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
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