Course Meeting Times
Lectures: 2 sessions/week, 1.5 hours/session
Prerequisites
Description
This course gives an introduction to analysis, and the goal is twofold:
- To learn how to prove mathematical theorems in analysis and how to write proofs.
- To prove theorems in calculus in a rigorous way.
The course will start with real numbers, limits, convergence, series and continuity. We will continue on with metric spaces, differentiation and Riemann integrals. After that, we will move on to differential equations.
Textbooks
Main Textbook
Brian S. Thomson, Judith B. Bruckner, and Andrew M. Bruckner. 2008. Elementary Real Analysis. 2nd ed. ISBN: 9781434843678
A screen-optimized PDF version of the textbook is available.
A print-optimized PDF version of the textbook is available.
Other Textbook
Rudin, Walter. 1976. Principles of Mathematical Analysis (International Series in Pure and Applied Mathematics). 3rd ed. McGraw-Hill. ISBN: 9780070542358
The latest edition is the 1976 third edition. It’s not available to purchase as an ebook, but it has been digitized by the Internet Archive. You can access the book by creating a free personal Internet Archive account. You can then log in and borrow the book (for one hour at a time, looks like).
Requirements
Problem Sets
The problem sets will be assigned weekly. They should be submitted on Tuesdays by 4 PM online. The graded assignments will be returned the following Tuesday. The lowest problem set grade will be dropped. We are planning on having ten sets of homework.
Exams
There will be one in-class midterm. We will have an honesty pledge on the first page to help with academic integrity. You may not use a computer or a textbook for the midterm or final, but you are allowed to bring one page of notes. The final exam will be three hours.
Collaboration
Collaboration on homework is very much encouraged. However, no collaboration on the midterm or final is allowed. Also, even though collaboration on homework is encouraged, everyone should hand in their own personal sets of homework.
Grading
The course grade will be determined as follows:
- Problem sets (50%)
- 1.5-hour midterm exam (20%)
- 3-hour final exam (30%)
