For questions whose answers can't be objectively evaluated as correct or incorrect, but which are still are relevant to this site. Please be specific about what you are after.

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3
votes
1answer
28 views

What is the discrete log used for?

Perusing Wikipedia, I stumbled on the discrete logarithm. I looks interesting that we'd be able have a function that could solve $b^k=g$ for integers $b,k,$ and $g$. However, Wikipedia says "No ...
1
vote
1answer
57 views

subtle/annoying fallacious proofs [duplicate]

I've been invited to a maths themed Xmas after party. I need to prepare a selection of interesting, and relatively simple fallacious proofs which other guests will try and find the flaw in. I'm trying ...
5
votes
2answers
86 views

How to select the right books? [on hold]

As the saying goes, "Give a man a fish, feed him for a day. Teach a man how to fish, feed him for life." I've always had a problem with selecting appropriate books. It could be a problem that I'm a ...
1
vote
0answers
37 views

Motivation for Putnam (soft question)

This question may be too specific and too vague. But I'm curious about this. How highly are the applicants evaluated in PhD admission if they were ranked above the cutoff of honorable-mention in ...
6
votes
0answers
58 views

Examples of useful, insightful and interesting hand-waving

I am really amused by the answers to this question on "Most harmful heuristic" posed on MathOverflow, from which I've benefited a lot. However, it seems to me that some hand-waving may be really ...
6
votes
2answers
102 views

How to explain to a layman why Fermat's Last Theorem involves non-trivial math?

Fermat's Last Theorem states, given$$x^n + y^n = z^n$$ no three integers $x,y,z$ will satisfy the equation given integer value of $n$ greater than two. On the surface this seems like something that ...
3
votes
1answer
42 views

Which courses should I take to prepare for PHD in Finance/Econ/OR

Since it's finally the end of the year, I would like to gain some insights about which course should I take that are most helpful to prepare for application to the PHD program in Finance/Financial ...
14
votes
0answers
82 views

Effective Research Notes

Note-taking for research is vital to your success as a mathematician. As I look back at some of my handwritten notes, I realized how poor they were. I had thought to myself, "What happened?" I was ...
4
votes
2answers
61 views

Sources for mathematics outside the mathematics world

In this question I would like to ask you about material showing the uses (or occurrences) of mathematics in the everyday world. The aim is to encourage with it a group of young undergraduate ...
1
vote
1answer
121 views

Why is the axiom of choice not taught from the start to mathematics undergraduates?

I've recently discovered that the following theorems require the axiom of choice to be proven: every surjective function has a right inverse. a real-valued function that is sequentially continuous ...
5
votes
0answers
19 views

Discrete analogue of Green's theorem

Following formula concerning finite differences is in a way a discrete analogue of the fundamental theorem of calculus: $$\sum_{n=a}^b \Delta f(n) = f(b+1) - f(a) $$ We can think about the Green's ...
1
vote
2answers
51 views

Probabilistic implications of the existence of non-measurable sets

Measure theory and probability theory are deeply connected through the interpretation of subset measures on the sample space as probabilities of events. A major (and somewhat disturbing) result from ...
3
votes
0answers
38 views

Why is the slope-intercept form of the equation of a line often written $y=mx+b$? Why $m$ instead of $a$?

After a quick google search, I read something about Conway suggesting the $m$ having to do with "modulus" ... This seems odd to me, but perhaps there is some mathematical reason? I've heard of the ...
-1
votes
0answers
42 views

List of simple, common functions with an incomplete domain or range on $\mathbb{C}$

This may seem like a strange question, but it's an interest of mine and I would appreciate the help of the community in addition to brainstorming on my own. As the question states, I'm looking for ...
4
votes
1answer
54 views

Is there a “unifying framework” for harmonic analysis?

