Math 10450: Glynn Mathematics Seminar – Fall 2021
Course Description: Mathematics is not about numbers and formulas, but about pattern and structures. According to Galileo, God wrote the world in the language of mathematics. In this course we will encounter the world of real mathematics with a particular focus on mathematical reasoning. This is not just being able to understand or prove theorems, but a general approach to framing, analyzing, and solving problems of many types. The ultimate goal is to think critically about the world, to question your assumptions, and master the power of logical deduction. The course will include set theory and the beginning of logic: logical connectives, truth tables, Venn diagrams, argument forms, soundness, validity, inductive and deductive arguments, translating natural language arguments, conditional statements, logical fallacies, syllogisms. You will develop the ability to construct, write, and explain mathematical proofs of various sorts: direct proofs, proofs by contradiction, mathematical induction, case analysis, and counterexamples.