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9
votes
0answers
128 views

Are NSA Mathematicians second-rate? [on hold]

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
32 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 ...
0
votes
0answers
34 views

Which Trigonometry Book is Recommended? [duplicate]

I'm taking trigonometry for this upcoming fall, and I want to get a good head start like I did with statistics a while back. I was recommended Cynthia Young' s Trigonometry book and Loney's book. ...
7
votes
7answers
191 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 ...
7
votes
1answer
55 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 ...
0
votes
0answers
50 views

What is way of getting good at math without math? [on hold]

What is way of getting good at math without math? I know this question might seem ridiculous, but It have been said that listening to Mozart can improve your math and science skills. I do not ...
10
votes
1answer
170 views

Soviet Russian Mathematical Books

The introductory part of the book briefly describes the popularity of mathematics in Soviet Russia, touches on Russian mathematical circles and generally how Russian society took to mathematics in a ...
1
vote
3answers
337 views

I'm forgetting maths.. [closed]

I'm 14, and I'm the Math topper in my grade. But suddenly, I've started loosing confidence, and I've started forgetting maths.. I am looking for a good solution. (If it helps, I'm forgetting a bit of ...
3
votes
0answers
96 views

Category of metric spaces versus category of non-empty spaces

Denote by $\mathbf{Met}$ the category of metric spaces with metric maps as morphisms. A function $(X,d)\xrightarrow{\ f\ }(X',d')$ is called metric if for every pair of points $x,y\in X$ we have ...
2
votes
1answer
86 views

The J programming language: is it useful for mathematics?

I just stumbled upon the J programming language, which has the description: J is particularly strong in the mathematical, statistical, and logical analysis of data. It is a powerful tool in ...
0
votes
3answers
141 views

How do we define equality in real numbers?

How do we define equality in real numbers? I know in logic we define equality by Leibniz's law. $$ \forall x \forall y[x=y \rightarrow \forall P(Px \leftrightarrow Py)] $$ But how do we define the ...
-1
votes
1answer
51 views

How does the research in theoretical physics differ from mathematics? [closed]

Cross post: http://physics.stackexchange.com/questions/123006/how-does-the-research-in-theoretical-physics-differ-from-mathematics I would like to know what is the difference between research in ...
16
votes
12answers
2k views

Gap year to study math

This is a plan in its earliest and thus least concise stage, so either bear with me or don't read the following babble (I bolded some of the important stuff): I am a high school graduate who is about ...
3
votes
1answer
24 views

Intuition behind prism operators to prove homotopy invariance of homology

I'm trying to understand the proof of homotopy invariance of induced maps on homology. However, I do not really understand the intuition behind this proof and especially what the prism operators (as ...
1
vote
3answers
53 views

Creating fractals through computers

What are some beginner softwares for creating fractals on computers?
2
votes
1answer
31 views

Introduction to nests

I've just read Chapter 7 of Alice in Numberland by Baylis and Haggarty, it's called "Nests - in which the rationals give birth to the reals and the scene is set for arithmetic in $\mathbb{R}$". ...
1
vote
0answers
46 views

Soft question (Etymology - Flatness)

Why where flat modules named "flat"? Is it because they are necessarily torsion free so in a "not convoluted" or circular like $\mathbb{Z}/n\mathbb{Z}$ is as a $\mathbb{Z}$-module?
1
vote
0answers
43 views

Should I use the minus sign when writing papers in characteristic two

Is there any consensus regarding whether one should write both "+" and "-" or only "+" when performing computations in characteristic two fields? To give some context, I am writing my thesis, which ...
7
votes
3answers
85 views

How to structure long proofs

How do you structure proofs that are longer than say half a page? I have already encountered a variety of styles (in my short math life), some of which I list below and I just hoped to hear some wise ...
5
votes
1answer
74 views

What makes “the topos $\mathbf{M}_2$” such a good counterexample?

I'd like to ask this question sooner rather than later; it might be a bit half-baked. So I'm sorry. It's just that there's a chance I'll be side-tracked from Topos Theory for a couple of months (with ...
4
votes
1answer
83 views

Lecture notes ready for $\LaTeX$

Are there on the internet lecture notes in calculus in .tex or .txt format, that is, ready to be edited/modified/re-used and compiled using $\LaTeX$? EDIT: now I am specifically asking for calculus, ...
0
votes
0answers
49 views

Complex analysis a good thing to take with algebra?

This is sort of a follow up to a question I asked awhile ago. I'm working out which courses to take my first semester of my second year of university. I've had linear algebra, calculus, and analysis ...
8
votes
4answers
795 views

How is addition different than multiplication?

Is there a fundamental difference in the things we call multiplication and those we call addition? In a field, both binary operations obey exactly the same rules (commutativity, associativity, ...
0
votes
0answers
39 views

Courses for Commutative Algebra

If I want to learn more about commutative algebra, which of the two courses will help me the most: coxeter groups or schubert calculus? Also, what kind of background is necessary these courses?
3
votes
0answers
24 views

Sufficient conditions for closed infinite pasting lemma

It's well known that the pasting lemma for infinitely many closed sets is false. It's reasonably easy to cook up examples such that for $X = \bigcup X_i$ with $X_i$ closed in $X$ such that $\left. ...
2
votes
5answers
659 views

What should I use Latex or Microsoft Word Professional? [closed]

What should I use Latex or Microsoft Word Professional for writing mathematics papers and documents and notes and courses...?
0
votes
1answer
76 views

The fourth pillar of mathematics? (analysis, algebra, geometry and …) [closed]

