For questions whose answers can't be objectively evaluated as correct or incorrect, but which are still are relevant to this site. Please be specific about what you are after.

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0answers
61 views

Pre-requisites for studying zeta functions

I want to start reading about zeta functions on my own, so i want to know what are the pre requisites that i need? P.S : I am an EE engineer and have done the basic college level mathematical ...
7
votes
4answers
4k views

Degree choice — Math or physics

I realize that it is of bad form to cross-post. However, on this matter I very much hope to hear arguments from all sides... I hope to become a physicist focusing mainly on the theoretical side in ...
3
votes
1answer
733 views

Relearn mathematics

I believe that this question is well known, but since I'm not a US resident and do wish to learn math according to the U.S. school syllabus I wish that somebody can help me. At my first eight years ...
4
votes
5answers
606 views

What is being researched on the frontiers of math and what are the expected applications for it?

I don't know if this is an acceptable question to make here, but I wanted to know what kinds of things are being researched that can lead to major breakthroughs in math. I'm not talking about usual ...
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2answers
199 views

Mathematical doodle games

Vi Hart's doodling videos and a 4 year old son interested in mazes has made me wonder: What are some interesting mathematical "doodling" diversions/games that satisfy the following criteria: 1) They ...
3
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3answers
430 views

Differential Calculus and Integral Calculus

Is differential calculus a prerequisite for integral calculus? Because almost always you see that differential is taught before integral. Does that have a specific reason? Would it be recommended to ...
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2answers
182 views

What does means the $\frown$ in sequence notation?

In the theorem 3.6 of Juhász's Cardinal Functions in General Topology appears the following symbol about sequence: $\frown$ The role context of it's appearance is the following: Theorem. Let X be an ...
2
votes
2answers
280 views

What about some engaging PDE topics for undergraduates?

Does anyone have any suitable PDE topics (research or otherwise) for an undergraduate math student? Consider the student has only completed an introductory class in PDE. The student also has ...
5
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4answers
665 views

What does “working mathematician” mean?

What does "working mathematician" mean? Is this term derogatory? What properties of a "working mathematician" are considered undesirable, and what attitude contrasts them?
21
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3answers
786 views

Swatting flies with a sledgehammer

Prompted by a recent exchange with Gerry Myerson, I was wondering if anyone has a favorite example of a relatively simple problem with a rather elementary (though perhaps complicated) answer for which ...
2
votes
3answers
103 views

Doubts about linearity of definite integration.

One of the first things about definite integration included in summaries is the linearity: $$\int_a^b (\alpha f + \beta g)(x) \, \textrm{d}x = \alpha \int_a^b f(x) \,\textrm{d}x + \beta \int_a^b g(x) ...
2
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2answers
97 views

Problems where the solution hinges on the correct definition

Recently, I realized that there are some famous problems in mathematics whose solution depended heavily on the right formulation of an intuitive concept. For example, there was no precise definition ...
3
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3answers
472 views

Soft question: Why freshmen feel linear algebra is abstract?

When I was a freshman, I have learnt linear algebra for two semester. I feel linear algebra is abstract and hard to truly understood. For example, my textbook introduce the concept "nonsigular" by ...
4
votes
1answer
97 views

What's the arity of the factorial and exponential operations?

I'm having a conflict with the concept of arity, I've read that the factorial is a unary operation and also that the exponentiation is a binary operation but I feel there's something strange, the ...
5
votes
5answers
704 views

Is mathematics the only language that is not subject of interpretation?

Do you know any other "language" that is used by people except mathematics and is not subject of interpretation? By subject of interpratation I mean e.g. that 1 000 000 people will undertand that 1 + ...
11
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3answers
386 views

Module Theory for the Working Student

Question: What level of familiarity and comfort with modules should someone looking to work through Hatcher's Algebraic Topology possess? Motivation: I am taking my first graduate course in ...
6
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3answers
462 views

Learning about the universe or special/general relativity

I have done a standard course in differential geometry/Riemannian geometry. Am I now able to understand the concepts people talk about when they say things like "spacetime is curved" and when I see ...
4
votes
1answer
95 views

Examples of concepts, definitions or areas of study that were later abandoned

I've been recently thinking about what I've learned in mathematics, and I realised that in contrast to physics (or the other sciences), I tend to take the concepts and definitions for granted in that ...
5
votes
2answers
287 views

Problem understanding math

sorry for my english but I am a foreigner. I'm writing to ask you for help with a problem I have with mathematics. I'm going to go to university physics but I have serious problems as regards ...
10
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5answers
750 views

Should I study algebra more?

