*(partial list)*

- AT&T
- CA Simmons Associates
- Fram Corporation
- HBO Company
- Raytheon
- School Districts (Various)
- Wall Street, NYC

*(partial list)*

- Boston College
- Brown University
- Dartmouth College
- Georgia Institute of Technology
- Harvard University
- New York University
- SUNY - Albany
- University of California - Irvine
- University of Wisconsin

The major consists of 10 required courses, beginning with a two-semester calculus sequence. These are followed by a four-course mathematics core and two major electives to be chosen from a specified list of alternatives.

The capstone course of the program is a problem-solving seminar which is designed to draw upon all courses in the foundation and to develop the student’s abilities in mathematical reasoning. Students are further advised to include courses in discrete mathematics, computer science and the history of mathematics in their studies.

Students wishing to teach mathematics at the secondary level must follow the Dual Major with Secondary Education and Mathematics. Students pursuing a double major in elementary education and mathematics may take either of the mathematics majors described below, but are encouraged to take the Dual Major with Secondary Education.

Majors pursuing a Bachelor of Science in mathematics must satisfy University Core Curriculum requirements and the College speech requirement, COMM 210. In addition, they must complete the following courses and a sufficient number of electives to total 120 credits. Majors are encouraged to apply electives toward a minor or second major.

Requirements for Bachelor of Science in Mathematics:

- MATH 213 Calculus I and Lab
- MATH 214 Calculus II and Lab
- MATH 221 Discrete Mathematics
- MATH 331 Linear Algebra
- MATH 351 Calculus of Several Variables
- MATH 371 Real Analysis
- MATH 390 Abstract Algebra
- MATH 421 Problem Seminar
- and two electives selected from: MATH 255, 301, 305, 315, 317, 330, 335, 340, 342, 370, 381, and 431.

The Mathematics and Secondary Education Dual Major

Majors pursuing a dual major for secondary education must satisfy University Core Curriculum requirements and the College speech requirement. In addition, they must complete the following courses and a sufficient number of electives to total 120 credits. Note that there are no electives among the mathematics courses required for the double major with secondary education.

Requirements for Bachelor of Science in Mathematics with Secondary Education Dual Major:

- MATH 213 Calculus I and Lab
- MATH 214 Calculus II and Lab
- MATH 221 Discrete Mathematics
- MATH 315 Probability and Statistics
- MATH 331 Linear Algebra
- MATH 335 Topics for Secondary Mathematics Education
- MATH 340 History of Mathematics
- MATH 351 Calculus of Several Variables
- MATH 390 Abstract Algebra
- COMSC 110 Introduction to Computer Science I and Lab

Requirements for the Minor in Mathematics

- MATH 213 Calculus I and Lab
- MATH 214 Calculus II and Lab
- and four Mathematics courses at the 200 level or above.

**MATH 110 - Mathematics in the Modern World**

Fulfills the University Core Curriculum requirement in mathematics

Survey of mathematics designed for students who are majoring in non-technical areas. Topics may include problem-solving techniques, an introduction to statistical methods, and an introduction to the mathematics of finance. (3 credits) Fall, Spring

**MATH 115 - Mathematics for Elementary Education I**

Fulfills the University Core Curriculum requirement in mathematics

Looks at mathematical topics necessary for elementary school teachers and helps students develop an adult perspective on the mathematics they will have to teach. Covers concepts in problem solving, sets and whole numbers, numeration, number theory, integers, fractions, decimals, proportional reasoning and statistics. (3 credits) Fall, Spring

**MATH 116 - Mathematics for Elementary Education II**

Fulfills the University Core Curriculum requirement in mathematics

This course looks at mathematical topics necessary for elementary school teachers and helps students develop an adult perspective on the mathematics that they will have to teach. Covers concepts in probability, algebraic reasoning, geometric figures, measurement, geometric transformations, congruence and similarity. (3 credits) Fall, Spring

**MATH 117 - College Algebra**

Fulfills the University Core Curriculum requirement in mathematics

Prerequisite: Placement by examination

Covers linear and quadratic equations and inequalities, systems of linear equations, polynomials and rational expressions, partial fractions, exponents and radicals, and introduces linear, quadratic, rational, exponential and logarithmic functions. (3 credits) Fall, Spring

