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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4 answers
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Problems for developing mathematical visualization expertise

Einstein stated that he often explored and reasoned visually and spatially, and only after achieving understanding cast his insights into algebraic form. He could just "see" the answer. There are ...
262 votes
29 answers
89k views

Mathematical games interesting to both you and a 5+-year-old child

Background: My daughter is 6 years old now, once I wanted to think on some math (about some Young diagrams), but she wanted to play with me... How to make both of us to do what they want ? I guess ...
13 votes
4 answers
977 views

Source for analysis of identification of structures in learner's mind and mathematical structures?

Concerning the structure of the learner's mind, psychologist Piaget claimed that There exists, as a function of the development of intelligence as a whole, a spontaneous and gradual construction of ...
Mikhail Katz's user avatar
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1 vote
3 answers
1k views

How to be a Great mathematician in prison/without a master? [closed]

Is it possible to be a great mathematician in our home with a laptop+poor internet+electronic books+some books+a little food +a little money or not? without having a constant job without studying P.H....
-1 votes
1 answer
649 views

Are manifolds typically taught to undergraduates outside mathematics (and possibly theoretical physics) tracks? [closed]

I'm writing my dissertation on symplectic structure-preserving algorithms for Hamiltonian systems simulation, and I'm trying to figure out how much exposition is necessary for it to be readable by ...
user8948's user avatar
  • 151
2 votes
3 answers
9k views

How can I combine my interests for pure mathematics and computer science in college? [closed]

I’m a high school senior who's gone through quite the self-introspection the past few months while applying for college, and I have a bit of a dilemma. All my life, I've loved & excelled at ...
Horse's user avatar
  • 169
7 votes
0 answers
587 views

How necessary is the knowledge of Lebesgue integral for non-analysts? [closed]

Recently I have learned that at some math department the introductory course to Lebesgue integration not obligatory. Thus in another course on introduction to Hilbert spaces the $L^2(0,1)$ space is ...
asv's user avatar
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15 votes
2 answers
5k views

What areas of algebra could be interesting to probability theorists?

I would like to find some topic of algebra (beyond linear algebra; algebraic number theory is fine) that would be interesting both to a student that wants to specialize in probability theory and to me ...
Mikhail Bondarko's user avatar
7 votes
1 answer
243 views

Five cubes, Hadamard and Shklyarskiy

Here is my(=bad) translation of from the paper about Shklyarskiy by Golovina: ... in 1937/38 Dodik presented to school students a complete proof of Abel's theorem about equations of degree 5. He ...
Anton Petrunin's user avatar
1 vote
1 answer
115 views

Expectation of changing the gift choice [closed]

Suppose we are given two boxes, with one of gift valued $n$ dollars and the other one valued twice as much. We can pick a box, and after open it we have the choice of switching to another box. Shall ...
Zhexiu Tu's user avatar
10 votes
1 answer
892 views

A proof without derivatives that a real polynomial of degree $n$ has at most $n-1$ local extrema

This question is about math education and is not research level, so do not hesitate to delete it if it feels inappropriate. I already asked it here a year ago: https://math.stackexchange.com/...
Mathieu Baillif's user avatar
49 votes
14 answers
6k views

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 ...
Uri Bader's user avatar
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95 votes
5 answers
8k views

Is there a database for tracking the dependencies of mathematical theorems?

Given a proof for a result, one could denote the proof as a node on a graph, and then draw arrows to the node from axioms and previous results that the proof uses, and then draw arrows from the node ...
Chill2Macht's user avatar
  • 2,622
12 votes
1 answer
2k views

Is there a way to embed Clifford algebras into the corresponding tensor algebra?

