Questions tagged [education]

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

2,504 questions
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Differential Geometry of curves and surfaces: bibliography?

Dear all, next year, I will probably teach a one-semester course of Differential Geomtry of curves and surfaces. Its content must be something along the lines of the first four chapters of Do Carmo's ...
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Why do we need to prove $e^{u+v} = e^ue^v$?

In this book I'm using the author seems to feel a need to prove $e^{u+v} = e^ue^v$ By $\ln(e^{u+v}) = u + v = \ln(e^u) + \ln(e^v) = \ln(e^u e^v)$ Hence $e^{u+v} = e^u e^v$ But we know from basic ...
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Why is $\pi$ equal to $3.14159…$?

Wait before you dismiss this as a crank question :) A friend of mine teaches school kids, and the book she uses states something to the following effect: If you divide the circumference of any ...
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Topic for a high school-level math elective?

I'm looking for ideas for a 15-hour mathematical enrichment course in a Chinese high school. What (fairly) elementary subject would you suggest as a topic for such a course? Background/considerations:...
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Need good material on multifractal analysis

I'm searching for some good reading material on multifractal analysis. Preferably something accessible that doesn't put the stress too much on mathematical proofs but rather on applications. As long ...
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How do you generate mathematical formulas programmatically using a server side language [closed]

We would like to generate simple mathematical formulas on the fly (e.g. $\sin^2 \theta$). The above function seems to be a MathJaX representation. Most of the solutions depend on writing mathematical ...
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Research Experience for Undergraduates: Summer Programs (that accept non-American applicants)

There are many summer research programs in the United States, targeted at good motivated undergraduate students majoring in mathematics. The main aspects that characterize such programs are: (a) a ...
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What is the meaning of the third derivative of a function at a point

(Originally asked on MO by AJAY.) What is the geometric, physical, or other meaning of the third derivative of a function at a point? If you have interesting things to say about the meaning of the ...
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What are or where can I find style guidelines for writing math?

I am a scientist writing my first manuscript with a substantial amount of mathematical methodological documentation. I am using LaTeX, but this is not my question. I would like to find a list of ...
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Geometry or Topology

So, I am a graduate student who is certain that he does not want to do analysis (I think...). What are the most exciting fields in mathematics right now? It seems to me that very generally, they are ...
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Motivating implications of the axiom of choice?

What are some motivating consequences of the axiom of choice (or its omission)? I know that weak forms of choice are sometimes required for interesting results like Banach-Tarski; what are some ...
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I wanted to ask these questions here, feeling that this place place is without doubt is better than anywhere else, feeling hesitant and shy to ask such question. For several reasons, the environment ...
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I would like to buy references in order to review and study mathematics [closed]

I am an ESL learner and most of the time I am able to understand English but In my courses, we don't study mathematics, and I think that it is a mistake or wrong. 1-What are really the best sources (...
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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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Quotient geometries known in popular culture, such as “flat torus = Asteroids video game”

In answering a question I mentioned the Asteroids video game as an example -- at one time, the canonical example -- of a locally flat geometry that is globally different from the Euclidean plane. It ...
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YARFMO (Yet another reposting from Mathoverflow) ;-) The more you know about math the more you find conceptions previously thought correct to be false: 1.) math is not as exact as many believe - in ...
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Books that develop interest & critical thinking among high school students

I heard about Yakov Perelman and his books. I just finished reading his two volumes of Physics for Entertainment. What a delightful read! What a splendid author. This is the exact book I've been ...
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Which discussion board is good for homework questions? [closed]

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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Why is negative times negative = positive?

Someone recently asked me why a negative $\times$ a negative is positive, and why a negative $\times$ a positive is negative, etc. I went ahead and gave them a proof by contradiction like so: Assume ...
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How do I explain 2 to the power of zero equals 1 to a child

My daughter is stuck on the concept that $$2^0 = 1,$$ having the intuitive expectation that it be equal to zero. I have tried explaining it, but I guess not well enough. How would you explain the ...
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Motivating infinite series

What are some good ways to motivate the material on infinite series that appears at the end of a typical American Calculus II course? My students in this course are generally from biochemistry, ...
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Why Doesn't This Series Converge?

I am teaching a Calc II course and came across the following series when finding the interval of convergence for the Taylor series of $f(x)=\sqrt{x}$ centered at $x=1$:  \sum_{n=2}^\infty \frac{1\...
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Best Cities for Mathematical Study

This may sound silly, but... Suppose an aspiring amateur mathematician wanted to plan to move to another city... What are some cities that are home to some of the largest number of the brightest ...
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False beliefs in mathematics (conceptual errors made despite, or because of, mathematical education)

Over on mathoverflow, there is a popular CW question titled: Examples of common false beliefs in mathematics. I thought it would be nice to have a parallel question on this site to serve as a ...
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Is most of the GM-AM Inequality in its codicil?

Let’s define the codicil of the Geometric Mean – Arithmetic Mean Inequality to be the statement that if the means are equal, then all the terms are equal. Then: I conjecture that most of the GM-AM ...
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What are good elementary examples for teaching/introducing/learning about Intuitionistic Logic or Heyting Algebras?

For example, I have heard of a topological one wherein negation means the interior of the complement (but still would like a reference).
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Is “locally linear” an appropriate description of a differentiable function?

In this answer on meta, Pete L. Clark said: I think the question concerns the idea that a differentiable curve becomes more and more like a straight line segment the closer one zooms in on its ...
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What are some deep questions that are applicable to first graders in regards to adding zero?

I'm trying to come up with some math problems (word or otherwise) that get to the meaning of adding zero, but I'm getting stuck because it seems just too simple to me. I have come up with questions ...
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How to assess a non-natively english speaking high-schooler's mathematical ability?

I'm a math PhD who has been asked to interview a high school student and determine what he/she is interested in and how strong the student is. Usually I would want them to talk as much as possible ...
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How to show every subgroup of a cyclic group is cyclic?

I'm teaching a group theory course now, and I wanted to give my students a proof that every subgroup of a cyclic group is cyclic. The easiest way I could think to do this is to say that any cyclic ...
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Elevator pitch for a (sub)field of maths?

When I first saw the title of this question, I forgot for a moment I was on meta, and thought it was asking about quick, catchy, attractive, informative one-or-two-liner summaries of various fields of ...
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