# Math 515

Math 515 course notes and homework

Project maintained by scoskey
Hosted on GitHub Pages — Theme by mattgraham
# Math 515 syllabus

Meeting times: M,W from 3:00–4:15pm

Meeting place: MB 124

Textbook: Sheldon Axler, *Measure, integration, and real analysis* (draft)

Web site: `scoskey.org/m515`

My email: `scoskey@boisestate.edu`

My office: MB 238-B

Office hours: M,W,F from 11:30am–12:00pm, Tu from 10:30–11:00, and by appointment

## Course topics

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.

## Anticipated learning outcomes

- Possess a working knowledge of Lebesgue measure theory, Lebesgue integration theory, Banach spaces, L^p spaces, and Hilbert spaces

## Grading

- Exam one 20%
- Exam two 20%
- Final (non-cumulative) 20%
- Homework 40%

## Tentative exam dates

- Exam one: Wednesday, September 19
- Exam two: Wednesday, October 24
- Final: Monday, December 10 from 2:30–4:30pm

## Homework

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*.