Algebra: A Computational Introduction by John Scherk
Algebra: A Computational Introduction - Table of Contents
- 1. Congruences and Modular Arithmetic
- 2. Permutations and Cycle Structure
- 3. Permutation Groups & Alternating Groups
- 4. Linear Groups and Matrix Representations
- 5. Groups, Homomorphisms & Isomorphisms
- 6. Subgroups, Lattices & Generators
- 7. Symmetry Groups and Geometric Isometries
- 8. Group Actions and Orbits
- 9. Counting Formulas and Burnside's Lemma
- 10. Cosets and Lagrange's Theorem
- 11. Sylow Subgroups and p-Groups
- 12. Simple Groups and Composition Series
- 13. Finitely Generated Abelian Groups
- 14. Polynomial Rings and Ideals
- 15. Symmetric Polynomials and Discriminants
- 16. Roots of Equations and Splitting Fields
- 17. Galois Groups and Automorphisms
- 18. Quartic Polynomials and Resolvents
- 19. General Equation of the nth Degree
- 20. Solution by Radicals & Solvability
- 21. Ruler-and-Compass Constructions
What You Will Learn in Algebra: A Computational Introduction
Algebra: A Computational Introduction by John Scherk is an authoritative, computationally grounded textbook published by CRC Press that provides undergraduate students with a concrete, algorithmic gateway into abstract group theory and Galois theory. This comprehensive volume guides readers through integer congruences, permutation cycle notation, general linear groups, subgroup structures, geometric symmetry groups, group action orbits, Burnside's counting lemma, coset partitions, Lagrange's theorem, Sylow p-subgroups, simple groups, finite abelian group decomposition, polynomial ring ideals, elementary symmetric polynomials, splitting field root analysis, Galois group computations, quartic equation solvability, Abel-Ruffini degree proofs, radical extensions, and classical ruler-and-compass geometric constructibility with exceptional clarity and logical precision.
Designed for undergraduate mathematics majors, computer science theorists, cryptography practitioners, and computational algebraists, this foundational text bridges concrete symbolic computation directly with abstract algebraic proof techniques. Scherk details step-by-step algorithmic approaches for calculating permutation products, determining Sylow subgroup counts, evaluating polynomial resultants, computing Galois groups of polynomials over rational fields, and verifying geometric constructibility limits. Whether you are studying cryptography background, preparing for graduate qualifying examinations in modern algebra, or implementing computer algebra software, this book offers an indispensable roadmap.
Recognized globally for its seamless blending of explicit computational examples alongside formal abstract proofs, it stands as one of the best introductory textbooks for mastering computational group theory and Galois theory. By connecting group actions directly to symmetric polynomials and radical solvability, it serves as an essential tool for learning computational abstract algebra with confidence.
Book Details & Specifications
Title:
Algebra: A Computational Introduction by John Scherk
Publisher:
Chapman and Hall
Year:
2000
Pages:
419
Type:
PDF
Language:
English
ISBN-10 #:
1584880643
ISBN-13 #:
9781584880646
License:
CC BY-NC-SA 2.5 CA
Amazon:
Amazon
About the Author: John Scherk
The author John Scherk
is Associate Professor Emeritus of Mathematics at the University of Toronto, Scarborough, widely respected for his research contributions to algebraic geometry, singularity theory, and computational approaches to abstract mathematics education.
Through Algebra: A Computational Introduction, Scherk delivers a clear, systematically structured presentation of modern group theory and polynomial field equations. His emphasis on explicit algorithmic calculations, concrete permutation examples, and accessible Galois theory derivations make this text a classic reference for computational algebra and group theory valued by students and educators worldwide.
Read or Downloadable Algebra: A Computational Introduction
Computational Algebra