Math 411 - Mathematical Analysis I
Description
Math 411 is the first course in the honors analysis sequence, 411/412. 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.
411 is not an equivalent course to 311; the two courses cover some similar topics but with key differences. 411 does analysis more abstractly, often in the setting of metric spaces or Euclidean space in any number of dimensions, while 311 is focused on analysis along the real line.
Topics covered
Topics usually covered in Math 411 include:
- Systems of numbers, especially the real number system
- Topology of metric spaces
- Sequences and convergence in metric spaces
- Series of real numbers
- Continuity in metric spaces
- Differentiation over the real line
- Derivatives of higher order and Taylor’s theorem
- Riemann–Stieltjes integral
Note that the exact list of topics may vary by instructor and semester. Additional topics may include construction of number systems.
Comments on prerequisites
Unofficial/suggested additional prerequisites: Math 311.
While not explicitly included as a prerequisite on the WebReg system, it is unlikely that you will be granted special permission for 411 without previously taking 311 with good performance (typically an A, though a B+ could be permissible in some cases). Historically, some students have received approval to take 411 without 311 (often by completing some unofficial summer work roughly equivalent to 311), but with changes in the Honors Advisor this pathway to 411 is no longer reliable.
Resources
Textbook
The usual textbook for the class is Principles of Mathematical Analysis by Walter Rudin.
Additional materials
Lecture notes from when the course was last taught by Mariusz Mirek may be found online at https://mathanalysis.org/411H/. Lecture notes are also available on a course webpage from when the course was taught by Kristen Hendricks in Fall 2024 at https://sites.math.rutgers.edu/~kh754/Math411.html.