The first half of the unit explores a variety of situations involving exponential growth and the second part explores a variety of situations involving exponential decay. Each component will explore geometric sequences, exponential functions in verbal, table, graph, and equation formats, and will then explore application problems of growth and decay. In between each component, the effect of k (which represents a positive or negative constant value) is explored as it transforms the behavior of the exponential graph. Each component will consist of approximately 8-9 days. The remaining days will include pre- and post-testing of standards. Properties of exponents are reviewed in warms-ups in the beginning of the unit. Vertical and horizontal translations are reviewed in warm-ups towards the middle or the unit.
explain the behavior of the graph when replacing f(x) by f(x) + k, and f(x + k) for specific values of k.
given the graph of a function in the form f(x) = a * rx and a transformed graph, determine the value k.
use appropriate technology to explore the effects of the value k on the function.
construct a graph of an exponential function from a table, sequence or a situation.
construct a table and/or a graph of a linear function with slope m and an exponential rate of change equal to the slope to identify the point where the exponential function exceeds the linear function.
evaluate exponential functions for given domains.
model an exponential relationship between two quantities with tables, graphs, and equations.
classify exponential functions as growth or decay.
compare/contrast properties and the graphs of linear and exponential functions.
create exponential models to represent real-life data.
interpret the graph and describe the pattern of change seen in the graph.
find solutions to exponential equations using the graph.
interpret what the parts of an expression tell you about a given situation.
determine the boundaries and choose an appropriate scale when graphing an exponential function.
determine the difference between the rate of change of a linear model (add each time) versus an exponential model (multiply each time)
given a situation recognize which sequence (arithmetic/geometric) should be identified to interpret the model.
recognize patterns to determine an arithmetic or geometric model for a sequence or problem. | 677.169 | 1 |
contemporary approach to liberal arts math breaks away from traditional instruction and moves towards a more "modern" course that stresses rich ideas, little review, and more visualization. This reader-friendly book offers an accessible writing style and mathematical integrity. Its unique three-part organization (Life, Society, the World) presents readers with sound, relevant mathematics, leaving them with the (correct) impression that math is useful and affects their lives in many positive ways30116904 MULTIPLE COPIES AVAILABLE-Very Good Condition-May have writing or
[...]
0130116904 | 677.169 | 1 |
{"name":"mathjs","version":"3.20.1","filename":"math.min.js","homepage":" is an extensive math library for JavaScript and Node.js. It features a flexible expression parser and offers an integrated solution to work with numbers, big numbers, complex numbers, units, and matrices.","author":"Jos de Jong ( | 677.169 | 1 |
§1.6, Exponential and Logarithmic
Functions#2P Some "loglog graph paper" is given, and students
must discover that a power relationship (y=AxB) appears as
a straight line of slope B on this graph paper. Further copies of the
graph paper may be printed to help with writeups if this problem is
assigned. CLICK FOR PDF.
§1.7, Technology: Calculators and Computers#3D Four computer-drawn graphs of x2
centered at (2,4) are displayed. Students are asked to explain the
results, and to give an example of a "straight line" which
could not result from this process. This problem was suggested by
G. Cherlin. Some answers are given as comments in the TEX file.
Possibly relevant to a later graphing section.
CLICK FOR PDF.
§2.5, Limits and
Continuity#5D Four limit situations are described which all
play on falsifying the conditions of continuity. Graphs are requested
of functions satisfying these situations. CLICK
FOR PDF.
§2.5, Limits and
Continuity#5E A piecewise defined function with two parameters
is given. Graphs are required for two pairs of values of the
parameters, one given, and the other requested to make the given
function continuous. CLICK FOR
PDF.
§2.7, Intermediate Value
Theorem#5C Graph x3 and a specific bounded
continuous function in an appropriate interval, appeal to IVT for a
root, and approximate the root. Understand what happens in general.
CLICK FOR PDF.
§2.7, Intermediate Value
Theorem#nan8 Tabular information is given about a
function and students are asked to investigate the number of
roots. Two specific examples are given to explore the situation.
CLICK FOR
PDF.
§2.7, Intermediate Value
Theorem#nan12 Students are asked why a specific cubic
polynomial has a root in [0,1]. This polynomial is perturbed and
students are asked to reconsider the number of roots.
CLICK FOR
PDF.
§3.1, Definition of the Derivative
#1Q Students must use a graphing calculator
here. One function is 3x at (0,1). The other function is
6x arctan((ln x)/(x3+2)) at (1,0). Graphs of the functions and two secant
lines are requested, as well as tables of slopes of secant lines. Then
equations for the tangent lines are requested. CLICK FOR PDF.
