Math 1d: Sequences and Series
Course Information: A Quick Summary
- Instructor: Padraic Bartlett.
- Class Time/Location: TTh 9-10am, Sloan 151.
- Office Hours: M, 2-3pm, T, 8-9pm; additional hours by appointment.
- Homework post date: Monday 4pm, biweekly (i.e. weeks 2,4,6,7.)
- Homework due date: Wednesday 4pm, in the Math 1d dropbox on the second floor of Sloan, a week and two days after the HW is posted (i.e. weeks 3,5,7,8.)
- Email: padraic at caltech dot edu.
Course Description:
Math 1d is a seven-week course on sequences and series for students previously enrolled in Math 1a, section 1. The main focus of this course is covering the Ma1a material omitted by your run of section 1; along the way, however, we'll see previews of the material you will see in ACM95/Ma2 , discuss the applications of series to fields as varied as CS, EE and Ph, and (maybe) encounter some open research questions in mathematics along the way. Our course will focus on a breadth of applications and topics, omitting some rigor in favor of covering more material.
Course Policies:
Grades: Math 1d is a pass-fail 5-unit course. Grades will be based on your performance on four biweekly HW sets. They will be posted by 4pm Monday on weeks 2,4,6 and 7, and be due by 4pm the Wednesday a week and two days from that time. Each problem set will feature between 5-8 problems, broken into two categories: (a) 1-3 non-collaboration problems, which you solve by yourself, and (b) 3-5 collaboration problems, which you can solve with your peers and ask detailed questions about in office hours. One quirk of the problem sets is that they will often list many problems, and allow you to choose a subset of these problems to solve: this structure is designed to allow students who prefer more or less rigor in their problems to pick questions that are closer to their own preferences.
Each student is allowed at most one late HW; notification that it will be late must be received before the HW itself is due, and its extension can be for at most a week. Extensions longer than a week or multiple extensions are excused only if they are accompanied by a note from the Deans or from the Student Health Center. (Relatedly: the student health center is remarkably friendly! Don't hesitate to go to them if you do get sick.)
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: Sequences of numbers.
- Week 2: Series of positive numbers.
- Week 3: Series of negative numbers; sequences of functions.
- Week 4: Series of functions; power series.
- Weeks 5-6: Taylor series.
- Week 7: Complex-valued series.
- Week 7: A Mathematica workbook for the Fourier series lecture.
Homework:
- Set 1: Sequences and series of positive numbers. Due Wednesday, January 23.
- Set 2: Sequences and series of functions. Due Wednesday, February 6.
- Set 3: Taylor series. Due Wednesday, February 20.
- Set 4: Fourier series and complex power series. Due Wednesday, February 27.