Math 504 Real Analysis (Graduate)
This course offers a rigorous study of the real numbers and associated functions in order to deepen students’ understanding of calculus and raise their ability to effectively formulate and communicate mathematics. It reviews concepts of real-valued functions defined on the real line and proceeds to extend these results as applicable to complex valued functions and metric spaces. It also includes a rigorous examination of properties of some important special functions.
Upon completion of this course, you should be able to:
- Analyze the construction and topology of the real line as a complete ordered field.
- Apply the concepts of convergence of sequences and series of numbers and functions.
- Determine the continuity, differentiability, and integrability of functions.
- Adapt concepts of real analysis to vector spaces.
- Compose solutions and rigorous proofs of results arising in real analysis.
- Examine God’s natural order in light of mathematical understanding (no graded assignments with this objective).
Prerequisite: A bachelor’s degree with a Mathematics major or must be state certified (in any state) to teach Mathematics at a secondary school level and show evidence of completing an undergraduate course in Introduction to Real Analysis with a minimum grade of “C.”
Prerequisite Courses: Undergraduate Real Analysis
Math 501 Linear Algebra (Summer II 2022 & Summer I 2023)
Math 502 Abstract Algebra (Summer I 2022 & Summer II 2023)
Math 503 Advanced Calculus (Winter/Spring I 2023)
Math 504 Real Analysis (Winter/Spring II 2022 & Winter/Spring II 2023)
Math 505 Statistical Methods I (Fall I 2022)
Math 506 Modern Geometry (Fall II 2022)