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 of Inference
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 the Second 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 Theorem. Coding Theory and Rings: Elements of Coding Theory, The Hamming Metric, The Parity Check, and Generator Matrices
Decoding with Coset Leaders, Hamming Matrices Rings and Modular Arithmetic: The Ring Structure – Definition and Examples, Ring Properties and Substructures, The Integers Modulo n