Math 311 - Introduction to Mathematical Analysis
Description
Math 311 is the introductory mathematical analysis class at Rutgers. Taking the course is required of all mathematics majors in order to satisfy the major’s analysis requirement, except in the case where permission to take a higher-level analysis course without having taken 311 previously was granted. Analysis studies many of the topics seen in a calculus course as well as related concepts, but in a more general and rigorous fashion; at its essence, it is about the rigorous study of approximation.
Topics covered
Topics usually covered in 311 usually include:
- Construction of the real numbers
- Topology of the real line (open and closed sets, connectedness, compactness)
- Sequences, series, and convergence
- Limits
- Continuity
- Derivatives
The topics and theorems in this class are typically presented and proven in a single dimension (i.e. over the real numbers)
Note that the exact list of topics may vary by instructor and semester. Additional topics may include the Riemann and Darboux integrals.
Resources
Textbook
Possible textbooks for the class include Understanding Analysis (2nd edition) by Stephen Abbott and Introduction to Analysis (5th edition) by Edward D. Gaughan. For honors sections, the book by Abbott is consistently used.
Additional materials
A course webpage from when an honors section of the course was taught by Kristen Hendricks in Spring 2021 may be found at https://sites.math.rutgers.edu/~kh754/Math311H.html. A sample syllabus, midterm, and final exam can also be found on the page with official information on 311, linked at the start of this page.