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0
votes
1answer
20 views

Preparation for a graduate commutative algebra course based on Eisenbud

I am an undergraduate with two semesters of algebra(groups,rings, Galois theory, etc) under my belt and I am planning on going through Atiyah and MacDonald's book over the summer. Is this sufficient ...
1
vote
3answers
80 views

Mental Math Tricks

What are some interesting mental math tricks that you know? Here's one that I got from my Grandmother who got it from a book: To square a two-digit number (from $26$ to $49$), take the number minus ...
7
votes
1answer
114 views

Create a Huge Problem

I am wondering if any problems have been designed that test a wide range of mathematical skills. For example, I remember doing the integral $$\int \sqrt{\tan x}\;\mathrm{d}x$$ and being impressed at ...
19
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8answers
6k views

Are there contradictions in math?

Someone told me that math has a lot of contradictions. He said that a lot of things are not well defined. He told me two things that I do not know. $1+2+3+4+...=-1/12$ what is infinity $\infty$? ...
2
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0answers
19 views

Revise high school material

Can you suggest me a comprehensive book to revise high school mathematics (up to besic calculus)? It should be extremely clear and complete and "scientific" (not like most high school books). Thank ...
13
votes
2answers
500 views

A problem V.I. Arnold solved as a primary school student

According to a 1995 interview that Vladimir I. Arnold gave to the Notices of the AMS, his primary school teacher I.V. Morozkin gave in 1949 (when Vladimir I. Arnold was 12 years old) to a Soviet ...
2
votes
2answers
36 views

Material for advanced highschooler

I'm a high school student who just finished elementary school.Though since I was into math I started going through advanced math while I was in elementary school and I pretty much finished most of the ...
14
votes
2answers
317 views

The double factorial notation

The double factorial is defined as $$n!! = \begin{cases} n \cdot (n-2) \cdot (n-4) \cdots 3 \cdot 1 = \dfrac{(n+1)!}{2^{(n+1)/2}((n+1)/2)!} & \text{ If $n \in \mathbb{Z}^+$, is odd}\\ n \cdot ...
0
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2answers
20 views

what are some typical systems of equations generating from practical problems?

I want to know some typical forms of system of equations generating from practical problems in engineering/economics/physics,etc. Some examples or research articles would be good. Specifically, I am ...
3
votes
4answers
482 views

Topological groups, why need them?

I'm reading through Munkres and Armstrong's books on topology. However, I find topological groups to be really complicated objects! I feel they are twice as hard to deal with then just groups and ...
1
vote
2answers
26 views

Cycloidal coincidence?

For the cycloid $$x=a(t-\sin t)\ ,\quad y=a(1-\cos t)$$ we have, as is easily seen, $$\frac{dx}{dt}=y\ .$$ Does this have any geometrical or physical significance? Or is it just a meaningless ...
318
votes
41answers
137k views

Visually stunning math concepts which are easy to explain

Since I'm not that good at (as I like to call it) 'die-hard-mathematics', I've always liked concepts like the golden ratio or the dragon curve, which are easy to understand and explain, but are ...
5
votes
0answers
44 views

Gap Year Advice-Becoming the Best I can be

I'm an undergraduate studying Mathematics at University of Cambridge. Very recently I had to take an intermit leave due to medical reasons during my second year as an undergraduate. During my time, I ...
3
votes
3answers
68 views

Things to do before starting math (or physics) at university

What is better to do before starting a math degree? I was thinking that maybe I should do something like: learning latex learning how to use matlab Any other suggestions?
26
votes
2answers
1k views

Development of the Idea of the Determinant

While I basically understand what a determinant is, I wonder how this idea was developed? What was the principal idea behind its origination? I would like to know this so that I can have a better ...
10
votes
8answers
297 views

$2\times2$ matrices are not big enough

Olga Tausky-Todd had once said that "If an assertion about matrices is false, there is usually a 2x2 matrix that reveals this." There are, however, assertions about matrices that are true for ...
8
votes
4answers
399 views

Is $\tan\theta\cos\theta=\sin\theta$ an identity?

