Abstract Algebra

NOTE EDITORE

Abstract Algebra: A Gentle Introduction advantages a trend in mathematics textbook publishing towards smaller, less expensive and brief introductions to primary courses. The authors move away from the ‘everything for everyone’ approach so common in textbooks. Instead, they provide the reader with coverage of numerous algebraic topics to cover the most important areas of abstract algebra. Through a careful selection of topics, supported by interesting applications, the authors Intend the book to be used for a one-semester course in abstract algebra. It is suitable for an introductory course in for mathematics majors. The text is also very suitable for education majors who need to have an introduction to the topic. As textbooks go through various editions and authors employ the suggestions of numerous well-intentioned reviewers, these book become larger and larger and subsequently more expensive. This book is meant to counter that process. Here students are given a "gentle introduction," meant to provide enough for a course, yet also enough to encourage them toward future study of the topic. Features Groups before rings approach Interesting modern applications Appendix includes mathematical induction, the well-ordering principle, sets, functions, permutations, matrices, and complex nubers. Numerous exercises at the end of each section Chapter "Hint and Partial Solutions" offers built in solutions manual

SOMMARIO

Elementary Number Theory Divisibility Primes and factorization Congruences Solving congruences Theorems of Fermat and Euler RSA cryptosystem Groups Definition of a group Examples of groups Subgroups Cosets and Lagrange's Theorem Rings Definition of a ring Subrings and ideals Ring homomorphisms Integral domains Fields Definition and basic properties of a field Finite Fields Number of elements in a finite field How to construct finite fields Properties of finite fields Polynomials over finite fields Permutation polynomials Applications Orthogonal latin squares Die/Hellman key exchange Vector Spaces De nition and examples Basic properties of vector spaces Subspaces Polynomials Basics Unique factorization Polynomials over the real and complex numbers Root formulas Linear Codes Basics Hamming codes Encoding Decoding Further study Exercises Appendix Mathematical induction Well-ordering Principle Sets Functions Permutations Matrices Complex numbers Hints and Partial Solutions to Selected Exercises

AUTORE

Gary Mullen is Professor of Mathematics, The Pennsylvania State University, where he earned his Ph.D. His main interest is finite fields, and is founder of the journal "Finite Fields and Their Introduction." He is also the Editor of The Handbook of Finite Fields published by CRC Press. James Sellers is Professor and Associate Head for Undergraduate Mathematics, The Pennsylvania State University, where he also earned his Ph.D. He has published many research articles and won awards related to his efforts to advance mathematics education.

ALTRE INFORMAZIONI

• Condizione: Nuovo
• ISBN: 9781482250060
• Collana: Textbooks in Mathematics
• Dimensioni: 9 x 6 in Ø 1.00 lb
• Formato: Copertina rigida
• Illustration Notes: 24 tables
• Pagine Arabe: 214