Department of Mathematics and Computer Studies

"You're a mathematics major? So, what are you going to do with it?"

The answer to this question is, "Whatever I want!" When you major in mathematics you are prepared to enter many different fields after graduation. One of our guiding philosophies is that if you couple your major (or minor) in mathematics with another major (or minor), your possibilities are endless. Some recent mathematics majors and minors at Salem have also completed undergraduate work in:

Our students have entered graduate and professional programs in mathematics, statistics, biometry, biology, chemistry, epidemiology, law, medicine, dentistry, economics, econometrics, accounting, religion, secondary education, educational statistics, public policy, nursing, secondary school administration, civil engineering, environmental engineering, and mathematics education. Our graduates have also found employment opportunities in a wide variety of fields after graduating from Salem, including public health, biostatistics, aviation consulting, fund raising, accounting, banking, financial planning, economics research, elementary, middle and secondary school teaching, and college and university faculty positions. We have alumnae who own their own businesses, who are well-respected artists, who have chaired boards, who are college professors, and who are award winning high school teachers.

Opportunities for internships and summer research experiences are available, both locally, nationally and internationally, and many of our students take advantage of study-abroad opportunities in places such as Hungary, Japan, Germany, Australia, Hong Kong, Greece, and the United Kingdom.

On-campus, mathematics majors and minors are active and visible participants in the Women in Science and Mathematics Program (WISMP), the Celebration of Academic Excellence, student life and student government.

Mathematics Placement and Academic Support

All undergraduate students entering Salem College take a Mathematics Placement Examination in order for the department to properly guide each student to the appropriate mathematics courses that satisfy Salem Signature requirements or that satisfy the requirements for her intended major. Students are encouraged to enroll in the course in which they are placed as early as possible during their Salem career so that they may benefit the most from the quantitative experience.

Academic support services are offered to students through the Office of Academic Support and through the QUEST Center for quantitative enrichment, science and technology. The QUEST Center offers on-line resources, live chat tutoring, and in-person tutoring for free to all Salem College students. The mathematics department also employs qualified work-study students whenever possible to provide free tutoring in many first- and second-year level courses.

Your Faculty

The mathematics faculty are active, engaged mathematicians that regularly participate in and present at national and international conferences and are committed to the undergraduate education of each Salem student, regardless of the student's major. With over 100 years of combined teaching experience at a variety of levels, and numerous teaching awards between them, you are assured a personal, professional, and individual experience, no matter how many mathematics courses you choose to pursue.

Professor Debbie Harrell (debbie.harrell@salem.edu), chair, received her BS in mathematics from Wake Forest University and her MS in applied mathematics from North Carolina State University. She teaches all levels of mathematics at Salem, and has a love for the history of mathematics and the Fibonacci numbers, and is dedicated to the use of technology in the teaching and learning of mathematics. She is a two-time recipient of the Omicron Delta Kappa (ODK) Teacher of the Year award at Salem College and has also received the HA Pfohl Award at Salem for her service and loyalty to the College and for her excellence in teaching. She loves to read, loves to travel within the United States and across the world, and has sponsored or co-sponsored numerous January Program travel courses.

Professor Wenzhi Sun (wenzhi.sun@salem.edu) came to Salem after receiving his PhD in mathematics from Pennsylvania State University, and also holds the BS and MS from Nanjing University in China. He has taught mathematics to students of all ages, and specializes in symbolic logic with interests in numerical analysis and graphical programming. In addition to teaching all levels of mathematics here, he currently is responsible for teaching our computer programming course which utilizes the Java language. He, too, has received the ODK Teacher of the Year award at Salem.

Professor Paula Grafton Young (paula.young@salem.edu) received her BS in mathematics from the University of Arkansas at Monticello, after which she earned the MS and the PhD in mathematics from the University of Arkansas, Fayetteville, with a specialization in functional analysis. Like her colleagues, she teaches all levels of mathematics at Salem and many of the courses that support the minor in statistics. She specializes now in metric spaces, particularly those that can be simplified and applied to realistic situations, and has interests in mathematical biology, along with applications of finite difference equations and dynamical systems. She has also received the ODK Teacher of the Year award and the HA Pfohl award, and served as the Salem Distinguished Professor for the 2002 - 2007 term.

Your Program

The department offers both a Bachelor of Arts and a Bachelor of Science degrees with a major in mathematics, as well as a minor in mathematics and a minor in statistics, each of which provides you with the opportunity for in-depth study and prepares you for a wide range of careers and post-graduate study. In consultation with the faculty in the department, you will choose appropriate elective courses and other on- or off-campus opportunities that complement your interests and prepare you for the goals you have set for your future. Our courses are taught in classrooms equipped with relevant technology, including computer algebra systems, object-oriented programming capability, dynamic geometry software, and state-of-the-art statistical computing environments.

