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### Abstract Algebra by Irena Swanson

MathSchoolinternational.com contain houndreds of Free Math e-Books. Which cover almost all topics of mathematics. To see an extisive list of Abstract Algebra eBooks . We hope mathematician or person who’s interested in mathematics like these books.

Abstract Algebra written by Irena Swanson . This is an other great mathematics book cover the following topics of Problem Solving.

• Definition and examples
• What follows immediately from the definition
• Bijections
• Commutativity
• Frequent groups and groups with names
• Group generators
• Subgroups
• Plane groups
• Orders of groups and elements
• One-generated subgroups
• The Euler φ function – an aside
• Permutation groups
• Group homomorphisms
• Group isomorphisms
• Group actions
• Cosets and Lagrange’s Theorem
• RSA public key encryption scheme
• Stabilizers, orbits
• Centralizer and the class equation
• External direct products/sums
• Normal subgroups
• Factor (or quotient) groups
• The internal direct product
• The isomorphism theorems
• Fundamental Theorem of Finite Abelian Groups
• Sandpile groups
• Rings
• Some unsurprising definitions
• Something new: ideals
• More that’s new: characteristic of a ring
• Quotient (or factor) rings
• (Integral) Domains
• Prime ideals and maximal ideals
• Division algorithm in polynomial rings
• Irreducibility
• Unique factorization domains
• Monomial orderings (all in exercises)
• Modules
• Finitely generated modules over principal ideal domains
• The Chinese Remainder Theorem
• Fields
• Splitting fields
• Derivatives in algebra (optional)
• Finite fields
• Appendix: Euclidean algorithm for integers
• Work out the RSA algorithm another time
• Appendix: Going overboard with factoring of X3
• ##### Math Books ABSTRACT ALGEBRA

Algebra by Michael Artin
• Free
• English
• PDF
• Page 634

• Algebra (2nd Edition) by Michael Artin
• Free
• English
• PDF 111
• Page 559

• A First Course on Abstract Algebra by John B. Fraleigh
• Free
• English
• Page 523

• Abstract Algebra by Joseph A Gallian
• Free
• English
• PDF 48
• Page 664

• Notes on Algebra by Donu Arapura
• Free
• English
• PDF 89
• Page 77

• Abstract Algebra by Robert B Ash by Robert B. Ash
• Free
• English
• PDF (Chapter wise) 71
• Page 200

• Abstract Algebra Lecture Notes by Dr David R Wilkins
• Free
• English
• PDF (chapter wise) 64
• Page 150

• Fields and Galois Theory by J.S. Milne
• Free
• English
• PDF 57
• Page 138

• Abstract Algebra by Irena Swanson
• Free
• English
• PDF 50
• Page 102

• Intro Abstract Algebra by Paul Garrett
• Free
• English
• PDF 49
• Page 200

• A History of Abstract Algebra by Jeremy Gray
• Free
• English
• PDF 38
• Page 412
##### SHORTCUT TRICKS (Division)
• Divisible by 2 Shortcut trick
• Divisible by 3 Shortcut trick
• Divisible by 4 Shortcut trick
• Divisible by 5 Shortcut trick
• Divisible by 6 Shortcut trick
• Divisible by 7 Shortcut trick
• Divisible by 8 Shortcut trick
• Divisible by 9 Shortcut trick
• Divisible by 10 Shortcut trick