Course Description and Grading Breakdown Course Meeting Time and LocationTuesday and Thursday 10:30  11:55 am 122 Math Building (Building 15)
Course Instructor Contact Information and Office Hours 2101 Math Building (Building 15)
Course Schedule and Textbook
Date  Topic  April 3  Introduction to C*algebras. Spectrum and spectral radius. Normal, selfadjoint, and unitary elements. Gelfand duality. See Section 1 of [1].  April 5  States on C*algebras. The GNS construction. The strong and weak operator topologies on B(H). See Section 1 and Section 2 of [1].  April 10  Characterization of (ultra)weakly continuous functionals. Spectral measures and the spectral theorem. Borel functional calculus. Isometries and partial isometries. Polar decomposition. See Section 2 and 3 of [1].  April 12  Von Neumann's bicommutant theorem.The predual of a von Neumann algebra. Characterization of normal states. Kaplanski's density theorem. See Section 3 of [1].  April 17  Spectral decomposition in von Neumann algebras. Projections in von Neumann algebras. Murrayvon Neumann equivalence. II_1 factors. The hyperfinite II_1 factor. See Section 3 of [1].  There is no official textbook. We list below some recommended reading containing most of the topics covered.
[1] C. Houdayer, An invitation to von Neumann algebras. Available at https://cyrilhoudayer.files.wordpress.com/2014/09/vngraduatecourse.pdf [2] C. Houdayer, An introduction to II_1 factors. Available at http://perso.enslyon.fr/gaboriau/evenements/IHPtrimester/IHPCIRM/Notes=Cyril=finitevonNeumann.pdf
Course Policies Late work 
Assignments Date Posted  Assignment  Due Date       
Midterm and Final Exam
Collaboration Table  Homework  Exams 

You may consult:    Course textbook (including answers in the back)  YES  YES  Other books  YES  NO  Solution manuals  NO  NO  Internet  YES  NO  Your notes (taken in class)  YES  YES  Class notes of others  YES  NO  Your hand copies of class notes of others  YES  YES  Photocopies of class notes of others  YES  NO  Electronic copies of class notes of others  YES  NO  Course handouts  YES  YES  Your returned homework / exams  YES  YES  Solutions to homework / exams (posted on webpage)  YES  YES  Homework / exams of previous years  NO  NO  Solutions to homework / exams of previous years  NO  NO  Emails from TAs  YES  NO  You may: 

 Discuss problems with others  YES  NO  Look at communal materials while writing up solutions  YES  NO  Look at individual written work of others  NO  NO  Post about problems online  NO  NO  For computational aids, you may use: 

 Calculators  YES*  NO  Computers  YES*  NO 
* You may use a computer or calculator while doing the homework, but may not refer to this as justification for your work. For example, "by Mathematica" is not an acceptable justification for deriving one equation from another. Also, since computers and calculators will not be allowed on the exams, it's best not to get too dependent on them. 