TEXT: Walter Rudin, Principles of Mathematical Analysis, 3rd Ed., McGraw-Hill, 1976, 007054235X.

COURSE DESCRIPTION:

This course introduces the student to a rigorous development of the real number system and the theory of Calculus on the real number line. Topics include: basic set theory, the real number system, sequences and series, limits and continuity, the derivative, the Riemann Integral, the Fundamental Theorem of Calculus, and sequences and series of functions.

PREREQUISITES: Modern Algebra ( MAT381 or equivalent).

TOPICS:

1. Introduction: N, Z, R, C (Ch. 1)
   • Fields, Orderings, Completeness
2. Basic Topology (Ch. 2)
   • Metric Spaces
   • Compact Sets, Connected Sets
3. Numerical Sequences and Series (Ch. 3)
   • Convergent Sequences and Cauchy Sequences
4. Continuity (Ch. 4)
   • Limits of Functions
   • Continuity and Compactness, Continuity and Connectedness
5. Differentiation and Integration (Ch. 5, 6)
   • Riemann-Stieltjes Integral
6. Sequences and Series of Functions (Ch. 7)
   • Uniform Convergence
7. Selected Topics (Time Permitting)
   • Integration of Differential Forms
   • Lebesgue Integral, Functional Analysis, Hilbert Spaces, Banach Spaces

OFFICE HOURS:

T,R 9-10 AM,     6-7 PM

DON 2275

GRADES:

Test (Feb. 9) Test (March 15) Test (April 12) Final (cumulative)

30 points 30 points 30 points 40 points

A+ >= 97 pts A = 93,...,96 pts A- = 90,...,92 pts etc.

The lowest test score will be dropped. A project successfully presented at a conference can optionally play the role of the final exam.