| Description |
1 online resource (viii, 467 pages) : illustrations |
| Contents |
1. On the product of sphere bundles and the duality theorem modulo two -- 2. Classes caracteristiques et i-carres d'une variete -- 3. Les i-carres dans une variete grassmannienne -- 4. On the realization of complexes in Euclidean spaces I -- 5. On the realization of complexes in Euclidean spaces III -- 6. On universal invariant forms -- 7. Theory of I*-functor in algebraic topology -- effective calculation and axiomatization of I*-functor on complexes -- 8. On the decision problem and the mechanization of theorem-proving in elementary geometry -- 9. Toward mechanization of geometry -- Some comments on Hilbert's "Grundlagen der Geometrie" -- 10. The out-in complementary principle -- 11. A constructive theory of differential algebraic geometry based on works of J.F. Ritt with particular applications to mechanical theorem-proving in differential geometries -- 12. Basic principles of mechanical theorem-proving in elementary geometries. 13. On zeros of algebraic equations -- an application of Ritt principle. 14. On the planar imbedding of linear graphs I -- 15. On the planar imbedding of linear graphs II -- 16. A mechanization method of geometry and its applications I -- 17. Recent studies of the history of Chinese mathematics -- 18. On Chern numbers of algebraic varieties with arbitrary singularities -- 19. Mechanical derivation of Newton's gravitational laws from Kepler's laws -- 20. A mechanization method of geometry and its applications II -- 21. A mechanization method of geometry and its applications III -- 22. On the foundation of algebraic differential geometry -- 23. On the genetic zero and Chow basis of an irreducible ascending set -- 24. Mechanical theorem proving of differential geometries and some of its applications in mechanics -- 25. On a finiteness theorem about optimization problems -- 26. On surface-fitting problem in CAGD -- 27. Central configurations in planet motions and vortex motions -- 28. On algebraico-differential equations-solving -- 29. On the construction of Groebner basis of a polynomial ideal based on Riquier-Janet theory -- 30. On "good" bases of algebraico-differential ideals |
| Summary |
This important book presents all the major works of Professor Wen-Tsun Wu, a widely respected Chinese mathematician who has made great contributions in the fields of topology and computer mathematics throughout his research career. The book covers Wu's papers from 1948 to 2005 and provides a comprehensive overview of his major achievements in algebraic topology, computer mathematics, and history of ancient Chinese mathematics. In algebraic topology, he discovered Wu classes and Wu formulas for Stiefel-Whitney classes of sphere bundles or differential manifolds, established an imbedding theory with an application to the layout problem of integrated circuits, and introduced the I*-functors which turned the "rational homotopy theory" created by D Sullivan into algorithmic form. In computer mathematics, he discovered Wu's method of mechanical theorem proving by means of computers, which has been applied to prove and even discover on the computers hundreds of non-trivial theorems in various kinds of elementary and differential geometries. He also discovered a new effective method of polynomial equations solving, which has been used to solve problems raised from the fields of robotics and mechanisms, CAGD, computer vision, theoretic physics, celestial mechanics, and chemical equilibrium computation |
| Bibliography |
Includes bibliographical references |
| Notes |
Partial text in French |
|
Print version record |
| Subject |
Wu, Wen-tsün
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| SUBJECT |
Wu, Wen-tsün fast |
| Subject |
Algebraic topology.
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Computer science -- Mathematics.
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Mathematics, Chinese -- History
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MATHEMATICS -- Topology.
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Algebraic topology
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Computer science -- Mathematics
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Mathematics, Chinese
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| Genre/Form |
History
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| Form |
Electronic book
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| ISBN |
9812791086 |
|
9789812791085 |
|
1281933678 |
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9781281933676 |
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