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35
votes
5answers
6k views

How hard should a mathematician work?

Of course I would never compare myself to, and don't expect to be, one of the great mathematicians. However, I am curious as to how my work habits, dedication and passion differs from theirs. How ...
0
votes
0answers
29 views

What are the patterns in the number of divisors $d(n)$ of the highly composite numbers?

I am trying to understand the patterns in the number of divisors $d(n)$ of the highly composite numbers. The numbers marked with an asterisk are the superior highly composite numbers. The first ...
0
votes
0answers
32 views

Text on Witt vectors that are accessible to undergraduate students

I am looking for a thorough text on Witt vectors that is accessible to an undergraduate student that have completed the following courses: Calc 1, 2, Linear Algebra and Abstract Algebra. (In Norway, ...
0
votes
0answers
119 views

Self-Contained Books / Series / Lectures for Comprehensive Introduction to College-Level Math for Someone with VERY Poor Math Foundation?

I've long been interested in various math related subjects (technology, philosophy, sciences, computer science, languages, etc.) without really invested time to actually any learn any of them. I ...
4
votes
2answers
138 views

Who invented or used very first the double lined symbols $\mathbb{R},\mathbb{Q},\mathbb{N}$ etc

Who invented or used very first the double lined symbols $\mathbb{R},\mathbb{Q},\mathbb{N}$ etc. to represent the real number system, rational number system, natural number system respectively?
1
vote
0answers
51 views

best introductory intuitive books for learning ODE

I want to know best introductory intuitive books for learning ODE (mainly interested in Picard' theorem, Gronowall's inequality and most importantly stability). I started with Philip Hartman. Not ...
6
votes
2answers
176 views

The best balance in studying Mathematics?

I'm a student studying Mathematics at a university level. I've completed Single Variable Calculus, Differential Equations, Multivariable Caculus, Real/Complex Analysis, and Linear Algebra and I've ...
5
votes
0answers
91 views

Helping a reluctant 12 year old. [closed]

My 12 year old daughter needs to strengthen her math skills. My strategy up until a year or so ago has been pretty relaxed. I subscribe to the idea that the best motivation for learning is the ...
4
votes
0answers
81 views

Problem solving strategy?

This question has always bothered me, and I've never had a maths coach to guide me along the way and show me what to do next. Nevertheless, I did make top 50 nationally in my national mathematics ...
6
votes
1answer
119 views

Coming up with short “magical” proofs

I was reading the solution to this problem: Prove that $f(n) = 2n$ is the only non-constant solution to $2f (m^2 + n^2 ) = (f (m))^2 + (f (n))^2 .$ The solution used these identities, pulled out of ...
12
votes
2answers
247 views

Is it normal that a pure math student doesn't know vector analysis?

Today I was watching a series of online video lectures about electromagnetism. At some point of the lecture, the professor used this vector calculus identity: $$ ...
1
vote
2answers
65 views

What are the various branches of Vectors?

I just wanted to begin learning 'Vectors'. But I am completely confused where I would have to start! There is vector Algebra, Vector geometry, Vector Analysis and what not. So, I want to know what ...
1
vote
0answers
61 views

Zuckerman's “Sets and Transfinite Numbers”

I am beginning a study in set theory and I found an old book in my school's library by Martin Zuckeman called Sets and Transfinite Numbers which was published in the 1970's. Has anyone used this text ...
0
votes
5answers
97 views

Some examples of applications of Game Theory

I'm approaching my junior year of HS now, and I'm looking for a good science fair project to do. I love mathematics, so I decided to a category of mathematics that can help base logical conclusions to ...
4
votes
1answer
78 views

Whatever Happened to Nearness Spaces?

I came across this paper about Nearness Spaces. It seemed to be at the time (1970-80s) a promising approach to general topology via category theory. I have found no posts at all on stackexchange ...
13
votes
4answers
221 views

Which mathematical ideas most influenced the way you think?

This is not a question about how you use a formula or mathematical method to solve quantitative problems - that is applied mathematics. Rather, I'd like to hear how deeper ideas gained through the ...
1
vote
0answers
36 views

Which Universities in US should I apply to study for a Masters in Statistics?

