Thread: number theory

please tell me that how should i improve my number theory concepts ? i am a programmer and number thoery is used too much in problems. algorithms , theorems , identities, formula etc are not known to me many time which other people already know. Please tell me any source or link from where i can study and improve my knowledge and thinking ability in this field ? thanks

Read Euclid's proof that there are an infinite number of prime numbers and appreciate its elegance. Once you fully grasp both its truth and its elegance, you are on your way. Everything there is to know about Number Theory can be known through knowlege of prime numbers. Everything there is to know about prime numbers can be known from your own head. Srinivasa Ramanujan is a perfect exemplar of this.

It's hard to know exactly where your knowledge stands, and so what resources would best serve you. Is a book on number theory at an undergraduate level too much? "Elementary Number Theory" by Burton is an example, but there are many such books.

One trick you could use is to look at the table of contents of an undergraduate number theory book, and then use the web to check out the topics mentioned, deciding which ones you think you'd like to learn about, and/or which book you think would be worth buying. If your google skills are good, virtually everything in an undergraduate course is explained somehwre on the web - most of it is on wikipedia and a few of the big math websites.

A course (having a knoweldgeable living person aid you with insights, and requiring a steady immersion for a few months) is always better than a book. A book (being self-contained in notation and logically structured/ordered) is always better than hodge-podge reading about topics on the web. However, you should be aware that the the web is a tool available to you.

SO johnsomeone what should i do according to you ? you have said both to use: now where should i go ? please can you clearify it more ? book or web ? if web ? then any solid links ? thanks if you can help me.

In order of what's most ideal (and also most expensive and perhaps impractical):
1) Take a college class in number theory
2) Get a book on number theory and go through it (chapter by chapter, from page 1, is best - plus problems)
3) Use the internet to read about individual little topics.

To make #2 and #3 most useful, you could maybe examine the Table of Contents of some number theory books first. That will tell what topics are out there, and let you do some inital investigation to decide what you already know, what you want to know, and what seem to advanced and demanding to be worthwhile to know. That will help you choose a textbook that's right for you, if that's what you decide to do, or give you some idea of the topics you might want to learn on your own just using the web.

Google something like: elementary number theory, or number theory textbook, and get copy of the textbook's table of contents.