Lecture Notes for MAT 236.00 - Elementary Abstract Algebra at Illinois State (ILSTU)

Notes Information

Material Type:Study Guide
Class:MAT 236.00 - Elementary Abstract Algebra
University:Illinois State University
Term:Fall 2003
  • Contrapositive
  • Identity Function
  • Definitions
  • Contradiction
  • Homework Problems
  • Generalized
  • Isomorphism
  • Trigonometric
  • Binary Operations
  • Cartesian Product
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Math 236 – Elementary Abstract Algebra Review for Test 1 Test 1 will consist in 4 problems and 2-3 theoretical questions (one for extra credit). Review the theory for each section, including the proofs for the theorems listed, and homework problems. 1.1 Logic and proof - Statements and non-statements; logic operations, truth tables; equivalence - Converse, contrapositive, negation; - Quantifiers, negating predicates - Structure of theorems (hypothesis, conclusion, proof); - Types of proofs: direct, indirect (contrapositive, by contradiction) 1.2 Sets - What is a set? (x∈S true or false), operations with sets (union, intersection, difference, Cartesian product); - Graphical representation (Venn diagrams) - Properties of operations: distributivity; - Families and collections of sets (Ex. partitions) 1.3 Real and complex numbers - Binary operations; R and C; closure relative + and x; order; subsets of reals - Rules for +,x on R and C: commutativity, associativity, distributivity; zero and unit; opposite and ...

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