**6**

votes

**0**answers

130 views

### When did people know that all real polynomials of degree greater than 2 are reducible? [migrated]

Admittedly, this may not be a research level question, but I am deeply curious about this.
Let $f(x) \in \mathbb{R}[x]$, and write $d = \deg f$. It is well known that if $\deg f > 2$, then $f$ is ...

**4**

votes

**1**answer

94 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 ...

**3**

votes

**1**answer

387 views

### What questions should -ologists of mathematics ask, in order to improve maths researcher training? [closed]

This question is part of a project funded by the International Council for Science, supported by the IMU (among other bodies). Answers gathered here on mathoverflow may be included in the final ...

**4**

votes

**1**answer

163 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 ...

**27**

votes

**12**answers

2k 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 ...

**46**

votes

**17**answers

10k 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
...

**2**

votes

**0**answers

102 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 ...

**1**

vote

**1**answer

186 views

### finding permutation matrix I which minimizes TRACE( I* C*( I^T)* D) matrix

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 ...

**26**

votes

**2**answers

1k views

### When exactly and why matrix multiplication became a part of undergraduate curriculum?

The story about Heisenberg inventing matrices and matrix multiplication in 1925 is very well known and well documented. Few weeks later Born and Jordan picked this and recognized the matrix ...

**4**

votes

**2**answers

610 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 ...

**33**

votes

**1**answer

2k 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?

**1**

vote

**1**answer

81 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 ...

**5**

votes

**1**answer

822 views

### Can one live without actual infinity? [closed]

The title of this question is the exact title of one of the sections of a book written by Alexandre Borovik: Mathematics under the Microscope. Under the title, we read:
How should we approach the ...

**1**

vote

**0**answers

384 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 ...

**2**

votes

**3**answers

939 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 ...

**-6**

votes

**1**answer

797 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 ...

**12**

votes

**5**answers

1k 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 ...

**56**

votes

**10**answers

11k views

### Is Euclid dead? [closed]

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!" ...

**42**

votes

**18**answers

6k 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 ...

**0**

votes

**3**answers

210 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 ...

**52**

votes

**8**answers

7k 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 ...

**40**

votes

**1**answer

3k 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 ...

**18**

votes

**14**answers

2k 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 ...

**18**

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 ...

**1**

vote

**2**answers

373 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 ...

**2**

votes

**3**answers

356 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 ...

**7**

votes

**2**answers

889 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 ...

**9**

votes

**7**answers

2k 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 ...

**2**

votes

**4**answers

1k 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 ...

**25**

votes

**3**answers

2k 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 ...

**28**

votes

**2**answers

1k views

### Schubert calculus, as lowbrow as possible

Starting in a week I'm going to be an instructor at a summer program for exceptionally mathematically talented high school students, and I'm going to be teaching a class on Schubert calculus. The ...

**23**

votes

**3**answers

2k views

### Nearly all math classes are lecture+problem set based; this seems particularly true at the graduate level. What are some concrete examples of techniques other than the “standard math class” used at the *Graduate* level?

In the fall, I am teaching one undergraduate and one graduate course, and in planning these courses I have been thinking about alternatives to the "standard math class". I have found it much easier ...

**-6**

votes

**3**answers

729 views

### Where is the belly button of the Universe? [closed]

It's fine and nice and wonderful when a part of learning mathematics is chaotic, ad hoc, spontaneous, social, ...
However it would be perhaps of fundamental value to know a very central point of ...

**11**

votes

**2**answers

753 views

### Anything special (historical?) about surface $x\cdot y\cdot z\ +\ x+y+z=0$?

QUESTION
I wanted to introduce and develop the complex logarithm from scratch. As the result I've arrived a couple of months ago at the following identity after which the road to complex logarithm is ...

**41**

votes

**19**answers

6k views

### Are there proofs that you feel you did not “understand” for a long time?

Perhaps the "proofs" of ABC conjecture or newly released weak version of twin prime conjecture or alike readily come to your mind. These are not the proofs I am looking for. Indeed my question was ...

**0**

votes

**1**answer

419 views

### Sierpinski Triangle and the Chaos Game

The chaos game is a way to construct (an approximation) of Sierpinski triangle. It's clear (using Thales' theorem!) that if we begin with a point on the sierpinski triangle, then we will never leave ...

**6**

votes

**5**answers

2k views

### What does a mathematician expect from mathematics education? [closed]

Consider that my question is not a personal and/or subjective question. Perhaps, you have hired a mathematics educator in your department and you are interested in finding a way to communicate with ...

**4**

votes

**4**answers

580 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 ...

**5**

votes

**1**answer

706 views

### Why do mathematicians prefer one definition over the other when they both define the same concept?

Here is a basic, though very important, example:
Hilbert takes as primary the notion of “congruence” (or “equal”) between segments. His first axiom of congruence “requires the possibility of ...

**10**

votes

**2**answers

938 views

### Reference for a nice proof of “undetermined coefficients”

I'm teaching an honors differential equations class and have been using linear algebra heavily. I thought it would be interesting to include a proof of the method of undetermined coefficients along ...

**8**

votes

**1**answer

722 views

### Topology, the board game

Edit: I am reposting this question fom math.stackexchange.com; there may be some professors here who have more experience teaching topology.
This is a math education question that I've been thinking ...

**5**

votes

**2**answers

681 views

### Faculty Handbook: Mentoring Undergraduates in Research and Scholarship

A few days ago I was asked by the director of the Center for Undergraduate Research and Scholarship at Georgia Regents University (formerly known as MCG and Augusta State) to contribute an article for ...

**3**

votes

**1**answer

648 views

### Math major at 36 [closed]

I decided to go for math at 36. Is this idea possible? I studied literature, political science and international relations and still I am not really sure what I am doing.
Since I was kid, I was not ...

**21**

votes

**10**answers

2k views

### Learning through guided discovery

I have been working through Kenneth P. Bogart's "Combinatorics Through Guided Discovery". You can download it from this page: http://www.math.dartmouth.edu/news-resources/electronic/kpbogart/
I've ...

**15**

votes

**2**answers

2k views

### What is the history of $\sqrt{}$

Why we use the symbol $\sqrt{}$ when we take square roots ? Anybody knows the history ?

**12**

votes

**7**answers

3k views

### Usage of set theory in undergraduate studies

I would like to ask my colleagues their thought on good practices concerning
set theorical framework in undergraduate studies. For example, have there been any attempt to use another mathematical ...

**6**

votes

**13**answers

6k views

### 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 ...

**6**

votes

**0**answers

2k views

### What can we do to raise awareness of reciprocity laws? [closed]

The study of reciprocity laws is a centerpiece of modern mathematics. Of the last ten Fields Medalists, two of them (Ngô Bảo Châu and Laurent Lafforgue) were awarded Fields Medals for their work on ...

**7**

votes

**4**answers

673 views

### Seeking a Geometric Proof of a Generalized Alternating Series' Convergence

Let $z \in \mathbb{C} \backslash \lbrace 1 \rbrace$ with $|z| = 1$. We consider the following infinite series, which necessarily converges:
$$S(z) := \sum_{n = 1}^{\infty}\frac{z^n}{n}$$
Note that ...

**16**

votes

**4**answers

3k views

### Is $x \, \tan(x)$ integrable in elementary functions?

I'm teaching Calculus and my students asked me to calculate the integral of $x \, \tan(x)$.
I spent quite a lot of effort to do this, but I'm now even not sure if the integral could be presented in ...