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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11
votes
2answers
421 views

Explaining why we can't “find” an antiderivative of $f(t) = e^{t^2}$.

We can't find $$ \int e^{t^2} \; dt $$ using basic tools from a calculus class. That is, we can't express an antiderivative of $f(t) = e^{t^2}$ using the basic operations. We can of course just ...
3
votes
3answers
229 views

Learning Combinatorial Species.

I have been reading the book conceptual mathematics(first edition) and I'm also about halfway through Diestel's Graph theory (4th edition). I was wondering if I was able to start learning about ...
28
votes
9answers
3k views

Is this way of teaching how to solve equations dangerous somehow?

Two years ago, I bought the book Mathematics for the Nonmathematican, by Morris Kline. There I learned a new way of solving equations, which is related to the principle that states that any ...
7
votes
2answers
607 views

Is it possible to learn mathematics right from the source instead of reading textbooks. By studying the masters and not their pupils

I was wondering if mathematics learning process require the use of textbooks. When I was a high school student, I read as a preparation for university, Legendre book on Elements of geometry and ...
7
votes
7answers
4k views

Easiest and most complex proof of $\gcd (a,b) \times \operatorname{lcm} (a,b) =ab.$

I'm looking for an understandable proof of this theorem, and also a complex one involving beautiful math techniques such as analytic number theory, or something else. I hope you can help me on that. ...
15
votes
2answers
2k views

Learning Mathematics using only audio.

Are there any mathematics audio books or other audio sources for learning mathematics. I ask this because I make about 1 hour from my house to the school and staring at a screen on the car makes me ...
1
vote
2answers
410 views

The Game of Nim alternative solutions

Nim has a mathematical solution which uses binary number system and addition modulo 2.I was wondering if there is an alternative solution to this game or at least another interpretation of the ...
5
votes
2answers
938 views

How can I make sure I never forget.

I am currently refreshing my Elementary Algebra using Schaum's Outlines. I find them useful as they are choc full of exercises (Which I now realize is the only way to master algebra). I am worried ...
3
votes
1answer
118 views

Course/homework management systems for computational math courses [closed]

I will be teaching a course which will be based on a mathematical software, (as in MATLAB, MAPLE, Mathematica). The question is how to manage homework. Ordinary email is not efficient it seems. I am ...
2
votes
3answers
172 views

Darboux integral too sophisticated for Calculus 1 students?

I strongly prefer Darboux's method to the one commonly found in introductory level calculus texts such as Stewart, but I'm worried that it might be a bit overwhelming for my freshman level calculus ...
2
votes
1answer
702 views

Complex division: polar form vs complex conjugate

The original problem In an electricity course which I volunteered to help with, the students solve circuits using phasors. Using phasors requires a good knowledge of complex numbers arithmetics, ...
2
votes
0answers
115 views

What is $0^0$? Should we define $0^0$ on its correctness or convenience? [duplicate]

What is $0^0$ ? I have read many debates about this question. The debate has been going on at least since the early 19th century. At that time, most mathematicians agreed that $0^0$ = 1, until in ...
2
votes
1answer
68 views

Why are variables typically given names like x in math?

Why do equations typically have variable names like x and y? In computer programming, we value meaningful names for variables. For example, if I were trying to calculate a square root, I would call ...
10
votes
5answers
352 views

High-School Level Introduction to Dynamical Systems

In one month I'll be giving a talk to motivated high schools students on a topic of my choice from dynamical systems and/or ergodic theory. I'm having trouble coming up with a topic compelling enough ...
2
votes
2answers
157 views

The shape of mathematical self-tutelage

I am interested primarily in physics, and I am generally self-taught in mathematics. However, this implies an inaptitude for rigorous proof. While I am confident that I can grasp the concepts and ...
0
votes
2answers
61 views

Profit loss or quantitative aptitude problem

At what percent above the cost price must an articles be marked so ás to gain $17$% after allowing a discount of $10$% ?
15
votes
2answers
732 views

How to deal with exercises with no solutions given?