I've decided that I want to join a masters programme that prepares graduates for industry work as opposed for a phd. At the same time, I also want to really understand the theory behind the ...
1
vote
0answers
30 views

To derive commutativeness of any group from the normality of all its subgroups & some other conditions

If a group is abelian then it is known that every subgroup of the group is normal ; is the converse true i.e. if every subgroup of a group is normal , then is it true that the grroup is abelian ? If ...
0
votes
3answers
61 views

Conceptually: A set whose elements can only be probabilistically characterized?

Sorry for the informality here, but was musing over the basic concepts around describing a set in real world usage: A finite set of explicitly named elements, this apple and that apple, nothing more ...
7
votes
1answer
132 views

Proof correctness problem

I was watching this talk by Vladimir Voevodsky which was given at the Institute of Advanced Study in 2006. In his talk the first slide he shows has the following written on it: ...
-1
votes
1answer
53 views

submit paper in two Journals due to the slow referring process [closed]

The paper is submitted,but the referring process is very slow, I can't wait for more months. What happen if I submit the paper to another Journal( if it will be accpeted quickly then I will withdraw ...
4
votes
2answers
64 views

Prerequisites to “Applications of Lie Groups to Differential Equations”

I'm currently a 4th year student at a university. I've become close with a professor and we talked about the topic of lie groups in differential equations. He then offered to do a reading course with ...
1
vote
0answers
54 views

Is the Annals of Global Analysis and Geometry a good journal?

I hope I'm not out of place asking such a question here. Anyway, I'll soon have my first real paper published in the Springer journal titled "Annals of Global Analysis and Geometry." Since I don't ...
2
votes
4answers
165 views

What if we removed all the irrational numbers from the real number line? [closed]

(1) Imagine drawing the real number line and tippexing out all the irrational numbers. What would the resulting shape look like- would there even be a line? (2) And what about if we ...
1
vote
0answers
103 views

Missing connection in real analysis?

I have long thought of real analysis as the consequences of mapping numbers to real numbers, thereby creating infinite sequences and series. From there, I can get to fairly elementary applications ...
1
vote
0answers
41 views

Developing Endurance

I realize many math problems solved by mathematicians require a tremendous perseverance over a period of years. My question is not about endurance over a long period of time, but over several hours. ...
2
votes
0answers
94 views

Science Fair project ideas? [closed]

It the summer for me right now, and I'm approaching my junior year. I'm attending a very rigorous high school in Florida in the Math, Science and Engineering program. The program requires that I ...
4
votes
2answers
45 views

Biconditional statements with an “easy” direction.

I was reading through Lax's Functional Analysis, when I came across the following statement: Theorem: X is a normed linear space over $\mathbb{R}$, $M$ a bounded subset of $X$. A point $z$ of $X$ ...
4
votes
1answer
194 views

Russian Texts on Geometry

I recently saw a question today pertaining to Russian mathematics and I have a similar question but of a slightly different flavor. I've always heard that the Soviet Union had a history of producing ...
3
votes
3answers
72 views

Best resource to learn quadratic reciprocity?

I took a very basic intro to number theory course last semester. We learned about many of the standard topics (gcd, primes, cryptography, congrences, pythagorean triples, etc), but we never learned ...
1
vote
1answer
52 views

Logic of steps in proofs

Whenever I read a textbook or get help with a proof, I'm always suggested a very obscure and tricky step which usually helps me immediately solve the rest of the proof because everything else seems to ...
7
votes
2answers
329 views

How would you change math notation? [closed]

Mathematical notation has been evolving for hundreds of years (really thousands, I guess, but most of the noteworthy examples seem to be only a few hundred years old). Sometimes we are stuck with old ...
2
votes
1answer
74 views

The number of partitions of $n$ and the $n$th Fibonacci number.

I'm very sorry if this is a duplicate in any way. There's a lot of material out there on connections between these sequences so it's a possibility . . . Let $P_n$ be the number of partitions of $n$ ...
37
votes
17answers
4k views

What exactly is a number?

