Logical development, precise notation, and written exposition are stressed. Includes axiomatic developments, set and function theory, division algorithm, congruence, completeness, Archimedean Principle, denseness, and infinite sets. Three hours of lecture and two hours of laboratory. Introduces the theory and application of ordinary differential equations. Problems from the natural and physical sciences are analyzed.
Emphasis is placed on finding and interpreting solutions.
Topics selected from separable equations, linear equations, power series solutions, Laplace Transforms, and systems of linear equations. Mth 331 Introduction to Real Analysis 4 credits Studies the basic analytic structure of real numbers. Topics include sequences, continuity, uniform continuity, properties of functions on closed bounded sets, and an introduction to metric spaces. Mth 341 Introduction to Algebraic Systems 4 credits Abstract groups are presented to demonstrate the fundamental strategies used to study algebraic structures such as subsystems, morphisms, and quotient systems. Includes a brief overview of some alternate algebraic systems.