What would be a good book to learn basic number theory? If possible a book which also has a collection of practice problems? Thanks.

What are some maths textbooks that follow the “axiomatic approach”? (I would call it “theorem-proof” approach, but I’m more after books that start from the complete basics in a branch of math) What I consider “axiomatic approach” books: e.g. Disquisitiones Arithmeticae, Euclid’s Elements

In almost every mathematical text there is a line as This was first proved by Gauss or This formula first appeared in a work of Riemann, but for me it’s more like My friend told me once that… For my Bachelor thesis and other papers I’m working on I would prefer to add a scan […]

I am searching for a real analysis book (instead of Rudin’s) which satisfies the following requirements: clear, motivated (but not chatty), clean exposition in definition-theorem-proof style; complete (and possibly elegant and explicative) proofs of every theorem; examples and solved exercises; possibly, the proofs of the theorems on limits of functions should not use series; generalizations […]

I am a graduate student of math right now but I was not able to get a topology subject in my undergrad… I just would like to know if you guys know the best one..

Allen Hatcher seems impossible and this is set as the course text? So was wondering is there a better book than this? It’s pretty cheap book compared to other books on amazon and is free online. Any good intro to Algebraic topology books? I can find a big lists of Algebraic geometry books on here. […]

All of us mathematicians after some time (and trial-and-error, of course) we are able to guess with reasonable accuracy whether or not a given function is elementary integrable (test yourself: $$\int\frac1{x\sin\bigl(\frac1x\bigr)}\,dx\quad\style{font-family:inherit;}{\text{vs.}}\quad\int\frac1{x^2\sin\bigl(\frac1x\bigr)}\,dx\ ;$$ surely the readers can give a lot more challenging and interesting examples). I would like to know what is the most comprehensive work […]

I am currently studying Introduction to Calculus and Analysis by Richard Courant and Fritz John.I would like to compare Courant’s book with Apostol’s and Spivak’s in terms of difficulty of the problems provided.After reading that book, should I go for one of the two above or should I study something else like Rudin?My focus is […]

I want to start signal processing and I need a book that satisfies my mathematical requirements: I am in the third grade of high school and I don’t know any useful thing about limit, differential, … Please help me.

I would like to see a proof of when equality holds in Minkowski’s inequality. The proof is quite different for when $p=1$ and when $1<p<\infty$. Could someone provide a reference? Thanks!

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Triangular matrices proof
Proving completeness of a metric space
Subgroup of an abelian group isomorphic to a given quotient group
Convex combination of projection operators
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What is $\mathbb Z]$? What are the double brackets?
explicitly constructing a certain flat family
The connection between differential forms and ODE
Easiest way to prove that $2^{\aleph_0} = c$
Need for inverse in $1-1$ correspondence between left coset and right coset of a group
Let $\pi$ denote a prime element in $\mathbb Z, \pi \notin \mathbb Z, i \mathbb Z$. Prove that $N(\pi)=2$ or $N(\pi)=p$, $p \equiv 1 \pmod 4$