Introduction to Classical Mathematics I: From the Quadratic Reciprocity Law to the Uniformization Theorem (Mathematics and Its Applications (70))

**`** Recommended for all libraries, this single volume may fill many gaps in smaller collections. **'** **Science & Technology** **`**The book is well-written, the presentation of the material is clear. ... This very valuable, excellent book is recommended to researchers, students and historians of mathematics interested in the classical development of mathematics. **'** **Acta Scientiarum Mathematicarum, 56:3-4** Front Matter....Pages i-xvii Congruences....Pages 1-10 Quadratic forms....Pages 11-22 Division of the circle (Cyclotomy)....Pages 23-34 Theory of surfaces....Pages 35-43 Harmonic analysis....Pages 44-58 Prime numbers in arithmetic progressions....Pages 59-66 Theory of algebraic equations....Pages 67-89 The beginnings of complex function theory....Pages 90-107 Entire functions....Pages 108-117 Riemann surfaces....Pages 118-136 Meromorphic differentials and functions on closed Riemann surfaces....Pages 137-153 The theorems of Abel and Jacobi....Pages 154-164 Elliptic functions....Pages 165-181 Riemannian geometry....Pages 182-209 On the number of primes less than a given magnitude....Pages 210-218 The origins of algebraic number theory....Pages 219-222 Field theory....Pages 223-231 Dedekind’s theory of ideals....Pages 232-250 The ideal class group and the group of units....Pages 251-261 The Dedekind ς-function....Pages 262-271 Quadratic forms and quadratic fields....Pages 272-280 The different and the discriminant....Pages 281-290 Theory of algebraic functions of one variable....Pages 291-306 The geometry of numbers....Pages 307-312 Normal extensions of algebraic number- and function fields....Pages 313-330 Entire functions with growth of finite order....Pages 331-341 Proof of the prime number theorem....Pages 342-358 Combinatorial topology....Pages 359-377 The idea of a Riemann surface....Pages 378-406 Uniformisation....Pages 407-416 Back Matter....Pages 417-453