My background is about third-year mathematics major, including linear algebra and abstract algebra. I'm now studying Atiyah's commutative algebra, but it lacks some concrete, easy examples and it's ...
13
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5answers
703 views

Finding a paper

Sometimes I have trouble finding particular papers. Does anyone have any general suggestions? I find myself in this situation frequently: An author references a paper. I find it on MathSciNet ...
5
votes
1answer
578 views

Why don't they teach Fundamental Theorem of Algebra in High School? [closed]

I am currently in AP Calculus BC and one more year to go, I have heard about Fundamental Theorem of Algebra several times, and with the resources that is out there today I tried to search and study ...
4
votes
1answer
101 views

Proof of existence of the number of solutions

I'm not sure how to tag this question, as I don't know what area of math covers these problems. For example, I know two or three ways of proving that $$ S=\sum_{k=0}^{\infty}p^{k}=\frac{1}{1-p} $$ ...
3
votes
1answer
354 views

Chapter V of Grothendieck's EGA

Grothedieck wrote, in the introduction of his EGA, Chapter V would be Procedes elementaires de construction de schemas(Elementary procedures for construction of schemes). I wonder what he meant by it. ...
5
votes
2answers
136 views

On the existence of number systems, and the extent to which we can extend them

The more I think about math, the less I realize I know. Learning about complex numbers has called me to re-evaluate how I think of negative numbers, or even natural numbers. I have to say the ...
1
vote
1answer
181 views

Average Amount Of Math or Math-oriented Courses Taken Each Semester [closed]

I was wondering, from all of you, what the average amount of math and\or physics courses you were/are able to tolerate in one semester.
3
votes
2answers
153 views

“Good” closure conditions

[Attention! This question requires some reading and it's answer probably is in form of a "soft-answer", i.e. it can't be translated into a hard mathematical proposition. (I hope I haven't scared away ...
27
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10answers
2k views

Contributions of Galois Theory to Mathematics

What are the major and minor contributions of Galois Theory to Mathematics? I mean direct contributions (like being aplied as it appears in Algebra) or simply by serving as a model to other theories. ...
9
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1answer
1k views

Choosing a Master Thesis Topic: Logic - Model Theory

I am a first-year graduate student in maths. Around these days, I feel I must decide on which exact part of mathematics I shall go through. Infact, I have narrowed down the suitable options but still ...
2
votes
1answer
85 views

Why do number rings have no endomorphisms

This question is about the analogy between number fields and function fields. It's a soft question and the title misrepresents the question. Consider the projective line over a field. This has many ...
2
votes
1answer
104 views

Finding a logical expression (under some constrains) s.t. it is equivalent to another one

In this question, it was made clear, when $\bullet$ some statement $A$ is stronger than another statement $B$, namely if $A\Rightarrow B$ holds; and when the statement $A$ is weaker than another ...
2
votes
3answers
910 views

Suggestions on Real, Fourier Analysis textbooks?

I'm new here, and I hope this is within the scope of the website. I'll try to ask few advisory type questions in the future... I'm a college junior, and I was wondering if you guys could offer any ...
0
votes
4answers
391 views

In mathematics is null == zero?

Kindly consider it soft question as I am a software engineer.and I know only software but I have a doubt in my mind that there would be something like null in mathmatics as well. If Mathematics ...
4
votes
1answer
210 views

Reading circle in mathematics?

How to learn about interesting topics in a small group of people?It seems very useful to broaden your mathematical background and get to know topics that are away from your field of specialization. ...
9
votes
1answer
334 views

Are integrations on forms “different” from Riemann integrations?

