The Sensual (Quadratic) Form
Published on 5. March 1998
Book
Hardback
166 pages
978-0-88385-030-5 (ISBN)
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Description
The distinguished mathematician John Conway presents quadratic forms in a pictorial way that enables the reader to understand them mathematically without proving theorems in the traditional fashion. One learns to sense their properties. In his customary enthusiastic style, Conway uses his theme to cast light on all manner of mathematical topics from algebra, number theory and geometry, including many new ideas and features.
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Content
Preface; 1. The first lecture: can you see the values of 2x2 + 6xy - 5y2?; 2. Afterthoughts: PSL2(Z) and Farey functions; 3. The second lecture: can you hear the shape of a lattice?; 4. Afterthoughts: Kneser's gluing method - unimodular lattices; 5. The third lecture:. and can you feel its form?; 6. Afterthoughts: feeling the form of a four dimensional lattice; 7. The fourth lecture: the primary fragrances; 8. Afterthought: more about the invariants - p-adic numbers; 9. Postscript: a taste of number theory; Bibliography.