Topics include numerical solutions of systems of linear equations, curve fitting, interpolation, numerical integration, solution of algebraic equations, and error analysis. The analysis sequence begins with the application of the infinitary methods of set theory to construct the uncountable continuum of real numbers, and then shows how the basic principles of calculus can be logically unfolded from a set-theoretic understanding of the continuum. MTH 286 MTH 432 Algebra II Algebra is the study of all possible sets of elements and all possible structure-preserving transformations between these sets. Topics include axioms of set theory, ordinals, transfinite induction, the universe of sets, cardinal arithmetic, large cardinals, and independence results. This course is an introduction to recent developments in foundational areas that have provided important new insights into the structure of the foundation of mathematics.
Specific topics covered in the course vary from year to year.
Students study topologies and their properties of separation, connectedness and compactness, topological mappings, and the fundamental group of a topological space.