Math 314, Spring 2023
Meeting times: T,Th from 12:00–1:15pm
Textbook: Stephen Abbott, Understanding Analysis 2nd ed
Lecture notes: Typed notes and Onenote class notes
Homework: Weekly exercises and Gradescope submission
Office hours: TBA, and by appointment
Real analysis is one of the core areas of modern mathematics. It the area of math that provides the foundations for introductory calculus. The course content is valuable for both aspiring math practitioners and future educators. This class will also focus on mathematical reasoning and problem solving, and the fundamentals of rigor 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 a key concept, the completeness of the real numbers. With an understanding of completeness, will be able to undertake a rigorous study of familiar concepts from calculus: limits, series, continuous functions, and of course derivatives and integrals. Our study of continuity will also take us on a short tour of the theory of topology—the abstract study of continuity and its properties.
Anticipated learning outcomes
- Appreciation of 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
- Possess and exhibit factual knowledge in content area
- Weeks 1-3: Chapter 1
- Weeks 4-7: Chapter 2
- Week 8: Midterm exam
- Weeks 9-11: Chapter 3
- Weeks 12-14: Chapters 4-7 selections
- Weeks 15-16: Review and final exam
The course will be delivered through synchronous remote class sessions. Each session will include a mixture of questions on previous material, discussion of new material, and an in-class activity.
Attendance, participation, and group activities 20%
You are expected to attend remote class sessions, and to be prepared to ask questions and discuss the material. Following the discussion, we will start a group activity, which will be submitted as a group. A portion of your grade will be based on your attendance, preparedness, attention, collaboration, and completion of these activities.
Homework assignments 40%
Homework will be assigned each week and collected the following week. Most exercises will be graded for both correcteness and mathematical style. Some will be graded for completeness only. You are encouraged to collaborate with your peers, and you are welcome to use online resources when you are stuck (please reference). But please keep in mind that you must always fully understand your solutions and most importantly write them in your own words.
Take-home exams 20% x2
Take-home exams will be given during the 8th week and the finals week of the class.