Description
Springer A Concrete Introduction To Higher Algebra 1995 Edition by L.N. Childs
This is an introduction to higher algebra for students with a background of a year of calculus. The book aims to give these students enough experience in the algebraic theory of the integers and polynomials to appreciate the basic concepts of abstract algebra. The main theoretical thread is to develop algebraic properties of the ring of integers: unique factorization into primes; congruences and congrunce classes; Fermat's theorem; the Chinese remainder theorem; and for the ring of polynomials. Concurrently with the theoretical development the book presents a broad variety of applications to cryptography error-correcting codes Latin squares tournaments techniques of integration and especially to elementary and computational number theory. Many of the recent advances in computational number theory are built on the mathematics which is presented in this book. Thus the book may be used as a first course in higher algebra as originally intended but may also serve as an introduction to modern computational number theory or to applied algebra. Table of contents : Unified General Relativity and Quantum Theory: Unified Symmetry: In the Small and in the Large; B.N. Kursunogammalu. Results from Quantum Cosmological Gravity; R.P. Woodard. The Very Early Universe: Baryogenesis from Electroweak Strings; M. Barriola. Reconstructing the Inflation Potential; E.W. Kolb et al. Beyond Potential Dominated Inflation; K. Freese J. Levin. Axitons; E.W. Kolb I. Tkachev. Power Spectrum of Cosmic String Perturbations on the Microwave Background; L. Perivolaropoulos. Progress in New and Old Ideas: Time Reversal for Spacetime and Internal Symmetry; E.C.G. Sudarshan. Superstring Fermion Vertex and Gauge Symmetry in Four Dimensions; L. Dolan. Massive String Status as Extreme; M.J. Duff J. Rahmfeld. Z' Diagnostics at Future Colliders; M. Cvetic. Aspects of Particle Physics: Siberian Snakes and Polarized Beams; L.G. Ratner. Polarized Lepton Experiments; D.G. Crabb. Progress in Neutrino Physics: A Survey of Experiments and Theory; S.L. Mintz M. Pourkaviani. Further Inspirations from the Electroweak Theory Supersymmetry Supergravity: Implications of Supersymmetric Grand Unification; V. Barger et al. Realistic Superstring Models; A.E. Faraggi. Flavor Mixing and the Generation of Mass; H. Fritzsch. Unification of Fundamental Interactions in Supersymmetry; P. Nath R. Arnowitt. Dynamical Problems of Baryogenesis; J.M. Cornwall. Conference Program. Index.