Math 361K (Introduction to Real Analysis), IBL (Inquiry-Based Learning) section, Fall 2011

This is the main page for section 55380 of Math 361K.

Inquiry-Based Learning

This is a special section, which will be organized differently from a standard lecture-based course. The basic principle is that you will discover the basic precepts of real analysis. So in a typical class meeting you will be working among yourselves in groups to solve the day's problems, presenting proofs on the blackboard and critiquing them, and both asking and answering questions. My main role, and that of the teaching assistant, will be to provide overall direction and guidance.


Broadly speaking, the goal is to cover: basic properties of the real numbers; sequences of real numbers, their convergence, and completeness of the real numbers; limits of functions; continuity and uniform continuity of real-valued functions in one variable; differentiation of real-valued functions in one variable; integration of real-valued functions in one variable. The treatment will be fully rigorous and proof-based. The syllabus and schedule are necessarily extremely tentative, since in an IBL course a lot of what we do will depend on the particular tastes and predilections of the class. Nevertheless, a rough plan follows (to be updated throughout the semester):


I am Andrew (Andy) Neitzke. You can contact me at My office hours are Tuesday 5:00-6:30p and Wednesday 4:00-5:00p, in RLM 9.134.

Teaching assistant

Our teaching assistant is Alice Mark. You can contact her at Her office hours are Monday 5:30-6:30p, Thursday 5:00-6:00p and Friday 4:00-5:00p, in RLM 13.150.


Class meetings are Tuesday and Thursday, from 9:30a-11:00a, in RLM 6.126. Excluding Thanksgiving and the 1 midterm exam (see below) this gives a total of 27 meetings.


An important feature of IBL is that you should not consult a standard real analysis textbook, nor any Internet resources; the idea is to struggle with the material yourselves rather than just reading the answers somewhere.

A special text has therefore been developed for this course, which contains some of the basic definitions and helpful advice, but leaves most of the real work to you.

I will post this text in sections here as we go:


The course grade will be determined based on class participation (30%), homework (40%) and exams (30%). It will be assigned using the +/- system.


There will be one in-class midterm exam (on Thu Oct 13) and a final exam. Here is a practice midterm. Here is the final exam.


Homework will be assigned during most class meetings, due at the following meeting. Most of the homework problems will ask you to prove statements given in the text. Not every problem will be graded, but we will grade as many as practicable. Working together on the homework is strongly encouraged, but you must write out your own solutions individually, and you must not use any resources other than your classmates, the text, or us.

Here is a list of assignments so far:


A Web forum for the course is hosted on the department's Moodle server, here.


The University of Texas at Austin provides upon request appropriate academic accommodations for qualified students with disabilities. For more information, contact the Office of the Dean of Students at 471-6259, 471-4641 TTY.