# Course Listings

**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.