Stage 3 Introductory Number Theory

Introductory Number Theory:
Gauss once said "mathematics is the queen of sciences and number theory the queen of mathematics." G..H. Hardy once said in A Mathematician's Apology that, "If the theory of numbers could be employed for any practical and obviously honourable purpose, if it could be turned directly to the furtherance of human happiness or the relief of human suffering, as physiology and even chemistry can, then surely neither Gauss nor any other mathematician would have been so foolish as to decry or regret such applications. But science works for evil as well as for good (and particularly, of course, in time of war); and both Gauss and less mathematicians may be justified in rejoicing that there is one science at any rate, and that their own, whose very remoteness from ordinary human activities should keep it gentle and clean." He wrote it on November 1940. It turned out coding theory, where algebra and number theory are applied, played a key role in the World War II.

• Adler A. and Cloury J.E. Theory of Numbers: A Text and Source Book of Problems
• Baker A. Algebra and Number Theory [.pdf] (FREE!)
• Burton D.M. Elementary Number Theory - One of the better books for an introduction.
• Chen W.W.L. Elementary Number Theory (FREE!)
• Clark W.E. Elementary Number Theory [.pdf] (FREE!)
• Coppel W.A. Number Theory: An Introduction to Mathematics: Part A, B - You may leave Part B to the next stage.
• Dantzig T. and Mazur J. Number: The Language of Science - Non-mathematical treatment indeed.
• Dirichlet P.G.L. Supplements by Dedekind R. Lectures on Number Theory
• Erdos P. and Suranyi J. Topics in the Theory of Numbers
• Everest G. and Ward T. An Introduction to Number Theory
• Fine B. and Rosenberger G. Number Theory: An Introduction via the Distribution of Primes
• Ikenaga B. Number Theory (FREE!)
• Joens G.A. and Jones J.M. Elementary Number Theory
• Moser L. An Introduction to the Theory of Numbers (FREE!)
• Nathanson M.B. Elementary Methods in Number Theory
• Niven I., Zuckerman H.S. and Montgomery H.L. An Introduction to the Theory of Numbers
• Parent D.P. Exercises in Number Theory
• Redmond D Number Theory
• Rosen K.T. Elementary Number Theory - See the website for supplementary material.
• Santos D. Number Theory Notes [.pdf] (FREE!)
• Sato N. Number Theory [.pdf] (FREE!) - IMO level.
• Shoup V. A Computational Introduction to Number Theory and Algebra (FREE!)
• Silverman J.H. A Friendly Introduction to Number Theory - See the web for extra material.
• Stein W. An Explicit Approach to Elementary Number Theory (FREE!)
• Stein W. Elementary Number Theory (FREE!)
• 李華介：基礎數論 (FREE!)