**MATH 101 Calculus I**

Limits, Continuous functions.
The derivative, formulas of differentiation, differentials. Related rates,
Extrema. Rolle’s and mean value theorems. Graph sketching Optimization.
Indefinite integrals, definite integrals, fundamental theorem of calculus.
Applications of definite integrals to find area, volume and arc length.

**MATH 102 Calculus II**

Logarithmic and exponential
functions. Inverse trigonometric and hyperbolic functions. Techniques of
integration. Indeterminate forms and improper integrals. Conic sections. Plane
curves and polar coordinates. Vectors and surfaces in R3.

**MATH 111 Linear Algebra**

Matrices: matrix operations,
inverse of a matrix, solving systems of linear equations. Determinants:
definition and properties, cofactor expansion and applications. Vectors in R2
and R3 , scalar and cross products, lines and planes, applications. The vector
space Rn . subspaces, linear independence, basis and dimensions, orthogonality.
Gram-Schmidt orthogonalization process. Rank of matrix. Eigenvalues and
eigenvectors, diagonalization of a matrix.

**MATH 126** **Computer Programming I**

Basic computer concepts. Data types. Control structures.
Repetition statements. Programme development methods. Programming style.

**STAT 201 Statistics for Science and Engineering**

Organizing and summarizing data. The probability of an event.
Random variables. Special distributions. Sampling and sampling distributions.
Confidence intervals Testing statistical hypotheses. Simple linear and
regression and correlation.

**STAT 210 Introduction to Probability**

Probability. Random variables. Mathematical expectation.
Special discrete distributions. Special continuous distributions. Joint
distribution. Conditional distributions. Product moments.

**MATH 211 Calculus III**

Sequences, infinite series,
partial differentiation and its applications. Multiple integrals and its
applications, Green's and Divergence theorems.

**MATH 221 Introduction to Mathematics of Economics and
Finance**

Mathematical models in economics. Interests and capital growth.
Marginal cost. Profit maximization. Elasticity of demand. Efficient small firm.
Portfolios, arbitrage portfolio and state prices. IS-LM analysis. Input-output
models. Consumer surplus.

**MATH 240 Ordinary Differential Equations**

Origin of
differential equations in science. Differential equations of first order. Linear
differential equations of higher order. Power series and Laplace transform
methods. Applications.

**MATH 250 Introduction to Foundations of
Mathematics**

Algebra of propositions, mathematical induction, operations
on sets, binary relations, equivalence relations and partitions, denumerable
sets, Cardinal numbers, partial order. Boolean algebra.

**STAT 250 Operations Research I**

Modeling in
Operations Research and mathematical approaches to optimization of functions
subject to linear constraints (linear program) and its extensions including
transportation, assignment, transshipment and network models.

**MATH 271 Mathematics of Economics and
Finance**

First-order recurrences. The Cobweb model. Contours and
isoquants. Optimisation in two variables. Vectors, preferences and convexity.
Constrained optimization, elementary theory of the firm, Cobb-Douglas firm.
Lagrangeans and the consumer, elementary theory of the consumer. .Second-order
recurrences, dynamics of economy, business cycles. Ordinary differential
equations, continuous-time models, market trends and consumer demand.

**MATH 272 Quantitative Finance**

Financial markets.
Quantitative methods: binomial trees and arbitrage, spreadsheets to compute
stocks and option trees. Continuous time models: Black-Scholes. Hedging. Bond
models and interest rate options. Computational methods for bonds. Currency
markets and foreign exchange risks.

**STAT 310 Stochastic Processes (I)**

Classification of
stochastic processes. Markov chains. The Bernoulli process. Classification of
the states of a Markov chain. Recurrence times and their properties. The
Stationary distributions of Markov chains. The Poisson process

**MATH 316 Elements of Mathematical Modelling**

The
basic idea of mathematical modeling of real world problems. Modeling using
graphs; proportionality; fitting, and optimization, experimental modeling.
Dimensional analysis and similitude, simulation modeling; modeling using the
derivative, interactive dynamic systems.

