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4
votes
1answer
154 views

Consequences of Pontryagin Duality?

What are some interesting corollaries and consequences of the Pontryagin Duality theorem? My question can be taken as broadly as you'd like, even up to including any philosophy introduced specifically ...
10
votes
4answers
783 views

Short forms like “haven't”, “don't”, “let's” [closed]

Is it true that short forms like "haven't", "don't", "let's" should not be used in serious mathematical texts?
2
votes
0answers
59 views

Can a rate be proportional to a shape?

This question may be a little vague, but it has a point. I woke up this morning with an idea. Let's say I wanted to design a projectile that has a velocity proportional to its 'shape'. When the ...
13
votes
2answers
1k views

Studying mathematics efficiently

I am particularly angry at myself for the last few days. I noticed how inefficiently I work. Here is the general scenario: I decided to study abstract algebra and analysis some days back. I tried ...
7
votes
4answers
6k 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 ...
0
votes
1answer
71 views

What's the meaning of “condition for $a$, $b$, $c$ to be in geometrical progression”?

I'm reading Sawyer's Prelude to Mathematics, from page 34-35: [...]Prove that, if¹ $$\frac{ac-b^2}{a-2b+c}=\frac{bd-c^2}{b-2c+c^2}$$ Then the fractions just given are both equal to: ...
2
votes
2answers
543 views

Intuition for the Product of Vector and Matrices: $x^TAx $

When I took linear algebra, I had no trouble with the mechanical multiplication of matrices. Given the time to write things out and mumble a bit about ith and jth rows, I can do the products no ...
5
votes
3answers
2k views

Advice for choosing an MSc or PhD.

I have recently graduated from the University of Warwick with a 1st Class in my Master of Mathematics(MMath) degree and would really like to continue my education in mathematics by doing a PhD. The ...
25
votes
4answers
2k views

What are the dangers of visual exposition of mathematics?

I've heard several times (such as this one) that it's dangerous to learn/prove/teach mathematics through images. I've also read somewhere that showing mathematics through images helps one's intuition ...
6
votes
3answers
128 views

How detailed does a proof have to be and is the format constrained to text and equations?

Given that somebody claims a proof to a problem and you ask 100 highly qualified mathematicians whether this proof is valid, will they all agree that it's valid or all claim it's invalid? In other ...
4
votes
5answers
2k views

Is it possible to practice mental math too often? [closed]

I'm far from a mathematician, but the field I'm trying to break into (management consulting) requires a fair amount of mental arithmetic. I'm okay, but I'm not even close to as good as I need to be in ...
3
votes
1answer
5k views

Confused about Effective Rate of Discount- Theory of Interest

I'm currently reading Kellison's book, The Theory of Interest. I've reached the chapter on Effective Rate of Discount and it's somewhat confusing. The book explains it as a loan where interest is paid ...
4
votes
4answers
523 views

Examples of partial functions outside recursive function theory?

My math background is very narrow. I've mostly read logic, recursive function theory, and set theory. In recursive function theory one studies partial functions on the set of natural numbers. Are ...
2
votes
2answers
756 views

Application of maths in economics

What are the branches of maths where we can see undoubtful connections with economics? Where can we use mathematical methods or models and apply them to analyze economic concepts?
4
votes
1answer
114 views

Is $\Delta^2V$ one of the nature's favourite patterns?

I was reading Sawyer's Prelude to Mathematics, he says that there's one suposed nature's favourite pattern which is: $$\Delta^2V$$ He also says that this pattern is found in a dozen areas: conection ...
1
vote
2answers
391 views

I've heard that some kinds of mathematics are so abstract, what's the point in it?

Some days ago, a friend - who's studying civil engineering - told me something about the mathematics of the theoretical mathematics degree: It's strange, their math is so abstract. What should ...
17
votes
1answer
2k views

Why did a famous mathematician say that algebraic topology was dead?

