MA 441 - Intro to Mathematical Analysis
This course introduces students to the fundamentals of mathematical analysis at an adequate level of rigor. Topics include fundamental mathematical logic and set theory, the real number systems, sequences, limits and completeness, elements of topology, continuity, derivatives and related theorems, Taylor expansions, the Riemann integral, and the Fundamental Theorem of Calculus.
Prerequisites: MA 227
MA441 and MA442 are capstone courses for mathematics majors. The two courses supply basic preparation for either graduate school or for application of mathematics to problems of science and engineering.
There are a number of different approaches to this course. The exact content of the course is not as important as the development of mathematical maturity by the students. Accordingly course outcomes are based on Bloom’s taxonomy.
- Know: Recall definitions and statements of theorems.
- Comprehend: Be able explain and restate theorems and definitions in different contexts and as they apply to special cases.
- Apply: Use the theorems and techniques taught in the course to solve problems.
- Analyze: Recognize which theorems and definitions apply to various situations.
- Synthesize: Be able to construct proofs.
The outcomes are repeated for each of the three major divisions of the course, namely
- Properties of the real numbers;
- Sequences, series, continuity;
- Differentiation and integration.
Thus there are altogether fifteen course outcomes.
Walter Rudin, Principles of Mathematical Analysis
John O’Connor, A First Analysis Course
Frank Morgan, Real Analysis