### Contact

For questions about the program, please contact:

**Amanda Hattaway**

Chair of Applied Mathematics

Ira Allen 319 | 617-989-4368

hattawaya@wit.edu

## Applied Math Course Descriptions and Notes

**Math 1030 Statistics **

This course is designed to introduce students to statistical concepts relating to engineering design, inspection, and quality assurance. Topics covered include probability, normality, sampling, regression, correlation, and confidence intervals in reliability.

4 Credit Hours

Required for construction management majors.

**Math 1000 College Math 1**

Algebra and trigonometry, including algebraic fractions, systems of linear equations, quadratic equations, literal equations, word problems and their solutions, right triangles, and vectors. Applications will be stressed. Prerequisite: High School Algebra II.

4 Credit Hours

Required for: management, facilities management, construction management, computer networking, engineering technology, architecture, and computer information systems majors.

**Math 1007 Application in College Math 1**

This is a class designed to provide additional enrichment applications for students enrolled in Math 205. Algebra and trigonometry, including algebraic fractions, systems of linear equations, quadratic equations, literal equations, word problems and their solutions, right triangles, and vectors. Students will take leadership roles in this class to work on advanced problems and look at how College Math 1 fits in with the rest of their major’s curriculum

1 Credit Hour

**Math 1020 Plane and Solid Geometry**

A survey of elementary Euclidean geometry including lines and angles, measurement and units, properties of triangles, parallelograms, trapezoids, regular polygons, circles, conic sections, spheres, cylinders, pyramids, polyhedra, areas, and volumes.

4 Credit Hours

Required for interior and industrial design majors

**Math 1500 Precalculus**

Topics include: polynomial and rational functions, exponential and logarithmic functions, trigonometric functions, parametric equations, analytic trigonometry, multivariable systems, and applications and modeling. Prerequisite: MATH 100 College Math I.

4 Credit Hours

Required for: construction management, computer networking, engineering technology, architecture, and computer information systems majors.

**Math 1550 Methods and Topics in Applied Math I**

Problems, methods and recent developments in applied mathematics will be discussed. Topics include: introduction to proof, probability, cryptography, game theory and the analysis of economic phenomena. Students will gain familiarity with technical word processors such as LaTeX, spreadsheet software such as Excel and also with mathematical software packages such as MATLAB and R. Students will also hear guest speakers describe the role that mathematics plays in their respective careers.

4 Credit Hours

Required course for BSAM majors

**Math 1575 Methods and Topics in Applied Math II**

Problems, methods and recent developments in applied mathematics will be discussed. Topics include: formulation of models for phenomena in biology and engineering, their solutions, traffic flow, Geographic Information Systems (GIS), and introduction to graph theory. Students will also hear guest speakers describe the role that mathematics plays in their respective careers.

4 Credit Hours

Required course for BSAM majors

**Math 1700 Calculus I**

Topics include: introduction to limits, definition of the derivative, differentiation of algebraic and transcendental functions, implicit differentiation, applications of the derivative and introduction to integration. Prerequisite: MATH 1500, Precalculus

4 Credit Hours

Required course for engineering technology majors.

**Math 1800 Calculus II**

Techniques of integration, the fundamental theorem of calculus, area, L'Hopital's Rule, improper integrals, and applications of definite integrals. Prerequisite: MATH 1700 Calculus I.

4 Credit Hours

Required course for engineering technology majors.

**Math 1802 Sequences and Series**

Topics include: sequences, summing an infinite series, convergence of sequences and series, power series and Taylor Series. This course is for students who are transferring into an engineering major who have taken MATH290 (a Calculus II course without sequences and series). This course and MATH 1800, Calculus II, are the equivalent of MATH 1850, Engineering Calculus II. Prerequisite: MATH 1800, Calculus II.

1 Credit Hour

**Math 2000 Calculus III**

Three dimensional Cartesian coordinate system, vectors, lines in three dimensions, planes and other surfaces, partial derivatives, directional derivatives, local extrema, polar coordinates, and multiple integrals in Cartesian and polar coordinates. Prerequisite: MATH 1800 Calculus II.

4 Credit Hours

Required course for engineering technology majors.

**Math 2002 Vector Fields and Line Integrals**

Topics include: vector fields, line integrals, and Green's Theorem. This course is for students who are transferring into an engineering major who have taken MATH 2000 (a Calculus III course without vector fields and line integrals). This course and MATH 2000, Calculus III, are the equivalent of MATH515, Multivariable Calculus. Prerequisite: MATH 2000, Calculus III.