Recently, I was exposed to a basic harmonic analysis course. Although the course is almost over, I still can't put my finger on what harmonic analysis is about. I have a vague idea that it is ...
0
votes
2answers
49 views

Self-Learning Geometry

I'm an undergraduate senior wondering where he should start in learning geometry. My university unfortunately offers no such course. Should i begin with riemann geometry or differential geometry and ...
0
votes
1answer
39 views

Probability in a Magical World

We know the frequentist definition of probability-the probability $p$ of an event $E$ is the limiting frequency the event happens when the associated random experiment is repeated large number of ...
1
vote
1answer
29 views

Request for Recommendation of a Handbook of pure Mathematics

I am looking for some books at undergrad level that give a good pedagogical coverage of of topics like topology,group theory,analysis,measure theory and probability with a nice exposition.Even books ...
6
votes
1answer
63 views

What level of math is needed to learn fractional calculus?

I was skimming through wikipedia pages and stumbled upon the fractional calculus page. My interest increased when I noticed it has applications in physics. I was wondering as an undergraduate who's ...
3
votes
1answer
30 views

Prerequisites for Hartshorne: Euclid and beyond?

as the title suggests, I am looking for the prerequisites to Hartshorne's Euclid and beyond. I just found this book and I think it's wonderful, but the downside is that I only know math up to single ...
-6
votes
0answers
38 views

study question master math [on hold]

How to master advanced mathematics ? Do you think that with hard work and quasi-absolute determination one can achieve that ? Thank you
6
votes
2answers
326 views

How can I pick up analysis quickly?

I have a 2-3 week recess from university for winter break. In this time, I would like to learn analysis, starting with Walter Rudin's Principles of Mathematical Analysis, and then, if at all possible, ...
1
vote
1answer
54 views

Book recommendations for topics leading upto Algebraic geometry

I'm interesting in studying algebraic geometry (specifically either from Shafarevich or Hartshorne). Assuming a high school and basic college math education, what should be the topics and the order ...
2
votes
1answer
51 views

Homotopy Type Theory prerequisites.

I've done some undergraduate level study of algebraic topology (most Hatcher's book) and the smallest amount of type theory in a foundations of mathematics course. Homotopy type theory sounds amazing ...
0
votes
1answer
53 views

Question about independent study in differential geometry for an undergraduate.

I am a senior undergraduate math and physics student applying to graduate school in math for this upcoming fall. I have had classes in: Abstract Algebra (Rings, Fields, and Groups), Point-Set ...
0
votes
0answers
22 views

Learning Stochastic Processing, Modeling, and Analysis: Any Available Workbooks?

Motivation behind the question: I took the upper-level probability course at my college, and did pretty well. Most of the time throughout the class, I found myself intuitively understanding the ...
0
votes
0answers
37 views

Order of study? Rudin, Spivak, Munkres?

I'm currently taking an analysis course at a top 10 four year university in which we use Baby Rudin as our primary text. I was curious to know the order in which I should continue my studies. That ...
7
votes
0answers
93 views

How to listen math lectures?

Many times, the lectures goes beyond the head and not easy to follow, (at least with me),mainly in the workshop/conferences, though the audience are eager to learn something from it. Also, most of ...
12
votes
2answers
117 views

Strategies to study apart from “books cover to cover.”

I have never really liked reading a book from cover to cover (because I usually get bored). Most of what I've learned so far has been picked up from forums like this one, or occasional reading from ...
0
votes
0answers
37 views

Inverse image of a functor

Suppose $F: \mathcal A \to \mathcal B$ is a functor. We can define a category $F^{-1}(\mathcal B)$ as follows: an object is an object of $\mathcal A$, and a morphism between objects $A_0$ and $A_1$ ...
0
votes
2answers
30 views

Continuous trapdoor functions?

Every trapdoor function I've seen has been a discrete function. Do there exist continuous trapdoor functions? If so, what's an example of a continuous trapdoor function? And if not, why not?
3
votes
1answer
62 views

Taking a Putnam (General Questions) [duplicate]

I've just discovered an undergrad math competition (William Lowell Putnam Competition) and that my school offers it. The competition looks extraordinarily difficult, but I thought I'd give it a go. ...
3
votes
2answers
111 views

Is “mixed math” a useful way to learn math?

I was reading a book about how mathematics was taught in Cambridge in the 19th century, and it struck me how much physics was included in the syllabus, and it wasn't optional but everyone had to learn ...
1
vote
2answers
95 views

How to upgrade Category Theory skills for Algebraic Geometry?

