Math 8 is a problem-solving methods course, meant to supplement Math 1a. While Math 1a is (by design!) a highly abstract course, Math 8 will be a more interactive, concrete approach to mathematical proofs and (single-variable) calculus.

Course Policies

Ma 8 is a 3-unit pass-fail course, graded entirely on attendance. Registered students must 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 Dean's Office or from the Student Health Center; make-up work for missed classes is not available.

You can attend the lectures, office hours, or send me emails even if you are not officially registered for the course.

Textbooks

There is no required textbook for the course. However, I recommend the following two books: Mathematical Thinking: Problem Solving and Proofs by John P. D'Angelo and Doug West and Calculus by Michael Spivak. They are fantastic introductions to proof-based mathematics and calculus; not only are they exceptionally well-written, they contain many interesting exercises.

Announcements

• The first session will take place on October 1st in Sloan 151.

Lecture Notes

• Week 1: Proofs and proof techniques.
• Week 2: Sequences.
• Week 3: Series, power series, limits and continuity.
• Week 4: Big O and little o notation, differentiation, the mean value theorem.
• Week 5: Midterm practice problems.
• Week 6: Integration, C^k functions, Newton's method.
• Week 7: Fundamental Theorem of Calculus, Taylor Series and approximations.
• Week 8: Optimization, critical points and extrema, convex functions.
• Week 9: Complex numbers.
• Week 10: Final review questions.

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