Math 108b: Classical Analysis

Instructor: Anton Gorodetski
Office: 282 Sloan
Phone: 395-4350
E-mail: asgor@caltech.edu
Office Hours: Friday, 12-1 p.m., and by appointment.
 

Teaching Assistants: Anna Maltsev and Dmitry Pavlov
Office:  Sloan 155 (Anna), Sloan 158 (Dmitry)
E-mail: amaltsev@caltech.edu, dmitry@caltech.edu
Office Hours: Friday, 4pm - 5pm (Anna), Sunday, 7pm-8pm (Dmitry)

The second term of Ma 108 covers a wide assortment of topics in real analysis:

• Integration. The Riemann integral. The Riemann-Stieltjes integral.
• Lebesgue measure. Measurable functions. The Lebesgue integral.
• The L^p spaces.
• The Hibert spaces.
• Introduction to Fourier series.
• Ergodic Theorem and applications.

Prerequisites: Calculus of one variable, Ma 108a or its equivalent.

Main texts:

• N.L.Carothers, Real Analysis (Required).
• W. Rudin, Principles of Mathematical Analysis. Third edition (Recommended).

Additional references will be given for a few topics not covered by these books.

Grading: Weekly homework 50%, midterm exam 10%, final exam 40%.

Collaboration Policy: You may discuss homework problems with other students, but solutions should be written up individually in your own words. Take-home exams must be your own work.

Homework

• Homework #1                                                                   
• Homework #2                
• Homework #3                
• Midterm                         
• Homework #4                
• Homework #5                
• Homework #6                
• Homework #7                
• Final                                Solutions
• COURSE   SURVEY  (Please complete this survey and return them with the final exam; place surveys only in bottom slot outside of 255 Sloan.)
• Final exam survey (Please send the answers to me by e-mail or just put in my mail box)