Bücher von Alan Baker

For Alexandra Drummond, senior year of high school was supposed to be about boys, parties, and spending time with friends. Living in a small suburban town, in a small suburban home, with her parents and baby sister she lived the quintessential small suburban life. That was, of course, until she lost everything in the blink of an eye. Traveling down a road they should never have been on; Alexandra and her family get into a brutal car accident. Barely surviving the crash, she finds herself face to face with the angel of death himself as he pulls the souls of her dead family from their mangled bodies. In the coming weeks he would haunt her almost daily. Alexandra desperately looks for a way to stop his pursuit and rid herself of the terrifying demon. Eventually she learns that in order to defeat him she would have to gamble with her own life. If successful, she would change everything. If she fails, she risks giving death what he'd been after all along; her own soul.

First published in 1975, this classic book gives a systematic account of transcendental number theory, that is those numbers which cannot be expressed as the roots of algebraic equations having rational coefficients. Their study has developed into a fertile and extensive theory enriching many branches of pure mathematics. Expositions are presented of theories relating to linear forms in the logarithms of algebraic numbers, of Schmidt's generalisation of the Thue-Siegel-Roth theorem, of Shidlovsky's work on Siegel's |E|-functions and of Sprindzuk's solution to the Mahler conjecture. The volume was revised in 1979: however Professor Baker has taken this further opportunity to update the book including new advances in the theory and many new references.

Developed from the author's popular text, A Concise Introduction to the Theory of Numbers, this book provides a comprehensive initiation to all the major branches of number theory. Beginning with the rudiments of the subject, the author proceeds to more advanced topics, including elements of cryptography and primality testing, an account of number fields in the classical vein including properties of their units, ideals and ideal classes, aspects of analytic number theory including studies of the Riemann zeta-function, the prime-number theorem and primes in arithmetical progressions, a description of the Hardy-Littlewood and sieve methods from respectively additive and multiplicative number theory and an exposition of the arithmetic of elliptic curves. The book includes many worked examples, exercises and further reading. Its wider coverage and versatility make this book suitable for courses extending from the elementary to beginning graduate studies.

**Winner of a Koestler Trust Silver Award*** and the only book of its kind by a serving lifer.

In this book, Professor Baker describes the rudiments of number theory in a concise, simple and direct manner. Though most of the text is classical in content, he includes many guides to further study which will stimulate the reader to delve into the great wealth of literature devoted to the subject.