Mathematics in India

Preface

List of Abbreviations

Chapter 1. Introduction

1.1. Background and aims of this book

1.2. History and South Asia

1.3. Sanskrit literature and the exact sciences

Chapter 2. Mathematical Thought in Vedic India

2.1. The Vedas and Mathematics

2.2. The Sulba-sutras

2.3. The Vedas and astronomy

2.4. The Jyotisa-vedanga

2.5. Vedic India and ancient Mesopotamia

Chapter 3. Mathematical Traces in the Early Classical Period

3.1. Numbers and numerals

3.2. Astronomy, astrology, and cosmology

3.3. Mathematical ideas in other disciplines

3.4. Mathematics in Jain and Buddhist texts

Chapter 4. The Mathematical Universe

4.1. An introduction to geocentric astronomy

4.2. Evolution of the siddhanta and astronomical schools

4.3. Astronomical calculations in siddhantas

4.4. Other texts for astronomical computation

4.5. Geometric models in astronomy

4.6. The problem of origins

Chapter 5. The Genre of Medieval Mathematics

5.1. Chapters on mathematics in siddhantas

5.2. The Bakhshali Manuscript

5.3. The Ganita-sara-sangraha

Chapter 6. The Development of "Canonical" Mathematics

6.1. Mathematicians and society

6.2. The "standard" texts of Bhaskara (II)

6.3. The works of Narayana Pandita

6.4. Mathematical writing and thought

Chapter 7. The School of Madhava in Kerala

7.1. Background

7.2. Lineage

7.3. Infinte series and other mathematics

7.4. Astronomy and scientific methodology

7.5. Questions of transmission

Chapter 8. Exchanges with the Islamic World

8.1. Indian mathematics in the West

8.2. Mathematical encounters in India

8.3. Influence and synthesis

Chapter 9. Continuity and Changes in the Modern Period

9.1. Individuals, families, and schools

9.2. Contacts with Europe

9.3. Mathematics and astronomy, 1500-1800

9.4. Conclusion

Appendix A. Some Basic Features of Sanskrit Language and Literature

A.1. Elements of spoken and written Sanskrit

A.2. The structure of Sanskrit verse

A.3. The documentary sources of texts

A.4. Meaning and interpretation: caveat lector!

A.5. Glossary of transliterated technical terms

Appendix B. Biographical Data on Indian Mathematicians

Bibliography

Index