[.ca] Three Pearls of Number Theory (ISBN 0486400263)

Come on, professors, write more like this!:
This book is actually a letter from a Russian professor to a student sent off to war. It's short, but won't be an easy read. These are "pearls" but getting the oyster open is going to be tough. It's also remarkable for it's candid revelation of the mathematical process of professional practitioners at various universities in different countries. The first pearl is about a young student name van der Waerden. Yep, the guy who went on to prove so many results in Abstract Algebra and wrote the classic text on the subject influencing Artin and Noether. It's interesting to note, van der Waerden used finite differences in his proof recounted in the first pearl, and he's the only author I know that included finite differences in his abstract algebra text book. Both the candid historical confessions and the conversational exposition make this a great book. It's style and methods should be widely imitated. Come on, professors, write more like this! Future archaeologist of the 20th century will be glad this document is available for it's revelation of the habits of homo professorus mathematicus.

If you like number theory you I think you will enjoy this bo:
A Y Khinchin was one of the greatest mathematicians of the first half of the twentieth century. He was also famous as a teacher and communicator. Fortunately, several of the books he wrote are still in print in English translations, published by Dover. Like William Feller and Richard Feynman he combines a complete mastery of his subject with an ability to explain clearly without sacrificing mathematical rigour. This is a short book of three chapters: Chapter 1. Van der Waerden's theorem on arithmetic progressions. Chapter 2. The Landau-Shnirelmann hypothesis and Mann's theorem. Chapter 3. An elementary solution of Waring's problem. These are all difficult problems from the theory of numbers and I think that the elementary proofs that Khinchin describes here are original. This book is a challenging but enjoyable read. I also recommend his other book on number theory: "Continued Fractions".