1 Credit Hour

**Math 2400 Applied Differential Equations**

Introduction to the solution of ordinary differential equations. Topics will include Euler's method, solving first-order ODEs and higher order linear ODEs with constant coefficients, using Fourier series, and using Laplace transforms Applications will include growth and decay, RLC circuits, and driven/damped motion. Prerequisite: MATH1800 Calculus II.

4 Credit Hours

Required course for engineering technology majors.

**Math 2402Series Solutions to Differential Equations**

Introduction to the solution of ordinary differential equations. Topics will include Euler's method, solving first-order ODEs and higher order linear ODEs with constant coefficients, using Fourier series, and using Laplace transforms Applications will include growth and decay, RLC circuits, and driven/damped motion. Prerequisite: MATH 1800 Calculus II.

1 Credit Hour

**Math 1750 Engineering Calculus I**

Limits, continuity, differentiability, the limit definition of the derivative, differentiation, linearization and some integration of algebraic and transcendental functions, implicit differentiation. Intended for engineering majors or advanced technology students.

4 Credit Hours

Required course for BSAM, computer science and engineering majors.

**Math 1755 Applications in Engineering Calculus I**

This is a class designed to provide additional enrichment applications for students enrolled in Math 1850. Limits, continuity, differentiability, the limit definition of the derivative, differentiation, linearization and some integration of algebraic and transcendental functions, implicit differentiation.. Students will take leadership roles in this class to work on advanced problems and look at how Engineering Calculus 1 fits in with the rest of their major’s curriculum

1 Credit Hour

**Math 1850 Engineering Calculus II**

Define integrals as a limit of Riemann sums, computation of definite and indefinite integrals using the techniques of integration, improper integrals, convergence of sequences and series, and approximating functions and estimating the error using Taylor and Maclaurin series. Prerequisite: MATH 1750, Engineering Calculus I or special permission.

4 Credit Hours

Required course for BSAM, computer science and engineering majors

**Math 4998 Exposition in Applied Math**

This course covers readings, and oral and written presentations of seminal papers in applied mathematics. Students will also work with problems obtained from industry and academia. Students will gain experience in presenting and writing mathematics papers.

1 Credit Hour

Required Course for BSAM majors

**Math 1900 Introduction to Operations Research**

This course serves as an introduction to the field of Operations Research (OR). The course will cover deterministic (non-probabilistic) methods of operations research (linear programming, network flows, and integer programming) and their applications to resource allocation problems in business and networking

4 Credit Hours

Required Course for Computer Information Students. This course does not count substitute for Math 3700 below.

**Math 3700 Operations Research**

An introduction to operations research, with topics chosen from linear programming, transportation and assignment problems, network models, queuing theory, simulation, decision analysis, game theory, inventory theory, and Markov chains. Prerequisite: MATH 2100, Probability and Statistics for Engineers.

4 Credit Hours

*Counts towards the Applied Math Minor

Required Course for BSAM majors

**Math 3900 Introduction to Numerical Analysis**

Analysis of algorithms frequently used in mathematics, the sciences, engineering and industry. Topics include: root-finding, interpolation, linear systems, numerical differentiation and integration, solution of initial value problems. Numerical experiments will be conducted with C, Matlab, Java, Python or another appropriate high-level language. Prerequisites: COMP128, Computer Science I, and MATH 1750, Engineering Calculus II.

*Counts towards the Applied Math Minor

Required Course for BSAM majors.

**Math 2990 Independent Study**

This course investigates a topic of special interest to faculty and students that is outside regular course offerings. Prerequisite: Consent of department head and instructor.

0 to 4 Credit Hours

*Counts as a technical elective for BSAM. (Four 4-credit technical electives are required)

**Math 3800 Special Topics**

This course investigates a topic of special interest to faculty and students that is outside regular course offerings. Prerequisite: Consent of department head and instructor.

1 to 4 Credit Hours

*Counts as a technical elective for BSAM. (Four 4-credit technical electives are required for BSAM.)

**Math 2300 Discrete Math**

Topics of this course to be chosen from: elementary logic, sets, permutations and combinations, induction, relations, digraphs, functions, trees, Warshall's Algorithm, and Boolean algebra. Prerequisite: MATH 1500 Precalculus or MATH 1065 College Math C.

4 Credit Hours

Required Course for BSAM majors and for computer science majors.

