University of Rhode Island MTH436: Mathematical Analysis and Topology I
Spring 2019
General Information
Course Goals
Course Schedule
Assignments






Graph of Sin(1/x)

Course Topics

Here are (some of) the topics that will be covered in this class.

Continuity

  • Uniform Continuity
  • Monotone Functions

Differentiation

  • Definition of the derivative
  • Mean Value Theorem
  • Taylor's Theorem
  • L'Hospital's Rule

Darboux Integral

  • Definition
  • Integrable and non-integrable functions
  • Fundamental Theorem of Calculus
  • Improper Integrals
  • Some light measure theory?

Sequences of Functions

  • Pointwise and Uniform Convergence
  • Convergence Tests
  • Properties of Uniform Limits
  • Series of Functions

Metric Spaces

  • Continuity of functions
  • Compactness

Optional Further Topics

e.g Vector Analysis, definition of a derivative in several variables, more metic spaces/basic topology,...

Course Goals

By the end of the course, you should be comfortable with all the standard material of Real Analysis: sequences, continuity, derivatives and integrals. You should also have a basic understanding of metric spaces and how they generalise the notions of real analysis.