Modern Mathematics: Proof, Sets, Logic, and Abstract Algebra

Catalog description

Prerequisite: one year of high-school or college calculus, with experience in methods and concepts from single- variable differential and integral calculus This course will begin with an exploration of advanced mathematical foundations, including logic, set theory, methods of proof, and properties of real numbers and functions. Each of these topics will bridge both theoretical mathematical structures and applications to a broad range of real-world problems. We will then build on the methods and concepts of pre-college algebra to analyze abstract systems that consist of mathematical objects (for example, numbers, functions, matrices, or permutations) and operations on them. By assuming a small number of basic properties—called axioms—of these systems, we will deduce other, more complex properties that can help us analyze a diverse number of abstract systems that, perhaps surprisingly, have common properties. Specific topics in abstract algebra will include groups, isomorphisms, symmetries, permutations, rings, and fields. Conference work may focus on any advanced topic relating to mathematics, including theoretical mathematical ideas or their applications to problems outside of mathematics. Spring portion may be repeated for credit, with instructor approval. Mathematics for Everyday Life: A Compassionate Approach