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 (8/21 - 8/25)

Monday Wednesday Friday
  • Crisis in Mathematics
  • Notes
  • Mathematical Logic
  • Notes

Week 2 (8/28 - 9/1)

Monday Wednesday Friday
  • Basic Set Operations
  • Notes

Week 3 (9/4 - 9/8)

Monday Wednesday Friday
  • Labor Day

Week 4 (9/11 - 9/15)

Monday Wednesday Friday
  • The Completeness Axiom I
  • Notes
  • The Completeness Axiom II
  • Notes

Week 5 (9/18 - 9/22)

Monday Wednesday Friday

Week 6 (9/25 - 9/29)

Monday Wednesday Friday
  • Exam 1
  • Convergence of Sequences
  • Notes

Week 7 (10/2 - 10/6)

Monday Wednesday Friday
  • Monotone Sequences
  • Notes

Week 8 (10/9 - 10/13)

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

Week 9 (10/16 - 10/20)

Monday Wednesday Friday
  • Uniform Continuity I
  • Notes
  • Uniform Continuity II
  • Notes

Week 10 (10/23 - 10/27)

Monday Wednesday Friday
  • The Mean Value Theorem I
  • Notes
  • The Mean Value Theorem II
  • Notes
  • L'Hoptials Rule I
  • Notes

Week 11 (10/30 - 11/3)

Monday Wednesday Friday
  • L'Hoptials Rule II
  • Notes

Week 12 (11/6 - 11/10)

Monday Wednesday Friday
  • Exam 2
  • The Riemann Integral
  • Notes
  • Properties of the Riemann Integral
  • Notes

Week 13 (11/13 - 11/17)

Monday Wednesday Friday
  • Fundamental Theorem of Calculus I
  • Notes
  • Fundamental Theorem of Calculus II
  • Notes
  • Convergence of Infinite Series
  • Notes

Week 14 (11/20 - 11/24)

Monday Wednesday Friday
  • Thanksgiving
  • Thanksgiving
  • Thanksgiving

Week 15 (11/27 - 12/1)

Monday Wednesday Friday
  • Convergence Tests
  • Notes
  • Pointwise Convergence
  • Notes

Week 16 (12/4 - 12/8)

Monday Wednesday Friday
  • Uniform Convergence
  • Notes
  • Exam 3