Reddit mentions of Elementary Number Theory (Springer Undergraduate Mathematics Series)

Everyone will tell you something else. It all depends on what you like. Going through undergrad and even the first couple years of grad school is like a spirit walk through math where you find yourself and your interests, and believe me they will change like the wind during that time. Just take as many proof-based classes as you can, if it's a class without proofs then it's not math and will not help you toward your goal. From your list, only Linear Algebra has the potential to be a math class, the rest is glorified engineering.

If you don't have time to focus on all these classes, learn to read math books and proofs. This is a good introduction to Number Theory and proof concepts in general. Once you have more experience under your belt you can try for things like Algebra, Combinatorics, Set Theory, Logic, Topology or Analysis.

Just be curious, keep an open mind and remember that Number Theory is the most superior and enlightening math subject =)

Liebeck's Concise Introduction to Pure Mathematics is a great text for introducing students to the basic tools required in abstract algebra, number theory and analysis, but doesn't go into great depth.

It's kind of a standard text but for abstract algebra I think Dummit and Foote is remarkably clear.

Ireland and Rosen's Classical Introduction to Modern Number Theory is a classic, but maybe more intermediate.

Elementary Number Theory by Jones is very good.

Mathematics papers aren't really a good place to get an introduction to branches of mathematics as they tend to cater to the advanced reader. The most accessible you might find would be Mathematics Magazine or similar.

You would fare far better with an undergraduate level textbook. Springer publish a lot of pretty good undergraduate level texts so you might find something like this or this helpful (although I have not personally read either of those specifically so I cannot speak to their quality, but I find Springer books are usually good).

You might get better advice asking in the main sub (/r/math) as people like to give reading there.

EDIT: or maybe something like this would be more suited to what you're looking for?

I would say that it would depend on the problem. If you cannot solve the first ten, I would be worried, as they can all be solved by simple brute force methods. I have a degree in Astrophysics, and some of the 300 and 400 problems are giving me pause, so if you are stuck there you are in good company.

There are elegant solutions to each problem, if you want to delve into them, but the first handful, the first ten especially, can be simply solved.

Once you get beyond the first ten or so, the mathematical difficulty ratchets up. There are exceptions to that rule of course, but by and large, it holds.

If you are interested in Number Theory, the best place to start is a number theory course at a local university. Mathematics, especially number theory, is difficult to learn by yourself, and a good instructor can expound, not only on the math, but also on the history of this fascinating subject.

Gauss, quite arguably the finest mathematician to ever live loved number theory; of it, he once said:

> Mathematics is the queen of sciences and number theory is the queen of mathematics. She often condescends to render service to astronomy and other natural sciences, but in all relations she is entitled to the first rank.

Although my personal favorite quote of his on the subject is:

> The enchanting charms of this sublime science reveal themselves in all their beauty only to those who have the courage to go deeply into it.

If you are interested in purchasing some books about number theory, here are a handful of recommendations:


Number Theory (Dover Books on Mathematics) by George E. Andrews


Number Theory: A Lively Introduction with Proofs, Applications, and Stories by James Pommersheim, Tim Marks, Erica Flapan


An Introduction to the Theory of Numbers by G. H. Hardy, Edward M. Wright, Andrew Wiles, Roger Heath-Brown, Joseph Silverman


Elementary Number Theory (Springer Undergraduate Mathematics Series) by Gareth A. Jones , Josephine M. Jones

and it's companion


A Classical Introduction to Modern Number Theory (Graduate Texts in Mathematics) (v. 84) by Kenneth Ireland, Michael Rosen

and a fun historical book:


Number Theory and Its History (Dover Books on Mathematics) Paperback by Oystein Ore

I would also recommend some books on

Markov Chains

Algebra

Prime number theory

The history of mathematics

and of course, Wikipedia has a good portal to number theory.

Get ahold of this book:
http://www.amazon.com/Elementary-Number-Theory-Gareth-Jones/dp/3540761977/ref=sr_1_2?ie=UTF8&s=books&qid=1255891222&sr=8-2