BSc in Applied Mathematics, Statistics, and Data Science

MATH 111 Calculus I (3-1-4)
Prerequisite: MATH 002 or placement test

This course will introduce students to the theory and techniques of single variable differential and integral calculus. Applications of single variable differential calculus for modeling, and solving, real-world problems in science and engineering will also be included. Students will be expected to demonstrate an understanding of the underlying principles of the subject, in addition to being able to apply the techniques of calculus in a problem-solving context.

MATH 112 Calculus II (4-0-4)
Prerequisite: MATH 111 (C grade or higher)

This is a second semester calculus course for students who have previously been introduced to the basic ideas of differential and integral calculus. Over the semester we will study the following topics: Applications and methods of integration, infinite sequences and series and the representation of functions by power series, conic sections, polar and parametric equations and curves.

MATH 214 Mathematical and Statistical Software (3-0-3)
Prerequisite: ENGR 112; MATH 213
Co-requisite: MATH 211

This course provides students with an introduction to the two major software packages used in the Applied Mathematics and Statistics program, and its concentrations. Students will receive significant hands-on training in the use of MATLAB for mathematical applications, and R for statistical applications.

MATH 242 Introduction to Probability and Statistics (3-0-3)

Prerequisite: MATH112

This course introduces students to basic probability models and statistical methods for data analysis. The course will cover introductory probability theory, discrete and continuous probability distributions, elements of descriptive statistics, and different statistical inference methods such as estimation for the mean and the variance, hypothesis testing for the mean and the variance.

MATH 243 Probability and Statistical Inference (3-0-3)

Prerequisite: MATH112

This course provides a mathematically rigorous introduction to probability theory and inferential statistics. Numerous real-world applications are presented throughout the course. After covering random variables/vectors, expectation/variance, and limit theorems, students are introduced to inferential statistics, including point estimation and interval estimation in the presence of nuisance parameters, and simple hypothesis testing.

MATH 244 Probability (3-0-3)

Prerequisites: MATH101; MATH112

This course introduces the mathematical theory of probability at an undergraduate level of rigor. The course covers basic concepts of axiomatic probability and conditional probability, random variables/vectors and their distribution, moments, and various models of random variables. Students will also study classical probability inequalities and limit theorems in large sample theory.

MATH 245 Mathematical Statistics (3-0-3)

Prerequisite: MATH 242 or MATH 243 or MATH 244

This course provides a rigorous introduction to classical statistics. Probabilistic concepts and tools are used to present inferential statistics methods, including sampling distributions, parametric point estimators and their properties, interval estimation, hypothesis testing and regression models. Students study some elements of Bayesian statistics.

MATH 252 Introduction to Applied Statistics (3-0-3)

Prerequisite: MATH 112

This course introduces students to basic probability and statistical methods. The course will cover descriptive statistics, random variables, basic discrete and continuous distributions, point and interval estimation, tests of hypotheses, regression and basic design of experiments. Applications to biosciences and engineering will be given throughout the course.

MATH 315 Advanced Linear Algebra (3-0-3)
Prerequisite: MATH 211

Survey of the mathematical structure of vector spaces and linear transformations within a scientific and engineering context. Topics include: vector spaces, matrices, linear mappings, scalar products and orthogonality; symmetric, Hermitian, and unitary operators, eigenvalues and eigenvector theorems, diagonolization and the spectral theorem; applications: convex sets, separating hyper-planes, and the Krien-Milman theorem.

MATH 316 Partial Differential Equations (3-0-3)
Prerequisites: MATH 314 

The course introduces the modern theory of partial differential equations in both classical and variational formulations. Students will have the opportunity to study some of the following topics: Series solutions of ODEs, Legendre’s and Bessel’s ODEs, PDEs and their classifications, Well-posedness, Green’s functions and integral representations, Non-linear PDEs, Sobolev spaces and related Theorems, Variational formulation of PDEs, Weak solutions and the Lax-Milgram formulation.

MATH 317 Nonparametric Statistics (3-0-3)
Prerequisite: MATH 214, MATH 314

The course provides an overview of modern nonparametric statistics and aims at familiarizing students with a wide range of ideas in this field. A combination of theoretical results and computational techniques will be presented with the clear goal of developing a thorough understanding of a number of useful methods for analyzing data.

MATH 318 Multivariate Statistics (3-0-3)
Prerequisite: MATH 211, MATH 212, MATH 214

This course provides a thorough introduction to multivariate statistical analysis methods. Particular emphasis will be placed on methods for analyzing categorical data. All methods will be illustrated with real data sets using the open-source software R.