Probably most people will acknowledge the importance of doing exercises when reading a mathematical textbook. Here I am talking about a textbook of similar level as those ones listed in GTM. However, ...
17
votes
5answers
943 views

Alternative set theories

This is a (soft!) question for students of set theory and their teachers. OK: ZFC is the canonical set theory we all know and love. But what other, alternative set theories, should a serious student ...
2
votes
3answers
139 views

teaching concept of “subspace” to linear algebra students

I'm currently a T.A. for an introductory combined linear algebra & differential equations course geared toward engineering students. One major problem I've run across is that most of my students, ...
7
votes
1answer
709 views

How does one visualize a function with a discontinuous second derivative?

Let us assume that all functions are continuous. I was teaching my calculus students the other day. We were talking about what points of non-differentiability look like. Two ways a function can fail ...
8
votes
1answer
142 views

Proof vs Practice

I've been brushing up on a lot of basic arithmetic, algebra, and logic as I work towards a review of calculus (and beyond), and I keep noticing that in order to fully understand many principles in the ...
0
votes
1answer
347 views

Name of odd powered polynomial graph (Opposite of parabola(ic))

I am writing an assignment and have to describe the graphs for when the powers are even and when they are odd. I described the even power graphs as being parabolic or parabolas. The only problem is, I ...
0
votes
1answer
98 views

How would I take multiple single bit binary numbers and convert it into a single binary array number?

So lets say I have these: 101010101001 Now lets also say I didn't count them you should count binary, lets say I counted that number at 6 because their are 6 1s and the 0s don't count. Now how would ...
11
votes
2answers
1k views

Etymology of the word “normal” (perpendicular)

While the word "normal" is one of the most overloaded mathematical terms, in linear algebra, it is usually associated with the notion of being perpendicular to something, as in "normal vector" or ...
9
votes
1answer
273 views

General question: What one can do to help students one is grading?

Due to unknown reason I was assigned as a grader this semester for a certain proof writing class in my universtiy. The class size is 65 and students took it usually comes from a computer science ...
0
votes
1answer
997 views

Learning a foreign language for math PhD

Many graduate programs in math require students to pass a foreign language exam in French, German, or Russian. Why is this so? Haven't the important mathematical works in these languages been ...
12
votes
1answer
303 views

Algebraic structures associated to flexagons?

Flexagons strike me as objects that would admit investigation in a first course in modern algebra. I'm surprised to be unable to find a reference discussing flexagons using modern algebra language. ...
0
votes
1answer
16 views

Representing expression through a Summatory

I need represent this expression $L_{u_3}u(k-1)+L_{u_2}u(k-2)+L_{u_1}u(k-3)$ by using a summatory, $L_{u}$ is a vector that contains d elements $L_u=\begin{pmatrix}L_{u_1} L_{u_2} ...
10
votes
4answers
2k views

Should I try to change the way Abstract Algebra is taught at my university? If so, how?

[This (soft) question should be Community Wiki.] Background: A year ago, I did a one-semester long course on Abstract Algebra at my university. When we started, I was excited, because I knew the ...
16
votes
4answers
479 views

Mathematical Habit

Whenever I have to do proofs or understand a concept, I start with examples and generalize. As an aspiring mathematician, I have fears that it might hurt me, especially when we have so many ...
555
votes
153answers
34k views

What was the first bit of mathematics that made you realize that math is beautiful? (For children's book)

I'm a children's book writer and illustrator, and I want to to create a book for young readers that exposes the beauty of mathematics. I recently read Paul Lockhart's essay "The Mathematician's ...
2
votes
2answers
1k views

What are the drawbacks of multiple-choice questions? [closed]

I can easily understand the advantage of multiple-choice questions for instance in grading and so. A drawback is that real life problem don't have multiple choice questions all the time for instance ...
3
votes
2answers
177 views

Which set of subjects has the most algebraic 'flavour' to it?