§3.2, The Derivative as a Function#3E A rational function with two parameters is
given. Find parameter values so that a given line is tangent at a
given point. Graph the resulting curve with the line. CLICK FOR PDF.
§3.2, The Derivative as a
Function#1C A graph of a (bizarre!) function is given, and
students are asked about continuity, differentiability, and the graph
of the derivative.
See also problems 49 and 74 in §3.2.
CLICK FOR PDF.
§3.2, The Derivative as a
Function
#nan14 The parabola y=x2 is flipped and
pushed up: what "push" is needed to have orthogonal intersections?
Then the parabola is translated left/right: what translates give
orthogonal intersections?
CLICK FOR PDF.
§3.3, Product and Quotient Rules#1B Tabular information is given about two
functions and their derivatives. Values of algebraic combinations of
the functions and derivatives of these combinations are
requested. See also problems 49–52 of §3.3.
CLICK FOR PDF.
§3.3, Product and Quotient Rules#3Z A formula (quotient of quadratic and exp) is
given. Then a graph is requested, and a tangent line and estimates of
{largest|smallest} values. The derivative verifies the estimates.
CLICK FOR PDF.
§3.4, Rates of Change#3X Four containers with identical volume but
different profiles are given. They are filled at a constant
rate. Students graph and analyze (continuous?
differentiable?) the liquid's height in each container.
Volume change is constant here but see also problems 52–54 of
§4.4. CLICK FOR PDF.
§3.7, The Chain Rule
#2H Tabular information is given about a function
and its first two derivatives. Find values of the function and the
first two derivatives for f(x2), (f(x))2, and
f(f(x)). Also there's a linear approximation part which can be omitted
if the material has not yet been covered. CLICK
FOR PDF.
§3.8, Implicit
Differentiation#4X A point moves on a parabola. The x and y
velocities are studied. What happens if the horizontal velocity is
constant? What happens if the vertical velocity is constant?
CLICK FOR PDF.
§3.8, Implicit
Differentiation#nan15 Two families of curves are defined. Students
are asked to sketch some members of each family and then are requested
to verify that the members of the families intersect orthogonally.
CLICK FOR PDF.
§3.9, Derivatives of Inverse
Functions#1K Verify that a given integer linear fractional
transformation is invertible. Compute values of the functions
(original and inverse) and derivatives at corresponding points.
CLICK FOR PDF.
§3.11, Related Rates#3T A ladder slides down a wall. The end of the ladder
goes faster than the speed of sound, and then, faster than light: a
simple mathematical model extrapolated to silliness.
See also problems 19–23 of §3.11. CLICK FOR PDF.
§4.1, Linear Approximation and Applications#sg48 A classical formula for body surface area due
to Dubois & Dubois is analyzed. What happens if body weight changes?
What happens if body height changes? Understand how linear
approximation can give some information. CLICK
FOR PDF.
§4.2,
Extreme Values#3A This problem is a more subtle version of the
model workshop problem included in the Rutgers version of the
textbook. A piecewise-defined function is analyzed and minimized.
CLICK FOR PDF.
§4.3, The Mean Value Theorem and Monotonicity#3R The graph of the derivative of a function is
given, and its value at a point. Careful use of the Mean Value
Theorem, combined with the Intermediate Value Theorem, shows the
existence of a root of the function. An elaborate problem. CLICK FOR PDF.
§4.4, The Shape of a Graph#1H Real data: the monthly rate of inflation for the
U.S. in the last half of 1920 is given. What do these numbers mean
about the first and second derivatives of consumer prices? What is a
real-world translation of the numbers in terms of prices? CLICK FOR PDF.
§4.4, The Shape of a Graph
#1M A point on an implicitly defined curve is given. What is the concavity of the curve at that point? (Second derivative via implicit differentiation; a good example where an explicit formula for y in terms of x exists and is very unwieldy.)
CLICK FOR PDF.
§4.4, The Shape of a Graph#3N A first derivative graph is given, and students
must find where the function is {in|de}creasing, has local extrema, is
concave {up|down}, and has points of inflection. The graph of the
original function is requested. CLICK FOR PDF.
§4.4, The Shape of a
Graph#2R A parameterized family of functions is given:
(x2+c)ex. Graphs drawn with the help of a
machine motivate investigation of the number of inflection points of
these graphs.
CLICK FOR PDF.
§4.7, L'Hôpital's Rule#3H Three sorting algorithms are given with their
average running times. Which is better for various values of inputs,
and which is best asymptotically as list size goes to ∞?
CLICK FOR PDF.
§4.8, Newton's
Method#3M Asks for a Newton's method approximation to an
equation, then discussion about the positive roots of
1/(1+x2)=tan(x).
