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Mathematical Omnibus: Thirty Lectures on Classic Mathematics

Dmitry Fuchs University of California, Davis, CA
Serge Tabachnikov Pennsylvania State University, University Park, PA
Available Formats:
Hardcover ISBN: 978-0-8218-4316-1
Product Code: MBK/46
List Price: $69.00 MAA Member Price:$62.10
AMS Member Price: $55.20 Electronic ISBN: 978-1-4704-1812-0 Product Code: MBK/46.E List Price:$65.00
MAA Member Price: $58.50 AMS Member Price:$52.00
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $103.50 MAA Member Price:$93.15
AMS Member Price: $82.80 Click above image for expanded view Mathematical Omnibus: Thirty Lectures on Classic Mathematics Dmitry Fuchs University of California, Davis, CA Serge Tabachnikov Pennsylvania State University, University Park, PA Available Formats:  Hardcover ISBN: 978-0-8218-4316-1 Product Code: MBK/46  List Price:$69.00 MAA Member Price: $62.10 AMS Member Price:$55.20
 Electronic ISBN: 978-1-4704-1812-0 Product Code: MBK/46.E
 List Price: $65.00 MAA Member Price:$58.50 AMS Member Price: $52.00 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$103.50 MAA Member Price: $93.15 AMS Member Price:$82.80
• Book Details

2007; 463 pp
MSC: Primary 00;

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.

• 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

• Reviews

• The authors manage to breathe new life into topics that at first glance appear to be old hat.

• This is an enjoyable book with suggested uses ranging from a text for a undergraduate Honors Mathematics Seminar to a coffee table book. It is appropriate for either It could also be used as a starting point for undergraduate research topics or a place to find a short undergraduate seminar talk. This is a wonderful book that is not only fun to read, but gives the reader new ideas to think about.

MAA Reviews
• Dmitry Fuchs and Serge Tabachnikov display impeccable taste in their choice of the material, level of exposition, and the balance between concrete and more conceptual mathematical themes. Each of the thirty lectures tells a unique mathematical story, each with a display of mathematical narrative art, with great care for the details, revealing masters of their craft at work. Both novice and more experienced readers will find many pleasant surprises at all levels of exposition. ...[A] book suitable for such a noble and demanding goal to serve as an introduction to the world of 'serious mathematics' for new generations of mathematicians. ...[E]very page has one or more diagrams, graphs, and pictures illustrating the material. ...[T]he special artistic spirit and atmosphere the book owes to numerous, witty, humorous, and mysterious illustrations of the artist Sergey Ivanov. Without much exaggeration, one may say that these provocative, yet mathematically correct drawings can alone serve as a layman's guide to the beauty and mystery of mathematics. Summarizing, we can say that Mathematical Omnibus is a 'desert island book,' a 'coffee table book,' a book to share with friends, colleagues, and students, a gift for a beginner and an expert alike. In short, it is a wonderful addition to our personal, school, and university libraries.

Rade T. Zivaljevic, The American Mathematical Monthly
• Requests

Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
2007; 463 pp
MSC: Primary 00;

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.

• 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 authors manage to breathe new life into topics that at first glance appear to be old hat.