An important objective of the course is mastery of the reasoning characteristic of abstract mathematics. Required for the major in mathematics. This course is a continuation of the study of algebraic systems begun in MATH 375. Among the topics covered are rings, fields, principal ideal domains, unique factorization domains, Euclidean domains, field extensions, and finite fields. The latter portion of the course emphasizes applications of group, ring, and field theory drawn from such areas as error-correcting codes, exact computing, crystallography, integer programming, cryptography, and combinatorics.
Topics covered include propositional and sentential logic, logical proofs, and models of theories.
Examples are drawn mainly from mathematics, but the ability to deal with abstract concepts and their formalizations is beneficial. This course covers the fundamentals of point set topology, starting from axioms that define a topological space. Some topics from algebraic topology, such as the fundamental group, might also be introduced. Prerequisite MATH 331 or permission of the instructor. This course presents a careful study of various concepts of analysis.