**Math 2800 Finite Math**

Set theory and logic, matrix notation and manipulation, linear programming and simplex method are studied. An introduction to probability and statistics is provided. Problem-solving by computer. Prerequisite: MATH 1500 Precalculus.

4 Credit Hours

Required course for computer networking majors.

**Math 2850 Linear and Vector Algebra**

This course is an introduction to linear and vector algebra with computer science applications. Topics include: vector and matrix operations, linear transformations, curves and surfaces. Prerequisite: MATH 1500

4 Credit Hours

Required course for computer science majors.

**Math 4400 Introduction to Abstract Algebra**

Topics include groups, subgroups, and factor groups, homomorphisms, rings and fields, and applications that may include symmetry groups, frieze groups, and crystallographic groups and/or introductions to algebraic coding theory. This course is recommended for students intending to go to graduate school for mathematics or a mathematics-related discipline. Prerequisite: MATH 2300, Discrete Math.

4 Credit Hours

*Counts as a technical elective for BSAM or as an elective for the Applied Math minor.

(Four 4-credit technical electives are required for BSAM.)

**Math 2100 Probability and Statistics**

Topics studied are basic probability and a variety of probability distributions used in engineering modeling and reliability (expected life of products); linear regression and correlation; and hypothesis testing. Prerequisite: MATH 1800 Calculus II.

4 Credit Hours

Required course for BSAM, most engineering majors, and applied math minors.

**Math 2025 Multivariable Calculus**

Three dimensional Cartesian coordinate system, vectors, lines in three dimensions, planes and other surfaces, partial derivatives, directional derivatives, local extrema, polar coordinates, and multiple integrals in Cartesian and polar coordinates, vector fields, line integrals, and Green's Theorem. Prerequisite: MATH 1850, Engineering Calculus II or special permission.

4 Credit Hours

Required course for BSAM and engineering majors.

**Math 4475 Actuarial Math**

This course is designed to prepare students for the Society of Actuaries' exam P/CAS Exam 1. We will develop knowledge of the fundamental probability tools for quantitatively assessing risk with an emphasis on problems encountered in actuarial science. Prerequisite: MATH 2100 with a grade of B or better.

4 Credit Hours

*Counts as a technical elective for BSAM or as an elective for the Applied Math minor (Four 4-credit technical electives are required for BSAM.)

**Math 4575 Complex Variables**

Complex algebra and functions; analyticity; contour integration, Cauchy's theorem; singularities, power series; residues, evaluation of integrals; multivalued functions, potential theory in two dimensions, conformal mapping. Prerequisites: MATH 2025 and MATH 2500.

4 Credit Hours

*Counts as a technical elective for BSAM or as an elective for the Applied Math minor (Four 4-credit technical electives are required for BSAM.)

**Math 4675 Topology**

This course covers some basic notions of point-set topology, such as topological spaces, metric spaces, connectedness and compactness, Heine-Borel Theorem, quotient spaces, topological groups, groups acting on spaces, homotopy equivalences, separation axioms, Euler characteristic and classification of surfaces. If time permits, additional topics including the study of the fundamental group will follow.

4 Credit Hours

*Counts as a technical elective for BSAM or as an elective for the Applied Math minor (Four 4-credit technical electives are required for BSAM.)

**Math 4875 Real Analysis I**

Topics include introductory proof writing, the real number system, limits, continuity, properties of real-valued functions, differentiation, elementary theory of integration. This course counts as a technical elective for BSAM majors and minors

4 Credit Hours

*Counts as a technical elective for BSAM or as an elective for the Applied Math minor (Four 4-credit technical electives are required for BSAM.)

**Math 2750 Differential Equations and Systems Modeling**

Linear systems, matrix algebra, eigenvalues and eigenvectors, solutions of first and second order ordinary differential equations, stability and equilibrium solutions, Laplace transforms, state space models and simulation. Prerequisite: MATH 1800, Calculus II or MATH 1850, Engineering Calculus II or special permission.

4 Credit Hours

* Required course for the Applied Math Minor. You can take this or Math 2500. Required course for biomedical engineering majors.

**Math 2500 Differential Equations**

Introduction to the solution of ordinary differential equations (ODEs). Topics will include Euler's method, first-order OEDs and higher order lineral OEDs with constant coefficients, using Fourier series, using Laplace transforms, and applications. Prerequisite: MATH295, Engineering Calculus II or special permission.

4 Credit Hours

* Required course for the Applied Math Minor. You can take this or Math 2750.

Required course for BSAM, most engineering majors, and applied math minors.

