Mathematics Educators Stack Exchange
Mathematics Educators Stack Exchange

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Is it possible to improve logical thinking and problem solving abilities?

I'm from Italy and I'm 13 years old. I'm good in Math and I'm good in languages (I know Italian, English and Russian and I think I'm good at them). I'm a programmer and I know HTML, CSS, JS and Python. I've created some program (like webapp), but…
Blind
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Ideas for teaching a bit of linear optimization to advanced undergraduates?

I am interested in ideas what to teach when the task is to teach a bit of (linear) optimization to third year undergraduate mathematics students. More specifically: Assume 'a bit' means I'd have about eight hours of lecturing time. The students…
quid
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How can I implement the principles of deliberate practise in my mathematical studies?

I have been reading a lot of books about deliberate practise recently like Angela Duckworth's "Grit", "Talent is Overrated" - Colvin and "Peak" - Ericsson and Pool. I want to apply these principles. Can you suggest some concrete steps to implement…
Saikat
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Communicating to students the meaning of extremely large numbers

I'm planning on showing my students a "deep zoom" video of the Mandelbrot set. The video is about 15 minutes long and, at the end, shows an image that is zoomed by a factor of $10^{220}$. I'd like to convey somehow just how staggeringly huge that…
mweiss
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Is there a literature database like MathSciNet for Mathematics Education?

Is there a literature database like MathSciNet for mathematics education?
Christian
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How can one motivate the adjugate matrix?

The adjugate matrix of an $n \times n$ matrix $A$ is defined by $(\mathrm{adj}\ A)_{k\ell} = (-1)^{k+\ell}\,\det M(\ell,k)$, where $M(\ell,k)$ is the minor matrix obtained from $A$ by deleting row $\ell$ and column $k$. The obvious application of…
Mark Wildon
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Why is multivariable analysis often omitted?

Related but not duplicate: What courses require multivariable analysis? By multivariable analysis I mean the rigorous version of multivariable calculus (something equivalent to Ch.9-10 in baby Rudin or topics cover in Analysis on Manifolds by…
user2139
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How important is it to show students an application of the topics seen in an undergraduate course?

I am currently designing a proof-based Math course for my University. I already designed and ordered all of the theoretical content in the course and included some ad hoc exercises for practicing each of the particular topics in the course. However,…
Martin Copes
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What does maths teach you that logic does not?

[Source:] Having studied maths gives you a particular way of thinking through problems that Intro to Logic just doesn't. Will someone please explain and explicate the quote above? Please pardon me if I ought to have posted this in Philosophy SE;…
user155
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What topics should be included in a course matching these specifications?

I posted this question on m.s.e., where I upvoted the two answers, both of which said rather little by comparison to what the question asks. Hence this present posting. Say you have a calculus classroom full of liberal-arts majors who are not…
Michael Hardy
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Could you suggest books, papers or problems that could be used as good "general" motivating examples of calculus application?

I would like to stress the kind of reference I am looking for: In statistics there are lots of motivating (and sometimes unexpected) examples that are interesting for everyone such as Birthday Problem, Simpson Paradox, secretary problem, St…
DanielTheRocketMan
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Substitution in recurrence relations

Let's say we study a reccurence relation such as $$a_{n+1}=a_{n}+n, n \geq 1$$ I find many students are having difficulties when you ask them to find $$a_{n}$$ in terms of $$a_{n-1}$$ where they just have to replace $n$ by $n-1$ in the above…
amarius8312
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What are the mathematical prerequisites to quantum mechanics?

Which topics - what skillset in mathematics need the students to possess to be able to proceed with learning quantum mechanics without hitches like need for explaining notation or understanding the underlying calculations? I.e. what should a…
SF.
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How to show that a radical can be partially simplified

While going over how to simplify expressions with radicals with my precalculus class, I ran into the problem of how to explain that $\sqrt[4]{9}$ can be simplified to $\sqrt{3}$. The best I could come up with was along the lines of you "just have to…
Mike Pierce
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Why is distribution prioritized over combining?

In every algebra (or basic analysis) book that I've seen, three properties of real numbers are taken as axiomatic: commutativity, association, and distribution of multiplication over addition [$a(b + c) = ab + ac$]. What's bothered me for a long…
Daniel R. Collins
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