Prerequisites

Although this course is self-contained, familiarity with elementary probability will clearly help. Moreover, students of this course must be know the following concepts.

Basic logic (implication, quantifiers, etc.)
Sets and their operations
Cartesian product
Relations and functions
Power set
Finite vs infinite sets
Countable vs uncountable sets
Natural, rational, real numbers
Induction principle
Basic combinatorics
Binomial and multinomial coefficients
Basic topology of \mathbb{R}^n (open sets, closed sets, bounded sets)
Sequences and series
Convergence and absolute convergence
Monotone functions
Continuous functions
Differentiable functions
Elementary linear algebra
Linear functions
Convex functions
Convex sets
Riemann integration

The interactive nature of the course will require knowledge of \LaTeX. Students are strongly encouraged to learn it as soon as possible.