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4
votes
3answers
349 views

participation in 1st year introductory pure maths classes

I have just started teaching a very elementary class for 1st year students on introductory pure mathematics. ( classes at my institution are groups up to 20 students and supplement the lectures. The ...
8
votes
2answers
263 views

How are more difficult proofs discovered?

Are there any resources that show how are the various proofs of important theorems in mathematics are invented? I don't understand how can anyone come up with this method for proof for example. I want ...
11
votes
1answer
191 views

Weil conjectures - motivation?

Can anyone explain (heuristically, intuitively is fine) what the importance of the Weil conjectures is? I realize they have motivated much of recent algebraic geometry. I don't really understand why ...
6
votes
0answers
320 views

formulating theories in math

One of my profs mentioned that sometimes people formulate theories about some type of object, but then later realize that those objects do not exist. Can someone given me an example of such a theory? ...
3
votes
2answers
445 views

Crackpots who turned out to be right. [closed]

Are there any examples of mathematical crackpots who turned out to be right? By crackpot, I mean someone who is not a mathematician whose mathematical theories were not taken seriously, but turned out ...
8
votes
2answers
3k views

Rudin against Pugh for Textbook for First Course in Real Analysis

So as I have said before in a previous question, I am taking a first course in Mathematical Analysis, and I'm quite excited. I just found out though that unlike the other professors at my university, ...
8
votes
5answers
5k views

Good software for linear/integer programming

I never did any linear/integer programming so I am wondering the following two things What are some efficient free linear programming solvers? What are some efficient commercial linear programming ...
1
vote
2answers
151 views

The importance of parallel arrows in a commutative square

I noticed that whenever there is a commutative square, the relation it imposes on parallel morphisms is usually very important (e.g. natural transformations, pullbacks). In contrast, there's usually ...
0
votes
1answer
131 views

Best classes to take [closed]

I want a class that will help me improve my intuition on geometric spaces. All the math classes I have taken this far has been computational heavy and didn't help me understand the concepts other than ...
11
votes
6answers
572 views

Strategies to prevent my math abilities from fading?

This is not a math question per se, but I think that it is relevant to a number of people. I am currently in the process of applying to graduate school, but not feeling super confident that I will get ...
5
votes
2answers
716 views

Follow-up to Baby Rudin

I would like to continue my study of analysis, albeit temporarily in self-study, and I was wondering what would be the best "sequel" to baby Rudin. Thank you very much for your advice.
8
votes
1answer
622 views

Differential Forms in Spivak vs Rudin

Can anyone give me the gist of the difference of the treatment of Stokes' Theorem in Spivak versus baby Rudin (chapter 4 in spivak, chapter 10 in rudin)? I need to do some problems from Rudin but ...
3
votes
2answers
163 views

Stochastic Processes…what is it?

My university is offering stochastic processes next semester, here is the course description: Review of distribution theory. Introduction to stochastic processes, Markov chains and Markov processes, ...
22
votes
1answer
782 views

Given a group $ G $, how many topological/Lie group structures does $ G $ have?

Given any abstract group $ G $, how much is known about which types of topological/Lie group structures it might have? Any abstract group $ G $ will have the structure of a discrete topological group ...
1
vote
1answer
88 views

What is meant by “orbit” in this question?

I was reading "Prove that Anosov Automorphisms are chaotic," and the answer and a few of the comments talked about orbits. I'm curious what is meant by "orbits" in the given context. Is it analogous ...
2
votes
1answer
69 views

Using the notation $m^{O(1)}$

$m^{O(1)}$ denotes the set of functions $\mathbb{N} \to \mathbb{N}$ which are polynomially bounded. (Is that what is usually means?) Now it used as follows: $$ f(m) \leq m^{O(1)}$$ To express that ...
0
votes
1answer
107 views

Why do we need tactics, reflection and other techniques when we have Curry-Howard for theorem proving?

