Life of Fred: Abstract Algebra

ISBN: 978-1-937032-64-7, hardback, 224 pages

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List of Topics Covered:

Binary operations.  Groupoids.  Semigroups.  The Generalized Associative law.  Monoids.  Groups with left and right inverses, right cancelation, permutations.  Symmetric groups.  Cayley's theorem.  Subgroups and the Subgroup test.  Eleven facts about Cosets.  Partitions.  Lagrange's theorem and the order of a group.  Normal groups.  Factor groups.  Three super functions: isomorphisms, homomorphisms, and automorphisms.  Simple groups.  Hamiltonian groups.  Sporadic groups.  The Monster Group.  Inner automorphisms.  Kernels.  Fundamental Isomorphism Theorem of Group Homomorphisms. Center of group.  Centralizers.  Normalizers.  Direct product of groups.  Cyclic groups.  Fundamental Theorem of Finite Abelian Groups.  Sylow's three theorems.  Cauchy's theorem.  Rings.  Subrings.  Centers.  Direct sums.  Ideals.  Quotient rings.  Polynomial rings.  Integral domains.  Norm functions.  Euclidean domains.  Unique factorization domains.  Fields.  Field extentions.  Fundamental Theorem of Field Theory.  Algebraic and Transcendental extensions.  Vector spaces.

The full 10-book Extra High School and College Math series includes:

1. Life of Fred: Logic
2. Life of Fred: Calculus Expanded Edition (freshman and sophomore year of college)
3. Life of Fred: Statistics Expanded Edition
4. Life of Fred: Life of Fred: Five Days of Upper Division Math: Set Theory, Modern Algebra, Abstract Arithmetic, Topology
5. Life of Fred: Abstract Algebra
6. Life of Fred: Linear Algebra Expanded Edition (junior year of college)
7. Life of Fred: Real Analysis
8. Life of Fred: Complex Analysis
9. Life of Fred: Numerical Analysis
10. Life of Fred: Metamathematics 

Life of Fred: Chemistry can also be read near the end of High-School or early College.