For questions related to the teaching and learning of mathematics. Note that Mathematics Educators StackExchange may be a better home for narrowly scoped questions on specific issues in mathematics education.

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Why is Cauchy condition for convergence not formulated in a simpler way?

The standard definition of a Cauchy sequence (e.g. it's given in Wikipedia and most textbooks I remember; admittedly those are mostly older ones) is: for every positive real $ε > 0$ there is a ...
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3k views

What is a standard precalculus syllabus?

I'm about to start teaching a calculus I class next week and I was wondering what I can expect from my students. I'm a Brit teaching in the US so I am unfamiliar with the system. I am hoping that ...
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79 views

Does $x = \left(x + \frac {(y - x)} 2\right)$ go on forever?

Basically, if you have x which lets say is 50 and y is 100. Now if I were to keep doing $x = \left(x + \dfrac {(y - x)} 2\right)$ until x = y would it be going forever? And if not, when will it stop? ...
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1answer
106 views

Best book for preparation to read The Art of the Computer Programming

I decided to read The Art of the Computer Programming by Donald Knuth. The problem is, that i'm in high school now, so i need a help with mathematics oriented book which help me to be prepared for ...
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141 views

What topics to include on a first course in number theory

I need to teach a course in elementary number theory next academic year. What topics should be included on a first course in this area? What is best order of doing things? The students have a minimum ...
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128 views

Help on French Math Education Paper

I am looking for very basic (probably I should say very elementary) papers in french designed for elementary school teachers and elementary school educators. I would appreciate if someone can provide ...
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776 views

Where does binary arithmetic/manipulation enter the mathematics/engineering curriculum?

Binary arithmetic is both an educational basis for elementary logic and an pervasive tool for practical mechanics in managing computer systems (at a very particular level). That is the state of ...
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1answer
106 views

Basic examples of probabilistic method

I'm looking for a truly basic example of probabilistic method proof which could be presented without a board (i.e. speaking only), that is, even moderately complicated calculations are not allowed. ...
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95 views

Euclidean Geometry in Physics

I've started tutoring my 13 year old niece in math. She learning geometry this year (it's a year-round school). Obviously, it'll just be basic Euclidean geometry -- though I might try to get to a ...
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154 views

Advice on taking a Course in Logic.

Is a course in Mathematical Logic necessary for a well-rounded Mathematical education? I asked a question about taking a Set Theory course before and was advised to do so. However the course offered ...
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62 views

How to understand the words “More algebraically”

How to understand the words More algebraically When seeing one proof about the theorem that rational set is countable, I saw this More algebraically , but ...
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91 views

Integrating a school homework question.

Show that $$\int_0^1\frac{4x-5}{\sqrt{3+2x-x^2}}dx = \frac{a\sqrt{3}+b-\pi}{6},$$ where $a$ and $b$ are constants to be found. Answer is: $$\frac{24\sqrt3-48-\pi}{6}$$ Thank you in advance!
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convert decimal 1024 to hexadecimal

I need to convert the decimal number 1024 to an hexadecimal number, I do this using these steps http://www.wikihow.com/Convert-from-Decimal-to-Hexadecimal#steps However, whenever I divide 1024 by 16 ...
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185 views

Why begin with distributions and then move to tempered ones?

After reading several books on distribution theory, I got a strange feeling. Why do they all begin with the theory of distributions and then move on to tempered distributions? Why can't we just start ...
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1answer
455 views

Getting a masters in Mathematics

I'm not entirely sure that this is the right medium for this question, so feel free to close it at will. I'm basically wondering where there are some strong programs to get a masters in mathematics. ...
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4answers
358 views

Which discussion board is good for homework questions?