I found Novikov said that algebraic topology was dead in the early 1970's in this article. Segal had been one of Atiyah's first students, working on equivariant K-theory, and then other ...
3
votes
2answers
572 views

Interesting or non-obvious finite subsets of the natural numbers

I was recently explaining to someone how to prove that there are infinitely many prime numbers, and I mentioned to them that it's not immediately obvious, upon first encountering the natural numbers, ...
3
votes
2answers
758 views

Good reference texts for introduction to partial differential equation?

As the title, are there any good reference texts for introduction to partial differential equation?
1
vote
1answer
221 views

Taking Differential Topology concurrently with Analysis

So I'm trying to finalize my schedule for this semester. I can't decide whether I should enroll in a grad level Differential Topology (Milnor) class or just the undergrad general topology one. The ...
5
votes
1answer
582 views

Rings' second isomorphism theorem

I am thinking about the proof of the second isomorphism theorem, and something isn't very clear to me. Let $R$ be a ring ,$S\subset R$ a subring and $I\subset R$ an ideal. We have the natural ...
105
votes
7answers
16k views

Tablet for reading textbooks and writing math by hand?

I am a math student. I'd like to find out if tablets (iPads, Galaxy Note 10.1) are worth the cost. How good are tablets for the purposes of reading textbooks as PDF and writing mathematics with a ...
1
vote
1answer
1k views

Looking for supplemental book or papers for honors high school student learning geometry proofs.

My child is taking honors geometry in high school this year and the teacher is starting them off with proofs with is great, however this being their first introduction to proofs it needs to be done ...
5
votes
1answer
1k views

Relevance of Euclidean geometry to modern mathematics

I'm interested whether, barring the reasons such as the importance of historical narrative and having an illustrative example, one should learn (synthetic) Euclidean geometry. To make such an inquiry ...
35
votes
7answers
5k views

What are some good math specific study habits?

What are/ were some of your good mathematician's study habits that you found really worked for you? I'm a CS major at a respected school and have a solid GPA... However, I definitely lack when it ...
0
votes
4answers
213 views

What sets satisfy $V = V^V$?

I'm not sure if said set exist or whether it is unique, but what name could I use to find more about it and what kind of interesting properties does it have? Clarification edit: I meant a set $V$ ...
2
votes
1answer
1k views

Application of various fields of mathematics to others

I have, only in recent times, taken seriously to mathematics.While reading a bit of real analysis(to be precise, flipping through the pages of Professor Abbott's Understanding Analysis) I asked myself ...
15
votes
1answer
319 views

How long should I insist?

While studying math, I usually get stuck on some topics, how long should I insist trying to understand it alone? What are the strategies for when this happens?
59
votes
12answers
6k views

Is it morally right and pedagogically right to google answers to homework? [closed]

This is a soft question that I have been struggling with lately. My professor sets tough questions for homework (around 10 per week). The difficulty is such that if I attempt the questions entirely ...
2
votes
1answer
133 views

Separation of mathematics and metamathematics

I recall reading that it's important to separate mathematics and metamathematics. What exactly does this mean, and why is it so? I understand that this question may make no sense without more ...
9
votes
1answer
728 views

Sex, Crime and Functional Analysis?

Ever since a friend told me about this book titled Sex, Crime and Functional Analysis: Part I. Functional Analysis, I have been looking for a copy of this book, but in vain. SO does this book ...
5
votes
2answers
247 views

How to motivate inner product spaces

What is the most motivating way to introduce general inner product spaces? I am looking for examples which have a real impact. For Euclidean spaces we relate the dot product to the angle between the ...
3
votes
0answers
311 views

Reading mathematical notation

Does there exist any site which can parse a series of mathematical symbols and translate them into english text? For example: For all $N$ of the set $I$...
8
votes
2answers
475 views

Classgroup of $\mathbb{Q}(\sqrt{2},\sqrt{-13})$

How would you compute the classgroup of the biquadratic number field $\mathbb{Q}(\sqrt{2},\sqrt{-13})$? I would prefer a method as "from scratch" as possible. Please avoid, if possible, quoting ...
37
votes
6answers
2k views

Is Complex Analysis equivalent Real Analysis with $f:\mathbb R^2 \to \mathbb R^2$?