Also problem 28 in this section would probably
be a good workshop problem. CLICK FOR PDF.
§5.6, Substitution Method#5R Students compute antiderivatives of sqrt(1+sqrt(x)) and
sqrt(1+sqrt(1+sqrt(x))). The latter can't be computed by current hand-held devices. They are asked to discuss the antidifferentiation of
sqrt(1+sqrt(1+sqrt(1+sqrt(x)))) which currently (December 2007) can't be done with the default settings of Maple
and Mathematica.
CLICK FOR PDF.
§5.8, Exponential Growth and Decay
#4A A certain radioactive substance when affected by (hypothetical) gamma ray flux has faster decay. Determine when to turn on the flux to obtain a specific amount of the substance after a specific time.
CLICK FOR PDF.
§5.8, Exponential Growth and Decay
#5I "Lab data" for growth of bacteria has some missing entries. The missing information must be reconstructed. Some of the text's problems in this section would be good workshop problems.
CLICK FOR PDF.
§7.1, Numerical
Integration#6L The graph of a function and its first four
derivatives are given. An estimate of the definite integral from the
graph is requested, following by use of the graphical information to
get error bounds for the Trapezoid Rule and for Simpson's
Rule. Note that the default location for four of the graphs is
on the next page. CLICK FOR
PDF.
§7.2, Integration by Parts#4R The function e–Ax is considered on
[1,2]. As A→∞, the integral of f(x), xf(x), and
(1/1+5x48)f(x) all→0. The second result needs integration
by parts, and the third is done by estimation. CLICK FOR PDF.
§7.2, Integration by
Parts#4S The function exsin(Nx) is considered
on the interval [0,1]. Graphs for N=5, 10, and 100 are requested, as
is the definite integral of the function. What happens as N→∞?
CLICK FOR PDF.
§7.2, Integration by
Parts#5O Integrate cos(mx)cos(nx) from 0 to 2Pi. Use this
to find a sum of cosines when given the values of the integrals of the
function multiplied by some cosines (an elementary aspect of Fourier
series). CLICK FOR PDF.
§7.2, Integration by
Parts#5Q Find the line through the origin which best
approximates (least mean square error) sin(x) on [0,1]. Sketch the
line and sin(x) and the tangent line at x=0 to sin(x) on
[0,1]. CLICK FOR PDF.
§7.6, The Method of Partial Fractions
#4M The area of a region under
(5+x)/(x2+4x+3) is computed exactly and by calculator. The
volume obtained when the region is revolved about the x-axis is
computed exactly and by calculator. CLICK FOR
PDF.
§7.6, The Method of Partial Fractions
#5P The integrals from 1 to 2 of 1/x2 and
1/(x(x–m)) and
1/(x2+m) for n and m small and positive are computed. What
happens as m→0+ and n→0+? Illustrate with a
sketch. CLICK FOR PDF.
§7.7, Improper Integrals
#5X Consider the region bounded by y=0,
y=x–a, and x=1. For which a's does this region have finite
area? Revolve the region about the x-axis (respectively, the
y-axis). For which a's are each of these volumes finite? CLICK FOR PDF.
§7.7, Improper Integrals
#5H Explain why two rational integrals, one
improper, are equal. Either compute both integrals or show they are
equal using a change of variables (substitution). CLICK FOR PDF.
§7.7, Improper Integrals
#6M The integral of x–ln(x) from 0 to
∞ is investigated. The limits of the integrand as
x→0+ and x→∞ are requested. The integral is
evaluated depending on the value of the integral of
e–x2 from –∞ to ∞: an integral
which "can't" be computed using the default configuration of Maple. CLICK FOR
PDF.
§7.7, Improper Integrals
#sg18 Here the integral
∫0∞(sin(x)/x)dx is evaluated by a complicated use of
differentiation under the integral. This problem may be too difficult
to assign, but the technique here and in sg50, the previous problem,
is discussed nicely by K. Conrad in this paper:
(the URL
is also available as a comment in the TEX file). CLICK FOR
PDF.
§8.1, Arc Length and Surface
Area#5Z Is the area of the surface obtained by revolving
y=e–x, x>0, about the x-axis finite? Only yes/no is
asked, but an exact answer is given as a TeX comment. CLICK FOR PDF.
§8.4, Taylor
Polynomials#sg7 Suppose f(x)=ex2+sin(x).
Information about values of f(j)(0) is given, along with
some graphs. Then Taylor polynomials of f(x) centered at 0 are
requested along with an error estimate.
CLICK FOR
PDF.
§9.1, Solving Differential Equations
#6Z A separable ODE is given, and the solution of a
specific initial value problem is requested. The student must graph
the solution curve and state its domain. CLICK
FOR PDF.
