Life of Fred Mathematics

Life of Fred: Abstract Algebra

• 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 extensions
• Fundamental Theorem of Field Theory
• Algebraic and Transcendental extensions
• Vector spaces

Unlike most other Abstract Algebra programs, this one also has:
• Fortune Cookies
• Palm Trees
• Duck comes back.
• The Wildflower Theory
• Alligator, cow, fish, bird, goat, mouse, rhino, and sheep
• Alexander the Great and Don Quixote

Click here to view a sample lesson (Opens in a new window or tab)

Life of Fred Abstract Algebra is a hardcover textbook containing 224 pages. This book is not consumable. All answers are written on separate paper or in a notebook.

Life of Fred Abstract Algebra contains 21 chapters. All answers are included.