Am I correct in noticing that Complex Analysis seems to be a synonym for analysis of functions $\mathbb R^2 \to \mathbb R^2$? If this is the case, surely all the results from complex analysis carry ...
1
vote
1answer
76 views

Sources of these questions?

I recently stumbled on preprint "36 unsolved problems in number theory", ArXiv:math/0010143. and I was wondering what does 'Gamma $\underline{\phantom{abcbdbe}}$' refer to? (I'm interested in some of ...
22
votes
6answers
1k views

What am I losing if I decide to perform all math by computer?

I solve mathematical problems every day, some by hand and some with the computer. I wonder: What will I lose if I start doing the mathematical problems only by computer? I've read this text and the ...
57
votes
15answers
12k views

Why do we need to learn integration techniques?

After a lifetime of approaching math the wrong way, I took two college math courses this quarter with a newfound zest for math. These classes are integral calc and multivariable calc. Integral calc ...
11
votes
3answers
416 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 ...
22
votes
1answer
2k views

What is magical about Cartan's magic formula?

Why is Cartan's magic formula $$\mathscr{L}_X\omega = i_Xd\omega + d(i_X\omega)$$ called "magic"? Should it be considered a highly surprising result? Does it "magically" prove several other ...
3
votes
3answers
335 views

What math branches are there? [closed]

This might be too general question, but still, I think this may be some useful question. So, what math branches are there generally? (for example, one branch would be abstract algebra, differential ...
2
votes
0answers
174 views

Preparation for a foray into noncommutative geometry

I am applying for a short undergraduate/honours research project, and am trying to decide on preferences for a topic. One of the possible topics is noncommutative geometry. I like the sound of this, ...
12
votes
1answer
2k views

Using distance formula to find slope, any reason to use the concluding equation?

So, today I was observing a class that I will be a TA for this semester and the professor started to talk about the distance formula $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$. Well, my mind wandered a little ...
1
vote
2answers
2k views

How to find ALL cluster points of a sequence?

The task of finding a limit point of a sequence is 'simple'; if the sequence converges, we locate the limit point by inspection and proved that it the sequence converges to that point. By uniqueness, ...
7
votes
4answers
2k views

Expanding problem solving skill

I have a great passion for Math but my lack in problem solving skill always keeps me away from the "good stuff". I always wanted to be better at Math and one of the things I figured out was to keep ...
7
votes
1answer
157 views

When do modifiers denote sub or super? Pseudo-, quasi-, ultra-, strong-, well-, pre-, c0- …

One only needs to search MMA.SE, math journals, wikipedia, or god-forbid, n-cat lab, for keywords listed in the title, which can be extended with: uniform-, regular-, complete-, local-, partial-, non- ...
5
votes
4answers
4k views

When is linear algebra usually taught

Just curious, when should I learn linear algebra in college? And when is linear algebra usually taught? What precedes linear algebra and what usually goes after linear algebra courses?
89
votes
10answers
12k views

Math and mental fatigue [closed]

Just a soft-question that has been bugging me for a long time: How does one deal with mental fatigue when studying math? I am interested in Mathematics, but when studying say Galois Theory and ...
9
votes
6answers
11k views

Math Textbooks for High School

I'm a high school student who is trying to figure out a complete course of self study for each year of high school. Is there a way to self learn grades of math without devoting too much time? For ...
1
vote
1answer
95 views

What preposition to use when fitting data?

Please could some real experts give an opinion on this question on English.SE: What preposition to use when fitting data? Do we fit data with, by, or as a linear function? Forgive me as I do ...