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0answers
63 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 courses....
5
votes
2answers
2k 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 ...
6
votes
3answers
2k 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
890 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
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3answers
740 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
247 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
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2answers
382 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
821 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
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3answers
115 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
123 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
991 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
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3answers
544 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
108 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 ...
12
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2answers
530 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 ...
12
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2answers
718 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
854 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 + ...
108
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4answers
12k 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
98 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
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3answers
626 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 ...
16
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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
311 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
146 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 ...
26
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
407 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. ...
2
votes
1answer
90 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 ...
9
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1answer
2k 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 ...
55
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9answers
4k views

Is memory unimportant in doing mathematics?

The title says it all. I often heard people say something like memory is unimportant in doing mathematics. However, when I tried to solve mathematical problems, I often used known theorems whose ...
3
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3answers
1k 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 ...
15
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3answers
1k views

Careers in Math

I am a highschool freshman, and I really like to have goals for my life, one of the big ones is my career of choice. Previously, I have always wanted to be a programmer, and I have written a lot of ...
0
votes
2answers
211 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 ...
0
votes
4answers
683 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
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1answer
261 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. ...
0
votes
1answer
829 views

Real Analysis 1 vs Real Analysis 2?

Note: I am not sure if this is the correct place to ask these types of questions, so please let me know if I should remove my question. I'm taking Real Analysis 1 this semester, and was thinking of ...
11
votes
1answer
1k views

“The Music of Pi” [closed]

I'm curious about this piece in the oct/nov MAA Monthly Supplement about The Music of Pi, and have wanted to share it here. I'm curious for many reasons, including the composer's choice to represent ...
195
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28answers
27k views

Too old to start math [closed]

I'm sorry if this question goes against the meta for posting questions - I attached all the "beware, this is a soft-question" tags I could. This is a question I've been asking myself now for some ...
4
votes
1answer
131 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
423 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
337 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 ...
12
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11answers
3k views

Good examples for mathemathical problems/statements that are easely solvable/provable in one theory and hard to solve/prove in another

Let $P$ be a mathematical statement or a mathematical problem. I am looking for a couple of nice examples for $P$ that satisfy the following criteria: Given two (or more) mathematical points of view ...
9
votes
4answers
294 views

Hyperreal field extension

In non-standard analysis, assuming the continuum hypothesis, the field of hyperreals $\mathbb{R}^*$ is a field extension of $\mathbb{R}$. What can you say about this field extension? Is it ...
46
votes
13answers
7k views

List of interesting integrals for early calculus students

I am teaching Calc 1 right now and I want to give my students more interesting examples of integrals. By interesting, I mean ones that are challenging, not as straightforward (though not extremely ...
4
votes
1answer
461 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 ...
10
votes
1answer
2k views

How can I explain the seven Millennium 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 ...
26
votes
4answers
2k views

How much time is too much (to put into a single problem)?

As a self-studier, I have no due dates and no time pressure. This is partly a good thing since I do have a life outside of my pursuit of mathematics. However, the lack of pressure is also a bad ...
3
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5answers
1k 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. ...
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6answers
4k views

How to interpret material conditional and explain it to freshmen?

After studying mathematics for some time, I am still confused. The material conditional “$\rightarrow$” is a logical connective in classical logic. In mathematical texts one often encounters the ...
1
vote
1answer
4k views

What is the best way to compare probabilities?

If you have two different events with different (known) probabilities, what is the best way to compare the probabilities? For example, the relationship between $0.5$ and $0.7$ is not the same as ...
10
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3answers
593 views

Why do people care about principal bundles?

I've started to learn a little about principal bundles (in the smooth category) and while I see how notions like connections and curvature are abstracted from the setting of vector bundles and brought ...
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 $$ S=\sum_{k=0}^{\infty}p^{k}=\frac{1}{1-p} $$ ...