Your Results

When you graduate with a major or minor in mathematics or a minor in statistics, you will have the quantitative and technological skills necessary to go right into the workforce or right into graduate or professional school. You will be well-equipped to communicate mathematical concepts and ideas, to use appropriate technological tools, and to succeed in whatever goals you have set for yourself.

Mathematics Courses (MATH)

The study of mathematics affords excellent training in rigorous deductive logic and familiarizes the student with results and techniques widely applied in science and industry. Students who major or minor in math are prepared for many different experiences after graduation. Some pursue graduate work in mathematics or an allied field. Other students obtain jobs with various industrial and research-oriented firms.

020. College Algebra One course

Structure of algebraic properties of real numbers, polynomials and their roots, rational expressions, exponents and radical expressions, binomial theorem, solution of equations and inequalities, properties of functions and graphing. The course is designed to prepare first-year students for further mathematics courses, such as MATH 025 and MATH 070. Some familiarity with basic algebra is expected. Not included in the major. Prerequisite: placement. Fall, alternate years.

025. Elementary Functions and Graphs One course

Functions, including the trigonometric functions, exponential functions and logarithmic functions, will be studied in detail. In addition, topics in analytic geometry, including conic sections and solutions of systems of equations using matrices will be covered. This course is designed to prepare the student for calculus. Prerequisite: MATH 020 or placement. Not included in the major. Fall.

060. Introduction to Finite Mathematics One course

A course in mathematics that is applicable in a variety of fields, including business, accounting and the social sciences. Topics include sets, Venn diagrams, probability, statistics, linear functions, linear regression, systems of linear equations and matrix algebra. Applications are used throughout the course. Other topics such as graphic linear programming, the Simplex method, the mathematics of finance, the game theory, logic and Markov processes may be included at the discretion of the instructor. Some familiarity with basic algebra is expected. Prerequisite: one year of high school algebra or placement. Fall and Spring.

070. Essential Calculus One course

An algebra-intensive introduction to calculus with emphasis on applications to business, accounting and social sciences. Derivatives and integrals of polynomial, rational and exponential and logarithmic functions will be discussed. Applications include optimization, price elasticity of demand, point of diminishing returns and producer and consumer surplus. Not included in the mathematics major. Students may not receive credit for both MATH 070 and MATH 100. Prerequisite: MATH 020 or placement. Spring.

100. Calculus I One course

Functions, limits, continuity, the derivative and its applications and The Fundamental Theorem of Calculus. Prerequisite: Placement or a grade of C or better in MATH 025. Fall and spring.

101. Calculus II One course

Applications of the integral, integration techniques, inverse trigonometric functions, exponential and logarithmic functions, L’Hopital’s Rule, improper integrals, conic sections, parametric and polar equations. Prerequisite: MATH 100. Fall and spring.

102. Calculus III One course

Infinite series, vectors and vector algebra, surfaces in space, lines and planes in space, vector-values functions and an introduction to partial differentiation. Prerequisite: MATH 101. Fall.

103. Calculus IV One course

Partial differentiation, properties of the gradient, optimization of multivariate functions, the method of Lagrange multipliers, multiple integrals in rectangular spherical and cylindrical coordinates, vector fields, line and surface integrals, Greens Theorem, the Divergence Theorem and Stokes theorem. An introduction to differential equations may also be included. Prerequisite: MATH 101. Spring.

110. Introductory Linear Algebra One course

Vector methods in geometry, real vector spaces, systems of linear equations, linear transformations and matrices, equivalence of matrices and determinants. Prerequisite: MATH 101. Spring.

122. Probability One course

Probability theory, including discrete and continuous random variables, moments and moment-generating functions, bivariate distributions, the Central Limit Theorem, Chebychev’s Inequality and the Law of Large Numbers. Required for secondary certificate. Prerequisite: MATH 101. Fall, alternate years.

132. Mathematical Statistics One course

A calculus-based treatment of both descriptive and inferential statistics. Topics will include organizing data, sampling distributions, hypothesis testing, estimation theory, regression, correlation and analysis of variance. Emphasis will be placed on both theory and applications. Prerequisite: MATH 122. Spring, alternate years.

140. Introduction to Numerical Analysis One course

Solutions of equations in one variable, interpolation and polynomial approximation, numerical differentiation and integration, solutions of linear systems and initial value problems for ordinary differential equations. Examples will be taken from the physical and biological sciences. Prerequisite: MATH 102 and CPSC 140. Offered as needed.