First of all, I apologize if this question is slightly misplaced, but this seemed the best place to ask it given the mathematical/theoretical nature of the discussion. Given that the Curry-Howard ...
2
votes
0answers
67 views

Resolutions over finite dimensional algebra

Let $A$ be a finite dimensional algebra over a field $k$ and global dimension of $A$ is finite. I want to study $A$ as a bimodule i.e. as $A^e=A \otimes A^{op}$-module. It is easy to see that ...
9
votes
3answers
523 views

Removing noise when the signal is not smooth

Suppose we have (an interval of) a time series of measurements: We assume it can be explained as a "simple" underlying signal overlaid by noise. I'm interested in finding a good algorithm to ...
2
votes
4answers
335 views

Is there any research in mathematical biology that isn't heavy in differential equations?

I'm near the end of my pure math undergrad trying to decide what sort of math I'm interested in for graduate school. I've always thought the idea of mathematical biology was cool, but it seems like a ...
2
votes
1answer
320 views

Getting Practice on Finding Charts for a Manifold

I just want to ask for a suggestion on the study of differential geometry. When I study it I understand the theorems, their proofs, I understand perfeclty the concepts and so forth, but I'm having ...
4
votes
5answers
201 views

Are CASs useful in mathematics?

I understand that computer-algebra systems are useful for physists, engineers, or other users of mathematics. But are they useful in mathematics itself? Specifically, Are they usually taught in ...
3
votes
2answers
1k views

Why is Goldbach's conjecture not included in the millenium prize problems

As we all know, the Goldbach's Conjecture is one one of the oldest and best-known unsolved problems in mathematics. I was going through some of the attempts made to solve it and got fascinated as to ...
2
votes
1answer
104 views

Differential Equations background

What are the prereqs for differential equations? Do you need to know integral calculus too, and if so, to what extent? I want to learn about DE's as quick as possible but I'm not sure if I'm ready ...
4
votes
4answers
147 views

Transition from introduction to analysis to more advanced analysis

I am currently studying intro to analysis and learning somethings about basic topology in metric space and almost finished the course . I am thinking of taking some more advanced analysis. Would it be ...
3
votes
5answers
287 views

Why do you need to specify that a coin is fair?

This sounds like the kind of etherial question that generally gets dropped from stack exchange sites, but I don't know of a better venue to ask so I'm hoping this question will help other folks with a ...
1
vote
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 ...
4
votes
2answers
988 views

What are the prerequisites for Stochastic Processes

I'm a first-semester mathematics student, however I already feel the need of a certain goal, or rather an area I'd like to specialize in. For a quite a while, that's been the study of stochastic ...
5
votes
3answers
1k views

Which methods are used by actuaries in practice?

Recently I read a comment from an actuary that a lot of the math they studied as part of the program they never actually used. I'm not interested in becoming an actuary, but I'm interested in ...
3
votes
1answer
768 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 ...
3
votes
3answers
498 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 ...
1
vote
2answers
200 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
295 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
votes
4answers
712 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?
2
votes
3answers
105 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
votes
2answers
98 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 ...
4
votes
5answers
685 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 ...
3
votes
3answers
485 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
104 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 ...
10
votes
2answers
399 views

What are some motivating examples of exotic metrizable spaces

Among topological spaces, the metric spaces are usually considered to be the tame animals. Describing the topological notion of closeness by a distance is so intuitive (as opposed to the abstract ...
10
votes
2answers
549 views

Fast paced book in point-set topology to move on to algebraic topology

I am sorry, if this is a repetition of previous questions. But my case is sightly different. I am a physics undergrad who wants to shift to pure maths, and I want to study topology. The supreme ...
5
votes
5answers
742 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 + ...
87
votes
4answers
9k views

How do I convince someone that $1+1=2$ may not necessarily be true?

Me and my friend were arguing over this "fact" that we all know and hold dear. However, I do know that $1+1=2$ is an axiom. That is why I beg to differ. Neither of us have the required mathematical ...
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 ...
6
votes
3answers
514 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 ...
14
votes
7answers
2k views

Films about math: a question about math education and motivation for learning math [closed]

I'm interested in movies about or related with mathematics or physics, I mean not documentaries which I also consider movies, but artistic or mainstream films about math. Now I have the following in ...
5
votes
2answers
291 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 ...
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 ...
28
votes
8answers
4k views

Math every mathematician should know [closed]

This question is meant as a companion to previously asked questions like Proofs every mathematician should know. More and more I'm beginning to see that there is just too much math to learn. ...
3
votes
1answer
369 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. ...