 |
| by: Dmitry Fuchs, Serge Tabachnikov |
Mathematical Omnibus: Thirty Lectures on Classic Mathematics
by: Dmitry Fuchs, Serge Tabachnikov,
* Publisher: Amer Mathematical Society
* Number Of Pages:
* Publication Date: 2007-10-18
* Sales Rank: 1304670
* ISBN / ASIN: 0821843168
* EAN: 9780821843161
* Binding: Hardcover
* Manufacturer: Amer Mathematical Society
* Studio: Amer Mathematical Society
* Average Rating:
* Total Reviews:
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.
Readership
Undergraduates, graduate students, and research mathematicians interested in mathematics.
Table of Contents
Algebra and arithmetics
Arithmetic and combinatorics
* Can a number be approximately rational?
* Arithmetical properties of binomial coefficients
* On collecting like terms, on Euler, Gauss, and MacDonald, and on missed opportunities
Equations
* Equations of degree three and four
* Equations of degree five
* How many roots does a polynomial have?
* Chebyshev polynomials
* Geometry of equations
Geometry and topology
Envelopes and singularities
* Cusps
* Around four vertices
* Segments of equal areas
* On plane curves
Developable surfaces
* Paper sheet geometry
* Paper Möbius band
* More on paper folding
Straight lines
* Straight lines on curved surfaces
* Twenty-seven lines
* Web geometry
* The Crofton formula
Polyhedra
* Curvature and polyhedra
* Non-inscribable polyhedra
* Can one make a tetrahedron out of a cube?
* Impossible tilings
* Rigidity of polyhedra
* Flexible polyhedra
Two surprising topological constructions
* Alexander's horned sphere
* Cone eversion
On ellipses and ellipsoids
* Billiards in ellipses and geodesics on ellipsoids
* The Poncelet porism and other closure theorems
* Gravitational attraction of ellipsoids
* Solutions to selected exercises
* Bibliography
* Index
http://rapidshare.com/files/48188228/Mathematical.Omnibus-Thirty.Lectures.on.Classic.Mathematics.pdf
