MATH 440 - Math Structures and Proofs

4 Credits
This course serves as a bridge from lower level undergraduate mathematics courses (calculus sequence, differential equations, linear algebra) which concentrate on applications to the upper level proof-based courses (especially Real Analysis, Algebraic Structures) which concentrate on concepts and the writing of proofs. In particular, it models, motivates and leads the student through the writing of proofs involving sets, functions, concepts of abstract algebra (equivalence relations, modulo arithmetic, groups), concepts of real analysis (limit, continuity, sequences), and the infinite.

Prerequisite(s): MATH 215
Course Learning Outcomes:
1. Solve problems requiring creativity and critical thinking involving numbers, sets, functions, equivalence relations, groups, limits, continuity, sequences, and the infinite.
2. Communicate mathematical ideas in written and oral form using mathematical symbols and terms and proper grammatical structure.
3. Construct mathematical proofs including direct proofs, contrapositives, proofs by contradiction, and inductive proofs.
4. Find flaws in alleged proofs and construct counterexamples.