I was amazed by the power of integration on forms when I learned that the Stokes' theorem can be written in a beautiful way (don't assume that I know more than this fact itself): $$ ...
4
votes
1answer
121 views

Seek results in group theory obtained by applping algebraic topology tools

After studying the first section, especially the section 1.3 (covering spaces) in Hatcher's book, it is obvious that many classical topics in group theory, especially in infinite group theory, have ...
3
votes
0answers
330 views

Microsoft Surface for reading textbooks and writing math by hand?

As a PhD student I am increasingly wanting to get a tablet and the new Microsoft Surface tablets appeal to me greatly as I am a big fan of the UI. I wonder if anybody has got hold of it yet and what ...
1
vote
1answer
68 views

can somebody tell me the name of the next theorem?

I am looking for the name of the next simple fact(theorem): let $M$ be some matrix and let $k$ be some combinatorial rectangle in $M$. denote the matrix of $k$ by $M_k$. It holds that: $Rank(M)\ge ...
6
votes
1answer
278 views

Set theorist as a physicist or physicist as a set theorist?

I'm majoring physics, but really interested in mathematics. I liked physics since it was really beautiful to have an analysis on a nature with mathematical tool. However, the more i study, the more ...
2
votes
2answers
490 views

Study Strategy: broad/depth; abstract/intuitive

Research Interest: Chaos, Dynamical System, PDE. Study style: Shallowly Broad: Quickly absorb as many branch as possible [master more 'toolbox'] OR Narrowed Depth: Carefully focus on ...
3
votes
1answer
177 views

Order of elements in group

Given $G$ is a group, and $ab=ba$ for $a,b\in G$, we know $o(a)=12,o(b)=18$, in order to calculate $o(ab),o(ab^2),o(a^2b^3)$. Do we need to assume group is a cyclic group in order to use formula ...
4
votes
1answer
371 views

A High-School Freshman's Journey Into Calculus

The short version: What path should I take to learn Calculus in High-School? The long version: I am a high-school freshman, and I am enamored with mathematics, and I just see beauty in many things ...
7
votes
3answers
1k views

Significance of eigenvalue

When I represent a graph with a matrix and calculate its eigenvalues what does it signify? I mean, what will spectral analysis of a graph tell me?
3
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5answers
829 views

Common sense in mathematics

Are there any claims and counterclaims to mathematics being in some certain cases a result of common sense thinking? Or can some mathematical results be figured out using just pure common sense i.e. ...
7
votes
1answer
1k views

How can I explain the seven Millenium Prize Problems to a layman?

I'm writing an email to a friend, who asked me to explain what higher level mathematics is like. Since I'm still an undergraduate student, I referred him to this Wikipedia page, saying that I assume a ...
2
votes
2answers
57 views

Quick criterion to decide whether a limit of functions in $W^{1,p}(\Omega)$ is in that space

Let $\Omega\subset \mathbb R^N$ be an open set. Suppose we are given a sequence $u_n$ in $W^{1,p}(\Omega)$, $1<p\leq+\infty$, such that $u_n\to u$ in $L^p(\Omega)$ and such that $(\nabla u_n)$ is ...
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2answers
127 views

Why isn't cognitive psychology part of a math undergrad/grad program? [closed]

I think it is good for math students to have a cognitive psychology course. Foreign languages are often required. If a student knows how his mind works he would use it more efficiently. Insight, for ...
8
votes
3answers
660 views

Which of these courses to take if one intends to go to grad school in pure math (rank please)

could you rank these classes in terms of necessity to take if I intend to pursue a Ph.D in pure math? I don't know if I can fit everything, but I want to make sure I take the most important ones: ...
10
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2answers
2k views

*Recursive* vs. *inductive* definition

I once had an argument with a professor of mine, if the following definition was a recursive or inductive definition: Suppose you have sequence of real numbers. Define $a_0:=2$ and ...
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0answers
143 views

Can a batsman's score be predicted in the sport of cricket?

I was browsing The Signal and the Noise in bookstore and chanced upon a chapter about predictions in baseball and found out about Moneyball and sabermetrics. I understand the closest to predicting a ...