# Tagged Questions

For questions in Mathematics Education as a scientific discipline. For more hands-on questions on teaching Mathematics, please use the tag teaching. There is also a Stack Exchange community http://matheducators.stackexchange.com/

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### Reasons for the importance of planarity and colorability?

Could it have been foreseen that - exemplarily - planarity and colorability would turn out to be such important concepts in graph theory (there's almost no textbook on graphs without two chapters ...
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### Where and when did “transition to abstraction” courses start?

I often find myself debating the content and structure of such courses and I would find it useful to know the basic history. I don't remember any such offerings during my own undergraduate days in ...
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### Good ways to engage in mathematics outreach?

Greetings all, I have often heard that it would be good if we as a community did more in the way of mathematics outreach: more to explain what it is we do to the community at large, more to expose ...
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### Pedagogical question concerning $\Gamma(z)$

Pedagogically speaking, I see two problems with defining $\Gamma(z)$ (at least for real $z$) by the limit $$\Gamma(z)=\lim_{m\to\infty}\frac{m! m^z}{\prod_{i=0}^m (z+i)}$$ as compared with the formula ...
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### What is the simplest, most elementary proof that a particular number is transcendental?

I teach, among many other things, a class of wonderful and inquisitive 7th graders. We've recently been studying and discussing various number systems (N, Z, Q, R, C, algebraic numbers, and even ...
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### Best examples of physics providing insight into math [duplicate]

Possible Duplicates: Examples where physical heuristics led to incorrect answers? Examples of using physical intuition to solve math problems V. I. Arnold argues (http://pauli.uni-muenster.de/~...
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### How To Present Mathematics To Non-Mathematicians?

(Added an epilogue) I started a job as a TA, and it requires me to take a five sessions workshop about better teaching in which we have to present a 10 minutes lecture (micro-teaching). In the last ...
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### A learning roadmap for Additive combinatorics.

Hello, I'd love to learn more about the field of additive combinatorics. From what I've understand, there's a book by Tao and Vu out on the subject, and it looks fun, but I think I lack the ...
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### Mathematics Graduate Student Summer Opportunities

I am currently a mathematics graduate student at Western Kentucky University in Bowling Green, KY. I am looking for some kind of summer opportunity to participate in during summer 2011. Does anyone ...
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### How quickly will billiard trajectories cluster?

Suppose you launch $n$ point-particles on distinct reflecting nonperiodic billiard trajectories inside a convex polygon. Assume they all have the same speed. Define an $\epsilon$-cluster as a ...
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### Is the boundary $\partial S$ analogous to a derivative?

Without prethought, I mentioned in class once that the reason the symbol $\partial$ is used to represent the boundary operator in topology is that its behavior is akin to a derivative. But after ...
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### What topics should be included in a calculus-for-the-liberal arts course?

I have in mind a course taken by liberal-arts students who will probably never take another math course. I would like such a course to convey some of the way mathematical thinking is done (i.e. not a ...
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### Name for a basic principle of calculus?

$$[\text{size of boundary}] \times [\text{rate of motion of boundary}] = [\text{rate of change of size of bounded region}]$$ This differs from the fundamental theorem of calculus in that it does not ...
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### Does any textbook take this approach to the isomorphism theorems?

Below, I present an outline of a proof of the first isomorphism theorem for groups. This is how I usually think of the first isomorphism theorem for ______, but groups will get the points across. My ...
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### (How) should I take notes on a subject for self-study?

Suppose I am interested in really learning / thoroughly reviewing some subject (e.g. the basic theorems of infinite Galois theory, or the classification of compact Lie groups). One approach I might ...
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### How do I explain the number e to a ten year old? [closed]

Hardly a research level question, but interesting nonetheless, I hope. Pi is easy, but not e. Where could I start?
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### Teaching proofs in the era of Google

Dear members, Way back in the stone age when I was an undergraduate (the mid 90's), the internet was a germinal thing and that consisted of not much more than e-mail, ftp and the unix "talk" command ...
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### Categories First Or Categories Last In Basic Algebra?

Recently, I was reminded in Melvyn Nathason's first year graduate algebra course of a debate I've been having both within myself and externally for some time. For better or worse, the course most ...
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### If you could redesign a high school mathematics curriculum from the ground up, what would you include? [closed]

Let's assume that we also get to redesign our high school mathematics teachers as well, in the sense that we can assume that they know and can teach whatever material we choose to cover. This is ...
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### Analysis from a categorical perspective

I have not studied category theory in extreme depth, so perhaps this question is a little naive, but I have always wondered if analysis could be taught naturally using categories. I ask this because ...
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### Who should teach the mathematics subjects in the engineering curriculum? [closed]

Should mathematics courses in Engineering Degree Programs, particularly those which are covered in licensure examinations, be taught by someone whose background is mathematics, or by someone whose ...
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### an engineering Ph.D. teaching math in college

I have a friend who has been teaching college-level math (e.g., all levels of calculus) for about 4 years, although all of his education, including his Ph.D., was in engineering. Now he is ...
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### To what extent can algorithms in undergraduate linear algebra be made continuous/polynomial/etc.?

