College Maths I

General Overview An introduction to various mathematical concepts. This course covers such topics as sets, logic, functions, and mathematical systems. 1 Sets I: A study of sets, symbols, roster and set builder notation in defining sets, with emphasis on identifying sets. 2 Sets II: A further study of sets: power sets, disjoint sets, intersection and union, relative complements of a set, and unary and binary operations. 3 Sets III and Logic I: A completion of sets: (infinite sets) and an introduction to logic, defining statements, and quantifiers. 4 Logic II: Defining the truth as a statement, using a Venn diagram, identifying logically true statements, and logically false statements. 5 Logic III: Another study of logical reasoning: conditional statements, biconditionals, variations on the conditional, and tautologies. 6 Deductive Reasoning: An introduction to deductive reasoning: the validity of arguments, theorems, indirect proofs, and invalid arguments. 7 Relations and Functions: A study in relations and functions, with ways of representing functions, inverses, and special functions. 8 Compositions of Functions and Binary Operations: A study of the composition of functions and binary operations. 9 Groups: A study of groups: definitions, proving theorems about groups, subgroups, and group generators. 10 From Groups to Fields: A further study of the isomorphisms of groups, rings and subrings, and integral domains and fields.

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