§9.1, Solving Differential Equations
#6S Decide which two of four ODE's are separable and
then solve an initial value problem for each of them. Also explain why
one of the other ODE's is not separable. CLICK FOR PDF.
§9.1, Solving Differential Equations
#6T A function explodes at b if
lim→b–f(x) is +∞ or
–∞. After some examples, solutions of y´=y2
have their "explosions" analyzed (that is, how domains of solution
curves depend on initial conditions is investigated). CLICK FOR PDF.
§9.2, Models involving y´=k(y–b)
#6T Find the initial temperature of an object
subject to Newton's Law of Cooling if two data points are known. Some
of the text's problems in this section would be good workshop
problems. CLICK FOR PDF.
§9.3, Graphical and Numerical Methods
#6K A separable ODE is analyzed. Which values of the
integration constant correspond to solutions? What is the domain of
the solution curves? How does the direction field interact with
solution curves? CLICK FOR
PDF.
§9.3, Graphical and Numerical Methods
#6W The direction field for a first order linear ODE
is given. The equation can't be solved explicitly using standard
functions. Students are asked to sketch a solution curve and to
analyze any possible critical points of the solution
curve. CLICK FOR PDF.
§10.1, Sequences
#4Z Repeated square roots of 5 followed by
subtracting 1 and multiplying by powers of 2 approximate
ln(5). Explain this, and show how ln's can be "computed" generally
with this method. CLICK FOR
PDF.
§10.1, Sequences
#5J Several variations on the sequential definition
of e are given. Numerical values for the first terms are
requested, and then the limiting values are found using
L'Hôpital's Rule. CLICK FOR
PDF.
§10.1, Sequences
#5K A recursively defined sequence is analyzed
graphically, and students are asked to cite a specific result which
will guarantee convergence ("Monotone bounded sequences ...") and must
find the limit. CLICK FOR
PDF.
§10.1, Sequences
#5L A recursively defined sequence is analyzed
algebraically. It is increasing and bounded. Students are asked to
cite a specific result which will guarantee convergence ("Monotone
bounded sequences ...") and must find the limit. CLICK FOR PDF.
§10.2, Summing an Infinite Series
#7J The centers of the sides of a square are joined
to form a smaller square. In turn, the centers of the sides of that
square are joined ... What is the total length of the figure? (Our
only pictex figure.) CLICK FOR PDF.
§10.3, Convergence of Series with Positive Terms
#7D Inequalities relating to the Integral Test are
used to investigate infinite tails of convergent series whose
jth terms are 1/j5 and
je–2. Finally, an approximation of the whole sum
of one of the series is requested. CLICK FOR
PDF.
§10.3, Convergence of Series with Positive Terms
#4G Several computed partial sums of a series are
reported, and students are asked to verify that the series converges
to a specific number, with an error tolerance. The Integral Test
should be used.The next problem, 6R, is a companion to this problem.
CLICK FOR PDF.
§10.3, Convergence of Series with Positive Terms
#6R Several computed partial sums of a series are
reported, and students are asked to verify that the series converges
to a specific number, with an error tolerance. A comparison to a
geometric series is suggested. This is a companion to the previous
problem, 4G. CLICK FOR
PDF.
§10.4, Absolute and Conditional Convergence
#4O Consider a series whose absolute value is a
geometric series with 3 as first term and 1/3 as ratio. Students are
asked if sign choices (+ or –) can make the series diverge, sum to
3.5, or sum to 2.25. CLICK FOR
PDF.
§10.4, Absolute and Conditional Convergence
#4N A Fourier sine series is analyzed. The graph of
a partial sum is given. Questions about convergence, periodicity, and
the accuracy of the graph are asked. A comment in the TEX file gives the sum of the series (verification
is possible with Euler's identity). CLICK FOR
PDF.
§10.4, Absolute and Conditional Convergence
#7Q Three series are offered as candidates for the
alternating series test. For those series which qualify, partial sums
within 10–8 are requested, and the value of one such
partial sum is desired. CLICK FOR
PDF.
§10.5, The Ratio and Root Tests
#4K Several computed partial sums of a series are
reported, and students are asked to verify that the series converges
to a specific number, with an error tolerance. A quantitative version
of the Ratio Test can be used. CLICK FOR
PDF.
§10.5, The Ratio and Root Tests
#7P Students are asked to compare the rates of
growth of several functions. Ideas needed combine the ratio test and
perhaps L'Hôpital's Rule. See also the discussion of "<<" in
section 4.7. CLICK FOR
PDF.
