Math 341: Foundations of Analysis
Professor: Kiril Datchev
Section 407 CRN 26304
Lectures: Mondays, Wednesdays, and Fridays, 8:30 to 9:20 am, in UNIV 219.
Office hours: Mondays, Wednesdays, and Fridays, 10:30 to 11:30 am, Tuesdays 12 to 1 pm, or by appointment, in MATH 602.
Textbook: Introduction to Analysis by Arthur Mattuck. The first three chapters and Appendix A are available online. See also some online lists of corrections to the various printings, here, here, and here.
The topics we will cover include real numbers, sequences, series, continuous functions, differentiation, and Riemann integration.
Grading is based on
Almost weekly homework assignments, worth 20% of the total grade,
two in-class midterm exams, on Monday September 27th and Friday November 5th, worth 40% of the total grade,
a final exam, on Saturday December 18th, from 8 to 10 am in SMTH 118, worth 40% of the total grade.
Homework is due on paper at the beginning of class on Wednesdays. Here are the assignments:
Homework 1, due September 1st.
Homework 2, due September 8th.
Homework 3, due September 15th.
The first midterm will be in class on Monday, September 27th.
Homework 4, due October 6th.
Homework 5, due October 15th. Note the unusual day of the week.
Homework 6, due October 20th.
Homework 7, due October 27th. See also the proof of the chain rule from Rudin's Principles of Mathematical Analysis.
The second midterm will be in class on Friday, November 5th.
Homework 8, due November 17th.
Homework 9, due December 1st.
Review problems for the final.
Some extra examples to supplement the book.
Below are some books recommended for further reading.
Analysis by Its History, by E. Hairer and G. Wanner, presents the material of this class in historical context, with many beautiful computations and examples.
Principles of Mathematical Analysis, by Walter Rudin, presents the material of this class in a more modern and general context, and has been the definitive reference on the subject for a long time.
Finally, a list of general policies and procedures can be found here.