I'm finishing my undergraduate mathematics programme this summer. The graduate program at my university requires that you specify a specialization on entry. This is very difficult for me and would ...
0
votes
1answer
98 views

Doing research on Google Matrix and PageRank algorithm

I'm doing research on Google Matrix and PageRank algorithm. In a paper, there are terms that I'm unaware of, such as stationary distribution, stochastic matrix, convex combination, markov matrix, ...
6
votes
2answers
221 views

What's the problem of using a “stand-up analogy” to demonstrate the concept of set?

I was reading this text about the new math movement, there's a line in which he says: Easy as it looked, teachers didn't always get the notion of "set" straight themselves, and could teach the ...
1
vote
0answers
150 views

Textbooks for PDE after Folland

I am a student who has just finished Folland's nice book Introduction to Partial Differential Equations. And I also read L. Craig Evan's textbook before. Could any expert here suggest a PDE book in ...
2
votes
2answers
111 views

Mathematically-based online games

I am looking for online games or puzzles which have a mathematical flavor and are suitable for general audiences. A classical example is the online version of Set Card Game. Or this game that has some ...
4
votes
2answers
172 views

Is it necessary to know a lot of advance math to become a good junior high/high school teacher?

By "advance math" I refer to Real Analysis, Abstract Algebra and Linear Algebra (to the level of Axler). I received mainly Bs in these courses with the exception of the intro-level Linear Algebra. ...
2
votes
0answers
82 views

Proving two Dedekind cuts represent the same number.

Hey guys I have a quiz soon and I really dont know how to prove this question. I tried my best but it is not working. Please help out with anything or hints. Let $(A'_1, A'_2)$ be a Dedekind cut of ...
-2
votes
2answers
342 views

Why mathematics has to be too much formal? [closed]

This is very general question I am asking here. But I think it really needs to be addressed. Whenever I come across a new concept in mathematics, I try to understand it by searching on the internet. ...
1
vote
3answers
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+. ...
9
votes
1answer
205 views

Difference between a Lemma and a Theorem [duplicate]

What essentially is the difference between a lemma and a theorem in mathematics? More specifically, suppose you come across a general result while solving a mathematical problem, what are the ...
5
votes
5answers
930 views

Motivation for the importance of topology

Starting from tomorrow, I will be tutoring some undergraduate students following a course in general topology. I am looking for examples motivating the importance of topology in mathematics which can ...
5
votes
3answers
142 views

Is there a simple geometrical description of $e$? [duplicate]

Of course I am not looking for a definition through $\int_1^e{1\over x} \, \mathrm{d}x=1$ or that slope of $a^x$ at $x=0$ is $1$ when $a=e$. I am looking for something understandable by a kid who has ...
1
vote
2answers
1k views

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 ...
1
vote
1answer
382 views

Chi-square degrees of freedom proof

I need to prove why we have the following result: When: $Y_i=\beta_0+\epsilon_i$, then: $\sum\frac{\epsilon_i^2}{\sigma^2}\sim \chi ^2(n-1)$ Thanks :)
0
votes
3answers
889 views

What is the most suitable function for a heart? [duplicate]

I have seen some codes to plot heart on matlab, e.g. first example second example How can I prove/find from the theory how to plot a perfect heart?
7
votes
5answers
336 views

Simplest error detecting/correcting codes for math newbies

Suppose you have been given the task of teaching some basic coding theory to folks who are interested in math but have not taken algebra, number theory, etc. If you want to introduce codes, you might ...
1
vote
1answer
109 views

What material is good for Atiyah-Singer index theorem [duplicate]

I want to ask what materials or books can I use to learn the proof of Atiyah-Singer index theorem? I hope such material contains enough preliminaries and background instead of proving the theorem ...
8
votes
1answer
341 views

Pedagogy of Teaching the Inverse Matrix Method

I am teaching a group of (ordinary rather than honours) second-year engineers and we are studying matrices. I told the class today that as far as I could see we were only studying matrices and, ...