Contents

Preface x i

Some histor y o f early mathematic s 1

1. Euclid-Archimedes-Diophantu s 3

2. Pythagora s and the Pythagorean triplets 11

3. Aryabhata–Brahmagupta–Bhaskar a 17

4. Irrationa l numbers : construction an d approximation 3 3

5. Arabi c mathematics 4 3

6. Beginning s of algebra in Europe 4 7

7. Th e cubic and biquadratic equations 5 5

Solution o f the cubi c an d biquadrati c equation s 6 3

8. Solutio n of the cubic equation 6 5

9. Solutio n of the biquadratic equation 8 7

Some theme s fro m moder n algebr a 9 3

10. Numbers , algebra, and the real world 9 5

11. Comple x numbers 9 7

12. Fundamenta l theorem of algebra 117

13. Equation s of degree greater than four 125

14. Genera l number systems and the axiomatic treatment o f algebra 127

References 137

Chronology 139

Index 14

IX