**MATH 124 - Basic Statistics**

Fulfills the University Core Curriculum requirement in mathematics

Emphasizes descriptive statistics, probability, estimation, hypothesis testing, regression and correlation. (3 credits) Fall, Spring

**MATH 136 - Precalculus**

Fulfills the University Core Curriculum requirement in mathematics

Prerequisite: Successful completion (C- or higher) of MATH 117 or placement by examination

The focus of this course is on functions, which are of central importance in Calculus. Topics include definitions, properties, and applications of algebraic, inverse, exponential, logarithmic and trigonometric functions. (4 credits) Fall, Spring

**MATH 141 - Finite Mathematics**

Fulfills the University Core Curriculum requirement in mathematics

This course is primarily designed for business majors and focuses on building algebraic skills while emphasizing applications, models, and decision-making from business and the social sciences. Topics include linear equations, functions, mathematics of finance, systems of linear equations, matrices, linear inequalities and linear programming. (3 credits) Fall, Spring

**MATH 207 - Applied Calculus for Business and Social Science**

Prerequisite: Successful completion (C- or higher) of MATH 136 or placement by examination

(A student cannot receive credit for both this course and MATH 213.)

This course covers fundamental notions of differentiation and integration of algebraic, exponential and logarithmic functions, with problems drawn principally from business situations. Topics include optimization, related rates, and simple applications and methods of integration. While covering traditional analytic methods, this course also emphasizes graphical and numerical approaches. This course may not be taken for credit by mathematics majors, minors or core concentrators. (3 credits) Fall

**MATH 213 - Calculus I and Lab**

Fulfills a course requirement in the Mathematics Core Concentration

Fulfills the University Core Curriculum requirement in mathematics

Prerequisite: Successful completion (C- or better) of MATH 136 or placement by examination

Covers the differential calculus of a single variable and introduces integration. Topics include limits and continuity, differentiation of algebraic and transcendental functions, applications of derivatives to rates of change, optimization, and curve sketching, and the Fundamental Theorem. The laboratory component involves use of computer algebra software. (4 credits) Fall, Spring

**MATH 214 - Calculus II and Lab**

Fulfills a course requirement in the Mathematics Core Concentration

Fulfills the University Core Curriculum requirement in mathematics

Prerequisite: Successful completion (C- or higher) of MATH 213

Covers the integral calculus of algebraic and transcendental functions and its applications. Topics include elementary differential equations, computation of areas, volumes, work and other physical quantities, integration techniques, improper integrals, and infinite series. The laboratory component Involves use of computer algebra software. (4 credits) Fall, Spring

**MATH 218 - Applied Calculus for Life Sciences**

Prerequisite: Successful completion (C- or higher) of MATH 213

(A student cannot receive credit for both this course and MATH 214.)

This course covers core concepts of integral calculus, important notions of linear algebra and multivariable calculus. It strongly emphasizes their applications to life sciences. Topics include techniques of integration, differential equations, matrix algebra, eigenvalues and eigenvectors, stability of equilibrium points and mathematical models such as the predator-prey, Leslie and microbial growth models. (3 credits) Fall, Spring

**MATH 221 - Discrete Mathematics**

Fulfills a course requirement in the Mathematics Core Concentration

Fulfills the University Core Curriculum requirement in mathematics

Prerequisite: Successful completion (C- or higher) of MATH 136 or placement by examination

Focuses on concepts and techniques in mathematics that play a fundamental role in the study of computer science. Sets, functions and relations, algorithms, proof by induction, recursive functions, and elementary combinatorics and graph theory are studied. (3 credits) Spring

**MATH/BIO 250 - Introduction to Biostatistics**

Cross-listed with BIO 250

Fulfills the statistics requirement for the Biology, Marine Biology and Environmental Science Majors

Fulfills a course requirement in the Mathematics Core Concentration

Prerequisite: MATH 136, BIO 104 and sophomore standing or consent of instructor

The course is a team-taught introductory course in statistics with applications to biological problems. Students will learn statistical concepts and the technical details behind those concepts as well as when and how to apply particular procedures. This class is a mix of theoretical understanding of statistical principles and problem application using statistical software. Particular topics include the following: Measures of the central tendency and of dispersion and variability, hypothesis testing, Analysis of Variance and linear, multiple and polynomial regression. (3 credits) Fall

