Math 504: Real Analysis

Course Information

Professor: Kiril Datchev
Lectures: Mondays, Wednesdays, and Fridays, 11:30 to 12:20, in UNIV 101.
Office hours: Wednesdays 1:30 to 2:30, Thursdays 2:00 to 3:30, or by appointment, in MATH 602.
Problem Session: Thursdays 9:30 to 10:20 in REC 103, run by our TA Alison Rosenblum.
TA Office hours: Wednesdays 10:30 to 11:30 in MATH G144, starting 8/31.

Textbook: Principles of Mathematical Analysis, Third Edition, by Walter Rudin. See also these notes on the text by George Bergman.

We will cover the following topics: Completeness of the real number system, basic topological properties, compactness, sequences and series, absolute convergence of series, rearrangement of series, properties of continuous functions, the Riemann–Stieltjes integral, sequences and series of functions, uniform convergence, the Stone–Weierstrass Theorem, equicontinuity, the Arzelà–Ascoli Theorem.

Grading is based on
  • Almost weekly homework assignments, worth 1/3 of the total grade,
  • two in-class midterm exams, on dates to be announced, worth 1/3 of the total grade,
  • a final exam, as scheduled here, worth 1/3 of the total grade.

  • Homework

    Homework is due on paper at the beginning of class on Fridays. Here are the assignments:

    Homework 1, due September 2nd.
    Homework 2, due September 9th.
    Homework 3, due September 16th.
    The first midterm will be in class on Monday September 26th.
    Homework 4, due October 7th.
    Homework 5, due October 14th.
    Homework 6, due October 21st.
    The second midterm will be in class on Monday October 31st.
    Homework 7, due November 11th.
    Homework 8, due November 18th.
    Homework 9, due December 2nd.
    The final exam will be on December 13th, as scheduled here.

    Additional Resources

    Below are some books recommended for further reading.

    Introduction to Analysis by Arthur Mattuck is a gentler beginning analysis book, with more examples, computations, and motivation, but does not go as far.

    Analysis by Its History, by E. Hairer and G. Wanner, presents the basic material of this class in historical context, with even better examples, computations, and motivation.

    The properties of sets and numbers taken for granted in our course are examined in The Structure of the Real Number System by Leon W. Cohen and Gertrude Ehrlich. For those interested in getting to the bottom of things, a good starting point is The Foundations of Arithmetic by Gottlob Frege.

    Finally, a list of general policies and procedures can be found here.