A friend of mine, who is a high school teacher, called me today and asked the question above in the title. In an abstract setting, this boils down to asking whether an expression like "$f=g$" is ...
9
votes
4answers
331 views

Application of computers in higher mathematics

Currently the main application of computers in mathematics seems to be to compute things, i.e. to solve equations, evaluate integrals, etc. It is at all possible to delegate the thinking of a ...
2
votes
1answer
40 views

Does memorizing a proof help to provide the intuition behind it?

To be clear, I'm $\bf{\text{not}}$ talking about rote memorization. If I can follow a proof, follow each step on its own, but still have trouble believing that the result is true. I usually try to ...
8
votes
1answer
238 views

Toddler introductions to higher mathematics

I bought my youngest (now 10 months old) "Introductory Calculus For Infants" by Omi Inouye a while back. It's actually an ABC book about the letter x and how no one ever plays with him until he meets ...
1
vote
3answers
29 views

Which discrete mathematics book to read for a software engineer?

I'm a computer science student, but I lack a good mathematics background. So I decided to start working on that. I was searching in the topic and I found that for computer science a good knowledge of ...
8
votes
6answers
9k views

“Where” exactly are complex numbers used “in the real world”?

I've always enjoyed solving problems in the complex world during my undergrad. However, I've always wondered where are they used and for what? In my domain (computer science) I've rarely seen it be ...
9
votes
1answer
491 views

Are there “mental calculator” persons that can recognize closed-form expressions?

There are people, sometimes called mental calculators, who is capable of performing fast calculations in their head, involving multiplication, factorization, finding logarithms and roots of a high ...
2
votes
0answers
46 views

Changing research area in grad school

I'm a PhD student about to close out my third year. My current research area is operator algebras. At the beginning of this semester I completed my qualifying exams (this was accomplished a semester ...
20
votes
7answers
460 views

“Here's a cool problem”: a collection of short questions with clever solutions

This game will be familiar to many mathematicians, and it is always good fun to play. I am looking to find a list of good questions with short, when-you-see-it solutions. The kind of question one ...
0
votes
1answer
31 views

In which course one learns Lie Group&Algebra and to which category of mathematics this subject belongs?

I'm a junior and i have never leanred this subject. I think "Lie Group&Algebra" is really deep and massive theory since the wikipedia page for it is quite long. Nevertheless, i'm not sure ...
1
vote
0answers
26 views

What courses require multivariable analysis?

For which undergraduate and introductory graduate mathematics courses is a rigorous course in multivariable analysis an essential prerequisite?
1
vote
0answers
30 views

Analogy between linear basis and prime factoring

I recall learning that we can define linear systems such that any vector in the system can be represented as a weighted sum of basis vectors, as long as we have 'suitable' definitions for addition and ...
1
vote
0answers
38 views

Applications of PDEs

I teach an undergrad ODE course. As I have completed basically all the material, I thought it would be nice to give the students a brief introduction to PDEs. At the end of the lecture, I said that ...
56
votes
14answers
5k views

A good way to retain mathematical understanding?

What is a good way to remember math concepts/definitions and commit them to long term memory? Background: In my current situation, I'm at an undergraduate institution where I have to take a lot of ...
2
votes
2answers
69 views

Conditional events that are not in the event algebra?

The Wikip. page on conditional event algebra states that: David Lewis showed that in orthodox probability theory, only certain trivial Boolean algebras with very few elements contain, for any ...
5
votes
1answer
98 views

What happens if your manuscript is accepted as a filler?

I just got a responce from a journal of the MAA that my manuscript is accepted as a filler. The email says : "The Editorial Board likes your submission and has asked me to move it to the ...
74
votes
19answers
12k views

Visually deceptive “proofs” which are mathematically wrong

Related: Visually stunning math concepts which are easy to explain Beside the wonderful examples above, there should also be counterexamples, where visually intuitive demonstrations are actually ...
4
votes
2answers
123 views

Is it still possible for mathematicians to contribute to the theory of music?