§10.6, Power Series
#4F A Bessel function series is investigated. After
verifying convergence, students are asked to show that one value of
the series is positive and another value is negative. CLICK FOR PDF.
§10.6, Power Series
#7E The geometric series formula is used to find
power series for several functions. One of these series is then used
to write a definite integral as the sum of an infinite
series. CLICK FOR PDF.
§10.6, Power Series
#6U A power series is analyzed: its interval of
convergence, and an ODE it satisfies. Solving the ODE gives a formula
for the sum of the series. A possible continuation asks for an
error bound (using alternating series) between the function and a
specific partial sum. CLICK FOR
PDF.
§10.6, Power Series
#7F Two graphs are given, one with a jump
discontinuity and one with a cusp. In each case, what is the largest
possible radius of convergence of a power series whose sum is the
function with displayed graph? CLICK FOR
PDF.
§10.6, Power Series
#sg31 A problem from Knuth's The Art of Computer Programming. It relates power series "convolved" with the harmonic series and an integral: an abstract problem difficult for students.
CLICK FOR PDF.
§10.7, Taylor Series
#7L The first 10 terms of the Maclaurin series of
(1+x+x2)sin(x3) are requested, as well as the
10th derivative of this function at 0. Some of the text's
problems in this section, especially the integrals, would be good
workshop problems. CLICK FOR
PDF.
§10.7, Taylor Series
#7M Use Maclaurin series to compute a limit which
would take 9 applications of L'Hôpital's Rule. Some of the
text's problems in this section, especially the integrals, would be
good workshop problems. CLICK FOR
PDF.
§11.1, Parametric
Equations#6A Equations defining a collection of parametric curves
with a loop and self-intersection are given, and students must
identify the unique curve in this collection where the
self-intersection is orthogonal. Some of the text's problems in this
section would be good workshop problems. CLICK
FOR PDF.
§11.1, Parametric
Equations#6B Five different parametric descriptions (using
"simple" geometric parameters) are requested for
y=x2. Five is too much, and perhaps select three of
the five for a workshop problem. Some of the text's problems in this
section would be good workshop problems. CLICK
FOR PDF.
§11.1, Parametric
Equations#6F A parametric curve must be sketched, and the tangent
lines which are parallel to the coordinate axes and to y=x are
requested. Some of the text's problems in this section would be good
workshop problems. CLICK FOR
PDF.
§11.2, Arc Length and
Speed#6G A parameterized collection of parametric curves is
given. Students must sketch some representative curves, find some
tangent lines, and find the length of a loop in one of
them. CLICK FOR PDF.
§11.4, Area and Arc Length in Polar
Coordinates#7N Deduce speed formula in polar coordinates given the
formula in rectangular coordinates. Then deduce the connection between
speed and the magnitude of acceleration for uniform circular
motion. CLICK FOR PDF.
§14.1, Functions of Two of More
Variables#sg27 An absurd problem modeled after post office
specifications for allowable package sizes. The answer (the domain of
allowable package sizes) is a bit surprising. (One of my favorite
problems.) CLICK FOR PDF.
§14.4, Differentiability, Linear
Approximation, and Tangent
Planes#sg45 Coefficients of a polynomial are symmetric
functions of it roots. In this problem, students are asked to write
these functions for a cubic polynomial, and then find the first
derivatives and accompanying linear approximations. They are then
asked to consider the inverse problem, and find linear approximations
to the roots if the coefficients are perturbed. CLICK FOR PDF.
§14.6, The Chain Rule#sg43 This problem is too difficult and too long and
suitable almost surely only for ambitious honors students. It first
discusses the linearity of the one-dimensional wave equation, and then
introduces the Korteweg-de Vries equation, together with some
historical setting. KdV is non-linear.
CLICK FOR PDF.
§14.6, The Chain
Rule#ers9 A bug crawls on a metal plate with specific
temperature. What are the first and second derivatives of the
temperature with respect to time at a specific time and
location. CLICK FOR PDF.
§14.7, Optimization in Several Variables#sg24 Two parameterized lines are given, and the
distance between the points specified by parameter values is
investigated. Are there critical points, and, if so, what kind? What
is the geometric feature of the critical point found? CLICK FOR PDF.
§14.7, Optimization in Several Variables#sg25 A rectangle is dissected into four rectangles by
two lines parallel to its sides. Find the configurations so that the
sums of the areas of the subrectangles are largest and
smallest. CLICK FOR PDF.
§14.7, Optimization in Several Variables#ers16 A function with a simple local and absolute
maximum is perturbed and students are asked to locate one critical
point of the perturbed function and explain the
situation. CLICK FOR PDF.
