Questions tagged [mathematics-education]

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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Abstract Algebra True or False [closed]

Hope you are all well, Im posting this on behalf of a friend and her first language is not english, i will relay any help given to her however im not familiar with the math formulas and terms, however ...
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How to explain to an engineer what algebraic geometry is?

This question is similar to this one in that I'm asking about how to introduce a mathematical research topic or activity to a non-mathematician: in this case algebraic geometry, intended as the most ...
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0answers
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A taxonomy of proof methods [closed]

I am looking for a taxonomy of proof methods in mathematics. For basic proof methods I would think of proof by contradiction, mathematical induction, structural induction (yes I am a computer ...
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261answers
234k views

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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Online courses for mathematics [closed]

I'm sorry if I'm posting this in the wrong forum. My background is in biology and medicine. I am looking to re-learn undergraduate-level mathematics, in particular discrete mathematics, calculus, and ...
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9answers
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How do you not forget old math?

I am trying to not forget my old math. I finished my PhD in real algebraic geometry a few years ago and then switched to the industry for financial reasons. Now I get the feeling that I want to do a ...
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15answers
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Useless math that became useful

I'm writing an article on Lychrel numbers and some people pointed out that this is completely useless. My idea is to amend my article with some theories that seemed useless when they are created but ...
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17answers
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PhD dissertations that solve an established open problem

I search for a big list of open problems which have been solved in a PhD thesis by the Author of the thesis (or with collaboration of her/his supervisor). In my question I search for every possible ...
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Engineering mathematics course and the order of the teaching of its topics

I am going to teach a course names "Engineering Mathematics" and the topics in it, are: Fourier series and integrals; including the motivation and computational aspects and their ...
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3answers
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Why is the standard definition of a $(p, q)$-tensor so bizarre?

At time of writing the first definition of a $ (p, q) $-tensor on the Wikipedia page is as follows. Definition. A $ (p, q) $-tensor is an assignment of a multidimensional array $$ T^{i_1\dots i_p}_{...
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10answers
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effective teaching

Eric Mazur has a wonderful video describing how physics is taught at many universities and his description applies word for word to the way I learned mathematics and the way it is still being taught, ...
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81answers
128k views

Video lectures of mathematics courses available online for free

It can be difficult to learn mathematics on your own from textbooks, and I often wish universities videotaped their mathematics courses and distributed them for free online. Fortunately, some ...
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6answers
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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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13answers
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How misleading is it to regard $\frac{dy}{dx}$ as a fraction?

I am teaching Calc I, for the first time, and I haven't seriously revisited the subject in quite some time. An interesting pedagogy question came up: How misleading is it to regard $\frac{dy}{dx}$ as ...
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4answers
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Some interesting and elementary topics with connections to the representation theory?

I'm going to give a talk to talented high school seniors (for nearly 1.25-1.75 hours, maybe a little bit longer). They know some abstract algebra (groups, rings, modules...), linear algebra (...
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2answers
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Which W W Sawyer titles exist in non-English language editions?

In this community question asking about books that teach the practice of mathematics, the author mentions the works of W W Sawyer. Which of Sawyer's books were translated into languages other than ...
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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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8answers
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How to memorise (understand) Nakayama's lemma and its corollaries?

Nakayama's lemma is mentioned in the majority of books on algebraic geometry that treat varieties. So I think Ihave read the formulation of this lemma at least 20 times (and read the proof maybe ...
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76 views

Classical papers in linear algebra suitable for an undergraduate reading group?

I'm interested in collecting some of the classical papers in linear algebra over the years. To be more specific, I'm looking for interesting and useful results that extend beyond what is typically ...
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5answers
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When exactly and why did matrix multiplication become a part of the undergraduate curriculum?

The story about Heisenberg inventing matrices and matrix multiplication in 1925 is very well known and well documented. A few weeks later, Born and Jordan read this work and recognized matrix ...
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Studying the vast world of Number Theory [closed]

I'm a high school student, interested in mathematics, especially in number theory. While preparing for the IMO test, and thinking about generalizations or the root of many olympiad problems led me to ...
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1answer
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Probability that a stick randomly broken in five places can form a tetrahedron

Edit (June 2015): Addressing this problem is a brief project report from the Illinois Geometry Lab (University of Illinois at Urbana-Champaign), dated May 2015, that appears here along with a foot-...
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3answers
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What aspects of math olympiads do you find still useful in your math research?