I am doing a second advanced graduate course in Algebraic Geometry, with Hartshorne as a textbook. The skillset I am least satisfied with is the application of the Category Theory to Algebraic ...
3
votes
1answer
46 views

Good confusion-avoiding notation for iterated commutators?

I am doing some complicated and tedious calculation on iterated commutators. A typical term in my calculation looks like $$[x_a,[[[x_b,x_c]-x_d,x_e],[x_f,x_g]]]\text{.}$$ (I am considering ...
1
vote
1answer
27 views

Applications of Singular Functions

For our purposes here, a singular function is a continuous function such that the part which is absolutely continuous with respect to Lebesgue measure is zero. For example, the Cantor function or ...
27
votes
7answers
4k views

Genius mathematicians who never published anything

Amongst philosophers, Socrates is an example of a genius with a great influence on human history who never wrote anything. Almost all facts which are known about his revolutionary ideas are written by ...
1
vote
1answer
69 views

What topics have complex analysis among their prerequisites?

I have one spot left in my bachelor's curriculum and am trying to decide between complex and functional analysis. What the latter is good for, is more or less clear to me: e.g. for advanced ...
5
votes
1answer
83 views
+50

Good source on current 'views and thoughts' on mathematics

Recently I've become interested in the history of the way people think about mathematics. What I mean by this is for example how Godels proof basically put an end to the whole school of thought ...
2
votes
2answers
31 views

Restrictive definition of diagonalizable matrix

There is a theorem that says that every matrix of rank $r$ can be transformed by means of a finite number of elementary row and column operations into the matrix $$D=\begin{pmatrix} I_r & O_1 \\ ...
5
votes
0answers
79 views

How important is Differential Geometry for Number Theory?

The title pretty much says it. To elaborate slightly, I am, of course, aware of the huge role played by Algebraic Geometry in Number Theory but I'm not so sure about Differential Geometry. I would be ...
1
vote
2answers
63 views

What are the suggested prerequisites for topology?

I am interested in topology but I don't know if I can learn it without learning something else first. I've done: Algebra 1 and 2 Euclidean Geometry Calculus Is that enough if not please tell me what ...
1
vote
1answer
38 views

A book with heuristics or general techniques used in real analysis?

I have been looking for a book with some good heuristics for real analysis and point set topology. Any ideas?
1
vote
3answers
118 views

Best book for a casual pure mathematician? [closed]

I'm looking for an interesting book on pure mathematics... I would also accept books that are about certain topics, like number theory or graph theory. I'm a second-year engineering student and I'm ...
1
vote
4answers
49 views

Applying math knowledge [closed]

Currently I'm in the middle of my first year of college studying informatics engineering. I was never great at math, but if I put some effort, I understand it and constantly get good grades. However, ...
4
votes
2answers
73 views

Why do we focus so much in math on functions (as a subclass of relations)?

Why is it that math so focuses on the subclass of relations known as functions? I.e. why is it so useful for us in nearly all branches of mathematics to focus on relations which are left-total and ...
31
votes
20answers
2k views

Ways to write “50” [closed]

A really good friend of mine is an elementary school math teacher. He is turning 50, and we want to put a mathematical expression that equals 50 on his birthday cake but goes beyond the typical ...
6
votes
2answers
78 views

Which mathematical topics is knot theory related to?

I wonder if knot theory is related to any other topic in mathematics. I've not read much about it, but it seems to be living isolated. I also wonder if there any particular mathematical background ...
4
votes
3answers
78 views

Should I go back and start with a more “proof” based approach?

So I'm currently a calculus student, next semester I'll take calculus 2. I'm wondering if I should go to a book like the one by Spivak which is entirely different from the book used for my course, and ...
1
vote
1answer
48 views

What does “if and only if” mean in definitions?

Consider the following definition: A sequence $\{p_n\}$ is Cauchy if we have that for every $n, m \ge N$: $$|p_n - p_m| < \epsilon$$ Although if and only if is not used, we know that if a ...