I'm a CompSci university student and i want some help for my math questions. Therefore i am looking for a good discussion board for math homework questions. I don't know any (good), because I come ...
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1answer
97 views

New idea to solve $\int x^n e^x dx$

I have this problem $$\int x^n e^x dx= x^ne^x -nx^{n-1}e^x +n(n-1)x^{n-2}e^x- \cdots+(-1)^nn!e^x $$ my try was to use integration by part . $$I_{n}=\int x^n e^x \, dx=e^x x^n -\int (nx^{n-1})e^x \, ...
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135 views

Explaining multiplication of fractions

The best way I've been able to describe multiplication is as $$ a\times b = \sum^a_{i=1} b$$ But my definition does not account for things such as $2.99792458\times8.987551787$ and ...
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66 views

$f(x)=\log x\Leftrightarrow f^{-1}(x)=e^x$. Why $e=2.73\cdots$?

$$f(x)=\log x\Leftrightarrow f^{-1}(x)=e^x.$$ Ok, $\log x$ is defined as the function $f(\cdot)$ such that: $f'(x)=\dfrac{1}{x}$. How to get, from this, the inverse of it $f^{-1}(x)$? And why ...
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48 views

Why are the areas non-positive?

I learnt that the integral of a function $f(\cdot)$ is the measure of an area, i.e. $\int\limits_{a}^{b}f(x)\,\mathrm{d}x$ is the area of the intersection of $x=a$, $x=b$, and $y=f(x)$. How come some ...
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56 views

The graph of the function is $g(x)=x^3-2x^2+x+1$ and the tangent to the curve is at $x=2$?

a) Find the equation of the tangent to the curve at $x=2$ HELP and then b) Determine the angle that this tangent makes with the positive direction of the $x$-axis Please help I really need to ...
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1k views

How to explain why a parabola opens up or down

I am being ask to explain in 2 ways why is it that y=ax^2+bx+c parabola opens up if a is positive and why is it that y=ax^2+bx+c opens down when a is negative. One of the explanations has to be ...
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1answer
116 views

A way to teach Archimedean property

A student asked me how to understand the Archimedean property, I tried to re-read with him what he has already done in class (well, actually copy from the blackboard in class). However I think I'm not ...
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1answer
124 views

How to teach the division algorithm?

What is the best way to introduce the division algorithm? Are there real life examples of an application of this algorithm. At present I state and prove the division algorithm and then do some ...
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148 views

Where could I learn basic math terminology?

I am an english learner and I would like to learn the etymology of Mathematics. I would like to know the most common phrases in Algebra, and Geometry as well. I want to know at a level of UK's A+. ...
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91 views

Can anyone explain the method used for finding the answer to this question?

I was practising questions on principles on mathematics. I stumbled onto this question and I don't know where to start. Can anyone please help?? If $P_1\,P_2\,\ldots\,P_n$ is a regular polygon in ...
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266 views

Mathematical disciplines [closed]

Once I spoked to a mathematician about mathematics and he asked me what was my favourite area in Maths. My answer was "Chaos Theory" and he said this is not a discipline in Mathematics. What is a ...
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1answer
39 views

Proving Odd & Even Functions

For the following: If $f(x)$ is an odd function, then $|f(x)|$ is _______. If $f(x)$ is an odd function and $g(x)$ is an even function then, $(f~o~g)(x)$ is _______. If $f(x)$ is an odd ...
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1answer
110 views

Difference between maths in physics degree and maths in a maths degree

I asked this question on the Physics site, but it got closed, so I'll try here. Basically, I was wondering what are the main differences between the maths you learn in a mathematics degree and the ...
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1answer
100 views

Is it ill-advised to read books casually for entertainment? [closed]

I'm a student who has about a year (and a few months) to go before entering a university and I've been reading some math books recently. I'm on Chapter 6 on Rudin's PMA, Chapter 5 in Munkres' Analysis ...
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29 views

Help Finding the Equation of a Line with a Given a Point and a Slope

I have been receiving a lot of help today and I really appreciate it, I am nearing the end of my class and need help studying for my final. In my review I came across a problem that i am having ...
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78 views

Is self study of proof-based mathematics difficult?

