Math 314 syllabus
Meeting times: T,Th from 9:00–10:15pm
Meeting place: MB 139
Textbook: Stephen Abbott, Understanding analysis, 2nd edition
My office: MB 238-B
Office hours: Monday 10:30–11:30, Thursday 1–2, and by appointment
Real analysis is one of the core areas of modern mathematics. It is also the subject that provides the foundations for introductory calculus. It is important for aspiring math practitioners and educators alike to become familiar with real analysis. In this class we will also be exposed to rigorous mathematical thinking, reasoning, problem solving, and proof.
We will begin by discussing a simple but surprisingly deep question: what are real numbers? The answer to this question will lead us to the key concept of completeness. And with this concept in hand, will be able to undertake a rigorous study of the most familiar concepts from calculus: limits, series, continuity, and derivatives. (Sadly we will not have much time for integration.) Our study of continuity will take us on a short tour of the theory of topology—the study of abstract spaces where, like on the real line, continuity makes sense.
Anticipated learning outcomes
- Appreciation for beauty in abstract concepts
- Fluency in the language of mathematics
- Comfort with mathematical discovery in content area
- Write rigorous and readable proofs in content area
- Weeks 1–3: Chapter 1, 8.6
- Weeks 4–7: Chapter 2
- Weeks 8–10: Chapter 3
- Weeks 11–13: Chapter 4
- Weeks 14–15: Chapter 5, 8.2
- Exam 1 25%
- Exam 2 25%
- Exam 3 (non-cumulative final) 25%
- Daily prep and classwork 5%
- Homework 20%
Tentative exam dates
- Exam 1: Thursday, February 14
- Exam 2: Thursday, March 28
- Exam 3: Tuesday, May 7 from 9:30–11:30am
Daily prep and classwork
Reading will be assigned prior to each class. You are expected to arrive prepared to ask questions and discuss the material. All homework assignments will be started in-class as group work. Daily participation and collaboration are required. A small discretionary portion of your grade will be based on your attendance, attention, and collaboration.
All homework assignments will be started as in-class group work, which will take place following the daily lecture. Your written solutions will be turned in the following Tuesday. All work will be evaluated for completeness, and certain items will be evaluated for correcteness and mathematical style. You are encouraged to collaborate with your peers inside and outside of class, and you are free to use online resources when you are stuck. But please keep in mind that you must always fully understand your solutions and most importantly write them in your own words.