In Math 310 we will learn to reason clearly and precisely about the underlying foundations of calculus. We will learn about the topology of the real numbers, then define metric spaces, which are the setting in which all limits and calculus make sense. We will then use this to study limits of sequences and functions, continuity, derivatives, series, and integrals.
During the course, students will learn to make precise and rigorous arguments about real numbers, and clearly write and communicate these arguments.
The course syllabus is available here.
Course NotesComplete Notes
- Section 1: The Real Numbers
- Section 2: Metric Spaces
- Section 3: Special Types of Metric Spaces
- Section 4: Limits of Functions and Continuity
- Section 5: Integrals of Real Functions
- Section 6: Sequences of Functions
- Homework 1, due Friday September 7
- Homework 2, due Friday September 14
- Homework 3, due Friday September 21
- Homework 4, due Friday September 28
- Homework 5, due Wednesday October 3
- Homework 6, due Friday October 19
- Homework 7, due Friday October 26
- Homework 8, due Friday November 2
- Homework 9, due Monday, November 12
- Homework 10, due Monday, November 19
- Homework 11, due Monday, December 3
- Test 1 (Tentatively October 5)
- Test 2 (Tentatively Wednesday November 14)
- Final Exam (Friday, December 14 at 8:30 AM)
There is no mandatory textbook for this course. I will post complete lecture notes and homework assignments on this page, and you do not need to purchase a textbook.I will be using several textbooks as I prepare notes for this course.
- The primary reference I will be using is Introduction to Analysis by Maxwell Rosenlicht. It is available on Amazon for about $13.
- The secondary reference I will be using is Basic Analysis I by Jiří Lebl. It is available for free online. If you want a hard copy, you can get one from Amazon for $13. It is also available from Lulu, at a normal size for $13 or a larger size for $15.
There are a couple other books you may find it useful to reference from time to time, which are freely available online.
- Mathematical Analysis Volume I by Elias Zakon approaches the material from a somewhat more advanced perspective. You can find a free online copy here.
- How We Got from There to Here: A Story of Real Analysis by Robert Rogers and Eugene Boman provides a very different and more historical approach. I don't like it as much as a reference but it might give you a different way of thinking about much of the material. You can find a free online copy here.