CIS 6930, Math for Intelligent Systems II, Spring 2009

Instructor:
Prof. Arunava Banerjee
Office: CSE E336.
E-mail: arunava@cise.ufl.edu.
Phone: 392-1476.
Office hours: Wednesday 2:00 p.m.-4:00 p.m. or by appointment.

Pre-requisites:

• Math for Intelligent Systems I is the official Pre-requisite for this course. However, if you have not taken it, please come and talk to me. I can give you a sense of whether you will be able to handle the course.

References:
Calculus of Variations, I. M. Gelfand and S. V. Fomin,
Convex Optimization, S. Boyd and L. Vandenberghe, Available online here
Principles of Mathematical Analysis, W. Rudin,
Probability and Measure, P. Billingsley
Probability: Theory and Examples, R. Durrett, Chapter 1 that will suffice for this course is available online here

The goal of this course is to cover several topics in mathematics that is of general interest to people pursuing a Ph.d in intelligent systems. The course will focus on conceptual clarity.

Please return to this page at least once a week to check updates in the table below

Evaluation: The final grade will be based on two midterm exams (30% each) and several assignments (remaining 40%).

Course Policies:

• Late assignments: All homework assignments are due before class.
• Plagiarism: You are expected to submit your own solutions to the assignments. Feel free to discuss the concepts underlying the questions.
• Attendance: Their is no official attendance requirement. If you find better use of the time spent sitting thru lectures, please feel free to devote such to any occupation of your liking. However, keep in mind that it is your responsibility to stay abreast of the material presented in class.
• Cell Phones: Absolutely no phone calls during class. Please turn off the ringer on your cell phone before coming to class.

Academic Dishonesty: See http://www.dso.ufl.edu/judicial/honestybrochure.htm for Academic Honesty Guidelines. All academic dishonesty cases will be handled through the University of Florida Honor Court procedures as documented by the office of Student Services, P202 Peabody Hall. You may contact them at 392-1261 for a "Student Judicial Process: Guide for Students" pamphlet.

Students with Disabilities: Students requesting classroom accommodation must first register with the Dean of Students Office. The Dean of Students Office will provide documentation to the student who must then provide this documentation to the Instructor when requesting accommodation.

List of Topics covered

Week	Topic	Additional Reading	Assignment
Jan 04 - Jan 10	Constrained optimization with equality constraints: Lagrange Multiplier Calculus of Variations
Jan 11 - Jan 17	Calculus of Variations continued. The Euler Lagrange Eqn: Euler's Technique
Jan 18 - Jan 24	Calculus of Variations continued. Differential of a functional Vectors, Covectors, Tensors The Euler Lagrange Eqn: Lagrange's Technique		Assignment 1. Due on Jan 29th. (Now extended to Feb 3rd) (Now extended to Feb 5th)
Jan 25 - Jan 31	Convex Optimization Definitions: convex, affine, convex optimization problem, etc Operations that preserve convexity
Feb 1 - Feb 7	Convex Optimization continued The lagrange dual problem Weak duality, Strong duality, Constraint qualification (Slater) KKT is necessary
Feb 8 - Feb 14	Convex Optimization continued KKT is sufficient Examples		Solution sketch for Assignment 1.
Feb 15 - Feb 21	Support Vector machines: Convex Optimization formulation The Dual problem The kernel Trick Mercer's theorem and Reproducing Kernel Hilbert Spaces		Assignment 2. Due on Mar 5th.
Feb 22 - Feb 28	Basic Topology Open and Closed sets, Compact sets Proofs of various properties
Mar 1 - Mar 7	Midterm I
Mar 8 - Mar 14	Spring Break
Mar 15 - Mar 21	Mathematical Probability Theory Measurable space: Sample Space, Sigma algebra/ring Limit Supremum and Infimum
Mar 22 - Mar 28	Mathematical Probability Theory continued Measure space Various theorems, Boole's inequality, Borel Cantelli
Mar 29 - Apr 4	Borel sigma algebra, random variables Simple functions, Definition of Expectation Started Monotone Convergence theorem
Apr 5 - Apr 11	Finished Monotone Convergence theorem Convergence in distribution, convergence in probability, almost sure convergence.		Assignment 3. Due on Apr 21st.
Apr 12 - Apr 18	Markov and Chebychev's inequalities Weak Law or Large numbers Kolmogorov's Strong Law of Large numbers
Apr 19 - Apr 25	Midterm II (tuesday)