Abstract Algebra for Beginners Table of Contents Since the announcement that I will soon be releasing Abstract Algebra for Beginners, I’ve had several requests for more information about the book. I decided to post he table of contents, so that you can see exactly what topics will be covered in the book. Remember, to be added to the notification list, simply send an email to steve@SATPrepGet800.com with “Notify me” written in the subject line. Now, here is the full table of contents: Lesson 1 – Sets and Subsets Describing Sets Subsets and Proper subsets Basic Theorems Involving Subsets Power Sets Transitivity of the Subset Relation Equality of Sets Cartesian Products Basic Set Operations Properties of Unions and Intersections Arbitrary Unions and Intersections Problem Set 1 Lesson 2 – Algebraic Structures Binary Operations and Closure Semigroups and Associativity Monoids and Identity Groups and Inverses Rings and Distributivity Fields Vector Spaces Over Fields Modules Over Rings Problem Set 2 Lesson 3 – Relations and Partitions Binary Relations n-ary Relations Orderings Intervals Equivalence Relations Partitions The Ring of Integers Mod n Problem Set 3 Lesson 4 – Functions and Equinumerosity Functions Injections, Surjections, and Bijections Inverse Functions Composite Functions Identity Functions Images and Inverse Images Groups and Monoids of Functions Equinumerosity Countable and Uncountable Sets Problem Set 4 Lesson 5 – Number Systems and Induction The Natural Numbers Well Ordering and the Principle of Mathematical Induction The Integers The Rational Numbers The Real Numbers The Complex Numbers Exponential Form of a Complex Number Problem Set 5 Lesson 6 – Substructures Structures and Substructures Subspaces of Vector Spaces Substructures Generated by a Set Problem Set 6 Lesson 7 – Homomorphisms and Isomorphisms Homomorphisms Isomorphisms Linear Transformations Matrices The Matrix of a Linear Transformation Images and Kernels Normal Subgroups and Ring Ideals Problem Set 7 Lesson 8 – Number Theory Divisibility Prime Numbers The Division Algorithm GCD and LCM Problem Set 8 Lesson 9 – Number Theoretic Applications Cyclic Groups Modular Arithmetic Solving Linear Congruences Problem Set 9 Lesson 10 – Quotients Cosets Quotient Groups Quotient Rings Quotient Spaces Problem Set 10 Lesson 11 – Structure Theorems Isomorphism Theorems Fundamental Theorem of Finite Commutative Groups Problem Set 11 Lesson 12 – Permutations and Determinants Permutations on Finite Sets The Alternating Group Permutation Matrices Determinants Matrix Groups Problem Set 12 Lesson 13 – Sylow Theory Conjugacy Classes Groups of Prime Power Order Sylow Subgroups Group Actions Problem Set 13 Lesson 14 – Polynomials Polynomials Over a Ring Polynomials Over a Field The Division Algorithm for Polynomials Principal Ideal Domains Unique Factorization Domains Polynomial Functions Problem Set 14 Lesson 15 – Field Theory Field Extensions Algebraic Elements Field Extensions as Vector Spaces Splitting Fields Problem Set 15 Lesson 16 – Galois Theory Field Automorphisms The Galois Correspondence Solvability Problem Set 16 If you think your friends might be interested in this information, please share it with them on Facebook: Thank you all for your continued support! Comments comments