MATH 3161
Real Analysis
Spring 2015

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 to your practice final have been posted below.
  • A practice final exam has been posted below; bring questions about it for Wednesday!
  • Solutions for Assignment 7 have been posted below.
Course Information

Course meets every MW from 2:00 p.m. - 3:50 p.m. in the basement of scenic Aspen Hall.

Instructor: Ronnie Pavlov
Office: Aspen Hall 715C
Phone: (303)-871-4001
Office hours: Wednesday 4-5, Thursday 1-2, or by appointment.

Graduate TA: Dennis Pace
Office: Aspen Hall 715
Office hours: Monday 4:15 - 5:15, Thursday 11-12, Friday 11-12.


Text: Understanding Real Analysis by Stephen Abbott.

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).

We will spend most of the term on Chapters 1-4 of Abbott, along with material on uniform convergence (section 6.2) and Riemann integration (7.2, 7.3, 7.6) if time permits. 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. Though Chapters 5 and 6 contain very important material, due to time constraints we will need to skip the vast majority of them.

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 a midterm April 27th and a final exam on June 1st. 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