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
Grading criteria.
| ACTIVITIES |
PERCENTAGES |
| Ten Problem Sets |
40% |
| Exam 1 |
15%
|
| Exam 2 |
15%
|
| Final Exam |
30% |
Calendar
Course 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 |
|