I feel like many of the algorithms that I learned — indeed, that I have taught — in undergraduate linear algebra classes depend sensitively on whether certain numbers are $0$. For example,...
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### What is your favorite isomorphism? [closed]

The other day I was trying to figure out how to explain why isomorphisms are important. I pulled Boyer's A History of Mathematics off the bookshelf and was surprised to find that isomorphism isn't ...
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### Journals for undergraduates

Are there math journals that are aimed for undergraduates? I don't mean here journals where students can publish their papers, but journals that publish introductory articles that an undergraduate can ...
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### Community experiences writing Lamport's structured proofs

About two years ago, I came across this paper by Lamport http://research.microsoft.com/en-us/um/people/lamport/pubs/lamport-how-to-write.pdf on writing proofs hierarchically. It changed how I wrote ...
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### Graphical representation of mathematical structures (in the spirit of unified modeling language)

In software engineering the unified modeling language ("UML") is a well established technique for providing overview of complex systems and an efficient means of communicating about them. There are ...
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### How to study a math text [closed]

Hello, recently I've been trying various attempts regarding how to approach a math book to learn in the best way. Should one memorize the theorems and proofs so that one can recite them? I tend to ...
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### Why linear algebra is fun!(or ?)

Edit: the original poster is Menny, but the question is CW; the first-person pronoun refers to Menny, not to the most recent editor. I'm doing an introductory talk on linear algebra with the ...
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### Why the Killing form?

I'm teaching a short summer course on algebraic groups and it's time to talk about the Killing form on the Lie algebra. The students are all undergrads of varying levels of inexperience, and I try to ...
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### What is Lagrange Inversion good for?

I am planning an introductory combinatorics course (mixed grad-undergrad) and am trying to decide whether it is worth budgeting a day for Lagrange inversion. The reason I hesitate is that I know of ...
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### The probabilistic method - reference to less challenging questions

I am teaching a course in combinatorics and large part of it is dedicated to the probabilistic method especially in the case of graphs. The course is an undergraduate level (almost none of the ...
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### The role of the mean value theorem (MVT) in first-year calculus.

Should the mean value theorem be taught in first-year calculus? Most calculus textbooks present the MVT just before the section that says that if $f'>0$ on an interval then $f$ increases on that ...
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### Good sources for linear algebra for convex optimization and graph analysis?

What are some good sources for linear algebra for convex optimization and graph analysis? In Particular, is Gilbert Strang's MIT course suitable, or some other online course? I prefer online courses (...
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### Theorems in Euclidean geometry with attractive proofs using more advanced methods

The butterfly theorem is notoriously tricky to prove using only "high-school geometry" but it can be proved elegantly once you think in terms of projective geometry, as explained in Ruelle's book The ...
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### Problem suggestions for polymath for undergraduates research

I'm inspired by the polymath project. It might be great for few undergraduates to work together on a research topic. What are some research problems with the following properties(Experimental ...
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### Euclid with Birkhoff

I'm looking for an short and elementary book which does Euclidean geomety with Birkhoff's axioms. It would be best if it would also include some topics in projective (and/or) hyperbolic geometry. ...
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### Yet another 'roadmap' style request- a second bite of the cherry

Okay, so I know MO has had a recent proliferation of this kind of question, and I know MO is not really for this type of question (though I suspect perhaps this is a phenomenon that is likely to ...
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### Undergraduate approach to learning math [closed]

I am going into my sophomore year as an undergraduate and I would like to ask the more experienced folks a couple questions about learning math and related things. What are your experiences and advice ...
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### Good combinatorics textbooks for teaching undergraduates?

Hello, can anyone recommend good combinatorics textbooks for undergraduates? I will be teaching a 10-week course on the subject at Stanford, and I assume that the students will be strong and motivated ...
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### Learning Roadmap for Software Engineer

Hi, I did some browsing around here on MathOverflow, but I feel that my question is different enough from others that it warrants its own question. Background: I'm a computer science major, with a ...
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### Uppercase Point Labels in High-School Diagrams: from Euclid?

I wonder if the convention of labeling points in geometric diagrams with uppercase symbols ultimately derives from Greek mathematics, which was originally written in "majuscule" (uppercase) Greek ...
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### What should we teach to liberal arts students who will take only one math course?

Even professors in academic departments other than mathematics---never mind other educated people---do not know that such a field as mathematics exists. Once a professor of medicine asked me whether ...
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### What would be good to know before starting my undergraduate studies to become a good mathematician?

First of all, I'm sorry if this isn't the kind of question that should be made in MathOverflow. I read the FAQ and I didn't consider this (that) inappropriate. I couldn't resist! People here are ...
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### Learning Algebra & Group Theory on my own [closed]

I'm learning Algebra & Group Theory, casually, on my own. Professionally, I'm a computer consultant, with a growing interest in the mathematical and theoretical aspects. I've been amazed with ...
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### Mathematics and autodidactism

Mathematics is not typically considered (by mathematicians) to be a solo sport; on the contrary, some amount of mathematical interaction with others is often deemed crucial. Courses are the student's ...
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### Why do we care about $L^p$ spaces besides $p = 1$, $p = 2$, and $p = \infty$?

I was helping a student study for a functional analysis exam and the question came up as to when, in practice, one needs to consider the Banach space $L^p$ for some value of $p$ other than the obvious ...
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### What are your experiences of handouts in mathematics lectures?

There are many different styles of lecturing, and many different aspects that are blended together to give a whole "lecturing style". That said, I'm particularly interested in hearing people's ...