Background
I am a college pass out. I have done my B.Tech in computer science and masters in quantum information. I am soon going to take up an industrial job. In the free time I got, after passing out from my college till now, ( few months ) I started reading Sipser's book on "Complexity and Computability theory". After reading it I wanted to learn more about it so I turned towards the book by Boaz and Barak on "Complexity theory". When I reached the chapter on "cryptography", I realized I did not know the fundamentals of number theory, so I started reading "Theory of numbers" by Hardy and Wright.
Question
I have read about one-third of Hardy and Wright. It got my really interested in elementary number theory. I am planning to read the complete book and pick it up as my hobby. The problem I am facing is, although till know I am able to follows the proofs on my own, I keep forgetting what I read earlier. For example I am currently reading about continued fractions and approximations of irrationals by rationals. But I don't remember the proofs, tricks, topic etc in detail that I read before it ( although I can always go back and remind myself ). As I read further I only remember the current topic that I read. And I feel if I read the book completely, at the end I would only remember the broad topics and only get a broader view. Also I try to read couple of pages everyday, but there are breaks of long number of days where I go without reading a single page. And when I again start reading I tend to forget even the current topic.
So I wanted to ask what is the correct way to learn number theory ? Should I read Hardy and Wright completely ( I have still to learn of many other topics like pell's equations, diophantine equations etc. ) ? Is there some other more practical way of learning number theory as a hobby ? How do I reach the threshold point of learning elementary number theory ?
Best Answer
I would not recommend continuing with Hardy and Wright. What you need is strength on the basics, not a tourist's view of a wide range of topics. I would focus on problem solving. Do lots of cool problems, taken from various sources, at a level that is reasonably challenging, but not way out of range, so as to develop your problem-solving and proof skills.