Syllabus

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Prerequisites

Multivariable Calculus (18.02); Differential Equations (18.03) or Honors Differential Equations (18.034)

Text

Amazon logo 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


ACTIVITIES PERCENTAGES
Ten Problem Sets 40%
Exam 1 15%
Exam 2 15%
Final Exam 30%

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