Review by Choice Review
The exhortation "read the masters'' usually refers to the likes of Newton, Euler, or Gauss, but the author's Fields Medal-winning work on transcendental numbers long ago established Baker (emer., Univ. of Cambridge, UK) as a true modern master. Now the idea of a 250-page "comprehensive'' introduction to number theory may seem audacious, but among mathematical writers, Baker manifestly possesses the powerful gifts for precision and concision that could even make it possible. Expanding on his famed A Concise Introduction to the Theory of Numbers (1984), the present volume speaks certainly to a more ambitious reader, but not necessarily (though likely) a more advanced one. Many a dedicated volume takes more pages to do less than Baker's work on the following topics (not an exhaustive list): congruences, elliptic curves, Diophantine equations, algebraic number theory, transcendental number theory, and analytic number theory. Such a book surely demands very careful study, but amazingly never seems rushed or artificially compressed. Despite a miraculous reach, some important topics receive little or no mention, for example, modular forms, so essential to Wiles's proof of Fermat's last theorem, and likewise any themes along the lines of those in H. Furstenberg's Recurrence in Ergodic Theory and Combinatorial Number Theory (1981). Summing Up: Highly recommended. Upper-division undergraduates and above. D. V. Feldman University of New Hampshire
Copyright American Library Association, used with permission.
Review by Choice Review
