Course Description The course includes concepts and applications of discrete mathematical structures as opposed to continuous mathematics studied in algebra and calculus. The topics presented in the course focus on Logic: propositional equivalences, predicates, sets, set operations, functions. Algorithms: integers and division, search algorithms. Coding theory: congruence, Euclidian algorithms, RSA method. Method of proof: mathematical induction, recursive definition, statement and connectives, logical equivalence. Basics of counting: permutations and combination. Relations and their properties: representing relations, equivalence relations, recurrence relations, generating functions. Graphs and trees: representing graphs, isomorphism, connectivity, Euler and Hamilton paths and circuits, trees, tree traversals, search algorithms, binary search. Combinatorial circuits: logical gates2. Section 1 Commentary: Write a half page (maximum) on the key concepts that you picked up up until the end of week 5 of the course. and how you feel about the competence you have gained in these topics. .3. Section 2 Self Reection: a) In 5-3 sentences. identify and describe the significant factors that have impacted your learning due to your experience in the course. b) In 6-3 sentences. discuss what smprised you with the realization of obtaining this new knowledge or improved your understanding of applying these concepts to your intellectual [scholarly] development. c) In 6-3 sentences. discuss how you could integrate and apply these insights into your educational. professional practice or both. Introduction to combinatorial problems and techniques Critical path analysis: PERT Combinatorial analysis Week 1 Sets, relations and functions Ch. 1 + Class notes Set operations Equivalence relations Sets, relations and functions Functions Week 2 Mathematical induction Ch. 2 Due- Challenge project-1 Mathematical Induction Coding theory O Week 3 Introduction Ch. 3 Due Resubmission-Challenge project-1 Due-Assignment-1 Coding theory Congruence O Euclidian algorithm Week 4 Ch. 3 Ciphering with the RSA methodWeek 5 Coding theory O Deciphering with the RSA methodo Error detecting and error correcting codes Graphs o Graphs and their representations: adjacent matrix and list, isomorphism o Paths and circuits o Euler path and circuit o Hamiltonian path and circuit