MATH 3161
Real Analysis
Spring 2018

This is the homepage for MATH 3161 (Real Analysis). This page will be updated throughout the term with important information for our course, including homework assignments, review materials, and more.


  • Solutions for your practice final have been posted.
  • A practice final exam and topics list for the final exam have been posted.
  • Assignment 9 (your last assignment!) has been posted and is due Friday, June 1st at 2:00 p.m., in my mailbox in Knudson Hall.
Course Information

Course meets every TR from 2:00 p.m. - 3:50 p.m. in Knudson 101.

Instructor: Ronnie Pavlov
Office: Knudson Hall 204
Office hours: Tuesday 10-11, Wednesday 9-10, Friday 1-2, or by appointment.

Graduate TA: Dennis Pace
Office: Knudson Hall 213
Office hours: Monday 3-5


Text: Understanding Real Analysis by Stephen Abbott, 2nd edition.

IMPORTANT: This book does have some typos/errors. Click this link for the current list of errata, and please notify me if you find any new ones!

This book is available at the DU Bookstore.

Course summary

Real analysis is concerned with properties of the set R of real numbers. These include properties of the numbers themselves (limits, sequences, series), the structure of R as a topological space (open and closed sets, compactness, connectedness), and the properties of functions on R (continuity, differentiation, integration).

In this course, we will cover Chapters 1-4 of Abbott, including least upper bounds, convergence of infinite sequences/series, open/closed/compact sets in R, and continuity. In the first couple of weeks, we will spend significant time on strengthening some fundamentals, in particular proof writing (techniques such as proofs by contradiction and proofs by induction) and familiarity with statements involving quantifiers. Further topics such as derivatives/integrals and uniform continuity/convergence are covered in MATH 3162 (Real Analysis 2).

Grading scheme

Your term grade will consist of written weekly homework assignments (which will mostly be taken from the text), short e-mail homework assignments (due most class days), one midterm exam, and one final exam, broken down in the following way.

30% Written homework
5% e-mail homework
30% Midterm exam
35% Final exam


You will have two types of homework for this course. One type will be standard written assignments, to be turned in at the BEGINNING of class on Tuesdays. Assignments turned in after the first 10 minutes of class will be counted as late, and subject to the usual late homework penalty scheme (described below.) These written assignments will be posted here at least one week in advance.

The second type of homework will be very short (shouldn't take longer than 15-20 minutes) e-mail assignments. These will be sent to you one day before every class (except for the first class day, midterm days, and a couple of other exceptions.) They can involve material we've covered, or extremely simple material from an upcoming section. They will very rarely (if ever) involve detailed proofs, and the solutions will usually consist of only a few sentences; the idea is to help with internalizing definitions and concepts so that class time will be more beneficial for you.

Late assignments will have a percentage subtracted according to the following policy:

2-3 days late: -50%
>3 days late: not accepted


You will have one midterm on Thursday, May 4th, and one final exam on Tuesday, June 5th. Both exams will be in our classroom during classtime. (2:00 p.m. - 3:50 p.m.)

Course Policies

Students in this course are expected to abide by the University of Denver’s Honor Code and the procedures put forth by the Office of Citizenship and Community Standards. Academic dishonesty - including, but not limited to, plagiarism and cheating - is in violation of the code and will result in a failing grade for the assignment or for the course. As student members of a community committed to academic integrity and honesty, it is your responsibility to become familiar with the DU Honor Code and its procedures: see

Students with Disabilities: If you qualify for academic accommodations because of a disability or medical issue, please submit a faculty letter to me from Disability Services Program (DSP) in a timely manner so that your needs may be addressed. DSP determines accommodations based on documented disabilities/medical issues. DSP is located on the 4th floor of Ruffatto Hall, 1999 E Evans Ave, 303-871-2278. Information is also available online at; see the Handbook for Students with Disabilities.

Religious Accommodations: University policy grants students excused absences from class or other organized activities for observance of religious holy days, unless the accommodation would create an undue hardship. Faculty are asked to be responsive to requests when students contact them in advance to request such an excused absence. Students are responsible for completing assignments given during their absence, but should be given an opportunity to make up work missed because of religious observance. Once a student has registered for a class, the student is expected to examine the course syllabus for potential conflicts with holy days and to notify the instructor by the end of the first week of classes of any conflicts that may require an absence (including any required additional preparation/travel time). The student is also expected to remind the faculty member in advance of the missed class, and to make arrangements in advance (with the faculty member) to make up any missed work or in-class material within a reasonable amount of time.