OVERVIEW
OVERVIEW

The Department of Mathematics is an academic unit within the College of Arts and Sciences. The department offers a BSc program in Applied Mathematics and Statistics with two optional concentrations in Financial Mathematics and Mathematical Biology. Students may choose to complete a broad program of study leading to the award of a BSc degree in Applied Mathematics and Statistics, or select one of the two concentrations in order to focus their final year in the program on a particular area of application.

The BSc in Applied Mathematics and Statistics program offers training in mathematical problem solving techniques with a reduced emphasis on abstract theory. The program is tailored to the student who will need to apply mathematical, statistical, and computational methods to practical problems.

Applied mathematics includes the theoretical portions of physics, chemistry, biomedicine, engineering, economics, finance, and a wide variety of other disciplines. Recent advances in computing technology have made the use of quantitative methods of even greater importance in these disciplines.

Prospects for employment opportunities for graduates in the mathematical and statistical sciences are excellent. There is a growing demand for professional mathematicians and statisticians in almost every sector of the job market, including the engineering and telecommunications industries; computer services and software development; actuarial and financial services; pharmaceutical industry and medical services; market research agencies; government laboratories and the military services; as well as academics and teaching.

Program Objectives
Student Outcomes

Students graduating with an Applied Mathematics and Statistics degree will have the following abilities:

(a)

An ability to apply knowledge of mathematics, statistics and computing.

(b)

An ability to design statistical experiments, as well as to analyze and interpret data.

(c)

An ability to read, understand and construct mathematical and statistical proofs.

(d)

An ability to function on a multi-disciplinary team as a member or leader.

(e)

An ability to formulate, and to solve, mathematical models of real-world problems.

(f)

An understanding of professional and ethical responsibility.

(g)

An ability to communicate effectively.

(h)

The broad education necessary to understand the strengths and limitations of mathematical and statistical models, and their solutions, in a global and societal context.

(i)

A recognition of the need for, and an ability to engage in, life-long learning.

(j)

A knowledge of contemporary issues.

(k)

An ability to select, and use, appropriate software packages and/or computer programming to solve mathematical models.

(l)

Familiarity with, and use of, sources of current research and an understanding of how new knowledge is generated.

STRUCTURE
COURSE DESCRIPTIONS

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 211 Differential Equations and Linear Algebra (4-0-4)
Prerequisites: MATH 112

An introduction to ordinary differential equations with a focus on the solution techniques for the first order equations, higher order homogeneous and nonhomogeneous linear equations with constant coefficients, linear and almost linear systems, and Laplace transforms. Basic topics of linear algebra, including linear systems, basic properties of matrices, vector spaces, and eigenvalues and eigenvectors.

MATH 212 Calculus III (4-0-4)
Prerequisites: MATH 112; ENGR 112

This course considers the development of differential, integral and vector calculus for functions of several variables. The course also includes the application of concepts from multivariable calculus to the study of curves and surfaces in space, the study of vector fields, optimization, areas, volumes and flux. The topics covered in this course are interesting, as well as important, with numerous scientific and engineering applications.

MATH 213 Probability and Statistics for Engineers (4-0-4)
Prerequisite: MATH 112

The course introduces students to probability models and statistical methods for data analysis. The course will cover introductory probability theory, several discrete and continuous probability distributions, and different statistical inference methods such as point estimation/interval estimation for the mean and the variance (based on one and two samples), hypothesis testing for the mean and the variance (based on one and two samples) and simple linear regression.

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 223 Probability and Statistical Inference (4-0-4)
Co-requisite: MATH 211

The course provides a mathematically rigorous introduction to the Theory of Probability and Inferential Statistics and presents numerous applications in various fields. It covers random variables/vectors, expectation and variance and probabilistic limit theorems. These (probabilistic) tools are then used to present inferential statistics methods, including point/interval estimation, Hypothesis Testing and regression models.

MATH 311 Probability and Statistics with Discrete Mathematics (4-0-4)
Prerequisite: MATH 112

An introduction to probability theory and statistics, with an emphasis on applications and problem solving. Probability and statistics is an important foundation for computer engineering fields such as artificial intelligence, data structures and algorithms, data communications and networking, and image processing and analysis. This course also covers an introduction to elementary discrete mathematics for computer engineering, emphasizing mathematical definitions and proofs as well as applicable methods.

MATH 312 Complex Variables and Transforms (4-0-4)
Prerequisite: MATH 211

This course provides students with a sound knowledge of complex variables and complex integrals, Laplace and Fourier transforms Fourier integrals and series along with a brief introduction to Partial Differential Equations (PDEs). After this course, students will be able to apply strong mathematical tools to model and solve a wide range of the practical problems in engineering and technology.  

MATH 313 Applied Engineering Mathematics (4-0-4)
Prerequisite: MATH 211

This course presents numerical and analytical methods to solve mathematical models in engineering science, including algebraic equations, ordinary differential equations, and partial differential equations. Applications will include wave motion and heat conduction. The course includes computer based projects.

MATH 314 Real Analysis and Probability (4-0-4)
Prerequisite: MATH 211, MATH 212, MATH 223

This course provides students with an introduction to the fundamental concepts and theory which underpin many of the applied mathematics and statistics courses that follow in the Applied Mathematics and Statistics Program.

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 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 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 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 450 Senior Project I (3-0-3)
Prerequisite: Successful completion of the first six semesters of the program

This is a two semester course in which students will conduct a research project under the close supervision of one faculty member. Typically, this will be an individual research experience for the student although small group projects, consisting of no more than two student members, may be considered in exceptional circumstances. Students will present the results of their research in the form of a written thesis and an oral presentation to faculty and students.

MATH 451 Senior Project II (3-0-3)
Prerequisite: MATH 450

Continuation of MATH 450.

TYPICAL STUDY SEQUENCE