MAT 319

Title: Foundations of Analysis

Description: A careful study of the theory underlying topics in one-variable calculus, with an emphasis on those topics arising in high school calculus. The real number system. Limits of functions and sequences. Differentiations, integration, and the fundamental theorem. Infinite series.

Prerequisite: C or higher in MAT 200 or permission of instructor; C or higher in one of the following: MAT 203, 205, 211, 307, AMS 261, or A- or higher in MAT 127, 132, 142, or AMS 161

Credits: 4

Textbook:

  • Elementary Analysis: The Theory of Calculus, by Kenneth Ross, 2nd edition

Major Topics Covered: 

  • Definition of Real Numbers
  • Completeness Axiom and Least Upper Bound
  • Bounded and Unbounded Sets
  • Limit of a Sequence
  • Cauchy Sequences
  • Subsequences
  • Bolzano-Weierstrass Theorem
  • Series
  • Convergence Tests
  • Continuous Functions
  • Intermediate Value Theorem
  • Derivatives, Mean Value Theorem
  • Riemann Integral and Fundamental Theorem of Calculus

Undergraduate Bulletin Course Information

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