**Math 4900 Partial Differential Equations**

An introductory course in partial differential equations which covers the methods of characteristics, separation of variables, Fourier Series, finite differences, Fourier Transforms and Green’s functions. Prereq: Math 2500

4 Credit Hours

*Counts as a technical elective for BSAM or as an elective for the Applied Math minor (Four 4-credit technical electives are required for BSAM.)

**Math 4950 Dynamical Systems and Chaos**

Introduction to dynamical systems and chaos with emphasis on applications in science and engineering. Topics include one-dimensional flows (fixed points, stability and bifurcations), two-dimensional flows (phase planes, limit cycles, and bifurcations), and chaos (Lorenz equations, maps, fractals and strange attractors). This course counts as a technical elective for applied mathematics majors and minors. Prerequisite: MATH 2400, Applied Differential Equations I,or MATH 2500, Differential Equations.

4 Credit Hours

*Counts as a technical elective for BSAM or as an elective for the Applied Math minor (Four 4-credit technical electives are required for BSAM.)

**Math 4050 Machine Learning**

Introduction to the field of machine learning. This course focuses on algorithms to help identify patterns in data and predict or generalize rules from these patterns. Topics include: supervised learning (parametric/non-parametric algorithms, kernels, support vector machines); unsupervised learning (clustering, decreasing dimensionality); model selection; and applications (such as speech and handwriting recognition, medical imaging, and drug discovery). Students who have basic programming skills and who have taken probability are encouraged to take this course. This course counts as a technical elective for BSAM majors and minors

*Counts as a technical elective for BSAM or as an elective for the Applied Math minor (Four 4-credit technical electives are required for BSAM.)

**Math 2200 Advanced Statistics**

Topics include: design of experiments, correlation and regression, analysis of variance, t-tests, nonparametric methods, failure, mode, and effects analysis. Prerequisite: MATH 2100, Probability and Statistics for Engineers.

4 Credit Hours

*Counts towards the Applied Math Minor; Students can take this or COMP611 Biostatistics.

Required Course for BSAM majors.

**Math 5000 Applied Math Final Year Design I**

Student will work alone and in small group projects to study, analyze, design, and sometimes build and test concepts in an applied mathematics subfield of their choosing. The study will be performed under thee direction of one or more faculty advisors. Projects from industry be encouraged to increase the interaction and cooperation with firms. Course requirements include regular oral and written progress reports throughout the semester. The final technical report by students may include a plan for the following Applied Mathematics Final Year Design II course. Prerequisite: Final year standing in BSAM program.

4 Credit Hours

Required Course for BSAM majors

**Math 5500 Applied Math Final Year Design II**

This course is a continuation of Applied Math Final Year Design I. Students will continue with their design and analysis (or with new designs and analysis) with emphasis on improvements and applications. Other faculty and local industry professionals will review the student work and make recommendations.

4 Credit Hours

Required Course for BSAM majors

**Math 2860 Linear Algebra and Matrix Theory**

Topics include the basic operations of n-tuples and matrices, geometric vectors, equations of lines and planes, systems of linear equations, row reduction of matrices, linear independence, determinants, and an introduction to basis, dimension, eigenvalues, eigenvectors, and vector spaces. Prerequisite: MATH 2000 Calculus III. 4 Credit Hours Required course for BSAM, most engineering majors, and applied math minors.

**Notes:**

- BSAM means Bachelor of Science in Applied Math.
- Click here to see the course sequence for BSAM students. (BSAM majors can complete the degree in three years but there is a four year option for students that would like more time.)
- Click here to see the 20 credits that are required for Applied Math minors.

- BSAM students have to take 8 credits of English, 20 credits of humanities and social science courses, two computer science courses (CS128 and CS201), 1 electromechanical engineering course (ELMC805) and a 8 credits of a science sequence. For descriptions of these other courses of the please see the Academic Catalogue: http://www.wit.edu/catalog/
- A total of 16 semester credit hours of technical electives must be taken as a part of BSAM. BSAM students may choose, after consultation with their faculty advisor, among the electives offered each semester. Technical elective courses will include biological, financial and physical science applications through courses offered by the Applied Mathematics Department (see courses listed above as technical electives) as well as courses offered by other departments besides the Applied Math Department (with approval from the Applied Math Department Chair and the student’s advisor); examples include: COMP310 Data Structures, COMP611 Introduction to Biostatistics with Applications and COMP411 Algorithm Design and Analysis.