§14.7, Optimization in Several Variables#ers17 Gene Speer's effort (the creator is identified by
the presence of a pictex image!) to introduce 251 students to the
special flavor of linear programming problems.
situation. CLICK FOR PDF.
§14.8, Lagrange Multipliers: Optimizing
with a Constraint
#sg41 Find the max of 3x+5y on
x2+y2=1 with an appropriate picture. Now do the
same analysis with constraint xn+yn=1
(n>0). What happens as n→∞? What happens as
n→0+? Draw the appropriate pictures. This problem
is delicate but can be rewarding. CLICK FOR
PDF.
§15.2, Double Integrals over More General
Regions#ers21 A provisional definition of convergent improper
integral for nonnegative functions over bounded two-dimensional
regions is given. Students then must consider whether three specific
improper integrals of functions over the unit square
converge. CLICK FOR PDF.
§16.2, Line
Integrals#ers26 Compare the values of the line integrals over two
given curves using three given integrands over two given curves. Do
this both by "reasoning" (without evaluation) and by direct
computation. CLICK FOR
PDF.
§16.3, Conservative Vector Fields#sg53 The student is asked to construct a 2-dimensional
vector field from geometric information, and then to compute a
specific line integral involving this vector field. CLICK FOR PDF. | 677.169 | 1 |
Course notes
We will more or less follow these course notes, written by Nuno Freitas and Adela Gherga. These course notes contain exercises at the end of each section, which will form some component of your homework grade. See the Homework page for more info.
Course description
This course serves as an introduction to basic number-theoretic concepts, such as divisibility, prime numbers, congruences, arithmetic functions, and other topics. We'll also discuss certain applications of number theory, such as cryptography. Emphasis will be placed on building proof-writing skills and developing mathematical intuition.
Important dates
Wednesday, January 17: Last day to withdraw without receiving a "W"
Friday, February 9: Last day to withdraw (with a "W")
Monday, February 12: Family Day, university closed
February 19 - February 23: mid-term break, no class
Friday, March 30: Good Friday, university closed
Monday, April 2: Easter Monday, university closed
General advice for success
Effort pays off! It is simply untrue that people have a fixed amount of math ability that determines how well they do. Just like any other skill, doing mathematics becomes easier with hard work, practice, and willingness to challenge yourself.
Stay caught up! Mathematics is a very cumulative subject: what we learn one week depends crucially on understanding what we learned the week before. Students who fall behind early struggle to catch up for the rest of the course. This is especially true in summer courses, in which the same amount of material is presented in roughly half the time.
Put in the hours! Remember the 2-to-1 rule for university courses: expect to spend an average of 2 hours outside of class for every 1 hour spent in class. In our course, that means 14 hours per week, in addition to coming to lectures, is quite reasonable (and some students will spend more than that). That seems like a lot, and it is, but I strongly encourage you to make the effort. Jump right in and start spending that time; don't wait until later in the course.
Work on the homework problems! Solving homework problems is the most direct way to practice for the exams. It's tempting to try to find some short cut to obtaining the answers, such as taking dictation from a fellow student, searching the internet, or using a friend's work from a previous term. Besides the fact that cheating in this way violates UBC's academic misconduct policies, it's important to realize that working on the homework is the primary way for you to learn the course material. Learning to do mathematics is like learning to do anything else: you can't learn how just by watching someone else do it. Take it from someone with years of experience teaching university courses: people who work through the homework problems do better on the exams. It's that simple.
Don't give up! In earlier math courses, everything we needed to be able to do might have been conveniently written in boxed formulas that we can instantly apply. In more advanced mathematics courses, however, we don't always immediately know the correct way to proceed; sometimes trial and error is necessary, and there's nothing at all wrong with this. Trying, struggling, going back to another idea, making mistakes, fixing them—these are all part of the learning process.
Use available resources! If you are stuck in the middle of a homework problem or a concept from the course, you are on the cusp of a great learning moment. Your fellow students (I imagine) and I are very happy to help you see the way past that obstacle. Additional resources, such as practice problems, will be posted here throughout the semester.
