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 This course covers the mathematical foundations of computer science and engineering. It provides an introduction to elementary concepts in mathematics such as definitions, logic, proofs, functions, relations and counting principles. The course also introduces students to elementary discrete structures such as sets, partial orders, graphs and trees.  Prerequisites: – Introduction to Set Theory 2

Topic Week Logic, Truth Table, Propositional equivalences1,2 Predicates and Quantifiers3 Sets and Functions4 Relations, Equivalences and Partial Orders5,6 Proofs: Induction, Contradiction, Contrapositives7,8,9 Counting Principles: Cardinality, factorials, permutations, Binomial coefficients, Inclusion-Exclusion, Pigeon-Hole Principle, sums and asymptotics 10,11,1 2 Graphs and Trees: Representation, degree sequences and hand shaking lemma, Euler tours, Planar graphs, Euler Formula. Properties of Tree, Spanning Trees 13,14 3

 Weekly Hours: 3 x 50 mins lectures, 0 lab hours  Textbook/References: Discrete Mathematics and Its Applications, 4th Edition, By Kenneth Rosen Invitation to Discrete Mathematics, 2nd Edition, By Jiri Matousek and Jaroslav Nesetril  Assessment Methods: Homework: 20% Quizzes: 10% Midterm: 30% Final: 40% 4

 Course Learning Outcomes (CLOs):  Be able to analyze complexity of algorithms  Be able to apply number theory to practical problems  Be able to synthesize elementary proofs  Be able to apply concepts of graph theory and trees to solve real world problems 5

 Relationship between CLOs and Student Outcomes: 6

 Relationship of Course to ABET Student Outcomes : 7