and Outline -- Indefinite Inner Products -- Orthogonalization and Orthogonal Polynomials -- Classes of Linear Transformations -- Canonical Forms -- Real H-Selfadjoint Matrices -- Functions of H-Selfadjoint Matrices -- H-Normal Matrices -- General Perturbations. Stability of Diagonalizable Matrices -- Definite Invariant Subspaces -- Differential Equations of First Order -- Matrix Polynomials -- …
to MuPAD -- Mathematical graphics with MuPAD -- to calculus of one variable -- Multivariable calculus -- Algebra with MuPAD -- Data visualization and elementary statistics -- A brief introduction to programming.The world of mathematics is probably one of the most fascinating creations of mankind. The world of mathematics with a Computer Algebra System, like MuPAD, is even more fascinating. With…
Free Resolutions and Hilbert Functions -- First Examples of Free Resolutions -- Points in ?2 -- Castelnuovo-Mumford Regularity -- The Regularity of Projective Curves -- Linear Series and 1-Generic Matrices -- Linear Complexes and the Linear Syzygy Theorem -- Curves of High Degree -- Clifford Index and Canonical Embedding.Algebraic Geometry often seems very abstract, but in fact it is full of co…
Beauville surfaces without real structures -- Couniformization of curves over number fields -- On the V-filtration of -modules -- Hecke orbits on Siegel modular varieties -- Ax-Kochen-Eršov Theorems for p-adic integrals and motivic integration -- Nested sets and Jeffrey-Kirwan residues -- Counting extensions of function fields with bounded discriminant and specified Galois group -- Classical a…
Basic Tensor Algebra -- Tensor Spaces -- to Tensors -- Homogeneous Tensors -- Change-of-basis in Tensor Spaces -- Homogeneous Tensor Algebra: Tensor Homomorphisms -- Special Tensors -- Symmetric Homogeneous Tensors: Tensor Algebras -- Anti-symmetric Homogeneous Tensors, Tensor and Inner Product Algebras -- Pseudotensors; Modular, Relative or Weighted Tensors -- Exterior Algebras -- Exterior Alg…
Straightedge and compass -- Euclid’s approach to geometry -- Coordinates -- Vectors and Euclidean spaces -- Perspective -- Projective planes -- Transformations -- Non-Euclidean geometry.For two millennia the right way to teach geometry was the Euclidean approach, and in many respects, this is still the case. But in the 1950s the cry "Down with triangles!" was heard in France and new geometry …
Field extensions -- Roots -- Galois theory -- A bit of group theory -- Applications -- Algebraic theory of differential equations.This unique textbook focuses on the structure of fields and is intended for a second course in abstract algebra. Besides providing proofs of the transcendance of pi and e, the book includes material on differential Galois groups and a proof of Hilbert's irreducibilit…
Infinite Galois Theory and Profinite Groups -- Valuations and Linear Disjointness -- Algebraic Function Fields of One Variable -- The Riemann Hypothesis for Function Fields -- Plane Curves -- The Chebotarev Density Theorem -- Ultraproducts -- Decision Procedures -- Algebraically Closed Fields -- Elements of Algebraic Geometry -- Pseudo Algebraically Closed Fields -- Hilbertian Fields -- The Cla…
A Fundamental Theorem -- Topics in Algebra -- Some Quadratic Problems -- The Genus of an Algebraic Curve -- Miscellany."... The exposition is not only clear, it is friendly, philosophical, and considerate even to the most naive or inexperienced reader. And it proves that the philosophical orientation of an author really can make a big difference. The mathematical content is intensely classical.…
Unary algebras and dualisability -- Binary homomorphisms and natural dualities -- The complexity of dualisability: three-element unary algebras -- Full and strong dualisability: three-element unary algebras -- Dualisability and algebraic constructions -- Dualisability and clones -- Inherent dualisability.Natural duality theory is one of the major growth areas within general algebra. This text p…