We've just been learning about complex numbers in class, and I don't really see why they're called numbers. Originally, a number used to be a means of counting (natural numbers). Then we extend ...
0
votes
0answers
31 views

Countable Baye's theorem?

Disclaimer: If this is a foolish question, I'm sorry.. this is the first time I've looked at probability theory in very many years, and have begun to re-read everything from scratch... Question: If ...
5
votes
3answers
347 views

Are vectors and covectors the same thing?

In Euclidean space, we usually don't distinguish between vectors and covectors (or dual vectors or 1-forms or whatever you want to call them) -- because the spaces overlap. However, a physicist ...
1
vote
0answers
229 views

What is the Kadison-Singer Conjecture [closed]

I recently heard on the news that Adam Marcus, Daniel A Spielman, Nikhil Srivastava have won the George Pólya Prize for proving the 1959 Kadison-Singer Conjecture. So I'm curious...what is this ...
14
votes
5answers
695 views

Understanding mathematical texts

Please could you comment on following: I always wanted to know what mathematicians mean by "understanding a piece of mathematics". For example, I have just finished the second chapter from Rudin's ...
3
votes
0answers
110 views

Abstract algebraic geometry vs complex algebraic geometry

Sorry in advance if my question is not precise enough. I'm currently trying to study algebraic geometry on my own. I've started by trying to read Harsthorne and Liu's book. And i found it very ...
2
votes
1answer
31 views

Frequency computation

I generate pulses using microcontroller with following method: Set $A=0$ With frequency $F$ execute the following code: 2.1. Add $S$ to $A$ 2.2. If $A\ge N$ then produce a pulse and ...
1
vote
1answer
58 views

Other Interesting solutions to $a=bq+r$? [closed]

The division algorithm says $a=bq+r$, with $r$ between $0$ and $b$. Are there interesting restrictions on $r$ using number-theoretic properties that make the equation $a=bq+r$ hold, or hold with ...
5
votes
5answers
393 views

About Trigonometry

Is there anything cool about trigonometry? I was just curious. I'm learning trig right now and I often find myself asking myself, "What's the point?" I feel if I knew what I was working on and why, ...
2
votes
3answers
116 views

a second course in abstract algebra

I recently read an abstract algebra textbook, "A first course in abstract algebra" by John Fraleigh. I am interested in continuing to do some more self studying. What is a good book for a second ...
4
votes
1answer
83 views

What is the difference between field theory and Galois theory

I am about to finish the book Galois theory by Harold Edwards. I am planning to study Galois theory at a more advanced level or field theory. I am unable to decide because I don't know the difference ...
1
vote
1answer
88 views

Where to post discovered formulae? [closed]

I have discovered an alternate formula for the Fibonacci sequence and I would like to find a way in which I can present this. Please could you give me suggestions on how I can go about posting this ...
7
votes
2answers
551 views

Derive or differentiate?

When the action is: Taking the derivative what verb should be used? to differentiate to derive I feel that deriving is not the correct word here. In my mind it's more a synonym of deducing. Am I ...
9
votes
0answers
189 views

Are NSA Mathematicians second-rate? [closed]

I recently read that the National Security Agency (NSA) is the single largest employer of mathematicians in the United States. Although spies and high-level secret government agents are glamorized in ...
0
votes
0answers
34 views

Koblitz - Are chapters III & IV independent of I & II

I am interested in learning about Modular forms and have heard many great things about Neal Koblitz's Introduction to Elliptic Curves and Modular Forms. However, Koblitz doesn't discuss modular forms ...
7
votes
7answers
232 views

Is $\mathbb{C}$ equal to $\mathbb{R}^2$?

Complex numbers are usually formally defined as pairs of real numbers. Although there are operations on $\mathbb{C}$, such as complex multiplication, which are not found in operations usually applied ...
8
votes
1answer
65 views

Parametrizing Walks on Sphere and Torus

This question is very underdeveloped, but I was wondering if there was a map from the sphere to the torus which preserves length of closed curves? I was just thinking about taking a walk on a ...