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3
votes
1answer
203 views

What's correspondence between the model theoric and the set theoric kernel of homomorphism?

A kernel of a mapping $h$ from $\mathfrak{A}$ to $\mathfrak{B}$, generally, is an equivalence relation $\{(a,a') \in \mathfrak{A} \times \mathfrak{A} \mid h(a)=h(a')\}$. However, in model theory, ...
8
votes
1answer
240 views

Construction(s) of new integral domains from “old ones”

Given an integral domain $D$, there are several ways how to construct a new integral domain related to D. For example, one can consider a ring of polynomials/formal power series/formal Laurent series ...
12
votes
3answers
542 views

Motivation for Jordan Canonical Form

I took linear algebra and understood the proof that linear operators on a vector space over an algebraically closed field have a Jordan Canonical Form. Why should I care about this theorem? I ...
2
votes
4answers
514 views

Resources for learning mathematics for intelligent people?

Could people recommend resources to help my wife learn more complicated mathematics? She had a really terrible maths education, and while she essentially OK with every day maths she keeps wanting to ...
3
votes
2answers
142 views

What's the correct name in english for “Analysis in $\Bbb R^n$”?

Well, this question may seem silly and I fear it's even out of topic here. My motivation to ask that is to know the correct terminology when talking about that here in Math.SE. The point is, here in ...
6
votes
1answer
290 views

Is there an integral form of Newton's method?

Warning : This seems like a silly sort of question, not the kind I'd ask out loud. The contraction mapping theorem is a basic tool for proving existence of, and finding solutions to, equations. Given ...
2
votes
2answers
584 views

What programming languages are used in (chaotic) dynamical systems and nonlinear phenomena research?

I'm currently considering pursuing postgraduate studies in the field of chaos/dynamical systems/nonlinear phenomena, and was wondering whether there are particular programming languages that are ...
7
votes
2answers
190 views

Usefulness of induced representations.

I am learning representation theory from Serre's book by myself. Currently I am reading about induced representations, but I don't understand the importance. The concept looks strange and the ...
9
votes
2answers
238 views

Ideas for a present to my topology teacher

Tomorrow is the my final lecture in my favorite course, algebraic topology. I want to give a present to my prof. as a keepsake, something along the lines of this only something I can make due ...
5
votes
4answers
698 views

Books for a beginner

I am a student of 11th grade and i have completed the syallabus of both 11th and 12th grade maths with complete understanding and it was possible coz of the love for this subject that i have. I don't ...
3
votes
1answer
110 views

What's next? $\text{Hom}(U,V)$, tensor product and so on

I don't think this question is as soft as soft-question tag, but if I not how to tag it, I would not be asking this question: I have taken second year linear algebra (Axler's Linear Algebra Done ...
5
votes
2answers
159 views

Were logical quantifiers not primarily motivated by infinite domains of discourse?

There is this quote by Hermann Weyl: "… classical logic was abstracted from the mathematics of finite sets and their subsets …. Forgetful of this limited origin, one afterwards mistook that logic for ...
5
votes
1answer
164 views

Algebra and skills needed for Hatcher

A couple of months ago I asked a professor by e-mail to mentor me on topology during the summer. He advised me to study general topology (Hausdorff spaces, connectedness, compactness) and algebraic ...
2
votes
0answers
49 views

Facing mostly-faced decks

In my day job, I am often called upon to take a large stack of—let's call them cards—and make sure that a large majority of them are facing in a particular direction. In most cases, there ...
3
votes
1answer
112 views

About having everything well under control [closed]

When I started doing maths I "rediscovered" some elemental things and listed them on a notebook. All things I learned were in there, like Pythagorean theorem, sine and cosine definitions, some ...
21
votes
5answers
934 views

Is there a deep reason why $(3, 4, 5)$ is pythagorean? [closed]

The triple $(3, 4, 5)$ is a pythagorean triple - it satisfies $a^2 + b^2 = c^2$ and, equivalently, its components are the lengths of the sides of a right triangle in the Euclidean plane. But of ...
17
votes
5answers
915 views

Questions about Listening To Presented Material [closed]

I find that during seminars I attend, I often feel like the slowest person in the room. For example when seeing a technical theorem on the board, I often forget it by the time we are but a few lines ...
3
votes
1answer
102 views

Would this be an effective way to study and comprehend text's?

