Undergraduate Programs
Undergraduate Home
Admissions and Financial Aid
Research Opportunities
Other Opportunities
Degree Programs
Course Descriptions
Current Courses
Honors Program
Applying to Graduate School
After Graduation
Math Links |
Undergraduate Courses
21-355 Principles of Real Analysis I Fall or Spring: 9 units The Real Number System: Field and order axioms, sups and infs, completeness, integers and rational numbers. Real Sequences: Limits, cluster points, limsup and liminf, subsequences, monotonic sequences, Cauchy's criterion, Bolzano-Weierstrass Theorem. Topology of the Real Line: Open sets, closed sets, density, compactness, Heine-Borel Theorem. Continuity: attainment of extrema, Intermediate Value Theorem, uniform continuity. Differentiation: Chain Rule, local extrema, Mean-Value Theorems, L'Hospital's Rule, Taylor's Theorem. Riemann Integration: Partitions, upper and lower integrals, sufficient conditions for integrability, Fundamental Theorem of Calculus. Sequences of Functions: Pointwise convergence, uniform convergence, interchanging the order of limits. 3 hours lecture. Prerequisites: 21-122 and 21-127. |