| ACTIVITIES | PERCENTAGES |
|---|---|
| Ten Problem Sets | 40% |
| Exam 1 | 15% |
| Exam 2 | 15% |
| Final Exam | 30% |
Table of Contents
Syllabus
Syllabus
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Prerequisites
Multivariable Calculus (18.02); Differential Equations (18.03) or Honors Differential Equations (18.034)
Text
Rudin, W. Principles of Mathematical Analysis. 3rd ed. McGraw-Hill Science/Engineering/Math, New York, NY: McGraw-Hill, 1976. ISBN: 007054235X.
Assignments
Weekly homework is due each Friday at 3 PM. Late homework will not be accepted, but the lowest score will be dropped.
Exams
There will be two midterms and a final exam.
Grading
Calendar
| WEEK # | TOPICS | KEY DATES |
|---|---|---|
| 1 | Sets and Fields, The Real Numbers | |
| 2 | Countability, Metric Spaces | Problem set 1 due |
| 3 | Closed Sets, Compact Spaces | Problem set 2 due |
| 4 | Compact Subsets of Euclidean Space | Problem set 3 due |
| 5 | Completeness, Sequences and Series | Problem set 4 due |
| 6 | Continuity | |
| Exam 1 | ||
| 7 | Continuity and Compactness | Problem set 5 due |
| 8 | Differentiability, Mean Value Theorem | Problem set 6 due |
| 9 | Taylor Series, Riemann-Stieltjes Integral | Problem set 7 due |
| 10 | Integrability, Fundamental Theorem of Calculus | Problem set 8 due |
| 11 | Sequences of Functions | |
| Exam 2 | ||
| 12 | Uniform Convergence | |
| 13 | Uniform Convergence, Equicontinuity | Problem set 9 due |
| 14 | Power Series, Fundamental Theorem of Algebra | Problem set 10 due |
| 15 | Final Review | |
| Final Exam |