Mathematical Omnibus : 30 lectures on classical mathematics

By: Dmitry, FuchsContributor(s): Tabachnikov, SergeMaterial type: TextTextPublication details: USA: American Mathematical Society, [c2013]Description: 459 pISBN: 9780821868850Subject(s): MathematicsLOC classification: QA37.3
Contents:
Algebra and arithmetics Chapter 1. Arithmetic and combinatorics Lecture 1. Can a number be approximately rational? Lecture 2. Arithmetical properties of binomial coefficients Lecture 3. On collecting like terms, on Euler, Gauss, and MacDonald, and on missed opportunities Chapter 2. Equations Lecture 4. Equations of degree three and four Lecture 5. Equations of degree five Lecture 6. How many roots does a polynomial have? Lecture 7. Chebyshev polynomials Lecture 8. Geometry of equations Geometry and topology Chapter 3. Envelopes and singularities Lecture 9. Cusps Lecture 10. Around four vertices Lecture 11. Segments of equal areas Lecture 12. On plane curves Chapter 4. Developable surfaces Lecture 13. Paper sheet geometry Lecture 14. Paper Möbius band Lecture 15. More on paper folding Chapter 5. Straight lines Lecture 16. Straight lines on curved surfaces Lecture 17. Twenty-seven lines Lecture 18. Web geometry Lecture 19. The Crofton formula Chapter 6. Polyhedra Lecture 20. Curvature and polyhedra Lecture 21. Non-inscribable polyhedra Lecture 22. Can one make a tetrahedron out of a cube? Lecture 23. Impossible tilings Lecture 24. Rigidity of polyhedra Lecture 25. Flexible polyhedra Chapter 7. Two surprising topological constructions Lecture 26. Alexander’s horned sphere Lecture 27. Cone eversion Chapter 8. On ellipses and ellipsoids Lecture 28. Billiards in ellipses and geodesics on ellipsoids Lecture 29. The Poncelet porism and other closure theorems Lecture 30. Gravitational attraction of ellipsoids Lecture 31. Solutions to selected exercises
Summary: The book consists of thirty lectures on diverse topics, covering much of the mathematical landscape rather than focusing on one area. The reader will learn numerous results that often belong to neither the standard undergraduate nor graduate curriculum and will discover connections between classical and contemporary ideas in algebra, combinatorics, geometry, and topology. The reader's effort will be rewarded in seeing the harmony of each subject. The common thread in the selected subjects is their illustration of the unity and beauty of mathematics. Most lectures contain exercises, and solutions or answers are given to selected exercises. A special feature of the book is an abundance of drawings (more than four hundred), artwork by an award-winning artist, and about a hundred portraits of mathematicians. Almost every lecture contains surprises for even the seasoned researcher.-- provided by publisher
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Item type Current library Collection Shelving location Call number Status Notes Date due Barcode Item holds
Book Book ICTS
Mathematic Rack No 4 QA37.3 (Browse shelf (Opens below)) Available Billno:IN 003 582; Billdate: 2018-01-11 00952
Total holds: 0

Algebra and arithmetics

Chapter 1. Arithmetic and combinatorics
Lecture 1. Can a number be approximately rational?
Lecture 2. Arithmetical properties of binomial coefficients
Lecture 3. On collecting like terms, on Euler, Gauss, and MacDonald, and on missed opportunities

Chapter 2. Equations
Lecture 4. Equations of degree three and four
Lecture 5. Equations of degree five
Lecture 6. How many roots does a polynomial have?
Lecture 7. Chebyshev polynomials
Lecture 8. Geometry of equations

Geometry and topology

Chapter 3. Envelopes and singularities
Lecture 9. Cusps
Lecture 10. Around four vertices
Lecture 11. Segments of equal areas
Lecture 12. On plane curves

Chapter 4. Developable surfaces
Lecture 13. Paper sheet geometry
Lecture 14. Paper Möbius band
Lecture 15. More on paper folding

Chapter 5. Straight lines
Lecture 16. Straight lines on curved surfaces
Lecture 17. Twenty-seven lines
Lecture 18. Web geometry
Lecture 19. The Crofton formula

Chapter 6. Polyhedra
Lecture 20. Curvature and polyhedra
Lecture 21. Non-inscribable polyhedra
Lecture 22. Can one make a tetrahedron out of a cube?
Lecture 23. Impossible tilings
Lecture 24. Rigidity of polyhedra
Lecture 25. Flexible polyhedra

Chapter 7. Two surprising topological constructions
Lecture 26. Alexander’s horned sphere
Lecture 27. Cone eversion

Chapter 8. On ellipses and ellipsoids
Lecture 28. Billiards in ellipses and geodesics on ellipsoids
Lecture 29. The Poncelet porism and other closure theorems
Lecture 30. Gravitational attraction of ellipsoids
Lecture 31. Solutions to selected exercises

The book consists of thirty lectures on diverse topics, covering much of the mathematical landscape rather than focusing on one area. The reader will learn numerous results that often belong to neither the standard undergraduate nor graduate curriculum and will discover connections between classical and contemporary ideas in algebra, combinatorics, geometry, and topology. The reader's effort will be rewarded in seeing the harmony of each subject. The common thread in the selected subjects is their illustration of the unity and beauty of mathematics. Most lectures contain exercises, and solutions or answers are given to selected exercises. A special feature of the book is an abundance of drawings (more than four hundred), artwork by an award-winning artist, and about a hundred portraits of mathematicians. Almost every lecture contains surprises for even the seasoned researcher.-- provided by publisher

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