The Integers -- Groups -- Rings -- Polynomials -- Vector Spaces and Modules -- Some Linear Groups -- Field Theory -- Finite Fields -- The Real and Complex Numbers -- Sets.Undergraduate Algebra is a text for the standard undergraduate algebra course. It concentrates on the basic structures and results of algebra, discussing groups, rings, modules, fields, polynomials, finite fields, Galois Theor…
Plane Algebraic Curves -- Ane Algebraic Curves -- Projective Algebraic Curves -- The Coordinate Ring of an Algebraic Curve and the Intersections of Two Curves -- Rational Functions on Algebraic Curves -- Intersection Multiplicity and Intersection Cycle of Two Curves -- Regular and Singular Points of Algebraic Curves. Tangents -- More on Intersection Theory. Applications -- Rational Maps. Parame…
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…
Results in Relativistic Quantum Mechanics -- The Construction of Fields -- Canonical Quantization -- Commutators and Propagators -- Interactions and the S-matrix -- The Electromagnetic Field -- Examples of Scattering Processes -- Functional Integral Representations -- Renormalization -- Gauge Theories -- Symmetry -- Spontaneous symmetry breaking -- Anomalies I -- Elements of differential geomet…