$\newcommand{\talg}{\mathcal{T}(V)}$$\newcommand{\clalg}{\mathcal{Cl}_q(V)}$$\newcommand{\qalg}{\mathcal{I}_q(V)}$Is there a way to embed Clifford algebras into the corresponding tensor algebra? There ...
Chill2Macht's user avatar
  • 2,622
3 votes
1 answer
2k views

Cambridge Mathematical Tripos papers from late 19th century

Are the scanned images of Cambridge Mathematical Tripos papers from late 19th century available anywhere on Internet?
vvn's user avatar
  • 33
15 votes
2 answers
4k views

A certain mathematical competition in the UK

There is a foreword, written by professor Snow, to the book A mathematician's apology. In the foreword, it is written some thing like the following: "Hardy was opposed to a certain mathematical ...
Ali Taghavi's user avatar
2 votes
2 answers
596 views

Math and social commitment [closed]

I am a master's student and am looking for ways that link a certain social commitment with serious math. Since I have not found such an overview yet and in order to raise public awareness of such ...
Leroy's user avatar
  • 119
1 vote
0 answers
98 views

Discrete Mathematics Uses [closed]

I am trying to explain how and why discrete maths is used in areas such as programming, correctness, data types, state transistion and conditionals. I'm having a really hard time articulating it ...
Chance212's user avatar
48 votes
5 answers
4k views

How do you mentor undergraduate research?

Lets say you had an undergraduate who wanted to do some advanced work and some research, possibly for a thesis, or things like that. There are two slightly more specific groups of questions I have ...
0 votes
1 answer
2k views

Everyday, real-life applications of mathematical concepts, and human intuition vs mathematical analysis [closed]

I'm working on an educational project about the applications of reasonably 'lofty', high-ish-level mathematical concepts in the real world. I've already scoured these links (1) (2) (3) after ...
Krister Janmore's user avatar
10 votes
1 answer
612 views

Problems which use S₄ → S₃

I need examples of problems which use, directly or indirectly, the homomorphism $S_4\to S_3$ in the solution (its kernel is $\mathbb{Z}_2\oplus\mathbb{Z}_2$). Obvious candidates: Lagrange resolvent (...
Anton Petrunin's user avatar
3 votes
2 answers
429 views

A logarithmic cotangent inequality

I must be a terrible googling searcher but I cannot find a reference to the following inequality: $$ \forall_{\phi\in(0;\frac \pi 4)}\ \ln(\cot(\phi)))\, <\, \cot(2\!\cdot\!\phi) $$ I have just ...
Włodzimierz Holsztyński's user avatar
78 votes
15 answers
9k views

Sophisticated treatments of topics in school mathematics

Sophisticated mathematical concepts typically shed light on sophisticated mathematics. But in a few cases they also apply to elementary mathematics in an interesting way. I find such examples ...
4 votes
1 answer
170 views

Numerical equality testing

I am working on developing an online homework system. One thing I would like to have is something which compares a student's answer (like $2\sin(x)\cos(x)$) with the intended answer (maybe $\sin(2x)$)...
Steven Gubkin's user avatar
5 votes
1 answer
428 views

How to teach generalizing the induction hypothesis? [closed]

I just finished teaching a class on using proof assistants (in this case, Agda) to write provably correct programs. Reflecting on how it went, the biggest difficulty I noticed the students having was ...
Neel Krishnaswami's user avatar
33 votes
15 answers
3k views

Historical (personal) examples of teaching-based research

The phrase "teaching-based research" brings to mind research about teaching, though important, it is not what I mean. Unfortunately, I couldn't come up with a better phrase, thus please bear with me ...
86 votes
33 answers
24k views

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 ...
4 votes
0 answers
227 views

Applications of Freiman's theorem?

What are some interesting applications of Freiman's theorem or, better-yet, its recent generalizations (eg Green-Ruzsa) that could be included in a graduate course in additive combinatorics? I'm ...
2 votes
1 answer
2k views

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 ...
math2014's user avatar
52 votes
5 answers
4k views

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 ...
Alexandre Eremenko's user avatar
9 votes
2 answers
3k views

Power series with funny behavior at the boundary

Consider a power series $$ \sum_{n=0}^{\infty}a_nz^n $$ where $a_n$ and $z$ are complex numbers. There is radius $R$ of convergence. Let us assume that is a positive real number. It is well known that ...
Giulio's user avatar
  • 2,324
36 votes
1 answer
3k views

Hilbert's Hotel

Hilbert's Hotel is a famous story about infinity attributed to David Hilbert (1862-1943). Is it documented that Hilbert's Hotel is in fact due to Hilbert, and if yes, where?
Loos's user avatar
  • 411
1 vote
1 answer
178 views