MATH 319 Numerical Analysis I (3-0-3)
Prerequisites: MATH 211; MATH 214

A survey of numerical methods for scientific and engineering problems. Topics include numerical solution of linear and nonlinear algebraic equations, interpolation and least squares approximation, numerical integration and differentiation, eigenvalue problems, and an introduction to the numerical solution of ordinary differential equations. Emphasis is placed on efficient computational procedures including the use of library and student-written procedures using MATLAB.

MATH 324 Real Analysis I (4-0-4)

Prerequisites: MATH101; MATH112

This course gives students a thorough understanding of essential concepts in analysis such as real numbers, limits, continuity, and convergence of sequences and series. The course also covers a rigorous definition of derivative and construction of the Riemann integral and their properties including the Fundamental Theorem of Calculus. Students are required to read and write proofs using a precise knowledge of definitions and theorems.

MATH 333 Applied Engineering Mathematics (2-3-3)

Prerequisites: ENGR112; MATH204; MATH206

This course provides students with the numerical and analytical methods to solve mathematical models appearing in engineering science including, but not limited to, nonlinear equations, systems of algebraic equations, extrapolation, and ordinary differential equations. Applications will include wave motion and heat conduction. The course includes writing computer codes.

MATH 352 Complex Functions (3-0-3)

Prerequisite: MATH231

This course provides students with a sound knowledge of analytic functions of a complex variable, infinite series in the complex plane and theory of residues in relation to Fourier integrals and transforms. The students will be introduced to several applications in engineering and science.

MATH 399 Internship (0-0-1)
Prerequisite: Junior standing and approval of department

Students are required to spend a minimum of eight continuous weeks on an approved internship program. The internship provides students with practical, on-the-job experience which allows them to integrate theory with “real world” situations. It is academically supervised by a faculty member and professionally supervised by the company’s internship supervisor who provides feedback to the university about the student’s progress. A formal report, that documents the work undertaken during the internship period, must be submitted to the Department within the first two weeks of the semester following the internship.  The report and the complete course activities are graded on a Pass/Fail basis by a faculty member.

MATH 410 Introduction to Topology (3-0-3)

Prerequisites: MATH231; MATH324

This course will introduce students to basic principles of point set topology. The course covers topological spaces, homeomorphisms, compactness, connectedness and metric spaces. It also prepares the students to undertake advanced courses in mathematics, such as algebraic topology, normed spaces and differential geometry.

MATH 411 Modern Algebra (3-0-3)
Prerequisite: MATH 315

This course provides students with a survey of properties of fundamental elements of modern algebra such as groups, rings, and fields and their applications to engineering. Topics include: sets and functions, fundamental theorems of groups, rings, and fields; homorphism theorems; Galois theory; applications to number theory and encryption, coding theory and error correcting codes.

MATH 412 Optimization (3-0-3)
Prerequisite: MATH 317; MATH 318

This course introduces the principal methods and algorithms for linear, nonlinear, and multi-objective optimization. Emphasis is on methodology and the underlying mathematical structures. Topics include the simplex method, convex optimization, optimality conditions for nonlinear optimization, interior point methods for convex optimization, Newton’s method, duality theory, Lagrange multiplier theory, multi-objective decision making, goal programming, stochastic optimization, fuzzy optimization, and applications in finance and management.

MATH 413 Game Theory (3-0-3)
Prerequisite: MATH 315

Introduction to mathematical theory of games and game theoretic analysis. Topics include: combinatorial and strategic games, Zermelo’s algorithm, strictly competitive games, minimax theorem; non-cooperative games and Nash equilibrium; games with mediated communication, repeated games and finite automata; common knowledge and incomplete information; applications: economics, biology, and political science.

MATH 414 Discrete Mathematics (3-0-3)
Prerequisite: MATH 315

Review of propositional and predicate calculus. Introduction to naïve set theory. Relations including equivalence relation and partial order. Cardinality including surjective and injective functions. Recursion and induction including well order. Boolean algebras, Knot Theory and Graph Theory.

MATH 415 Design of Experiments (3-0-3)
Prerequisites: MATH 317; MATH 318

A review of simple designs and analysis of variance, followed by an introduction to block designs, Latin Squares and Related Designs, Full Factorial Designs, 2-level Full Factorial and Fractional Factorial Designs, Response surface methods and designs, Designs with Random Factors, Nested Designs, and split-plot Designs.

MATH 416 Sample Survey Design and Analysis
Prerequisite: MATH 214

This course will focus on methodological issues regarding the design, implementation, analysis, and interpretation of surveys and questionnaires in variety of applied areas such as education, healthcare, social sciences, etc.

