Mat 320

Assignments

Assignment 1
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

9/1: Introduction, Set Theory, Section 0
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