Math 515 course notes and homework
Meeting times: M,W from 3:00–4:15pm
Meeting place: MB 124
Textbook: Sheldon Axler, Measure, integration, and real analysis (draft)
My office: MB 238-B
Office hours: M,W,F from 11:30am–12:00pm, Tu from 10:30–11:00, and by appointment
Measure theory: This is a cornerstone of real analysis which shows up in many pure and applied areas of math including geometry, calculus, probability, and physical science. I plan to spend up to two-thirds of the semester on measure theory. We will cover a selection of topics from Axler, chapters 1–5. This includes the classical Lebesgue measure, measurable functions, integration, and abstract measure theory.
Functional analysis: This is another area of analysis that is important in a wide range of fields including differential equations, noncommutative algebra, and quantum mechanics. I plan to spend roughly one-third of the course on functional analysis. We will cover topics from from Axler, chapters 6–9. This includes Banach spaces, L^p spaces, and Hilbert spaces.
Homework assignments will be given each week, and collected on the following Wednesday. All work will be evaluated for completeness, and certain problems will be evaluated for correcteness and mathematical style. You are encouraged to collaborate with your peers, you are welcome to use online resources when you are stuck. But please keep in mind that you must always fully understand your solutions and most importantly write them in your own words.