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Upper division (junior/senior) pure math is much different than calculus. No "word problems," no formulas to memorize, no concrete applications – just puzzles to solve. Instead of learning procedures, students create definitions, theorems, and …
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.
All answers are included in the textbook.
Technical Data
Cover
Hardcover Textbook
Number of Pages
244
Colour Content
Black and White
Reproducible
No
Number of Lessons
Answer Key
Included
Biblical Content
Occasional references - accepted by many USA Public and Charter schools.
