Concepts of Real Analysis

An introduction to rigorous analytic proofs involving properties of real numbers, continuity, differentiation, integration, and infinite sequences and series.

Week 1 (8/24 - 8/28)

Monday Wednesday Friday

Week 2 (8/31 - 9/4)

Monday Wednesday Friday
  • Proof by Induction
  • Notes

Week 3 (9/7 - 9/11)

Monday Wednesday Friday
  • Labor Day
  • No Class

Week 4 (9/14 - 9/18)

Monday Wednesday Friday
  • Review

Week 5 (9/21 - 9/25)

Monday Wednesday Friday
  • Exam I
  • Topology of the Reals
  • Notes
  • Topology of the Reals
  • Notes

Week 6 (9/28 - 10/2)

Monday Wednesday Friday

Week 7 (10/5 - 10/9)

Monday Wednesday Friday
  • Monotone Sequences
  • Notes

Week 8 (10/12 - 10/16)

Monday Wednesday Friday
  • Limits of Funtions
  • Notes
  • Continuous Functions
  • Notes
  • Properties of Continuous Functions
  • Notes

Week 9 (10/19 - 10/23)

Monday Wednesday Friday
  • Uniform Continuity
  • Notes
  • Uniform Continuity
  • Notes
  • Review

Week 10 (10/26 - 10/30)

Monday Wednesday Friday

Week 11 (11/2 - 11/6)

Monday Wednesday Friday
  • The Mean Value Theorem
  • Notes

Week 12 (11/9 - 11/13)

Monday Wednesday Friday
  • Properties of the Riemann Integral
  • Notes

Week 13 (11/16 - 11/20)

Monday Wednesday Friday
  • Properties of the Riemann Integral
  • Notes
  • Fundamental Theorem of Calculus
  • Notes
  • Fundamental Theorem of Calculus
  • Notes

Week 14 (11/23 - 11/27)

Monday Wednesday Friday
  • Thanksgiving
  • Thanksgiving
  • Thanksgiving

Week 15 (11/30 - 12/4)

Monday Wednesday Friday
  • Review
  • Exam III

Week 16 (12/7 - 12/11)

Monday Wednesday Friday
  • Convergence Tests
  • Notes
  • Uniform Convergence
  • Notes