2
votes
7answers
718 views

What are the most important functions every mathematician should know? [closed]

I am an undergrad in math and was wondering, what are for you the most important functions every mathematician should know? At the moment I think ...
3
votes
2answers
91 views

Show that $f(x,y)= \|x-y\|_2^2$ is differentiable

Problem: Show that $f: \mathbb{R}^n \times \mathbb{R}^n \to \mathbb{R}$ with $f(x,y)=\|x-y\|_2^2$ is differentiable and compute its differential at every point in the domain of $f$Note: $\| \cdot ...
0
votes
0answers
37 views

Intuition analysis-deconstruction-reconstruction.

The following question is a refinement of this question, which caused a lot of people to give answers that were missing the point entirely, probably because the question was not clear. Being human, ...
0
votes
1answer
107 views

Books (and supporting material) that are useful in deconstructing one's intuition?

I recently came across the following problem from Paul Zeitz's book The Art and Craft of Problem Solving. Given the image below, can you find a way to connect corresponding blocks (i.e. A to A, B to ...
5
votes
3answers
608 views

Why are we interested in irreducible representation but not faithful representation?

I am reading some materials of representation theory (of a group). The motivation of representation theory is to represent (by a homomorphism $h: G \to GL(V)$, from the group $G$ to a vector space ...
8
votes
1answer
217 views

“Easy” (maybe not) question about dual spaces (Lineal Algebra).

Hi everyone is my first time reading about dual spaces and in one part of the notes that I read, says: The dual of the quotient space $V/U$ is naturally a subspace of $V$, namely the annihilators of ...
16
votes
1answer
427 views

Learning Math Efficienctly and Succeeding in Grad School

I'm currently a second year Ph.D. student studying pure math. I've recently come to the conclusion that I must be studying wrong. Actually, more to the point, I must be thinking about mathematics ...
1
vote
1answer
224 views

Adjunctions via Universal Arrows: Understanding a Proof.

I've having trouble understanding something in Turi's Category Theory Lecture Notes from The University of Edinburgh, which can be found here. It's the proof of Theorem 7.1, part (3). Here's the ...
13
votes
1answer
402 views

How to improve mathematical creativity?

To introduce myself: I'm an undergraduate mathematics student in Germany. Currently I'm studying in the second semester and until now I'm doing well, but I still got the feeling that my ability to ...
6
votes
2answers
664 views

start mathematics from scratch

I'm sorry if this question goes against the site. I have completed my engineering in computer science; we were taught to get degrees only in our university :(. I love mathematics but time passed ...
155
votes
28answers
15k views

Too old to start math

I'm sorry if this question goes against the meta for posting questions - I attached all the "beware, this is a soft-question" tags I could. This is a question I've been asking myself now for some ...
42
votes
4answers
4k views

Do you prove all theorems whilst studying?

When you come across a new theorem, do you always try to prove it first before reading the proof within the text? I'm a CS undergrad with a bit of an interest in maths. I've not gone very far in my ...
5
votes
2answers
194 views

The area problem!

We have to find area of the quadrilateral formed by joining the point of intersection of the four quarter circles that are drawn from each vertex in a unit square. $\hspace{4cm}$ The challenge is ...
28
votes
13answers
10k views

Formerly good at math, but after 12 years I've lost most of my skills. Now I need them once again. Any advice to grow them back?

I love math, and I used to be very good at it. The correct answers came fast and intuitively. I never studied, and redid the demonstration live for the tests (sometimes inventing new ones). I was the ...