Math 63, Winter 2020

Real Analysis

General Information









Vladimir Chernov

Contact Information

Office: 304 Kemeny Hall

Telephone: (603) 646 2421



Course Meeting times: MWF 2:10-3:15 PM

(x-hour Thursday 1:20-2:10 PM)


Tentative Office Hours:

Monday 3:30-5 PM

Tuesday 2:30-4 PM

Friday 3:30-5 PM

and by appointment


105 Kemeny Hall

Text Book

W. Rudin: “Principles of Mathematical Analysis” 3rd edition

Course grade will be based on

Written Homework                        50 points

Midterm Exam                                100 points

Final Exam                                      150 points

Total                                              300 points


Late homework will not be accepted unless it is excused in advance for serious reasons. Unexcused late and missing homework counts zero.


* If requested, oral presentation of homework can be made in my office rather than in class; or even substituted to a written assignment with the student answering my questions on the written solution



ORC Description: This course introduces the basic concepts of real-variable theory. Topics include real numbers and cardinality of sets, sequences and series of real numbers, metric spaces, continuous functions, integration theory, sequences and series of functions, and polynomial approximation. Students may not take both MATH 35 and 63 for credit.


Prerequisites:  MATH 22 or MATH 24, or MATH 13 and permission of the instructor.


Exams: The take-home open-book Midterm Examination will be distributed on Wednesday January 29 and it will be due on Monday February 3 at class time. The take-home open-book Final Examination will be distributed on Friday March 6 and it will be due on Monday March 11 at noon. Do not make plans to leave Hanover before the end of the final exam week. The exams will not be given earlier to accommodate your travel plans.



Written homework will be assigned after each lecture. The written homework assignment can be found here. All homework  will generally be due at the class time on Wednesday following the week when it  was assigned, unless announced otherwise.

Late homework will not be accepted unless it is excused in advance for serious reasons. Unexcused late and missing papers count zero.

Honors Code: Colloboration on Homework is permitted and encouraged but NO COPYING. On the Exams  NO HELP given or received. In general, when in doubt, ask before doing.

Disabilities: Students with disabilities who may need disability-related academic adjustments and service for this course are encouraged to see me privately as early in the term as possible. Students requiring  disability-related academic adjustments and services must consult the Student Acessibility Service office (Carson Hall, Suite 125, 646-9900). Once SAS has authorized services, students must show the originally signed SAS Services and Consent Form and/or a letter on a SAS letterhead to their professor. As a first step, if students have question about whether they qualify to receive academic adjustments and services, they should contact the SAS office. All inquiries and discussions will remain confidential.


Mental Health: The academic environment at Dartmouth is challenging, our terms are intensive, and classes are not the only demanding part of your life. There are a number of resources available to you on campus to support your wellness, including your undergraduate dean ( ) and the Student Wellness Center ).


Student Religious Observances: Some students may wish to take part in religious observances that occur during this academic term. If you have a religious observance that conflicts with you participation in the course, please meet with me before the end of the second week of the term to discuss appropriate accommodations.