## MATH 115 - Introductory Discrete Mathematics I

An introduction to discrete Mathematics, with emphasis on topics that are closely related to computer science. Core topics include Counting, Logic and Quantifiers, Set Theory, Formal Reasoning and Induction, Functions and Relations, Number Theory. Additional topics to be covered may be selected from Trees, Growth of Functions, Automata Theory and Formal Languages.

Hours: 45 (Lecture Hours: 45)

Total Weeks: 15

Prerequisites:
BC Pre-calculus 12 or equivalent

Non-Course Prerequisites:
None

Co-Requisites:
None

Course Content:
- Counting
- Logic and Quantifiers
- Set Theory
- Formal Reasoning and Induction
- Functions and Relations
- Number Theory
- Additional Topics Selected from Trees, Growth of Functions, Automata Theory and Formal Languages.

Learning Outcomes:
Upon completion of this course students will have demonstrated:
- Counting: Rules of Sum and Product; Permutations and Combinations.
- Propositional Logic: Propositional Logic; The Laws of Logic; Rules of Inference; Quantifiers and Methods of Formal Proofs.
- Naive set theory: Sets and Subsets; Set Operations and Laws; Counting and Venn Diagram; Principle of Inclusion and Exclusion.
- Formal Reasoning and Induction: Mathematical Induction; Recursion.
- Functions and Relations: Cartesian Product and Relations; One-to-One Functions; Onto Functions, Composition of Functions; Inverse Functions.
- Number Theory: Division Algorithm: Prime Numbers; Great Common Divisor: The Euclidean Algorithm; The Fundamental Theorem of Arithmetic.
- Additional topics selected from Trees; Growth of Functions; Automata Theory and Formal Languages.