Math 8: Problem Solving in Calculus
Course Information: A Quick Summary
- Instructor: Padraic Bartlett.
- Class Time/Location: TTh 7:30-9pm, 107 Downs.
- Office Hours: Sunday 9-10pm, Sloan 156; by appointment.
- Email: padraic at caltech dot edu.
Course Description:
Math 8 is a problem-solving methods in calculus course, designed to support Math 1a. Where Math 1a is (by design!) a highly abstract course, Math 8 will have a much more interactive approach to proofs and calculus, focusing on lots of well-chosen examples. Lectures will cover everything from the art and language of mathematical proof to the nitty-gritty of set theory, Taylor series, epsilon-delta proofs and roots of unity; this course's aim is to illustrate the techniques and beauty of mathematical thinking through hundreds of examples.
Students who are new to the concept of formal proofs or who are otherwise concerned with meeting the levels of rigor in Math 1a are encouraged to attend.
Course Policies:
- Grades: Math 8 is a pass-fail 3-unit course, graded entirely on attendance. Registered students are required to attend at least 3/4 of the lectures to pass the course. Absences are excused only if they are accompanied by a note from the Deans or from the Student Health Center; make-up work for missed classes is not available. (Relatedly: the student health center is remarkably friendly! Don't hesitate to go to them if you do get sick.)
- Unregistered Students: If you're unregistered for Math 8, you are still more than welcome to attend whichever lectures you can make it to, send me emails, and go to office hours! More students are always welcome.
Textbooks:
- This course does not have a textbook. If you're looking for interesting mathematical texts on proofs and calculus, however, I would recommend the following two texts:
- Mathematical Thinking: Problem Solving and Proofs, by John P. D'Angelo and Doug West. A fantastic introduction to the world of proof-based mathematics; well-written and full of interesting problems.
- Calculus, by Michael Spivak. Contains some of the best mathematical exposition that I've ever read. Also, a ton of excellent problems.
Lecture Notes:
- Week 1: The art and technique of proof.
- Week 2: Sequences.
- Week 3: Series.
- Week 4: Limits and continuity.
- Week 5: Differentiation.
- Week 5: Midterm review notes(definitions).
- Week 5: Midterm review notes(examples).
- Week 6: Integration.
- Week 7: Integration techniques.
- Week 8: Assorted calculus tricks.
- Week 9: Taylor series.
- Week 10: Complex numbers and power series.
- Week 10: Practice final.
- Week 10: Practice final: solutions.