Math 1d: Series
Course Information: A Quick Summary
- Instructor: Padraic Bartlett.
- Class Time/Location: MW 9-10am, Sloan 153.
- Office Hours: Sunday 9-10pm, the 3rd-floor lounge in Sloan; MW, after class; by appointment.
- Homework due date: Monday 4pm, in the Math 1d dropbox on the second floor of Sloan, a week after the HW is posted.
- Email: padraic at caltech dot edu.
- TA: Daiqi Linghu.
- TA Office Hours/Location: 5-6pm Friday, Sloan 382; by appointment.
- TA email: dlinghu at caltech dot edu.
Course Description:
Math 1d is a course on 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 (hopefully) encounter some open research questions in mathematics along the way.
Based on survey results, our course will focus on a breadth of applications and topics, omitting some rigor in favor of covering as many examples and as much material as we can get to.
A syllabus for the course is available here.
Course Policies:
Grades: Math 1d is a pass-fail 5-unit course. Grades will be based on your performance on weekly HW sets, posted on or before Monday each week and due by 4pm the following Monday. Specifically, each problem set will feature between 5-7 problems, of which you will be asked to choose 3-4 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.
At the end of the quarter, your lowest 2 HW scores will be dropped, and the remaining 5 sets will be averaged together. Accordingly, because the lowest HW scores are dropped, our late policy is fairly strict: late HW 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 2: Sequences.
- Week 3: Series of positive numbers.
- Week 4: General series; pointwise and uniform convergence.
- Week 5: Power series and Fourier series.
- Week 6: Taylor series.
- Week 7: Complex numbers.
- Week 8: Generating functions and dice.
Homework:
- Week 2: Sequences.
- Week 3: Series of positive numbers.
- Week 4: General series; pointwise and uniform convergence.
- Week 5: Power series and Fourier series.
- Week 6: Taylor series.
- Week 7: Complex numbers.
- Week 8: Generating functions and dice.