For questions in Mathematics Education as a scientific discipline. For more hands-on questions on teaching Mathematics, please use the tag teaching.

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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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3answers
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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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6answers
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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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2answers
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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 ...
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17answers
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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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1answer
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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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3answers
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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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2answers
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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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20answers
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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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7answers
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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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2answers
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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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11answers
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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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0answers
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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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11answers
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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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6answers
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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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6answers
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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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7answers
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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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5answers
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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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6answers
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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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20answers
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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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4answers
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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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10answers
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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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9answers
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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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15answers
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Why do we care about L^p spaces besides p = 1, p = 2, and p = infinity?

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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16answers
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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 ...
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7answers
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On starting graduate school and common pitfalls…

Hi, I'll be starting graduate school soon, and when I look back at my college career, there are certain things I wish I could have done differently. In hindsight, I wished I wasn't in such a rush to ...
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4answers
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Less-known conjectures of significant influence and the contrary

In mathematics, it is common that theorems/results and problems appearing dull in one generation get revitalized and become the center of research in another one. Sometimes conjectures that are ...
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11answers
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Why does undergraduate discrete math require calculus?

Often undergraduate discrete math classes in the US have a calculus prerequisite. Here is the description of the discrete math course from my undergrad: A general introduction to basic ...
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1answer
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Websites hosting free math ebooks. [duplicate]

Possible Duplicates: Free, high quality mathematical writing online? Most helpful math resources on the web A lot has been said about different kinds of math resources here in MO. To ...
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14answers
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Making sure that you have comprehended a concept

Hi, I have a question that I've been thinking about for a long time. How can you assure yourself that you've fully comprehended a concept or the true meaning of a theorem in mathematics? I mean how ...
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3answers
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Applications of Group Theory Which Motivate Theoretical Questions?

I'm going to be a teaching assistant for an undergraduate class in abstract algebra next semester, for students who have not taken abstract algebra before. It will deal with group theory and linear ...
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How do undergrad students write papers by themselves?

Can a student write a paper and send it to a professor review?
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12answers
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Examples of undergraduate mathematics separation from what mathematicians should know

I'm looking for examples of four kinds of things: Material that is usually covered in standard undergraduate mathematics courses and/or in first-year graduate work (or tested in qualifying ...
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10answers
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A place to find original papers

I currently use scholar.google.com to find papers in cases like Sophus Lie's original papers on "Transformation Groups". Does anyone know of other places that collect original works like this, i.e. ...
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2answers
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Does A “Connections” Blog/Podcast exist for Math?

What I mean is this: Does there exist a mathematics podcast where a mathematician of some sort looks at undergraduate/graduate mathematical topics and look into the history (how those objects came ...
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5answers
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Resources for learning domain theory?

I'm a computer programmer who's caught on to denotational semantics. I mostly work with Ruby, JavaScript and C, but I know a little Haskell and ML. I've taken my first steps towards reasoning about ...
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2answers
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Which area of mathematics is the hardest to learn ? [closed]

I was asked this question by a friend's daughter a few days back, and I was interested to see what people here think. I realize of course that this is quite subjective, but still, I get the impression ...
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8answers
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Where have you used computer programming in your career as an (applied/pure) mathematician?

For background: I'm working on a book to help mathematicians learn how to program. However, I need to see some examples from people in the field that have done different kinds of things than I have. ...
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Math History books

I'm teaching a course over the summer (it's a sort of make-your-own course for non-majors) and I'm planning on organizing it as a math history course, hitting on major threads through about 1900, and ...
393
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179answers
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Examples of common false beliefs in mathematics

The first thing to say is that this is not the same as the question about interesting mathematical mistakes. I am interested about the type of false beliefs that many intelligent people have while ...
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3answers
795 views

Do rational numbers admit a categorification which respects the following “duality”?

I need to give a lot of quite basic background to this question because I think (at least from conversing with fellow graduate students) that most mathematicians have not really thought about ...
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0answers
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Good textbooks on probability and/or stochastic processes, emphasizing simulation

Any recommendations for textbooks on probability and/or stochastic processes that emphasize simulation? I'll be teaching this course in the Fall.
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18answers
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How should one present curl and divergence in an undergraduate multivariable calculus class?

I am a TA for a multivariable calculus class this semester. I have also TA'd this course a few times in the past. Every time I teach this course, I am never quite sure how I should present curl and ...
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7answers
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Good/Economical textbook for undergraduate intro to diff.eq. for engineers?

In the fall I will be teaching an intro to diff.eq.s course for undergrad engineers. The usual textbook is $150 with solution manual and it's not that great. There must be a cheaper alternative that's ...
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4answers
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The Interrelationship Problem Of Modern Mathematics- How To Deal With it In First Year Graduate Courses?

I was reading recently online Peter May's complaints (I'm a fan, you can tell, I'm sure) about teaching the third quarter of the graduate algebra sequence at the University of Chicago. This course ...
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Reference letters for graduate school after a couple years in the industry

How does one return to graduate school after spending a couple years in the industry? In particular, what are ways of getting good recommendations? I'm not concerned about the "adjustment" to the grad ...