# Mathematics Prerequisites for the MA Program

## 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.