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6
votes
3answers
120 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
1k views

Is it possible to practice mental math too often?

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
4k 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
420 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 ...
1
vote
2answers
610 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
112 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
370 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 ...
15
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
543 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, ...
4
votes
2answers
539 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
208 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 ...
4
votes
1answer
440 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 ...
94
votes
7answers
14k 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
783 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 ...
4
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 ...
33
votes
7answers
4k 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
185 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
917 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
2answers
303 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?
57
votes
12answers
5k 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
125 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 ...
8
votes
1answer
664 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
214 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 ...
2
votes
0answers
302 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
420 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 ...
33
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 ...
21
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 ...
54
votes
14answers
9k 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
394 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 ...
17
votes
0answers
1k 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
311 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 ...
1
vote
0answers
157 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, ...
10
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
1k 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
1k 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
153 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
3k 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?
79
votes
9answers
8k views

Math and mental fatigue

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 ...
6
votes
4answers
9k 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
87 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 ...
73
votes
34answers
5k views

Theorems with an extraordinary exception or a small number of sporadic exceptions

The Whitney graph isomorphism theorem gives an example of an extraordinary exception: a very general statement holds except for one very specific case. Another example is the classification theorem ...
2
votes
2answers
276 views

Resources for IMO

I am seeking an online resource or any book where I can find the questions of International Mathematical Olympiad questions chapter wise eg Number Theory problems grouped together. Like this site ...
10
votes
2answers
264 views

Articles on ideas in the history of mathematics notation?

I'm teaching a course this term on the history of scripts (writing systems) and rather than talking interminably about Semitic and Chinese and their spawn, I'd like to give students a more varied ...
8
votes
4answers
4k views

Advanced Linear Algebra courses in graduate schools

After studying general a linear algebra course, how would an advanced linear algebra course differ from the general course? And would an advanced linear algebra course be taught in graduate schools? ...
2
votes
3answers
245 views

Is there a reasoning behind the depiction of the numbers as they are $\{1$, $2$, $3$, $4$, $5$, $6$, $7$, $8$, $9\}$?

Is there a reasoning behind the depiction of the numbers as they are: $$\{1,2,3,4,5,6,7,8,9\}$$ Is there any other form of depiction for $6$ and $9$ other than $VI$ and $IX$?
4
votes
4answers
440 views

Strategies for arranging coins in a circle

Suppose you have $n$ identical circular coins and you would like to arrange them on the table so that their edges touch and their centers lie on a circle. Mathematically, there is no trouble. "Just" ...
4
votes
4answers
173 views

Why Does Finitely Generated Mean A Different Thing For Algebras?

I've always wondered why finitely generated modules are of form $$M=Ra_1+\dots+Ra_n$$ while finitely generated algebras have form $$R=k[a_1,\dots, a_n]$$ and finite algebras have form ...
6
votes
2answers
799 views

Personal advice ragarding Qualifying Exams

I am a Graduate student in Mathematics and in second Year. I have three qualifying exams in topics Abstract algebra, Real and Complex Analysis and Algebraic and differential topology.I already ...
1
vote
0answers
90 views

Where can I find a database with premade generalizations of mathematical structures?

Last question, I needed to use the general definition of a polynomial which is: $$a_nt^n+a_{n-1}t^{n-1}+\cdots+a_1t+a_0$$ But I needed to type it all, if I could find templates it would be ...