Consists of thirty lectures on diverse topics, covering much of the mathematical landscape. This title helps reader learn numerous results that often belong to neither the standard undergraduate nor graduate curriculum and discover connections between classical and contemporary ideas in algebra, combinatorics, geometry, and topology.
Consists of thirty lectures on diverse topics, covering much of the mathematical landscape. This title helps reader learn numerous results that often belong to neither the standard undergraduate nor graduate curriculum and discover connections between classical and contemporary ideas in algebra, combinatorics, geometry, and topology.
Product Details
Hardcover
English
American Mathematical Society
Oct. 30th, 2007
463
9780821843161
9.80 x 10.31 x 1.14 inches
0821843168
2.17 lbs
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 Mobius 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
Table of Contents provided by Publisher. All Rights Reserved.
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