# Department of Mathematics and Computer Studies

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.

### "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:

Accounting | Arts Management | Biology | Business Administration |

Chemistry | Communication | Computer Science | Dance |

Economics | Education | English | Finance |

French | German | History | Interior Design |

International Business | Music | Psychology | Religion |

Sociology | Spanish | Studio Art | |

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, the QUEST Program, 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. **Traditional-aged students** should click here for more information and Fleer Center students should click here for information and instructions. 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 Program for quantitative enrichment, science and technology. The QUEST Center offers on-line resources 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.

**Why Take More Mathematics than is Required by Your Major or by the Salem Signature General Education Program?**

Research continues to support the notion that women who take more mathematics courses in high school and in college experience a positive impact on future earnings. (See: Rose, Betz, *Math Matters: The Link Between High School Curriculum, College Graduation and Earnings*, 2001.) So, while you may only be *required* to take a single mathematics course for your major or for General Education purposes, we strongly encourage you to consider taking at least one additional course from our department in order to maximize your earnings potential, strengthen your applications for graduate or professional school, and increase opportunities for internships while a student at Salem College. Rest assured, we will help you and your advisor choose any and all mathematics courses which would be most beneficial to you based on your past mathematical experiences and your academic or career goals.

**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 nearly 70 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 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. Her office is SCIE 308.

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. Her office is SCIE 106.

Professor Wade Mattox (wade.mattox@salem.edu) received his BS, MS and PhD from Virginia Tech University. His dissertation, "Homology of Group Von Neumann Algebras", falls under the categories of group theory, group Von Neumann algebras, and homology. Joining Salem in August 2012, Professor Mattox will teach a full range of mathematics courses and will be responsible for MATH 221: Modern Algebra. His commitment to excellence in undergraduate teaching and professional activity are hallmarks of Salem's mathematics faculty--he received the 2011 Outstanding Graduate Teaching Assistant of the Year for Teaching Excellence from the Mathematics Department at Virginia Tech and was supported by an NSF grant each of his last two summers as a PhD candidate. We are pleased to welcome him as the newest member of Salem's mathematics department. His office is SCIE 309.

Emeritus 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 was also responsible for teaching our computer programming course which utilizes the Java language. He, too, has received the ODK Teacher of the Year award and the H. A. Pfohl Award. He retired at the end of the 2011 - 2012 academic year.

**Your Program**

Mathematics and Computer Science 4-Year Plan

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.

Each student who enters Salem is given a placement test in mathematics. Any student who places in or completes MATH 060 or higher cannot receive credit for MATH 020 or MATH 025 without special permission from the chair of the department.

Secondary licensure in mathematics requires courses beyond those required for the major. Refer to the section on Education and the Teaching, Schools and Society Major.

All mathematics majors must take at least three courses above the level of MATH 102 at Salem.

### Mathematics Major (B.A.)

The student who seeks the bachelor of arts degree with a major in mathematics must complete ten courses: MATH 100, 101, 102, 103, 110, 210, 221 and either 321 or 330, as well as CPSC 140: Introduction to Programming and at least one mathematics elective above the level of MATH 103.

### Mathematics Major (B.S.)

The student who seeks the bachelor of science degree with a major in mathematics must complete a total of 16 courses: MATH 100, 101, 102, 103, 110, 210, 221 and either 321 or 330, plus at least 3 mathematics electives above the level of MATH 103, CPSC 140: Introduction to Computer Programming, PHYS 210/220: General Physics I and II, and two courses above the 100 level in an allied discipline, such as Accounting, Biology, Chemistry, Economics, or Finance (listed under Business Administration).

### Mathematics Minor

The minor in mathematics requires the completion of five courses, including MATH 100 and 101, either MATH 102 *or* 103 and at least two electives above the level of MATH 102.

### Statistics Minor

The minor in statistics requires the completion of five courses, including MATH 122, 132, 142, 242 and either MATH 110, 140 or 262. Please see the most current edition of the Salem College academic Catalog for information regarding restrictions on courses that can be used to satisfy both the minor in mathematics and the minor in statistics. Also note that no more than three courses may be used to satisfy both a major and a minor.