**MATH 321 Financial Calculus**

Martingales and change
of measure in discrete time framework. Brownian motion and stochastic calculus.
Black-Scholes pricing formula. Stock price models with jumps and stochastic
volatility.

**MATH 322 Option, Futures and other
Derivatives**

Mechanics of futures, Hedging strategies, interest rates,
Mechanics of options, stock options, binomial trees, Black-Scholes model,
volatility, exotic options, Martingales, interest rate derivatives, credit
risk.

**MATH 333 Computational Linear Algebra**

Systems of
linears equations: direct methods: elimination and its matrix analysis, special
structured systems, Thomas and Choleski algorithms, iterative methods: Jacobi
and Gauss-Seidel, SOR, optimal SOR. The linear least-squares problem: normal
equations, QR-and SVD-decompositions, error analysis. Matrix eigenvalue problem:
power method, deflation, Given and Householder orthogonal transformations, the
QR-algorithm, reduction to Hessenberg form; eigenvalue problem for symmetric
matrices.

**MATH 340 Theory of Differential Equations**

Series
solutions near regular singular points. Nonlinear differential equations.
Systems of linear differential equations. The theory of first-order equations.
Stability of equilibria. Boundary value problems.

**MATH 352 Numerical Analysis**

Numerical solution of
nonlinear equations. Numerical solution of linear algebraic systems: direct and
iterative methods. Polynomial interpolation. Least-squares approximation.
Numerical integration

**MATH 363 Advanced Linear Algebra**

Vector spaces,
subspaces, linear independence. Linear transformations and their representations
via matrices. Kernel and range, dimension theorem and isomorphism theorem.
Direct sums of vector spaces. Duality and the interpretation of the adjoint
matrix. Characteristic polynomiaI and trace. An introduction to the theory of
linear transformations, polynomials in a linear transformation, eigenspaces,
cyclic spaces, nilpotent and semisimple transformations. Applications to
canonical forms.

**MATH 371 Mathematics of Financial Derivatives**

Basic
option theory, asset price random walks, Black-Scholes model, American options.
Numerical methods, finite-difference methods, methods for American options,
binomial methods. Further option theory, exotic, path-dependent, barrier, asian,
lookback options, transaction costs. Interest rate derivative products,
convertible bonds.

**MATH 415 Partial Differential Equations**

First and
second order linear partial differential equations. The method of
characteristics. Separation of variables and its application to linear partial
differential equations. Fourier series. Sturm-Liouville theory, Green’s
functions.

**MATH 416 Mathematical Modelling**

Selection of
mathematical models based on differential equations and linear systems. Analysis
of models, development of solution algorithms and sensitivity of models to
perturbations in data. Computer simulation for visualization and interpretation
of physical phenomenon governed by these models.

**MATH 422 Modeling Financial Derivatives**

Mathematical
modeling for financial products, in particular derivatives, using Mathematica.
Topics include: options, lookbacks, Asian and American options, exotics,
finite-difference schemes and the Black-Scholes equation, basket options and
Monte Carlo simulation, dividends, interest rates, modeling volatility by
elasticity

**MATH 423 Computational Financial
Mathematics**

Financial problems and numerical methods. Topics include:
Cash, modeling stocks and options, stock market data management and analysis,
option market data, American options, optimal portfolios.

**MATH 424 Financial Engineering**

Basic theory of
derivatives, path dependency, extending Black-Scholes, interest rates and
products, risk measurement and management, numerical methods.

**MATH 440 Integral Equations**

Basic concepts. Fredholm
and Volterra integral equations. Integral transformations. Approximation
methods.

**MATH 468 Numerical Ordinary Differential
Equations**

Numerical integration.Some basic rules. Gaussian and Romberg
integration. Numerical solution of ordinary differential equations. Initial
value problems. One step and multistep methods (convergence, absolute
stability). Boundary value problems.

**MATH 469 Numerical Partial Differential Equations**

Numerical solution of partial equations selected topics to be
chosen from: Theory of approximation, variational methods, Eigenvalue problems,
further linear algebra, integral equations.

**MATH 493 Topics in Financial Mathematics**

To be selected by the instructor.