0
votes
2answers
64 views

Doing for the first time a mathematical essay! Tips [closed]

I am an undegraduate and i though of doing my first essay on number theory!I kinda have the topic and i started selecting info from different references..but i dont want it to be just a copy paste ...
9
votes
4answers
510 views

Topics on Number theory for undergraduate to do a project

Im an undergraduate in the mathematics field ..So i wanna be alittle more productive and wanted to do an essay or project mostly on number theory or Algebra(Rings or Groups) and i want to ask if you ...
4
votes
0answers
140 views

start studying advanced topics in number theory

I am a first year undergrad and have had elementary course in Number Theory which includes only basic introductory topics like: divisibility,gcd-lcm,primes,congruences, number theoretic functions etc. ...
13
votes
0answers
1k views

What are some strong algebraic number theory PhD programs?

I am currently applying for PhD programs in the US. My main interests are number theory and algebra. More specifically, I am interested in algebraic number theory (number fields, Galois groups, ...
5
votes
2answers
348 views

What are some reasonable things to prove about the Collatz Conjecture?

I am writing an undergraduate paper on the $3n+1$ problem, and I am looking for some theorems related to the problem that would be reasonable for someone with my mathematical background to prove. I'm ...
5
votes
5answers
778 views

Multiplicative inverse of a complex number.

Find the multiplicative inverse of $1+ 3\sqrt{2}$ in the ring $\mathbb{Q}(\sqrt{2})$ and use it to solve the equation $(1+3\sqrt{2})x=1-5\sqrt{2}$. I think that the inverse is the conjugate, so it ...
6
votes
2answers
780 views

Learning roadmap for Class Field Theory and more

I consider to study Class Field Theory and Advance Number Theory by my self this next semester. However, there are many books, lecture notes... I would like to choose the most comprehensive book to ...
19
votes
7answers
2k views

Mathematical Career Advice to a young 16 year wannabe mathematician

I am a '94 born aspiring mathematician, programmer and a little bit of drummer from Nepal. I have been an avid follower and lover of mathematics since my seventh grade. Although I do not even consider ...