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.
Based on my experience in this subject, I have decided to study it further on my own.
I am planning to cover these topics: Primitive roots,Quadratic residues,binary quadratic forms, etc...
Can someone tell me in what sequence should I study these topics?
Though I have seen that in most books Primitive roots comes just before Quadratic Residues follwed by Binary quadratic forms ,And what other topics follow these three topics?
Second, What I want to have is knowledge in my favourite field of maths which is number theory, Is my approach to learn this is right? Or, should I first see which branch : Algebraic or Analytic interests me more and study only that particular branch?
And most important, Which books or other references like lecture videos should I refer to, suitable to learn the material step by step with exercises to work out?
What opinion you guys have about David Burton book and Alan Baker book?
I apologize if a similar question has already been asked by someone or if I haven't added appropriate tags or If I have asked too many questions in just one post.
And please do not recommend books like: introduction to the theory of numbers by Hardy and wright and another one by Niven, Zuckerman, their are- not at all suitable for someone studying the topics for the first time.
Thanks in advance to all.