Consciously address what you find hard! Why do some people get better quickly when they work hard, while others don't seem to progress as fast? One answer is that deliberate practice is much more effective than going through the work just for the sake of finishing it. From a Freakonomics blog post (boldface is my emphasis): "For example, in school and college, to develop mathematics and science expertise, we must somehow think deeply about the problems and reflect on what did and did not work. One method comes from the physicist John Wheeler (the PhD advisor of Richard Feynman). Wheeler recommended that, after we solve any problem, we think of one sentence that we could tell our earlier self that would have 'cracked' the problem. This kind of thinking turns each problem and its solution into an opportunity for reflection and for developing transferable reasoning tools." Stephen Chew lists several ways to develop and improve your study skills, summarized by "unplug and think hard about the meaning of the concepts you're studying". | 677.169 | 1 |
Introductory Functions
The Algebra - the Complete Course series covers all Algebra core curriculum topics from a basic overview to the more complex algebraic functions. Dr. Monica Neagoy, consultant to the Annenberg Foundation & Public Broadcasting Service, uses concrete examples and practical applications to show how a mastery of fundamental algebraic concepts is the key to success in today's technologically advanced world. In this lesson you will discover multiple applications of exponential functions. You will view two exponential explorations: "The Mythical Story of Chess" and "A Paper folding Activity". Students will learn to answer questions by functional exploration and to confirm answers by symbolic manipulation. | 677.169 | 1 |
Course Summary
Most culture's mathematics begins with the introduction of the counting numbers and their structure under addition, with multiplication following soon thereafter. In western mathematics these two operations (together with the usual comparisons) were the language in which mathematics was written for thousands of years. The inverses of these operations were also considered, though ``improper fractions" were socially accepted long before negative numbers were thought to have real meaning. Though one might expect the acceptance of negative numbers to far predate that for complex numbers, the two were finally considered ``natural'' around the same time when it was discovered that there are integer-coefficient cubic equations with real (positive) roots that nonetheless require square roots of negative numbers to be formulated (you might look up casus irreducibilis if you want to find out more about this). This was the first in a long line of discoveries that pointed to the fact that the nature of the complex numbers is important to understand, even if you think you only care about real phenomena.
The goal of this class is to learn what we can about functions of a single complex variable. In many ways this will mean attempting to translate familiar notions from calculus into the complex setting, and we'll see that there are certain surprises in the study of complex functions which one might not have predicted from studying real calculus. A constant theme in the course will be connecting the geometric understanding of the complex numbers with the algebraic operations we perform on them. By the end of the course we will understand the classical results on derivatives and path integrals for complex functions, and we will (hopefully) discuss one of the most important complex functions in all of mathematics: the Riemann zeta function.
Course Instructor
The professor for this class is Andy Schultz. His office is on the third floor of the Science Center, room S352. His office hours are Monday 1 to 2, Tuesday from 3 to 4, Wednesday from 11 to noon, Thursday from 9 to 10, and Friday from 1 | 677.169 | 1 |
Mathematics GCSE
What's covered?
This course is tailored to meet the requirements of Mathematics A Higher Tier Edexcel qualification. The course covers a wide range of contents which include: expressions and sequences, fractions, decimals
and estimations, angles and polygons, equations, area and volume, percentages, diagrams and graphs, algebra and Pythagoras' theory.
What do you need?
Learners are required to complete a diagnostic assessment at level 2 prior to the start of the course. Qualifications needed to access this course are either a D grade GCSE or Level 2 Functional Skills Maths.
How you are assessed
Learners are assessed by two exams: one calculator exam and one non-calculator exam.
How Long?
The course runs for 3 hours a week for 1 year.
What course next?
Success in this subject is necessary for a number of careers and courses. Students who need more advice on whether a grade C at GCSE mathematics is necessary for a given career or course should seek specialist advice. Any student who wants to take A Level mathematics following success at GCSE should discuss fully with their mathematics lecturer what this involves.
What could this lead to?
Learners are encouraged to build their skills and knowledge so that they can get a job, promotion or access university | 677.169 | 1 |
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If you are having problems with algebra and you cant find a simple way to learn, you must try Algebrator, you will never believe what its capable of doing15:
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Graph2Go - Graphing calculators are instrumental in teaching and learning mathematics. It is an environment that supports conceptual understanding of functions in general, and school algebra and real analysis in particular. Especially, it enhances connections between graphic and symbolic representations. A major objective of algebra teaching is equipping learners with tools to mathematize their perceptions. A multi-representational approach has the potential to shift the focus of solving even traditional problems from assigning and solving for an unknown to analyzing the various processes and relations among those processes. The integration of multiple representations of function creates opportunities for developing a wider range of solution methods to traditional problems. Zooming in on the use of the graphing calculator, researchers point on four patterns and modes of use: computational tool, data analysis tool, visualizing tool, and checking tool.
Dynamic transformations are a unique facility of Graph2Go.
Dynamic control involves the direct manipulation of an object or a representation of a mathematical object. As the driving input is the letter-symbolic one, the transformations are carried out on the numbers involved in the function's expression. Thus, by parameterizing an example we turn it into a family of functions. Research suggests that the kinesthetic relation between the user and the object on the screen can have an important role in developing a deeper understanding of the mathematical concept.
Basic features of Graph2Go:
* Graphs of single variable function expressions.