Many universities claim that there are three general areas in mathematics: analysis, which deals with continuous aspects of mathematics; algebra, which deals with discrete aspects; and geometry. If ...
-1
votes
0answers
33 views

What to ask to the director of the orientation course [closed]

I'm going to take part in an orientation course: that is, I will talk to some influential members of the faculty of mathematics and physics of a university. I would like to ask you (who are students ...
-3
votes
1answer
42 views

second derivative of discrete function

given function $y[n]$ what is the best way to define the second derivative? some background to the question: in linear systems we often sample a continuos signal to a discrete one with sample rate of ...
7
votes
3answers
711 views

Masters' thesis in group theory [closed]

I would like some ideas on topics in group theory which would be suitable for a masters' thesis. What sort of problems would be suitable for this level? Because it is at masters' level, no original ...
0
votes
0answers
18 views

Resources for mathematical biology

I´m goin to take an undergraduate course in Mathematical Biology. I´m goin to see themes like: Population dinamics The appear of patterns Philotaxia Turing´s bifurcation Genetics Chaos Neuronal ...
5
votes
0answers
69 views

Reference Request: Prereqs for Lecture Notes on “Abstract Linear Algebra”

I just found this set of lecture notes on linear algebra which seems to go over several things I've been wondering about as I study linear algebra. Unfortunately there are very few exercises in the ...
0
votes
2answers
107 views

Open Problems for High School Students

I am a homeschooled rising senior in high school, and I would like to research an open problem in mathematics. I have taken a number of undergraduate-level mathematics courses, including ...
0
votes
1answer
29 views

Unbounded Operators: Notation?

For continuous a.k.a bounded operators we have $\mathcal{B}(X,Y)$ stressing on boundedness and $\mathcal{L}(X,Y)$ stressing on linearity entailing $\mathcal{C}(X,Y)$. Is there a notation for ...
1
vote
3answers
66 views

Related Methods: Lagrange Multipliers

It really pains me to ask this question, but I was working on an optimization problem and wanted to show a friend how we could also use Lagrange Multipliers to solve it. I was considering the ...
1
vote
2answers
103 views

Linear Algebra without Matrices

How far could one get in linear algebra without matrices? It seems like the more I learn, the less I actually use them, but most of the basic theorems and invariants that learned first -- and still ...
3
votes
0answers
66 views

Is there any visual animation to show the basic concept of algebraic geometry? [closed]

Is there any visual animation to show the basic concept of algebraic geometry? There are rarely pictures in textbooks, so are there any animation to show basic but important concepts?
4
votes
1answer
57 views

Defining algebras over noncommutative rings

A definition of "algebra" (that is, an associative algebra, in the sense of ring theory) generally requires a commutative base ring. But there are cases where it's reasonable to consider algebras ...
2
votes
1answer
103 views

Changing streams in PhD

I've a masters degree from a reputed Indian university in pure mathematics, with a specialization in Algebraic Number Theory. However, I'd like to apply for a PhD in computational math/theoretical ...
3
votes
2answers
142 views

Bridging the gap of understanding function terminology in math for a programmer.

I'm a computer programmer by profession with no formal CS education. When I read in mathematics the terminology used around a function, I get confused. For example, I was reading up on some calc and ...
9
votes
3answers
200 views

Areas of contemporary Mathematical Physics

I have often heard that some developments in Physics such as Gauge Theory, String Theory, Twistor Theory, Loop Quantum Gravity etc have had a significant impact on pure Mathematics especially geometry ...
4
votes
3answers
296 views

Interesting Mathematical Fallacies [duplicate]

I recently volunteered to help with a summer math program at a local high school for which I thought would be a breeze. As it turns out, it isn't a program for those catching up (summer school) like I ...
25
votes
15answers
3k views

Ways to study mathematics while commuting

I spend approximately 3 to 4 hours on public transport everyday. I try to maximize the usage of this time by checking email etc on my phone. Are there any tips to study mathematics while commuting? ...
7
votes
3answers
139 views

Algebraically, What Does $\Bbb R$ get us?

In terms of the basic algebraic operations -- addition, negation, multiplication, division, and exponentiation -- is there any gain moving from $\Bbb Q$ to $\Bbb R$? Say we start with $\Bbb N$: ...
0
votes
0answers
40 views

Why Does $e^{ix}=\cos(x)+i\sin(x)$? [duplicate]

Something I've always wondered, but never had a good answer too (I accept there may not be one). I fully understand how to derive this, so I'm not looking for an analytic proof. But rather I cannot ...
2
votes
1answer
92 views

Best Less-Famous Texts for Forcing

There are many books, papers and lecture notes which give an introduction to forcing (e.g. Jech or Kunen's books) but here I am looking for some possibly less-famous useful comprehensive texts for ...
4
votes
6answers
156 views

Interviews of famous modern mathematicians

I was wondering, are there any good collections of interviews of famous modern mathematicians? It can be text interviews, or audio or video recordings. I am not sure what exactly I mean by "modern". ...
1
vote
3answers
51 views

Considering Vectors Geometrically

I have a few questions which a little research (searching the internet through Google) has not satiated. It seems that vectors are very important, even when considering them as the arrows which ...
4
votes
1answer
123 views

Humor in Math Textbooks

So, I was looking though a problem section in Dummit and Foote, and found this amusing "definition." I actually tried googling it, but I can't find any reference to these associated primes being ...
24
votes
8answers
2k views

Complex analysis is more “real” than real analysis

In physics, in the past, complex numbers were used only to remember or simplify formulas and computations. But after the birth of quantum physics, they found that a thing as real as "matter" itself ...