Fundamentals of Logic: Basic Connectives and Truth Tables, LogicalEquivalence, Logical Implication, Use of Quantifiers, Definitions and the Proof of Theorems.
Set Theory: Set and Subsets, Set Operations, and the Laws of Set theory,Counting and Venn Diagrams. Properties of the Integers: The well – ordering principle, Recursivedefinitions, the division algorithms, fundamental theorem of arithmetic.
Relations and Functions: Cartesian Product, Functions onto Functions,Special Functions, Pigeonhole Principle, Composition and Inverse Functions, Computational Complexity. Relations: Partial Orders, Equivalence Relations and Partitions. Principle of Inclusion and Exclusion: Principles of Inclusion and Exclusion,Generalization of Principle, Derangements, Rock Polynomials, Arrangements with Forbidden Positions.
Generating Functions: Introductory examples, definition and examplePartitions of Integers, exponential generating function, summation operator. Recurrence Relations: First – order linear recurrence relation, second – orderlinear homogenous recurrence relation with constant coefficients, Non homogenous recurrence relation, divide and conquer algorithms.
Algebraic Structures: Algebraic System – General Properties, semi groups,Monoids, homomorphism, Groups, Residue arithmetic, group codes and their applications.