Intro to Abstract Algebra by Paul Garrett
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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 :-
This book has following details information.
Title:
Intro to Abstract Algebra by Paul Garrett by NA
Publisher:
Paul Garrett
Series:
eBookDirectory
Year:
1998
Pages:
200
Type:
PDF
Language:
English
ISBN-10 #:
1584886897
ISBN-13 #:
978-1584886891
Country:
Pakistan
License:
N\A
Get this book from Amazon
About Author :-
The author NA
NA
Book Contents :-
conver the following topics.
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
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