Mathematics Prerequisites for the MA Program
Algebra
Polynomials, roots;
Sets: Definitions and operators;
Euclidean space, base vectors;
Vectors and matrices: definitions and operations, (determinant, inverse, etc.);
Matrix functions: determinant, bilinear and quadratic forms;
System of linear equations, Cramer's rule;
Calculus
Sequences, limits;
Function, inverse function, inverse function, curve;
Differences, differentials, derivatives, rules of derivation;
Partial and total derivatives;
Continuous compounding, logarithmic derivative, elasticity;
Unconstrained optimization: single variable, multiple variable
Constrained optimization of multiple variables: Lagrange multipliers;
Integration: indefinite, definite (Riemann).
Probability theory
Event space;
Combinatorics (basic);
Random variable: discrete, continuous;
Distributions of random variables: Bernoulli, binomial, normal, uniform;
Moments, independence, Bayes theorem;
Marginal, joint and conditional distribution;
Conditional expectation.
