SUNY Stony Brook

Office: 4-112 Mathematics Building

Phone: (631)-632-8274

Dept. Phone: (631)-632-8290

FAX: (631)-632-7631

MW 11:00am to 12:20pm, Physics P-122

Scheduled Final Exam Time Thursday, Dec 15, 11:15am-1:45pm

We will follow the book `Functional Analysis'
by Peter Lax, published
by Wiley. There is a wealth of material in the
book and ideally you
should know all of it. In practice, however, we shall have to make
some choices about what to cover. Some of the early sections on
linear algebra, Hahn-Banach, Hilbert spaces, uniform boundedness, should
be familiar to you from MAT 544 and 550,
so I plan to only review these.
Topics I hope to cover in greater depth include:

--- duality

--- weak convergence and its applications

--- convex sets and extreme points

--- Banach algebras

--- Compact maps and operators

--- Fredholm's theory

--- Spectral theory: Symmetric, Normal, Unitary, Self-Adjoint

--- Groups of Unitary Operators

--- Scattering therory

1 Week of Aug 29: Chapters 1,2,3,4 (Hahn-Banach)

2 Week of Sept 5: Chapter 5 (Normed spaces)

3 Week of Sept 12: Chapters 6,7 (Hilbert spaces)

4 Week of Sept 19: Chapters 8,9 (Duality)

5 Week of Sept 26: Chapters 10,11,12 (Weak convergence)

6 Week of Oct 3: Chapters 13,14 (Convexity)

7 Week of Oct 10: Chapters 15,16 (Bounded linear maps)

8 Week of Oct 17: Chapters 17,18 (Banach Agebra)

9 Week of Oct 24: Chapters 19,20 (Spectrum)

10 Week of Oct 31: Chapters 21,22,23 (Compact operators)

11 Week of Nov 7: Chapters 27,28,29 (Index theory, compact symmetric operators)

12 Week of Nov 14: Chapter 30 (Trace class and trace formula)

14 Week of Nov 28: Chapter 31 (Spectral theory)

15 Week of Dec 5: Chapters 32,33 (Self-adjoint operators)

Chapter 1: Problems 4,6,7 , Due Sept 7

Chapter 2: Problems 4,5,6 , Due Sept 7

Chapter 3: Problems --- ,

Chapter 4: Problem 2 , Due Sept 7

Chapter 5: Problems 3,4 , Due Sept 26

Chapter 6: Problems 1,2,3 , Due Sept 26

Chapter 7: Problems --- ,

Chapter 8: Problems 1,2,3 , ---

Chapter 9: Problems --- ,

Chapter 10: Problems 2,3,5 , Due Oct 24

Chapter 11: Problems 1,2 , Due Oct 24

Chapter 12: Problems --- , Due

Chapter 13: Problems 6,7,9 , Due Oct 24

Chapter 14: Problems 3,5,6 , Due---

Chapter 15: Problems 1,3,4,8,12 , Due---

Chapter 16: Problems 1,2,3,4 , Due---

Chapter 17: Problems 1,2,3 , Due

Chapter 18: Problems --- , Due---

Chapter 19: Problems 1,2 , Due December 17

Chapter 20: Problems 2,4,6 , Due December 17

Chapter 21: Problems 5,8, Due December 17

Chapter 28: Problems 1,2,3,4,5,9,10 , Due----

Chapter 29: Problems 2 , Due---

Grades will be based on the problem sets.

Send the lecturer (C. Bishop) email at:

Email MAT 551 students and instructor

Peter Lax Wikipedia page

Link to history of mathematics There are a lot of interesting articles here. If you know of other math related sites I should link to, let me know.