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Thirty-three Miniatures: Mathematical and Algorithmic Applications of Linear Algebra

About this Title

Jiří Matoušek, Charles University, Prague, Czech Republic

Publication: The Student Mathematical Library
Publication Year 2010: Volume 53
ISBNs: 978-0-8218-4977-4 (print); 978-1-4704-1636-2 (online)
DOI: http://dx.doi.org/10.1090/stml/053
MathSciNet review: MR2656313
MSC: Primary 15-01; Secondary 05A10, 05C70

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Table of Contents

Front/Back Matter

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Chapters

• Miniature 1. Fibonacci numbers, quickly
• Miniature 2. Fibonacci numbers, the formula
• Miniature 3. The clubs of Oddtown
• Miniature 4. Same-size intersections
• Miniature 5. Error-correcting codes
• Miniature 6. Odd distances
• Miniature 7. Are these distances Euclidean?
• Miniature 8. Packing complete bipartite graphs
• Miniature 9. Equiangular lines
• Miniature 10. Where is the triangle?
• Miniature 11. Checking matrix multiplication
• Miniature 12. Tiling a rectangle by squares
• Miniature 13. Three Petersens are not enough
• Miniature 14. Petersen, Hoffman–Singleton, and maybe 57
• Miniature 15. Only two distances
• Miniature 16. Covering a cube minus one vertex
• Miniature 17. Medium-size intersection is hard to avoid
• Miniature 18. On the difficulty of reducing the diameter
• Miniature 19. The end of the small coins
• Miniature 20. Walking in the yard
• Miniature 21. Counting spanning trees
• Miniature 22. In how many ways can a man tile a board?
• Miniature 23. More bricks—more walls?
• Miniature 24. Perfect matchings and determinants
• Miniature 25. Turning a ladder over a finite field
• Miniature 26. Counting compositions
• Miniature 27. Is it associative?
• Miniature 28. The secret agent and umbrella
• Miniature 29. Shannon capacity of the union: A tale of two fields
• Miniature 30. Equilateral sets
• Miniature 31. Cutting cheaply using eigenvectors
• Miniature 32. Rotating the cube
• Miniature 33. Set pairs and exterior products

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