Intro to Abstract Algebra by Paul Garrett
About this book :-
This textbook is best for advanced undergraduate or graduate students. It presents abstract algebra concepts in a more accessible way by focusing on examples and narratives rather than heavy symbolism. The book covers topics like number theory, polynomials, finite fields, and linear algebra. It also introduces advanced subjects such as cyclotomic polynomials, Galois theory, and basic complex analysis. Beyond standard topics like Lagrange's and Sylow's theorems, it delves into areas such as cyclotomic polynomials, Galois theory, and basic complex analysis. The book also focuses on broader background, including brief but representative discussions of naive set theory and equivalents of the axiom of choice, quadratic reciprocity, Dirichlet's theorem on primes in arithmetic progressions, and some basic complex analysis. Numerous worked examples and exercises throughout facilitate a thorough understanding of the material.
Book Detail :-
Title:
Intro to Abstract Algebra by Paul Garrett
Publisher:
Paul Garrett
Year:
1998
Pages:
200
Type:
PDF
Language:
English
ISBN-10 #:
1584886897
ISBN-13 #:
978-1584886891
License:
Linked Content Owned by Author
Amazon:
Amazon
About Author :-
The author
Paul Garrett
is a Professor in The department of School of Mathematics. at the University of Minnesota. Prof. Paul Garrett received his PhD in Nuclear Physics from McMaster University in 1993. He joined the Atomic and Nuclear Physics Group at the University of Fribourg, Switzerland, for his first post-doctoral position. He held a Staff Physicist position within the N-Division of Lawrence Livermore National Laboratory from 1998 to 2005. In 2004, he joined the Department of Physics at the University of Guelph as an Associate Professor, and in 2009 he was promoted to Professor.
Book Contents :-
1. Basic Algebra of Polynomials
2. Induction and the Well-ordering Principle
3. Sets
4. Some counting principles
5. The Integers
6. Unique factorization into primes
7. Prime Numbers
8. Sun Ze's Theorem
9. Good algorithm for exponentiation
10. Fermat's Little Theorem
11. Euler's Theorem, Primitive Roots, Exponents, Roots
12. Public-Key Ciphers
13. Pseudoprimes and Primality Tests
14. Vectors and matrices
15. Motions in two and three dimensions
16. Permutations and Symmetric Groups
17. Groups: Lagrange's Theorem, Euler's Theorem
18. Rings and Fields: de nitions and rst examples
19. Cyclotomic polynomials
20. Primitive roots
21. Group Homomorphisms
22. Cyclic Groups
23. Carmichael numbers and witnesses
24. More on groups
25. Finite elds
26. Linear Congruences
27. Systems of Linear Congruences
28. Abstract Sun Ze Theorem
29. The Hamiltonian Quaternions
30. More about rings
31. Tables
Similar
Abstract Algebra (Introduction)
Books