* Dynamic graphing of transformed expressions.
* Points of interest (maximum, minimum, inflection_ are marked and their numerical values are presented.
* Graph and expression of the derivative function.
* Graph, expression of the integral function's family.
* Area expressed by the integral of a given function.
* Zooming and rescaling options.
Graph2Go is a special purpose graphing calculator that operates for given sets of function expressions. The given families of function expressions and the tools that support easy changes of any given example have been designed for fast and easy use with the small keyboard.
Suggested Activities
Below is an interesting example that combines the use of visual thinking with an analytic task and has the potential to enhance procedural operations with conceptual understanding:
Prove or refute each of the following statements.
Explain and demonstrate your method and answer using Graph2Go, paper and pencil, or mental operations
* The derivative of a family of functions cannot be a single function.
* [k*f(x)]' is equal to k*[f(x)]'
* [k*(f(x)]' is equal to [f(kx)]'
If you study calculus with the support of graphing calculators, see the AP (Advanced Placement) calculus site for examples of calculus assessment problems (carried out with or without graphing tools).Fit2Go Fit2Go supports exploration and modeling activities. It supports data collection by proposing a model that can appropriately describe the user's data. The tool highlights the numeric aspects of a phenomenon. Together, Sketch2Go and Fit2Go provide a comprehensive view of models and modelingx_calc Universal free, every day use calculator with scientific features. One of top.
Good for simple and advanced calculations!
Calculator 4 M Everybody needs a calculator. "Calculator 4 M" easy to use and beautifully designed to do things better than your phone or handheld calculator ever didPowerful-Xcalculator About
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Scientific Calculator new Scientific Calculator new - Download Scientific Calculator for JAVA mobile - one of the best JAVA Apps. Download Scientific Calculator app free! You will certainly enjoy its fascinating features | 677.169 | 1 |
MT A120 College Algebra
Time/Place
General Description
The purpose of this course is to learn the elements of
algebra and some applications which will be useful
in your day-to-day lives. A key idea is the notion of a
function; we will learn how to analyze functions
using graphical methods, and will spend the majority
of the course looking at interesting examples and
their applications.
The course schedule link at the upper left of the page
will take you to a page containing
announcements of exams, homework assignments,
and other date-sensitive material. It is a good page to bookmark
and return to periodically.
There is also a very terse course description contained in the
SLU Undergraduate Catalog (PDF format).
The course prerequisite is a passing grade in MT A114 Intermediate
Algebra or two years of high school algebra.
We will study the mathematics behind the image on this page
later in the semester (Chapter 9, Conic Sections).
Textbook Information
The required text for the course is
College Algebra, 2nd edition by
Michael Sullivan
and
Michael Sullivan, III.
Students can buy the text from the
SLU Bookstore.
Graphing Calculator
Because we will be taking the graphical
point-of-view mentionedtimes TBA).
Optional equipment which you'll probably want:
translucent colored slide cases so you look fashionable
in class.
Homework and Exams
There will be some homework problems every week, unless otherwise
indicated. You should periodically check the
course schedule page for updates.
There will be three in-class exams given
September 20th, October 14th, and November 8th;
together these exams make up 50% of your final grade.
The final exam is scheduled for Monday, December 16th from
8:00-9:50AM;
it is comprehensive and is worth 35% of your final grade.
Class participation (group work) accounts for the remaining 15%.
Make-up exams will not be given.
The College of Arts & Sciences
has a policy concerning
academic honesty with which you
should be familiar.
Getting Help
The Mathematics Department offers help sessions run by
graduate students for all lower division courses.
These begin around the second week of classes
(Monday-Thursday 10AM-2PM, Friday 10AM-1PM in Ritter Hall Room 2).
This is a great (and underutilized) resource for math students!
Free tutoring is also available from
Student Educational Services in
the Academic Resources Center, Room 016, phone 977-3319.
There is a helpful handout distributed by the
Mathematics Department called
Success in Mathematics which
discusses study skills, problem solving techniques,
studying for and taking exams.
Most importantly, you should come to my office hours which are
10-11AM on Monday, Wednesday, and Friday in Ritter Hall 127. | 677.169 | 1 |
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UP Board class 10th Science chapter 19 notes(control and coordination in plants and animal)3rd part.It isIn this article you will get UP Board class 10th Science chapter 20 notes(nervous coordination in animals)2nd part.It isShort notes help student to revise the complete syllabus in minutes.UP Board class 10th science Key Notes clearly give you a short overview of the complete chapter as these UP Board chapter-wise key points are prepared in such a manner that each and every concept from the syllabus is covered in form of UP Board Revision Notes. | 677.169 | 1 |
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