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

**Mathematics Placement and Academic Support**

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

**Your Faculty**

**Your Program**

**Your Results**

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, and 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 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.

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.

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.

The mathematics faculty are active, engaged mathematicians who 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 seventy 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. Professor Mattox teaches 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. His office is SCIE 309.

The department offers both a bachelor of arts and a bachelor of science degree 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.

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.

Major/Minor ### Mathematics Major (BA)

### Mathematics Major (BS)

### Mathematics Minor

### Actuarial Science Minor

### Statistics Minor

Students may major in mathematics within the bachelor of arts degree or within the bachelor of science degree. Others may choose to pursue a minor in mathematics to complement their major course of study in preparation for graduate or professional school. The department offers a minor is statistics for those students who plan to pursue careers as researchers or statisticians and for those students majoring in other disciplines whose graduate study or professional goals require statistical analysis. An interdisciplinary minor in actuarial science is also offered in conjunction with the Economics program.

All math majors must take at least twelve semester hours above the level of MATH 102 at Salem.

The student who seeks the bachelor of arts degree with a major in mathematics must complete the following:

Required core courses:

- MATH 100. Calculus I (5 hrs)*
- MATH 101. Calculus II (5 hrs)*
- MATH 102. Calculus III (3 hrs)
- MATH 103. Calculus IV (3 hrs)
- MATH 110. Introductory Linear Algebra (4 hrs)
- MATH 210. Differential Equations (4 hrs)
- MATH 221. Modern Algebra (4 hrs)
- MATH 321. Real Analysis or MATH 330. Complex Variables (4 hrs)
- CPSC 100. Introduction to Programming with Java (3 hrs)

One additional MATH elective (3-5 hrs)

* For a student with a strong mathematics background, MATH 100 and 101 may be waived if proficiency standards are met through examination, and the total number of major requirements is reduced accordingly.

The student who seeks the bachelor of science degree with a major in mathematics must complete the following:

Required core courses:

- MATH 100. Calculus I (5 hrs)*
- MATH 101. Calculus II (5 hrs)*
- MATH 102. Calculus III (3 hrs)
- MATH 103. Calculus IV (3 hrs)
- MATH 110. Introductory Linear Algebra (4 hrs)
- MATH 210. Differential Equations (4 hrs)
- MATH 221. Modern Algebra (4 hrs)
- MATH 321. Real Analysis or MATH 330. Complex Variables (4 hrs)

- CPSC 100. Introduction to Programming with Java (4 hrs)
- PHYS 210. General Physics I (5 hrs)

Electives:

Select three MATH electives numbered 107 and above (3-5 hrs min. each)

Select one additional course (3-5 hrs)** in an allied discipline at the 100 level or above (ACCT, BIOL, CHEM, ECON, ENVS, FINC, or PHYS). Students may petition the chair of the department if she wishes to satisfy this requirement with a course from another discipline not listed here.

* For a student with a strong mathematics background, MATH 100 and 101 may be waived if proficiency standards are met through AP or IB examination, and the total number of major requirements is reduced accordingly.

** The course in an allied discipline must be at the 100-level or above; a student may petition the chair of the department of mathematics for permission to include two courses from another allied discipline not listed here.

The minor in mathematics requires the completion of the following:

Required courses:

- MATH 100. Calculus I (5 hrs)
- MATH 101. Calculus II (5 hrs)
- MATH 102. Calculus III or MATH 103. Calculus IV (3 hrs)

Two MATH electives above MATH 102 (3-4 hrs min.)

Two of the five classes must be taken at Salem.

Students who wish to pursue minors in both mathematics and statistics may not submit MATH 107, 122, 132, 140, 162, or 242 for completion of the minor in mathematics.

The minor in actuarial science requires the completion of the following:

Required courses:

- ECON 100. Introduction to Economics (4 hrs)
- ECON 220. Intermediate Microeconomics (3 hrs)
- MATH 122. Probability (4 hrs)
- MATH 132. Mathematical Statistics (4 hrs)
- MATH 162. Mathematics of Finance (3 hrs)

Select one of the following:

- MATH 107. Statistical Methods with R (4 hrs)
- ECON 320. Econometrics (4 hrs)

The minor in statistics requires the completion of five courses.

Required courses:

- MATH 107. Statistical Methods with R (4 hrs)

- MATH 122. Probability (4 hrs)
- MATH 132. Mathematical Statistics (4 hrs)
- MATH 242. Nonparametric Statistical Methods (4 hrs)

Select one of the following:

- MATH 110. Linear Algebra (4 hrs)
- MATH 140. Numerical Analysis (4 hrs)
- MATH 162. Mathematics of Finance (3 hrs)

Two of the five classes must be taken at Salem.

