A Modern Introduction to Ancient Indian Mathematics

Cover......Page 1
Title page......Page 2
Preface to the Second Edition......Page 5
Preface to the First Edition......Page 6
Contents......Page 9
1. The Decimal Place Value System......Page 11
2. Divisibility......Page 15
3. Greatest Common Divisor and Least Common Multiple......Page 25
4. Simple Continued Fractions......Page 30
5. The Euler phi-function......Page 36
6. The Möbius mu-function......Page 40
7. Congruences......Page 50
1. Some Questions of Divisibility......Page 69
2. Recurring Decimals......Page 75
3. Square......Page 85
4. Square Root......Page 92
5. Cube......Page 98
6. Cube Root......Page 100
1. Lemmas of BRAHMAGUPTA......Page 113
2. Examples......Page 116
3. CHAKRAVALA Method of BHASKARA......Page 118
4. Historical Remarks......Page 130
5. Continued Fractions......Page 131
6. Remarks on Pi......Page 145
7. Theorem of BHASKARA......Page 151
1. Geometry in the Sulba Sutras......Page 165
2. The Triangle......Page 178
3. The Cyclic Quadrilateral......Page 186
4. The Circle......Page 192
APPENDIX......Page 205
1. Multiplication and Division......Page 223
1. Introduction......Page 232
2. The Bhaskara Coefficients m... and h... for sqrt(D)......Page 233
1. Polynomial Rings......Page 242
2. Statement of the Fundamental Theorem on Symmetric Functions......Page 244
3. The Field Q of Algebraic Numbers......Page 245
4. Taylor Expansion for Polynomials......Page 247
5. Transcendence of e and Pi......Page 250
6. Dirichlet's Approximation Theorem, Siegel's Lemma......Page 261
7. Miscellaneous Theorem and Examples......Page 263
SUGGESTED READINGS......Page 269