## Mathematics Courses (MATH)

#### 020. College Algebra (1 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.

Note: This course does *not* satisfy the Salem Signature Liberal Arts Disciplinary Requirement in Mathematics or the Salem Signature requirement in Quantitative Interpretation/Evidence Based Thinking. This course is usually taken by students whose degree programs require a course in Calculus, either MATH 070 or MATH 100. This course is the minimum prerequisite for BUAD 240: Business Statistics, CHEM 110: General Chemistry, and SOCI 215: Social Statistics.

#### 025. Elementary Functions and Graphs (1 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.

Note: This course does not satisfy the Salem Signature Liberal Arts Disciplinary Requirement in Mathematics or the Salem Signature requirement in Quantitative Interpretation/Evidence Based Thinking. This course is usually taken by students whose degree programs require MATH 100. Placement in MATH 025 or higher satisfies the prerequisite for BIOL 100: Cell and Molecular Biology. Completion or placement out of this course satisfies a prerequisite for BIOL 205: Biometry. Placement in this course satisfies the prerequisite for CHEM 110: General Chemistry

#### 060. Introduction to Finite Mathematics (1 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.

Note: This course satisfies the Salem Signature Liberal Arts Disciplinary Requirement in Mathematics. This course satisfies a prerequisite for BUAD 240: Business Statistics, EXER 310: Exercise Physiology, EXER 320: Biomechanics of Sport and Exercise, EXER 330: Measurement, Assessment and Evaluation of Exercise and Sport.

#### 070. Essential Calculus (1 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.

Note: This course satisfies the Salem Signature Liberal Arts Disciplinary Requirement in Mathematics and the Interdisciplinary Dimensions Requirement in Quantitative Interpretation/Evidence-Based Thinking. This course also satisfies the requirements for the BS in Accounting, the BA in Biology, the BS and the BSBA in Business Administration, the BA in Economics, and the BS in Exercise Science. This course satisfies a prerequisite for ACCT 140: Intermediate Accounting I, a prerequisite for BIOL 205: Biometry, a prerequisite for BIOL 230: Genetics, BIOL 290: Honors Independent Study in Biology, BUAD 240: Business Statistics, FINC 302: Corporate Finance, CHEM 207: Solutions. Placement in this course satisfies the prerequisites for CHEM 110: General Chemistry; completion of this course satisfies a prerequisite for ECON 250: Mathematical Economics, ECON 320: Econometrics, and PHYS 201: General Physics I.

#### 100. Calculus I (1 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.

Note: This course satisfies the Salem Signature Liberal Arts Disciplinary Requirement in Mathematics and the Interdisciplinary Dimensions Requirement in Quantitative Interpretation/Evidence-Based Thinking. This course also satisfies requirements for the BS in Accounting, the BS in Biology, the BS and the BSBA in Business Administration, the BS in Chemistry, the BA in Economics, the BA in Teaching Schools and Society with the Mathematics Concentration, the BA in Environmental Studies with the Conservation Ecology Concentration, and the BS in Exercise Science. This course satisfies a prerequisite for ACCT 140: Intermediate Accounting I, a prerequisite for BIOL 205: Biometry, a perquisite for BIOL 230: Genetics, a prerequisite for BIOL 290: Honors Independent Study in Biology, BUAD 240: Business Statistics, FINC 302: Corporate Finance. Placement in this course satisfies the prerequisite for CHEM 110: General Chemistry, ECON 250: Mathematical Economics, ECON 320: Econometrics, and PHYS 210: General Physics I.

#### 101. Calculus II (1 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.

Note: This course satisfies the Salem Signature Interdisciplinary Dimensions Requirement in Quantitative Interpretation/Evidence-Based Thinking. This course also satisfies the requirements for the BA in Teaching Schools and Society with the Mathematics Concentration, and the BA in Environmental Studies with the Computational Environmental Analysis concentration.

#### 102. Calculus III (1 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.

Note: This course satisfies the Salem Signature Interdisciplinary Dimensions Requirement in Quantitative Interpretation/Evidence-Based Thinking. This course also satisfies the requirements for the BS in Chemistry. It is a prerequisite for CHEM 311: Physical Chemistry I.