Students who wish to pursue minors in both mathematics and statistics may not submit MATH 107, 122, 132, 140, 162, or 242 for completion of the minor in mathematics.

Courses ## Mathematics Courses (MATH)

### MATH 020. College Algebra (4 hrs)

### MATH 025. Elementary Functions and Graphs (4 hrs)

### MATH 060. Introduction to Finite Mathematics (3 hrs)

### MATH 070. Essential Calculus (4 hrs)

### MATH 100. Calculus I (5 hrs)

### MATH 101. Calculus II (5 hrs)

### MATH 102. Calculus III (3 hrs)

### MATH 103. Calculus IV (3 hrs)

### MATH 107. Statistical Methods with R (4 hrs)

### MATH 110. Introductory Linear Algebra (4 hrs)

### MATH 122. Probability (4 hrs)

### MATH 132. Mathematical Statistics (4 hrs)

### MATH 140. Introduction to Numerical Analysis (4 hrs)

### MATH 162. Mathematics of Finance (3 hrs)

### 200. Independent Study in Mathematics (1-4 hrs)

### MATH 202. College Geometry (3 hrs)

### MATH 210. Differential Equations (4 hrs)

### MATH 221. Modern Algebra (4 hrs)

### MATH 242. Nonparametric Statistical Methods (3 hrs)

### MATH 250. History of Mathematics (3 hrs)

### MATH 270. Internship in Mathematics (1-4 hrs)

### MATH 280. Special Topics in Mathematics (1-4 hrs)

### MATH 290. Honors Independent Study in Mathematics (3-4 hrs)

### MATH 321. Real Analysis (4 hrs)

### MATH 330. Complex Variables (4 hrs)

##

Structure of algebraic properties of real numbers, polynomials and their roots, rational expressions, exponents and radical expressions, solution of equations and inequalities, properties of functions and graphing. The course is designed to prepare first-year students for MATH 025 and MATH 070. Some familiarity with basic algebra is expected. Not included in the major; does not satisfy any Salem Signature requirements. Prerequisite: placement.

Functions, including the trigonometric functions, exponential functions and logarithmic functions, will be studied in detail. Additional topics will be included at the discretion of the instructor, including systems of equations, conic sections, and limits of functions. This course is designed to prepare the student for calculus MATH 100. Not included in the major; does not satisfy any Salem Signature requirements. Prerequisite: MATH 020 or placement.

A course in mathematics that introduces students to useful quantitative topics and techniques that are beneficial to many areas of study. 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, game theory, logic, and Markov processes may be included at the discretion of the instructor. Prerequisite: placement.

An algebra-intensive introduction to calculus with emphasis on applications to business, accounting, life sciences, 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’s and consumer’s surplus. Other applications to physical sciences may be included at the discretion of the instructor. Not included in the mathematics major. Students may not receive credit for both MATH 070 and MATH 100. Prerequisite: A grade of C- or better in MATH 020 or placement. (QI)

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. (QI)

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: placement or grade of C- or better in MATH 100. (QI)

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. (QI)

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. (QI)

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. Prerequisite: successful completion of General Education Requirement in mathematics.

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

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 Prerequisite: MATH 101.

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.

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 may be taken from the physical, life, financial, social, or statistical sciences. Students will develop and utilize computer programming techniques throughout the course, using a programming language or mathematical computing software of the instructor’s choice. Prerequisite: MATH 102.

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.

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 maximum total of twelve semester hours, no more than seven semester hours in any term.

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. Prerequisite: MATH 101.

Basic theory of ordinary differential equations with applications; linear differential equations and linear systems; numerical methods, solutions in series, Laplace transforms, existence and uniqueness theorems. Prerequisite: MATH 101. (QI)

Elementary theory of groups, rings, integral domains, and fields; properties of number systems; polynomials; and the algebraic theory of fields. Prerequisite: MATH 110.

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. Prerequisite: One of the following: BIOL 205, BUAD 240, ECON 320, MATH 107, MATH 132, PSYC 101, or SOCI 215.

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 of the Western tradition. The birth of calculus and selected topics from the nineteenth and twentieth 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.

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 of four semester hours per term; admission by application only.

Investigation of a topic, issue application, or problem in mathematics. Topics might include: mathematical modeling, dynamical systems, graph theory, combinatorics, biomathematics, or another topic chosen by the instructor.

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 eight semester hours.

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

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.