I heard from a renowned Mathematician that self study of proof based Mathematics is extremely difficult as there is not only right and wrong but also degree's of correctness. So without a teacher ...
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57 views

How to score a second try on a multiple choice test

Suppose a multiple choice question has $n$ answers. You allow a student $m$ tries. The student gets the correct answer on the $k$-th try. What is a "fair" score?
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1answer
20 views

how many fewer grames of caffeine is she consuming each week?

how many fewer grames of caffeine is she consuming each week? I try with the following 2*97*7 + 5 * 6 *7 = 1358 +210 = 1568 mg convert to gram = 1.568 but not correct , please help how calculate ...
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78 views

Abstract/formal interest of rings

I am about to introduce first year undergrads to the concept of rings, after spending some time looking at groups; and I would like to give them more than a practical motivation (the most usual rings ...
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1answer
44 views

Beyond calculating just as an exercise, are there any other reasons to calculate an indefinite integral?

Calculus textbooks often have us calculate indefinite integrals as exercises. However, beyond calculating just as an exercise, are there any other reasons to calculate an indefinite integral?
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88 views

What is not the second derivative of a parametric equation?

1142004    Consider the parametric equations $x=f(t)$ and $y=g(t)$. To "find" $\frac{d^2y}{dx^2}$, there are three ways to go: (1) the correct one, that is, ...
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1answer
117 views

Why are Fourier series important?

Are there any real life applications of Fourier series? Are there examples of Fourier series which have an impact on students learning this topic. I have found the normal suspects of examples in this ...
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1answer
139 views

Question about independent study in differential geometry for an undergraduate. [closed]

I am a senior undergraduate math and physics student applying to graduate school in math for this upcoming fall. I have had classes in: Abstract Algebra (Rings, Fields, and Groups), Point-Set ...
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2answers
156 views

How to teach Critical Thinking

I am currently tutoring a few students in an entry level physics course and had some trouble recently when it comes to helping them with problem solving. The students I am helping don't have many ...
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118 views

Do mathematics researchers regularly solve problems like this?

I'm not sure that this is the right exchange for this question. It asks about the possibilities of research in mathematics and computer science. Extended Background I am very interested in ...
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1answer
532 views

Gilbert Strang's books on calculus and linear algebra?Are they for math majors?

I would to know what are the best resources to use to teach and learn elementary subjects (calculus,linear algebra),I remember when learning calculus, I used Spivak's book which had wonderful ...
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1answer
151 views

Grade School Math: Bad math, or new meanings?

I came across this online quiz discussing the new Common Core education standards, and it all seemed pretty reasonable, until I came across this question: In the number below, how many times ...
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215 views

Convention verses memory: The quotient rule v product rule for derivatives

I have long wondered why the product rule is taught the way it is. ${ d(UV)=Udv+Vdu}$ Don't get me wrong, I am not a complete NOB when it comes to calc, but the quotient rule states $${d(\frac ...
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1answer
115 views

What is the contribution of group theory to topology?

An answer for a question on MathOverflow.net which asked for some recommendations on textbooks for books in topology received the following comment: "It's a great book to introduce applied ...
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31 views

significant figure representation?

I was wondering: Why does $1.30 \times 10^3$ have $3$ significant figures while $1300$ has $2$ significant figures (they are both the same number) Why is that distinction ? When should I use ...
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109 views

A Good Example of an Argument That Cannot Be Reversed

My students are having a hard time with assuming what they must prove. A good example of what they are doing is when one wishes to show that $\lim_{x\to 3}(2x+1)=7$. They will assume that ...
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966 views

A round table probability question

Hi guys I am writing my P exam for the second time and I remembered two question that confused me when writing the exam. I asked my prof. but it confused him as well. For simplicity I will ask one ...
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109 views

Explanation of math statement

This symbols are used to describe left recursion : $A\to B\,\alpha\,|\,C$$B\to A\,\beta\,|\,D,$ It is taken from : http://en.wikipedia.org/wiki/Left_recursion How can these symbols be ...
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185 views

Software for visualizing partial derivatives?

I'm whipping up a set of notes, and I want to include a diagram or two showing some partial derivatives. Specifically, a diagram would include: a 3D surface of the form z=f(x,y), a plane of the form ...