Introduction
This course provides an introduction to real analysis. The principles behind the real number system will be introduced. Sequences and series of numbers will then be discussed, and theorems presented to analyze their convergence properties.
The course will then proceed to mathematically define notions of continuity and differentiability of functions. Convergence of power series will be discussed. Time permitting, topics in metric spaces and integration will be covered. Throughout the course, the use of rigorous mathematical proof will be emphasized.
Course information
- Lecturer
- Chris H. Rycroft, chr@math.berkeley.edu. Offices: Evans 1083 (510-642-3523) and LBNL 50E-1520 (510-495-2857).
- Lectures
- Monday, Wednesday & Friday, 4pm–5pm in Evans 2
- Office hours
- Monday 5pm–6pm, Wednesday 2pm–4pm in Evans 1083
- Textbook
- Elementary Analysis: The Theory of Calculus, by Kenneth A. Ross
- Additional reading
-
Principles of Mathematical Analysis, by Walter Rudin
Real Mathematical Analysis, by Charles Pugh
Basic Analysis: Introduction to Real Analysis, by Jiří Lebl - Homework
- In general, there will be weekly homework posted on the course web page, which will be due in each Friday of class. Collaboration on the homework is encouraged, but each student must write solutions in his/her own words, and not copy them from anyone else. A random selection of the assigned homework will be graded. Homework solutions will be published on this web page. The homework will be graded on a scale from 0 to 10 points. Late homework will not be accepted, but the two lowest scores will be dropped when computing the grade.
- Midterms
- There will be two 50 minute in-class midterm exams, scheduled for Friday 2/24 and Wednesday 3/21 between 4:10pm–5pm. There will be no homework due on the weeks of the midterms. The final exam will be on Friday, May 11 between 8am–11am in Evans room 60. The exams are “closed book” – no textbooks, notebooks, or calculators allowed.
- Grade corrections
- The grades for exams will be changed only if there is a clear error on the part of the grader, such as adding up marks incorrectly. Problems must be brought to the attention of the lecturer immediately after the exams are returned.
- Grades
- The final grade will be based on homework
assignments (20%), midterm 1 (20%), midterm 2 (20%), and the final exam
(40%). The final exam score will override any lower midterm score.
Explicitly, this means that grades will be computed with the following
formula:
- Incomplete grades
- Incomplete “I” grades are almost never given. The only justification is a documented serious medical problem or genuine personal/family emergency. Falling behind in this course or problems with workload in other courses are not acceptable reasons.
- Special arrangements
- If you are a student with a disability registered by the Disabled Student Services (DSS) on UCB campus and if you require special arrangements during exams, you must provide the DSS document and make arrangements via email or office hours at least 10 days prior to each exam, explaining your circumstances and what special arrangements need to be done. Also, see the lecturer as soon as possible to make arrangements for the homeworks.