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MATH 327 - Real Analysis I

Suggested Syllabus

Course description and prerequisite informationsee UW General Catalog
Text: Varies by instructor.

Limits and continuity of functions, sequences, series tests, absolute convergence, uniform convergence.  Power series, improper integrals, uniform continuity, fundamental theorems on continuous functions, theory of Riemann integrals.

  • The Real Number System
    • ordered field axioms and completeness
    • elementary properties of real numbers
    • the Archimedean property
    • inf and sup
    • absolute values and the triangle inequality
  • Sequences of real numbers
    • convergence, infinite limits
    • algebraic limit theorems, squeeze principle
    • monotone convergence theorem
    • subsequences
    • Bolzano-Weierstrass theorem
    • Cauchy sequences
    • lim inf, lim sup
  • Series of real numbers
    • tests for convergence
    • absolute and conditional convergence
  • Functions
    • limits
    • continuity
  • Uniform Convergence
    • definition of uniform convergence of sequences of functions, examples
    • consequences of uniform convergence