**Mat 320**

**Assignments**

Assignment 2

Assignment 3

Assignment 4

Assignment 5

Practice Midterm [Solutions]

Midterm Solutions

Assignment 6

Assignment 7

Assignment 8

Assignment 9

Assignment 10

Assignment 11 ( Does not need to be handed in)

Practice Final [Solutions]

**Schedule**

9/8: Real Numbers, Natural Numbers, Countability, Sections 1.1-1.2

9/13: Countability, Topology of the real numbers, Sections 1.3-1.4

9/15: Convergent sequences, Cauchy sequences, completeness, Section 1.5

9/20: Continuous real valued functions and topological theorems, Section 1.6

9/22: Introduction to Lebesgue measure, Outer measure, Sections 2.1-2.2

9/27: Sigma algebras, Borel sets and measurable sets, Section 2.3

9/29: Approximation of measurable sets, countable additivity, Borel-Cantelli, Sections 2.4-2.5

10/4: Nonmeasurable Sets, Cantor set, Cantor function, Sections 2.6-2.7

10/6: Lebesgue measurable functions, Sections 3.1-3.2

10/11: Littlewood's Principles, Section 3.3

10/13: Midterm

10/25: Riemann integral review, Lebesgue integral, Sections 4.1-4.2

10/27: Lebesgue integral continued, Chebyshev, Monotone convergence, Sections 4.3-4.4

11/1: Fatou's Lemma, Dominated convergence theorem, Sections 4.4-4.5

11/3: Uniform integrability, convergence theorem, Section 4.6

11/8: Convergence in measure, Section 5.2

11/10: Characterization of integrability, Section 5.3

11/15: Monotone functions and differentiability, Section 6.1

11/17: Lebesgue's theorem, Jordan's theorem, Sections 6.2-6.3

11/22: Absolutely continuous functions, fundamental theorem of calculus, Sections 6.4-6.5

11/29: Hilbert and Banach spaces, Section 7.1

12/1: Cauchy-Schwarz and HÃ¶lder, Section 7.2

12/6: Completeness and density theorems for L^p spaces, Section 7.3