MATH 419 Numerical Analysis II (3-0-3)
Prerequisite: MATH 319

Introduction to the theory and practical methods for numerical solution of differential equations. Runge-Kutta and multistep methods, stability theory, stiff equations, boundary value problems. Finite element methods for boundary value problems in higher dimensions. Direct and iterative linear solvers. Discontinuous Galerkin methods for conservation laws.

MATH 421 Econometrics (3-0-3)
Prerequisite: MATH 317; MATH 318

Fundamentals of statistical time series analysis and econometrics are presented and developed for models used in the modern analysis of financial data. Techniques are motivated by examples and developed in the context of financial applications.

MATH 422 Stochastic Differential Equations (3-0-3)
Prerequisite: MATH 314

Stochastic Differential Equations are used extensively in economics and finance. Reflecting this, this course provides an introduction to stochastic differential equations emphasizing applications and computations. It considers strategies for exact, approximate, and numerical solutions of SDEs, and emphasizes the relationship with partial differential equations.

MATH 423 Financial Risk Analysis (3-0-3)
Prerequisite: MATH 412

This course aims to provide an overview of the main theoretical concepts underlying the analysis of financial risk and to show how these concepts can be implemented in practice in a variety of financial contexts. Additionally students will learn how to examine and manage risk and its impact on decisions and the potential outcomes.

MATH 424 Optimal Control Theory (3-0-3)
Prerequisite: MATH 412

This course aims to provide an overview of deterministic and stochastic control theory in both discrete and continuous time. We will apply the theory to relevant problems in finance and economics.

MATH 425 Financial Portfolio Management (3-0-3)
Prerequisite: MATH 412

This course concerns making sound financial decisions in an uncertain world. Increasingly, financial decision-makers are depending on optimization techniques to guide them in their decisions. Topics to be covered will include asset/liability management, option pricing and hedging, risk management, and portfolio selection. Optimization techniques to be covered will include linear and nonlinear programming, integer programming, dynamic programming, and stochastic programming.

MATH 426 Finance in Discrete Time (4-0-4)

Prerequisites: MATH214; MATH231; MATH243 or MATH245

The course gives a modern overview of the main concepts in mathematical finance in discrete time stochastic models. The course will focus on the Cox-Ross-Rubinstein (binomial) model. Topics include no-arbitrage pricing of financial derivatives, replication, hedging, self-financed portfolios, risk-neutral probability measures, and the Black-Scholes-Merton option pricing models. European and American options in discrete time and the numerical algorithms for their evaluation will also be presented.

MATH 431 Computational Methods in Biology (3-0-3)
Prerequisite: BMED 211
Co-requisite: MATH 419

This course presents an overview of important applications of computers to solve problems in biology. Major topics covered are computational molecular biology, modeling and simulation including computer models of population dynamics, biochemical kinetics, cell pathways, neuron behavior, and mutation and development of models of physiological systems using the compartmental framework. The final part of the course introduces techniques to analyze and interpret the “classical” models of theoretical ecology.

MATH 432 Mathematical Models in Biology (3-0-3)
Prerequisite: MATH 316; MATH 419; BMED 211

This course provides an introduction to the application of differential equations (ODEs and PDEs) to develop mathematical models of real-world phenomena in the biological sciences. Topics will include drug infusion, epidemics, chemical kinetics and enzymatic reactions, population growth and oxygen diffusion in muscles.

MATH 433 Biostatistics (3-0-3)
Prerequisite: MATH 318; BMED 211

This course provides an introduction to Biostatistics. In particular, methods and concepts of statistical analysis and sampling in the biological sciences are presented. A thorough coverage of Sequential Analysis methods and Survival Analysis methods, and their applications in Biology, are included.

MATH 434 Bioinformatics (3-0-3)
Prerequisite: MATH 433; BMED 202

Principles of protein structure, techniques within the framework of basic shell scripting and web-based bioinformatics databases/tools, principles of sequence alignment, automation/use of existing applications for the analysis of large datasets.

MATH 435 Mathematical Imaging (3-0-3)
Prerequisite: MATH 412

Mathematical Imaging provides a comprehensive treatment of the mathematical techniques used in imaging science. Students will become familiar with concepts such as image formation, image representation, image enhancement, noise, blur, image degradation, edge detection, filtering, de-noising, morphology, image transforms, image restoration, image segmentation, image quality measure, fractal image coding, with applications to Bio-imaging and Medical Imaging.

MATH 497 Senior Research Project I (3-0-3)

Prerequisite: Senior standing

MATH 498 Senior Research Project II (3-0-3)

Prerequisite: MATH497