#### 103. Calculus IV (1 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.

Note: This course satisfies the Salem Signature Interdisciplinary Dimensions Requirement in Quantitative Interpretation/Evidence-Based Thinking.

#### 110. Introductory Linear Algebra (1 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.

Note: This course also satisfies the requirements for the BA in Teaching Schools and Society with the Mathematics Concentration.

#### 122. Probability (1 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.

Note: This course also satisfies the requirements for the BA in Teaching Schools and Society with the Mathematics Concentration.

#### 132. Mathematical Statistics (1 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 (1 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 (1 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.

Note: This course also satisfies the requirements for the BA in Teaching Schools and Society with the Mathematics Concentration, and the BA in Environmental Studies core. It also satisfies the requirements for the Computational Analysis Concentration and the Conservation Ecology Concentration of the Environmental Studies major.

#### 162. Mathematics of Finance (1 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 2 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 (1 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.

Note: This course also satisfies the requirements for the BA in Teaching Schools and Society with the Mathematics Concentration.

#### 210. Differential Equations (1 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.

Note: This course satisfies the Salem Signature Interdisciplinary Dimensions Requirement in Quantitative Interpretation/Evidence-Based Thinking. This course also satisfies the requirements for the BA in Environmental Studies with the Computational Environmental Analysis concentration.

#### 221. Modern Algebra (1 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 (1 course)

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

#### 242. Nonparametric Statistical Methods (1 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 MATH 100 and either BIOL 205, BUAD 240, ECON 320, MATH 132, PSYC 101, or SOCI 215.

Note: This course also satisfies the requirements for the BA in Environmental Studies with the Computational Environmental Analysis concentration. It also serves as an elective for the major in Sociology.

#### 250. History of Mathematics (1 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 (1 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 (1 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 (1 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 (1 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 (1 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.

## Computer Science Courses (CPSC)

#### 140. Introduction to Programming I (1 course)

Computer programming in an object-oriented language such as Java for algorithmic problem solving. Programming concepts such as classes, objects, inheritance, variables and data types, methods, looping, strings, arrays, basic sorting, scientific computations and elementary drawing will be introduced. Requires competence in high school algebra. Spring.

#### 141. Introduction to Programming II (1 course)

Computer programming in an object-oriented language such as Java for algorithmic problem. Programming concepts not covered in Computer Science 140, such as collections, recursions, sorting, searching, input/output and exceptions, advanced drawing and elementary data structures will be introduced. Prerequisite: CPSC 140. Offered as needed.

### Mathematics Internships and Summer Research

*Below are internship and other off-campus opportunities completed by Salem Mathematics students:*

- Aon Consulting, intern
- American Red Cross, intern
- Argonne Labs
- Budapest Semester in Mathematics
- Bureau of the Census, intern
- Clare Booth Luce Foundation, intern
- Grand Valley State University Research Experience for Undergraduates
- Howard Hughes Medical Institute Science Exploration and Research Biology Program at North Carolina State University
- James Madison University Center for Materials Science
- Legal Aid Society of Forsyth County, intern
- Montana State University's Complex Biological Systems Summer Undergraduate Research Program
- NASA Jet Propulsion Laboratory, intern
- Research in Industrial Projects for Students at the Institute for Pure and Applied Mathematics at UCLA
- Statistical And Applied Mathematical Sciences Interdisciplinary Workshop for Undergraduates
- Summer Institute for Training in Biostatistics at Boston University and Harvard Clinical Research Institute
- Summer Program for Women in Mathematics at George Washington University
- Targacept, intern
- Tengion, intern
- Texas A&M University, Department of Chemical Engineering's Research Experience for Undergraduates
- United Space Alliance (formerly Rockwell International), 3 interns
- University of Nebraska Medical Center's Summer Research Program
- Wake Forest University Department of Biostatistics, intern
- Wake Forest University Department of Physics, Olin Physical Laboratory, intern
- Wake Forest University Department of Physiology and Pharmacology
- Wake Forest University Department of Public Health, intern
- Winston-Salem Police Department, intern