Distance between two distribution of image

I am looking for a common distance method to compare two distribution (ex: histogram of image). Please suggest to me some common method to do it. I found some method ex: Bhattacharyya distance , K-L ...
John's user avatar
  • 119
1 vote
0 answers
2k views

Is Independent University of Moscow recognized? [closed]

What graduate schools recognize the degree from Independent University of Moscow? It is not a university strictly speaking and their degree doesn't have any official status in Russia, but they claim ...
mosceo's user avatar
  • 111
10 votes
5 answers
3k views

Assessing effectiveness of (epsilon, delta) definitions [closed]

There is much discussion both in the education community and the mathematics community concerning the challenge of (epsilon, delta) type definitions in calculus and the student reception of them. The ...
Mikhail Katz's user avatar
  • 15.1k
-5 votes
1 answer
2k views

V.I. Arnold's high school problem [closed]

According to his interview to the Notices of the AMS, when Vladimir I. Arnold was 12 years old (in 1949) his teacher I.V. Morozkin, gave to his classroom (apparently 6th grade of a soviet primary ...
smyrlis's user avatar
  • 2,873
31 votes
9 answers
9k views

Recreational mathematics: where to search?

I am not sure I can strictly define recreational mathematics. But we all feel what it is about: puzzles, problems you can ask your mathematical friends, problems that will bother them for a couple of ...
85 votes
12 answers
21k views

Is Euclid dead?

Apparently Euclid died about 2,300 years ago (actually 2,288 to be more precise), but the title of the question refers to the rallying cry of Dieudonné, "A bas Euclide! Mort aux triangles!" (...
55 votes
18 answers
8k views

How can an extremely mathematically talented young person be helped to fulfill his/her potential?

Obviously, this question is not a research level mathematics question at all. But, I've just met an extremely mathematically talented $11$ years old student and I don't know how I can help him. For ...
1 vote
4 answers
387 views

Application for functions of the shape $r = f(\theta)$

A fairly ubiquitous object in elementary calculus is a function of the shape $r = f(\theta)$, where $r$ is the radius and $\theta$ the argument. Common examples include the cardiod and limacon, and of ...
Stanley Yao Xiao's user avatar
108 votes
9 answers
35k views

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 ...
60 votes
1 answer
6k views

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-...
Benjamin Dickman's user avatar
38 votes
18 answers
5k views

Insightful books about elementary mathematics

What are some books that discuss elementary mathematical topics ('school mathematics'), like arithmetic, basic non-abstract algebra, plane & solid geometry, trigonometry, etc, in an insightful way?...
23 votes
2 answers
2k views

Papers better than books?

Not so long ago I took a class called "Discrete analysis". I remember that I couldn't find any "novice" level material on Mobius functions in combinatorics. So then I went to the roots and read Rota's ...
0 votes
2 answers
840 views

Can one branch of mathematics be completely learned from the perspective of another branch of mathematics? [closed]

This arose from a discussion with a friend (people involved are two engineers) who argued that every result in mathematics should be transformable into another branch. For example, he argued that ...
3 votes
3 answers
2k views

Good Books on the history of Zero

I am looking for books that discuss the origins of the zero, specifically the differences in the use and concept of the zero number among different civilizations (considering also the Mesoamerican ...
D. Corro's user avatar
  • 221
7 votes
2 answers
1k views

How should you respond to a student who asks whether a very nice physical example constitutes a proof? [closed]

"Is this really a proof?" is the exact question e-mailed to me today from an undergraduate mathematics student whom I know as a highly competent student. The one sentence question was accompanied with ...
Amir Asghari's user avatar
  • 2,277
9 votes
7 answers
7k views

Review papers in mathematics

Are there review papers, literature reviews in mathematics that describe the recent developments in various fields for a newcomer? Or is the prerequisite knowledge always provided in research ...
4 votes
4 answers
2k views

When did you "meet Polya"? [closed]

I guess most of us didn't meet Polya in person (this is the answer to the title)! Perhaps, it is much easier to guess that most of us have met one of his writings (or alike) on problem solving, and ...
27 votes
3 answers
3k views

Is “problem solving” a subject to be taught?

I am witnessing a new curriculum change in my country (Iran). It includes the change of all the mathematics textbooks at all grades. The peoples involved has sent me the textbook for seven graders (13 ...