MATH 4331/6312 - Fall 2017
Introduction to Real Analysis

    Course Info. View syllabus. Office hours: PGH 604, Tu 11:30am-12:30pm, We 1-2pm.
      Week 1. The topology of Rn. Cauchy sequences and completeness. Open and closed sets.
        Homework Set 1 (Solutions), due date deferred to September 7.
          Week 2. Closure of a set. Compactness.
            Homework Set 2 (Solutions), due September 14.
              Week 3. Heine Borel property and other properties of compact sets. Limits and continuity of functions.
                Homework Set 3 (Solutions), due September 21.
                  Week 4. Discontinuous functions. Uniform continuity. Connected sets.
                    Homework Set 4 (Solutions), due September 28.
                      Week 5. Connectedness and the Intermediate Value Theorem in higher dimensions. Summary of the material in a handout.
                        Exam 1, October 5, in class. When you feel prepared, try a practice run (Solutions).
                          Week 6. Differentiablity and the Mean Value Theorem.
                            Homework Set 5 (Solutions), due October 19.
                              Week 7. The Riemann integral and its properties.
                                Homework Set 6 (Solutions), due October 26.
                                  Week 8. The Fundamental Theorem of Calculus, see handout. Normed vector spaces.
                                    Homework Set 7 (Solutions), due November 2.
                                      Week 9. Inner product spaces. Cauchy-Schwarz inequality. Relation between inner product and norm.
                                        Exam 2, November 9, in class. Covers material from the Intermediate Value Theorem (and its higher-dimensional generalization) to normed vector spaces. When you feel prepared, try a practice run.
                                          Week 10. Hölder and Minkowski inequalities for functions and sequences.
                                            Homework Set 8, due Tuesday, November 21.
                                              Week 11. Limits of sequences of functions. Uniform convergence. Completeness of C(K).
                                                Homework Set 9, due November 30.