**MATH 255 - Introduction to Mathematical Software**

Fulfills a course requirement in the mathematics major, minor, or core concentration

Prerequisite: Successful completion (C- or higher) of MATH 213

This course shows students how to use specialized software for mathematical and scientific problem solving, exploration and visualization. Students will learn how to take advantage of the capabilities of free, open source mathematical software in a variety of mathematical and modeling situations. (3 credits) Spring

**MATH 301 - Linear Programming**

Fulfills a course requirement in the Mathematics Core Concentration

Prerequisite: Successful completion (C- or higher) of MATH 213; or consent of instructor

Presents matrices, systems of linear equations, linear programming problems (diet, work scheduling, transportation, assignment and transshipment), the simplex algorithm, and dual linear programming problems. (3 credits) Alternate Spring

**MATH 305 - Mathematical Modeling**

Fulfills a course requirement in the mathematics major, minor or core concentration

Prerequisite: Successful completion (C- or higher) of MATH 214 or 218: or permission of instructor

Mathematical modeling is a powerful tool that helps us to understand a plethora of phenomena in various disciplines such as mathematical sciences, operation research, biology and engineering. The emphasis of this course is on applications to real-world problems. Both discrete and continuous modeling will be covered. Topics include modeling change (with difference equations), model fitting (least squares), optimization of discrete models and modeling with differential equations. (3 credits) Fall

**MATH 315 - Probability and Statistics**

Fulfills a course requirement in the Mathematics Core Concentration

Prerequisite: Successful completion (C- or higher) of MATH 214; or consent of instructor

Emphasizes probability, probability density functions, distributions, statistical inferences and estimation, correlation, and regression. (3 credits) Fall, Spring

**MATH 317 - Differential Equations**

Fulfills a course requirement in the Mathematics Core Concentration

Prerequisite: Successful completion (C- or higher) of MATH 214; or consent of instructor

Studies methods of solution of ordinary differential equations with applications in science and engineering. Extensive use is made of the method of Laplace transforms. (3 credits) Fall, Spring

**MATH 330 - Engineering Mathematics**

Fulfills a course requirement in the Mathematics Core Concentration

Prerequisite: Successful completion (C- or higher) of MATH 317; or consent of instructor

This is a course in mathematical methods for students majoring in engineering. Topics to be discussed include: vector calculus, the theorems of Green, Gauss and Stokes, power series, Fourier series and orthogonal polynomials. (3 credits) Fall

**MATH 331 - Linear Algebra**

Fulfills a course requirement in the Mathematics Core Concentration

Prerequisite: Successful completion (C- or higher) of MATH 213; or consent of instructor

Presents matrices, determinants, vector spaces, linear transformations, eigenvectors and eigenvalues, diagonalization, solution of systems of linear equations by the Gauss-Jordan method, and applications. (Completion of MATH 221 - Discrete Mathematics is recommended.) (3 credits) Spring

**MATH 335 - Topics for Secondary Mathematics Education**

Fulfills a course requirement in the Mathematics Core Concentration

Prerequisites: Successful completion (C- or higher) of MATH 214 and 221; or consent of instructor

Focuses on two areas of mathematics required for secondary mathematics education: number theory and geometry. Number theory topics to include: divisibility, primes, congruences, perfect numbers and the Fibonacci numbers. Geometry topics to include a review of Euclidean geometry, transformation geometry, and an introduction to several non-Euclidean topics: neutral geometry, Bolyai-Lobachevskian geometry, and Riemannian geometry. (3 credits) Alternate Fall

**MATH 340 - The History of Mathematics**

Fulfills a course requirement in the Mathematics Core Concentration

Prerequisites: Successful completion (C- or higher) of MATH 214 and 221; or consent of instructor

An introduction to the history of mathematics, focusing on the origins and development of algebra, geometry, trigonometry, and/or calculus. Includes the study of mathematical problems associated with the historical topics. (3 credits) Alternate Fall

**MATH 342 - Numerical Analysis**

Fulfills a course requirement in the Mathematics Core Concentration

Prerequisites: Successful completion (C- or higher) of MATH 214 and either COMSC 111 or MATH 317; or consent of instructor

