Sets and Subsets, Set Operations and the Laws of Set Theory, Counting and Venn Diagrams, A First Word on Probability, Countable and Uncountable Sets
Basic Connectives and Truth Tables, Logic Equivalence – The Laws of Logic, Logical Implication – Rules ofInference; The Use of Quantifiers, Quantifiers, Definitions and the Proofs of Theorems
Mathematical Induction, The Well Ordering Principle – Mathematical Induction, Recursive Definitions
Cartesian Products and Relations, Functions – Plain and One-to-One, Onto Functions – Stirling Numbers of theSecond Kind, Special Functions, The Pigeon-hole Principle, Function Composition and Inverse Functions;Properties of Relations, Computer Recognition – Zero-One Matrices and Directed Graphs, Partial Orders –Hasse Diagrams, Equivalence Relations and Partitions
Definitions, Examples, and Elementary Properties, Homomorphisms, Isomorphisms, and Cyclic Groups, Cosets,and Lagrange’s TheoremElements of Coding Theory, The Hamming Metric, The Parity Check, and Generator Matrices
Decoding with Coset Leaders, Hamming MatricesThe Ring Structure – Definition and Examples, Ring Properties and Substructures, The Integers Modulo n