This is probably a grey area question but I am going to test the waters anyway. What I am thinking of doing would be to basically record myself doing examples from textbooks and making lessons for ...
3
votes
2answers
137 views

Specific (algebraic) directions in NCG

Since my initial question (How much algebra is there in Noncommutative Geometry?), I got to study the basics of NCG and I now consider starting a PhD. program in NCG. I read Khalkhali's Basic NCG and ...
4
votes
0answers
111 views

Some long and good prerequisite textbooks to the graduate probability textbook by shiryaev and boas?

Some long and good prerequisite textbooks to the graduate probability textbook by shiryaev and boas? It seems that it have a big gap between this graduate textbooks and the easier ones.
3
votes
1answer
177 views

bests book of representation theory for algebraic number theorists

I am looking for some of the best books on representation theory for an algebraic number theorists> I would prefer a book that is more number theoretical (e.g, galois representations, p adic ...
3
votes
1answer
992 views

maths required to complete project euler

What math's will help one complete all if not most of project Euler questions? Last I've attempted project Euler I could not understand the questions/vocabulary, etc., and could only complete a few ...
2
votes
3answers
291 views

Usefulness of the concept of equivalent representations

Definition: Let $G$ be a group, $\rho : G\rightarrow GL(V)$ and $\rho' : G\rightarrow GL(V')$ be two representations of G. We say that $\rho$ and $\rho'$ are $equivalent$ (or isomorphic) if $\exists ...
4
votes
5answers
517 views

How important is a teacher / tutor?

I am doing fine in my classes and enjoy math. That is not the issue. During my spare time, I am doing more advanced stuff than my class is currently doing. My question is though, would I benefit more ...
40
votes
8answers
2k views

Intuitive meaning of Exact Sequence

I'm currently learning about exact sequences in grad sch Algebra I course, but I really can't get the intuitive picture of the concept and why it is important at all. Can anyone explain them for me? ...
2
votes
2answers
400 views

Question regarding the definition of direct sum decomposition of a representation

Please bear with me. I am trying to learn representation theory of finite groups from J.P. Serre's book by myself. Here, the author has used the word 'representation' for the homomorphism $\rho : ...
4
votes
1answer
781 views

Concrete Mathematics Prerequisite Question

I've been very interested in the book Concrete Mathematics (Graham,Knuth,Patashnik) and I've been reading it for the past few weeks. I'm at the chapter about Sums (Chapter 2), specificaly, the lesson ...
10
votes
3answers
3k views

Self teaching Galois Theory

At uni, I did a module in group theory which I really enjoyed. I also did one on number theory which had aspects of rings and fields in it and I enjoyed learning this. Now that I have finished uni, I ...
5
votes
2answers
519 views

Meaning of quote: “model theory = algebraic geometry - fields”?

On the wikipedia article for model theory, it says that a modern definition of model theory is "model theory = algebraic geometry - fields" and cites Hodges, Wilfrid (1997). A shorter model theory. ...
6
votes
1answer
121 views

Is there an easy way to get to a paper, given a citation?

This question isn't about math per se, but I hope it will be of general interest to people studying math so I feel reasonably comfortable asking here. Let me start with an example: Today I had the ...
4
votes
2answers
565 views

What is Ramsey Theory ? what is its own importance in maths?

3 days ago , i had a discussion with a close friend who studies physics - still a student - . and i was telling her about the biggest known numbers in maths , so i told her about numbers such googol ...
0
votes
1answer
85 views

What subject teaches derivation of trigonometric identities?

I'm a college student. In order to ace my single-variable calculus course, I have memorized many trigonometric formulas including $$\int \sin^m x \cos^n x dx = \frac{\sin^{m+1} x \cos^{n-1}x}{m+n} + ...
285
votes
29answers
43k views

My sister absolutely refuses to learn math [closed]

My 13-year-old sister has a problem which, given the way math is currently taught, I doubt is anything but all too common. She has a low grade in her math course and only ever attempts to memorize ...
7
votes
1answer
151 views

In what way is combinatorial game theory connected to the rest of mathematics?