Emphasizes iterative solution of linear and non-linear equations, numerical solution of linear systems, interpolation polynomials, curve-fitting, numerical differentiation, numerical integration, numerical solution of ordinary differential equations, and consideration of error estimations. (3 credits) Alternate Spring

**MATH 351 - Calculus of Several Variables**

Fulfills a course requirement in the Mathematics Core Concentration

Prerequisite: Successful completion (C- or higher) of MATH 214; or consent of instructor

Introduces functions of several variables including partial differentiation, multiple integrals, line and surface integrals, and the theorems of Green, Gauss, and Stokes. (4 credits) Alternate Fall

**MATH 370 - Advanced Calculus for the Physical Sciences**

Fulfills a course requirement in the Mathematics Core Concentration

Prerequisite: Successful completion (C- or higher) of MATH 214; or consent of instructor

Designed to develop a basic competence/maturity in each of many areas of mathematics needed in junior and senior level courses in mathematics, biology, chemistry and engineering. The focal objective of the course is to train students to formulate physical phenomena in mathematical language. Topics include complex variables, matrix algebra, Fourier series, and partial differential equations. (3 credits) Alternate Spring

**MATH 371 - Real Analysis**

Fulfills a course requirement in the Mathematics Core Concentration

Prerequisites: Successful completion (C- or higher) of MATH 221 and 351; or consent of instructor

In the 19th century, mathematicians from Cauchy to Cantor created a foundation for calculus which was as rigorous as the foundations of the other branches of mathematics. Topics include: definitions of convergence, continuity, differentiability, and integrability; the Intermediate, Maximum-Minimum, and Mean Value Theorems; Taylor’s Theorem and power series; uniform and pointwise convergence. (3 credits) Alternate Spring

**MATH 381 - Complex Analysis**

Fulfills a course requirement in the Mathematics Core Concentration

Prerequisite: Successful completion (C- or above) of MATH 351 or consent of instructor.

Emphasizes functions of one complex variable including the Cauchy-Riemann equations, contour integration, Cauchy integral formulas, the Residue Theorem, series representation, and mapping theorems. (3 credits) Alternate Spring

**MATH 390 - Abstract Algebra**

Fulfills a course requirement in the Mathematics Core Concentration

Prerequisite: Successful completion (C- or higher) of MATH 221; or consent of instructor

Focuses on groups, rings, and their homomorphisms. Topics include subgroups and quotient groups, group actions, ideals, quotient rings, Euclidean and principal ideal domains, and factorization. (3 credits) Alternate Fall

**MATH 421 - Problem Seminar**

Fulfills a course requirement in the Mathematics Core Concentration

Prerequisites: Successful completion (C- or higher) of MATH 331, 351, and 390; or consent of instructor

Designed to enhance students’ mathematical maturity as they work to solve specifically chosen mathematical problems. (3 credits) Alternate Spring

**MATH 431 - Special Topics**

Fulfills a course requirement in the Mathematics Core Concentration

Prerequisites: Successful completion (C- or higher) of MATH 221, 351 and 390; or consent of instructor

A variable content course, offered periodically when there is sufficient interest among students for in-depth coverage of a topic which is not included among the standard mathematics offerings. Possible topics include topology, number theory, or geometry. (3 credits) Special Offering

**MATH 450 - Research in the Mathematical Sciences**

Prerequisites: Prior departmental approval of a research proposal, 3.3 GPA or permission of the department

This course serves as a capstone experience for outstanding students in the major. Working closely with a full time faculty mentor, students engage in research on a topic of choice. The culmination of the course is a formal written thesis and a public oral presentation (1-3 credits) Fall, Spring

**MATH 451 - Senior Thesis**

Prerequisites: Prior departmental approval of a research proposal, 3.3 GPA or permission of the department, and MATH 450

Students actively participate in mathematical investigation and exposition, working in conjunction with a math faculty member on research questions. Review of relevant literature and research methods will be incorporated. Students are required to present their findings both in writing (consistent with the standards of the discipline) and in public presentations. Topics vary by instructor. (3 credits) Fall, Spring

Copyright 2014, Roger Williams University • One Old Ferry Road, Bristol, RI 02809

1-800-458-7144 • 401-253-1040

1-800-458-7144 • 401-253-1040