I was rereading the book Littlewood's Miscellany and this passage struck me: It used to be said that the discipline in 'manipulative skill' bore later fruit in original work. I should deny this ...
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1answer
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Finding permutation matrix $P$ that minimizes the trace of $P C P^T D$

I have a problem that is really important for my thesis and i am not studding math so i will be very glad if you help me in this case... thanks for your help in advance I want to find permutation ...
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2answers
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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 ...
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18answers
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Interesting and accessible topics in graph theory

This summer, I will be teaching an introductory course in graph theory to talented high school seniors. The intent of the course is not to establish proficiency in graph theory, per se. Rather, I hope ...
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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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29answers
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Parodies of abstruse mathematical writing

Perhaps under the influence of a recent question on perverse sheaves, in conjunction with the impending $\pi$-day (3/14/15 at 9:26:53), I recalled a long-ago parody of abstruse mathematical language ...
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3answers
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Mathematics for machine learning

I would like to know what mathematics topics are the most important to learn before actually studying the theory on neural networks. I ask that because I will start to learn about neural networks and ...
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3answers
759 views

Axioms for constructive Euclidean geometry

In the summer I will be teaching a course in (plane) Euclidean geometry to future high school teachers and I am looking for a suitable axiom system (unlike College (Euclidean) geometry textbook ...
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1answer
380 views

What are some problems for research in functional analysis that can possibly be solved by someone with basic knowledge of the subject? [closed]

I wanted to know are there any problems in Functional Analysis (FA) that can possibly be successfully tackled by someone like me who does not have any expertise in this area but is only familiar with ...
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13answers
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Pedagogical question about linear algebra

Last semester I taught a linear algebra class that is intended to introduce young students (at a sophmore-junior level) to "abstract mathematics". It seems that a major conceptual hurdle for many of ...
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21answers
7k views

One-step problems in geometry

I'm collecting advanced exercises in geometry. Ideally, each exercise should be solved by one trick and this trick should be useful elsewhere (say it gives an essential idea in some theory). If you ...
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17answers
15k views

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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28answers
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Cool problems to impress students with group theory [closed]

Since this forum is densely populated with algebraists, I think I'll ask it here. I'm teaching intermediate level algebra this semester and I'd like to entertain my students with some clever ...
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27answers
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Nontrivial question about Fibonacci numbers?

I'm looking for a nontrivial, but not super difficult question concerning Fibonacci numbers. It should be at a level suitable for an undergraduate course. Here is a (not so good) example of the sort ...
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34answers
72k views

Why is a topology made up of 'open' sets? [closed]

I'm ashamed to admit it, but I don't think I've ever been able to genuinely motivate the definition of a topological space in an undergraduate course. Clearly, the definition distills the essence of ...
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9answers
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Relating Category Theory to Programming Language Theory

I'm wondering what the relation of category theory to programming language theory is. I've been reading some books on category theory and topos theory, but if someone happens to know what the ...
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6answers
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Euclid with Birkhoff

I'm looking for an short and elementary book which does Euclidean geometry 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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7answers
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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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21answers
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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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25answers
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“Mathematics talk” for five year olds

I am trying to prepare a "mathematics talk" for five year olds from my daughter's elementary school. I have given many mathematics talks in my life but this one feels very tough to prepare. Could the ...
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14answers
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Interactive model of the hyperbolic plane for a general public lecture

The following is not quite a research level question, but I still find this site appropriate for asking it. I hope I get it right here. I am preparing a talk for a general public and I want to ...
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1answer
118 views

Generalized Fourier integral and steepest descent path, saddle point near the endpoints

I am looking forward to solving the integration in the following equation with the assumption that $ka$ is very large \begin{align} H = 2jka\int_{-\pi/2}^{\pi/2}\cos{(\varphi-\phi)}e^{jka[\cos{\...
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2answers
656 views

Books on the History of math research at European universities

Are there good books that cover the history of math and mathematical science (ex. physics, chemistry, computer science) PhD programs in the Occident? My primary motivation is to figure out how the PhD ...
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0answers
640 views

Probability in Math Education [closed]

Why is probability an under-emphasized subject in most math programs? Why does it seem that the hot topics these days are category theory and algebra? What do you think about the following: A student ...
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16answers
7k views

Short papers for undergraduate course on reading scholarly math

(I know this is perhaps only tangentially related to mathematics research, but I'm hoping it is worthy of consideration as a community wiki question.) Today, I was reminded of the existence of this ...
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4answers
931 views

Lecture on Fractals for Middle School Students

I'm going to have a one-hour lecture for middle school students next Monday. It will be about fractals. The students know virtually nothing about this subject. I'll show some fractal images and a few ...
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6answers
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Why isn't integral defined as the area under the graph of function?

In order to define Lebesgue integral, we have to develop some measure theory. This takes some effort in the classroom, after which we need additional effort of defining Lebesgue integral (which also ...
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1answer
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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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