Course Goals: To begin to indoctrinate students to the reasoning, language, and practice involved in higher-level mathematics.
Course Objectives:
- Develop a foundation of set theory concepts and notation
- Explore a variety of various mathematical structures by focusing on mathematical objects, operations, and resulting properties
- Develop formal logical reasoning techniques and notation
- Demonstrate the application of logic to analyzing and writing proofs
- Develop techniques for counting, permutations and combinations
- Develop the concept of relation through various representations (digraphs, matrices, lists)
Student Learning Outcomes: Students will be able to:
- Demonstrate a proficient understanding and ability to use basic concepts and notation of sets.
- Establish properties and identities of mathematical structures.
- Determine the truth value of compound statements
- Demonstrate simple proofs using standard rules of inference: direct, indirect, contradiction, and induction
- Demonstrate correct application of algorithms for counting permutation and combination for given contexts.
- Solve recurrence relations
- Determine properties of an abstract relation (reflexive, irreflexive, symmetric, etc) and establish equivalence relations.