142. Statistical Methods with R One course

This course presents statistical inference with a focus on statistical computing in the R environment. Topics include: graphical representations of data; measures of central tendency and dispersion; binomial, normal, Student’s t, chi2- and F-distributions as they apply to inferential statistics; sampling methods; linear and multi-linear regression, correlation; hypothesis testing; analysis of variance. Three lectures and a two-hour laboratory per week. Pre-requisite: MATH 100; CPSC 140 strongly recommended.

162. Mathematics of Finance One course

This course covers the basic mathematical concepts in consumer-related instruments and derivative asset pricing. The mathematical formulas associated with consumer instruments, including effective rates of interest, annuities, sinking funds, and amortized loans, will be derived and explained in detail. A discussion of the principal assets traded in financial markets, such as Arbitrage Pricing Theory, will be followed by detailed explanations and derivations of the formulas associated with bond valuation, and the pricing of options and derivative securities in the contexts of binomial probability trees and the Black-Scholes option-pricing model. Both American- and European-style options are included in the course. Pre-requisite: MATH 102.

200. Independent Study in Mathematics One-half to two courses

Independent study under the guidance of a faculty advisor. Open to students with a 2.0 cumulative average and permission of the chair of department. Independent study may take the form of readings, research, conference, project and/or field experience. Independent study may be taken for a total of four courses, no more than two in any term.

202. College Geometry One course

An axiomatic approach to the foundations of finite geometries, Euclidean, Hyperbolic and Elliptic geometries, transformational geometry in the plane, convexity and an introduction to topology. Additional topics, including graph theory, knot theory, fractal theory, projective geometry and Euclidean constructions, may also be included at the discretion of the instructor. Required for secondary certificate. Prerequisite: MATH 110. Spring, alternate years.

210. Differential Equations One course

Basic theory of ordinary differential equations of first order and first degree with applications; linear differential equations and linear systems; operational methods, numerical methods,solutions in series, existence and uniqueness theorems. Prerequisite: MATH 101. Falls, alternate years.

221. Modern Algebra One course

Elementary theory of groups, rings, integral domains and fields; properties of number systems; polynomials; and the algebraic theory of fields. Required for secondary certificate. Prerequisite: MATH 110. Fall, alternate years.

240. Topology One course

Point set topology, including basic topological properties, metric spaces, topological spaces and product spaces. Offered as needed.

242. Nonparametric Statistical Methods One course

This course is an introduction to the methods of statistical analysis appropriate to categorical and other data when no assumptions are or can be made about the parent distribution of the data. The Wilcoxon Rank-Sum test and other rank tests, goodness of fit tests and signed tests will be discussed. Data sets will be included from marketing, sociology, biology, psychology and education. Computer usage required, though students may use whatever statistical computing environment with which they are familiar. Pre-requisite: MATH 070 or 100 and either BIOL 205, BUAD 240, ECON 320, MATH 132, PSYC 101, or SOCI 215.

250. History of Mathematics One course

A general survey of the history and development of mathematical ideas and thought. Topics include Egyptian, Babylonian, Hindu-Indian, ancient Greek and Arabic mathematics, as well as mathematics from outside Western tradition. The birth of Calculus and selected topics from the 19th and 20th centuries will be included. Biographical and historical content will be supplemented by the study and application of techniques and procedures used in earlier eras. Thus, this will be a “working” course in which students will focus on doing sample problems in ways that illustrate important developments in mathematics. Prerequisite: MATH 101.

270. Internship in Mathematics One course

An opportunity to use the knowledge and skills the student has learned in coursework to solve problems in a real work setting; the apprenticeship aspect of the internship implies that the student has some base of knowledge and will increase her knowledge and skills by direct contact with an experienced, knowledgeable mentor. Open to sophomores, juniors and seniors with a 2.0 cumulative average; maximum credit per term is one course; admission by application only.

280. Special Topics in Mathematics One course

Investigation of a topic, issue or problem in mathematics. Topics might include: history of mathematics, mathematical modeling, dynamical systems, graphical programming.

290. Honors Independent Study in Mathematics One course

Advanced independent study under the guidance of a faculty advisor. Normally open to juniors and seniors with a 3.5 average in mathematics. Subject to the approval of the chair of the department. Honors work may be taken for a maximum of two courses.

321. Real Analysis One course

A rigorous treatment of the real number system, limits, continuity, sequences, series, differentiation and Riemann integration. Prerequisite: MATH 103. Spring, alternate years.

330. Complex Variables One course

The complex number system; complex-valued functions; limits and continuity; complex differentiation and analytic functions; complex integration and Cauchy Theory; infinite series. Prerequisites: MATH 102 and 110. Spring, alternate years.

Dr. Debbie Harrell