Algebra: A Computational Introduction by John Scherk
Algebra: A Computational Introduction - Table of Contents
Part-I Introduction to Groups
1. Congruences
2. Permutations
3. Permutation Groups
4. Linear Groups
5. Groups
6. Subgroups
7. Symmetry Groups
8. Group Actions
9. Counting Formulas
10. Cosets
11. Sylow Subgroups
12. Simple Groups
13. Abelian Groups
Part-II Solving Equations
14. Polynomial Rings
15. Symmetric Polynomials
16. Roots of Equations
17. Galois Groups
18. Quartics
19. The General Equation of the nth Degree
20. Solution by Radicals
21. Ruler-and-Compass Constructions
What You Will Learn in Algebra: A Computational Introduction
"Algebra: A Computational Introduction" is a practical textbook that teaches "computational algebra" with an emphasis on hands-on problem solving. Instead of focusing only on abstract proofs, the book introduces algebraic structures through explicit calculations and algorithms. Students learn how algebra works in practice by working with concrete examples and computational techniques.
Key topics include "groups", "rings", "fields", and "polynomial arithmetic", explained in a way that connects theory with computation. The book demonstrates how algebraic ideas are applied in areas such as cryptography and symbolic computation. By blending classical algebra with computational methods, it helps learners build intuition and practical problem-solving skills.
Overall, John Scherk’s textbook is ideal for students who want a modern and application-oriented introduction to algebra. It bridges the gap between abstract mathematics and computation, making complex ideas accessible and useful for further study in mathematics and computer science.
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 Professor at Department of Computer and Mathematical Sciences, Department of Mathematics. University of Toronto Scarborough, University of Toronto. He is known for his work in "algebra" and computational approaches to mathematics. His research focuses on making algebraic ideas practical through "computational methods" and structured problem solving. He has contributed to academic understanding of algebra and its applications in science and technology. He authored Algebra: A Computational Introduction, which explains algebra using a computational perspective. The book helps students grasp "algorithmic thinking", algebraic structures, and real-world applications. It is useful for learners seeking a practical introduction to modern algebra and mathematical computation.
Read or Downloadable Algebra: A Computational Introduction
Computational Algebra