Description
Book SynopsisConsists 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.
Table of ContentsAlgebra 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.