Is it still possible that mathematicians contribute to the theory of music? Is the mathematical foundation of music still an area of research? If yes, what new researches have been done regarding ...
0
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0answers
23 views

A nowhere zero point in a linear mapping and Research Resources

Conjecture: If $\mathbb{F}$ is a finite field with at least 4 elements and $A$ is an invertible $n\times n$ matrix with entries in $\mathbb{F}$, then there are column vectors $x,y \in \mathbb{F^n}$ ...
0
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0answers
58 views

Choosing between Universities for Mathematics

I am trying to advise a younger friend looking into colleges and I was wondering what others would think: Is it better to go for a prestigious university where the focus would be almost exclusively ...
4
votes
1answer
88 views

Forgetting mathematics. Memory problem [duplicate]

I got an A from Game Theory. But after that i forgot almost all the formulas and theorems. What should i do to prevent that? Do you forget math like i do?
1
vote
1answer
67 views

Uncertainty of Graduate Mathematics

I will be starting my graduate studies next semester right out of my undergrad and I am uncertain about courses that I am ready to take. The main courses of concern are algebra, analysis and applied ...
0
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0answers
25 views

Proving Maths Skills for MSc Data Science Degree

In September I'll be applying for a Master's degree in Data Science (2015 intake). With the degree I hold (BSc Psychology), I will forfil the entry requirements provided I have a "demonstrable ...
12
votes
1answer
632 views
+100

The Best Strategy and Highest Possible Score for the “Threes!” Game.

[There's still the strategy to go . . . ] Here's my description of the game: There's a $4\times 4$ grid with some random, numbered cards on. The numbers are either one, two, or multiples of three. ...
23
votes
5answers
2k views

Tell me problems that can trick you

I am looking for problems that can easily lead the solver down the wrong path. For example take a circle and pick $N$, where $N>1$, points along its circumference and draw all the straight lines ...
1
vote
1answer
364 views

Linear algebra and Multivariable calculus prerequisites for Stochastic Calculus

Which topics are considered "graduate-level" for the following subjects: Linear algebra Multivariable calculus On Internet, it is said that you need "graduate level" Linear algebra and ...
2
votes
0answers
60 views

Calculus book advice

I'm reading Thomas Calculus now but I don't think it includes Mellin transform or Riemann-Stieltjes integration... Can you recommend an advanced calculus book which includes all of this stuff?
2
votes
0answers
21 views

Pure Math or Stats undegrad for Stats Grad School

Hello I'm currently a first year undergrad double majoring in physics and math. My school offers both a pure math and a statistics concentration and I'm wondering which one would be better for ...
16
votes
11answers
762 views

Why limits work

I'm currently a first year student in electrical engineering and computer science. I know how to compute limits, derivatives, integrals with respect to one variable that is things from one variable ...
31
votes
4answers
2k views

How to write a good mathematical paper?

I hesitate to ask this question. However I read many advices from math.stackexchange, and I couldn't find anything similar. A good time always goes too fast! Two years are fled. In the third year of ...
0
votes
0answers
25 views
11
votes
7answers
872 views

When is something “obvious”?

I try to be a good student but I often find it hard to know when something is "obvious" and when it isn't. Obviously (excuse the pun) I understand that it is specific to the level at which the writer ...
4
votes
1answer
27 views

Surprising constructions in algebraic topology that facilitate one's understanding of underlying theory

I am recently come into the world of algebraic topology and find it a fascinating place with lots of beautiful constructions that challenge one's intuition. Also, understanding these constructions are ...
0
votes
0answers
30 views

The term $rank$ in methematics

Reading wikipedia's disambiguation page about the "rank" word I see many concept of rank of many different matematical object. I only know about the rank of a graded poset and the rank of a set that ...