- HW6 solutions are available here.
- Homework assignment 6, due on Thursday, April 6, is now posted.
- Next time (March 23), we will start Hilbert spaces. Please see here for more details.
- Midterm 2 solutions are available here.
- Midterm 2 was on Thursday, March 16. It covered everything from the Hahn-Banach theorem to weak and weak* convergence.
- Solutions to homework assignment 4 are available here. (Update, 03/14: a student has pointed out that the solution to Q2 was incomplete. This has now been corrected.)
**Office hours schedule change**: Office hours on Tuesdays have been moved to 1:30-2:30. Office hours on Thursdays are still 10-11.- Midterm 1 solutions are available here.
- Midterm 1 was on Tuesday, February 7, 11-12:30. The test covered all material done in class up to Jan. 30: Banach spaces, bounded linear operators, basic function spaces including L^p spaces (see the summary here). From Section 5.2, you are responsible for the definition of linear functionals, bounded linear functionals, and dual space, but not yet for the Hahn-Banach theorem.
**Classroom change**: Starting on Tuesday Jan. 10, classes will be held in MATX 1102.

- Contact information: Math Bldg 200, 604-822-4457, ilaba(at)math.ubc.ca
- Office hours: Tue 1:30-2:30, Thur 10-11, and by appointment, in MATH 200.
- The best way to contact the instructor is by email. Please note that email received on evenings and weekends will be answered on the next business day. If you cannot attend regular office hours due to schedule conflict, please make an appointment in advance. Drop-ins and same-day requests for appointments cannot always be accommodated.
- Course webpage: http://www.math.ubc.ca/~ilaba/teaching/math510_S2017
- Homework assignments: all assignments and solutions sets will be posted here.
- Current updates on course syllabus are posted here.

This cross-listed 4th year undergraduate and graduate course provides an introduction to functional analysis. It will be based on Chapters 5-8 of the textbook. Most of the emphasis will be on Chapter 5, with the main topics as follows:

- Normed vector spaces, Banach spaces
- Linear operators and linear functionals
- Operator spaces: strong, weak, and weak$^*$ topologies
- Hahn-Banach theorem, open mapping theorem, closed graph theorem
- Hilbert spaces and their geometry
- Operators on Hilbert spaces

- L
^{p}spaces - Radon measures and the Riesz representation theorem
- Fourier series and Fourier analysis

- John B. Conway,
*A Course in Functional Analysis*, 2nd ed., Springer, 2007. - Peter D. Lax,
*Functional analysis*, Wiley-Interscience, New York, 2002.

Additional links and resources:

- Please read the UBC policy on Student Conduct and Discipline.
- Mathematics Learning Centre: The Math Learning Centre (or MLC for short) is a space for undergraduate students to study math together, with support from tutors, who are graduate and undergraduate students in the math department. Please note that while students are encouraged to seek help with homework, the MLC is not a place to check answers or receive solutions, rather, their aim is to aid students in becoming better learners and to develop critical thinking in a mathematical setting. The MLC is located in Rooms 301 and 302 in the Leonard S. Klinck (LSK) Building, and is open Monday through Friday, 11:00am to 6:00pm. Check the website above for any changes to hours and announcements.
- Past final exam database
- UBC Math Club, located in Math Annex 1119, sells math exam packages (old exams together with solution sets) for a nominal price before each final exam session.

[Mathematics Department] [University of British Columbia]