Since my University library lists Conway's "Winning ways for your mathematical plays in the section "recreational mathematics" alongside books on origami and puzzles, I wondered to what extent game ...
5
votes
4answers
1k views

Meditation and Mathematicians [closed]

It is said that Yitang Zhang obtained his key insights by relaxing and putting the problem away. With this said, is meditation a task that mathematicians often do when they are stuck in a rut? ...
27
votes
8answers
2k views

“It looks straightforward, but actually it isn't”

In a previous topic, I asked about proof of statements which are simple but incorrect. Here, I ask about statements which seems, at a first glance, straightforward, but if we try to write a proof, ...
4
votes
1answer
93 views

Who introduced the term Homeomorphism?

Who introduced the term Homeomorphism? I was wondering about asking this question on english.stackexchange but I think this term is strongly (and maybe solely) related to mathematics.
2
votes
1answer
84 views

Does adding “monotone” change the meaning?

I wonder why math texts states "function is monotone increasing/decreasing" instead of "function is increasing/decreasing" without word "monotone". Nothing changes, right? Then, why?
8
votes
1answer
326 views

Question for mathematicians who started before the computer era: what constants did you have memorized, in what form, and why?

A former department chair at BYU, Wayne Barrett, would always amaze grad students by his vast knowledge of mathematical constants, like the radical form of $\cos(2\pi/5)$. I've never memorized ...
12
votes
3answers
301 views

New mathematical results in fiction work

On the surreal numbers page on Wikipedia it says: They were introduced in Donald Knuth's 1974 book Surreal Numbers: How Two Ex-Students Turned on to Pure Mathematics and Found Total Happiness. ...
5
votes
1answer
136 views

Ricci flow reference with pictures

I'm going to talk about the singularities of the Ricci flow for a group of physics students on Monday! To create a PowerPoint, I need a text or paper that contains photos and figures to raise the ...
2
votes
1answer
237 views

Why do we need continuous random variables since they can be approximated by discrete ones?

I do not understand the motivation of developing the theory of continuous random variables. Given simple discrete random variables, the continuous ones can be well approximated.
5
votes
2answers
257 views

Astonishing and innocent results with the axiom of choice

The product of nonempty sets is nonempty. I am fascinated that such a simple and seemingly intuitive statement can lead to rather astonishing results such as the Banach-Tarski paradox or the solution ...
6
votes
4answers
5k views

Two Different Approaches to Self-learn Calculus

Here's my situation: I'm a computer science student who has taken Calculus I twice. Not less than a week ago, I finished a second semester of the class and felt entirely defeated finishing the final. ...
4
votes
2answers
118 views

Suggestions for using a new text about a topic on which someone already possess a first course or advanced idea

The question is seeking the suggestions for using a new text about a topic on which someone already possess a first course or advanced idea. Of course then reading every lines of the text is a shear ...
6
votes
0answers
263 views

Comparing the U.S. undergraduate math education to the French “classes préparatoires”

Could anyone comment on how the math track of the "classes préparatoires" compares to the U.S. undergraduate major? I took a look at some of the French entrance exams and was rather intimidated. How ...
1
vote
0answers
29 views

looking for “invertibility and singularity”

Dear *friends* Many monts ago,i searched a lot the book of Robin Harte "invertibility and singularity". this book contains a lot of demonstrations that i need in my master. it focus on banach ...
4
votes
3answers
127 views

What mathematical objects permit “taking of limits”?

Background I have been reading a lot of abstract algebra recently (at the level of Artin/Dummit & Foote/Herstein Topics in Algebra for those of you familiar with these books). I have noticed ...
51
votes
19answers
5k views

Theorems' names that don't credit the right people

The point of this question is to compile a list of theorems that don't give credit to right people in the sense that the name(s) of the mathematician(s) who first proved the theorem doesn't (do not) ...
61
votes
26answers
5k views

Is there a great mathematical example for a 12-year-old?

I've just been working with my 12-year-old daughter on Cantor's diagonal argument, and countable and uncountable sets. Why? Because the maths department at her school is outrageously good, and set ...