Academic Dishonesty: See http://www.regulations.ufl.edu/chapter4/4017.pdf 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.

Tentative List of Topics to be covered

• Real analysis: Basic point set topology, convergence, continuity etc
• Vector spaces and Linear algebra
• Mathematical Probability theory: Sigma algebra, Random variables etc.
• Information Theory: Entropy, Mutual Information, etc.

List of Topics covered

Week	Topic	Additional Reading	Assignment
Aug 21 - Aug 27	Introduction Natural numbers, Rationals and Reals Least upper bound Countably infinite.	Paper on the Riemann Hypothesis Paper on the Johnson Lindenstrauss lemma	Assignment 1
Aug 28 - Sep 03	Reals are uncountable (Cantor's diagonalization proof) Rings and Feilds Convergence, Cauchy sequnece
Sep 04 - Sep 10	Reals are complete Limit Supremum and Limit Infimum		Assignment 2
Sep 11 - Sep 17	Limit Supremum and Limit Infimum continued. Convergence of bounded monotonic sequence Basic point set topology
Sep 18 - Sep 24	Basic point set topology continued; epsilon neighborhoods, limit points, interior points, open sets, closed sets Thm: Open iff complement is closed Thm: Arbitrary union of open sets is open Thm: Finite intersection of open sets is open Definition: Topological space Continuity, limit definition, epsilon delta definition Equivalence of limit and epsilon delta definition Dirichlet's function (discontinuous everywhere) Thomae's function (discontinuous only on rationals)
Sep 25 - Oct 01	Linear maps. Vector/Linear spaces. Span, Linear Independence, Basis Matrix representation of a linear map Matrix multiplication with vector and matrix, and relationship to linear maps and composition of linear maps
Oct 02 - Oct 08	Composition of linear maps and Matrix multiplication Review of material covered to date.
Oct 09 - Oct 15	Midterm I (Monday In-class) A vector space cannot have a n-dimensional basis and an m-dimensional basis. Gaussian Elimination
Oct 16 - Oct 22	Invertable linear transforms LU Decomposition Normed (+Complete=Banach) vector space		Assignment 3 Deadline extended to Thursday 5 pm. (Slip HW under door of E336) Matrix A has changed
Oct 23 - Oct 29	Inner product (+ Complete = Hilbert) Spaces. Tensors Orthogonality, Orthonormality
Oct 30 - Nov 05	Gram Schmidt Orthogonalization Orthonormal Basis Introducing the inner product first Fourier Series
Nov 06 - Nov 12	Eigen values and Eigen vectors Symmetric matrices: real eigen values and orthogonal eigen vectors Eigen value decomposition of a symmetric linear transform
Nov 13 - Nov 19	Singular value decomposition Volume as a rank n alternating tensor = determinant Mathematical Probability Theory: What is it all about? Measurable space, Measure space
Nov 20 - Nov 26	Borel sigma Algebra, random variable, Distribution function Basic Information Theory: Entropy of a discrete random variable		Assignment 4 Deadline extended to Thursday 4 pm (under my office door)
Nov 27 - Dec 03	Mutual information Kullback Leibler Divergence
Dec 04 - Dec 10	Midterm II (Monday, In-class)