Jacob Bernstein






Math 605: Real Variables

Course Description

This is the introductory graduate course in real analysis. Topics covered in the course will include, measure theory, theory of integration, and the basic theory of Hilbert spaces.

Course Information

Lectures are Monday and Wednesday 12:00-1:15 pm in Krieger 304. There will be 10 weekly problem sets, they will count for 50% of your final grade. There will also be two in class exams which will (together) count for the other 50% of the final grade.

Lecturer office hours: Tuesday 1:30-3pm or by appointment, in Krieger 408.

TA: Cheng Zhang. Office hours: TBA


The course text is
  • Real Analysis by E. Stein and R. Shakarchi, Princeton Lectures in Analysis III, Princeton University Press, Edition: 2005

Problem Sets

Problem sets will be due in class on Wednesday (see below for the assignments). They will count for 50% of your final grade No late homework will be accepted.


There will be two in class exams. The exam you score higher on will count for 30% of your final score and the one you score lower on will count for 20%.

The dates of the exames are
First Exam: Wednesday, October 17.
Second Exam: Wednesday, December 5.

(Tentative) Schedule

Week 0-1 (8/30 & 9/5):

Read: Chapter 1
No homework due.

Week 2 (9/10 & 9/12):

Read: Chapter 1
Problem Set 1 due. Do: Exercises 1, 2, 4, 5, 6, 10 from Chapter 1.

Week 3 (9/17 & 9/19):

Read: Chapter 1
Problem Set 2 due. Do Exercises: 8, 13, 14, 16, 26 and Problem 5 (on page 48) from Chapter 1.

Week 4 (9/24 & 9/26):

Read: Chapter 2
Problem Set 3 due. Do Exercises: 22, 23, 28, 32, 33, 37 from Chapter 1.

Week 5 (10/1 & 10/3):

Read: Chapter 2
Problem Set 4 due. Do Exercises: 1, 6, 9, 10, 11 from Chapter 2.

Week 6 (10/8 & 10/10):

Read: Chapter 2
Problem Set 5 due. Do Exercises: 2, 8, 12, 15 from Chapter 2 and Problem: 3 from Chapter 2.

Week 7 (10/15 & 10/17): First Exam

Read: Chapter 3
No homework due.
First Exam.

Week 8: (10/22 & 3/24)

Read: Chapter 3
Problem Set 6 due.

Week 9 (10/29 & 10/31):

Read: Chapter 3
Problem Set 7 due.

Week 10 (11/5 & 11/7):

Read: Chapter 4
Problem Set 8 due.

Week 11 (11/12 & 11/14):

Read: Chapter 4
Problem Set 9 due.

Week 12: Thanksgiving Break

Enjoy your break.

Week 13 (11/26 & 11/28):

Read: Chapter 4
Problem Set 10 due.

Week 14 (12/3 & 12/5): Second Exam

No homework due.
Second Exam.

Students with disabilities

Students with documented disabilities or other special needs who require accommodation must register with Student Disability Services. After that, remind the instructor of the specific needs at least two weeks prior to each exam; the instructor must be provided with the official letter stating all the needs from Student Disability Services.

JHU ethics statement

The strength of the university depends on academic and personal integrity. In this course, you must be honest and truthful. Ethical violations include cheating on exams, plagiarism, reuse of assignments, improper use of the Internet and electronic devices, unauthorized collaboration, alteration of graded assignments, forgery and falsification, lying, facilitating academic dishonesty, and unfair competition.

Report any violations you witness to the instructor. You may consult the associate dean of students and/or the chairman of the Ethics Board beforehand. Read the "Statement on Ethics" at the Ethics Board website for more information.

If a student is found responsible through the Office of Student Conduct for academic dishonesty on a graded item in this course, the student will receive a score of zero for that assignment, and the final grade for the course will be further reduced by one letter grade.

Fall 2018 -- Department of Mathematics, Johns Hopkins University.