Glynn Mathematics Seminar II

(4 Credit Hours) · Undergraduate

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 topics will vary each semester, but each year we 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. To start out the first semester 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. As the first semester continues and on into the second, we will focus on particular mathematical topics. These will vary somewhat from year to year, but the following are good examples: number theory, symmetry and group theory, topology of surfaces, notions of infinity, counting and combinatorics.