Internships ### 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

Success Stories

I was quickly won over by the genius, yet down-to-earth professors in the Math Department. My advisor, Debbie Harrell, is one of many unforgettable professors in the department who will give you all of the individualized attention you need to succeed. In College Geometry, Dr. Paula Young encouraged me to explore my love for sports in a class project where I looked at the fascinating geometry of basketball. In addition to the awesome faculty, class sizes are small and intimate. Your peer cohort is sure to bond as you triumph together through the Calculus course sequence, all the way into Real Analysis. The power of numbers is so strong, and mastering these techniques and problem-solving skills will give you an unparalleled confidence and sense of accomplishment.
Salem and its Department of Mathematics filled me with confidence to pursue what I thought was the unthinkable—six more years of school! Because of the relationships I formed, I was able to get amazing recommendation letters and had the credentials to get into a really great program for my field. I now do applied research on student-athletes at the national headquarters for the NCAA. I get to study the coolest topics relating to the college athlete experience such as academic performance, mental health and well-being, retention, major choice, relationships with coaches, and life after sport retirement.

Tiese L. Roxbury

**Class Year: **2004

**Major: **Mathematics

**Graduate Studies: **MS, PhD in educational research methodology

**Career:** Educational research scientist, NCAA

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, and 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 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.

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.

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.

The mathematics faculty are active, engaged mathematicians who 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 seventy 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. Professor Mattox teaches 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. His office is SCIE 309.

The department offers both a bachelor of arts and a bachelor of science degree 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.

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.

Students may major in mathematics within the bachelor of arts degree or within the bachelor of science degree. Others may choose to pursue a minor in mathematics to complement their major course of study in preparation for graduate or professional school. The department offers a minor is statistics for those students who plan to pursue careers as researchers or statisticians and for those students majoring in other disciplines whose graduate study or professional goals require statistical analysis. An interdisciplinary minor in actuarial science is also offered in conjunction with the Economics program.

All math majors must take at least twelve semester hours above the level of MATH 102 at Salem.

The student who seeks the bachelor of arts degree with a major in mathematics must complete the following:

Required core courses:

- MATH 100. Calculus I (5 hrs)*
- MATH 101. Calculus II (5 hrs)*
- MATH 102. Calculus III (3 hrs)
- MATH 103. Calculus IV (3 hrs)
- MATH 110. Introductory Linear Algebra (4 hrs)
- MATH 210. Differential Equations (4 hrs)
- MATH 221. Modern Algebra (4 hrs)
- MATH 321. Real Analysis or MATH 330. Complex Variables (4 hrs)
- CPSC 100. Introduction to Programming with Java (3 hrs)

One additional MATH elective (3-5 hrs)

* For a student with a strong mathematics background, MATH 100 and 101 may be waived if proficiency standards are met through examination, and the total number of major requirements is reduced accordingly.

The student who seeks the bachelor of science degree with a major in mathematics must complete the following:

Required core courses:

- MATH 100. Calculus I (5 hrs)*
- MATH 101. Calculus II (5 hrs)*
- MATH 102. Calculus III (3 hrs)
- MATH 103. Calculus IV (3 hrs)
- MATH 110. Introductory Linear Algebra (4 hrs)
- MATH 210. Differential Equations (4 hrs)
- MATH 221. Modern Algebra (4 hrs)
- MATH 321. Real Analysis or MATH 330. Complex Variables (4 hrs)

- CPSC 100. Introduction to Programming with Java (4 hrs)
- PHYS 210. General Physics I (5 hrs)

Electives:

Select three MATH electives numbered 107 and above (3-5 hrs min. each)

Select one additional course (3-5 hrs)** in an allied discipline at the 100 level or above (ACCT, BIOL, CHEM, ECON, ENVS, FINC, or PHYS). Students may petition the chair of the department if she wishes to satisfy this requirement with a course from another discipline not listed here.

* For a student with a strong mathematics background, MATH 100 and 101 may be waived if proficiency standards are met through AP or IB examination, and the total number of major requirements is reduced accordingly.

** The course in an allied discipline must be at the 100-level or above; a student may petition the chair of the department of mathematics for permission to include two courses from another allied discipline not listed here.

The minor in mathematics requires the completion of the following:

Required courses:

- MATH 100. Calculus I (5 hrs)
- MATH 101. Calculus II (5 hrs)
- MATH 102. Calculus III or MATH 103. Calculus IV (3 hrs)

Two MATH electives above MATH 102 (3-4 hrs min.)

Two of the five classes must be taken at Salem.

Students who wish to pursue minors in both mathematics and statistics may not submit MATH 107, 122, 132, 140, 162, or 242 for completion of the minor in mathematics.

The minor in actuarial science requires the completion of the following:

Required courses:

- ECON 100. Introduction to Economics (4 hrs)
- ECON 220. Intermediate Microeconomics (3 hrs)
- MATH 122. Probability (4 hrs)
- MATH 132. Mathematical Statistics (4 hrs)
- MATH 162. Mathematics of Finance (3 hrs)

Select one of the following:

- MATH 107. Statistical Methods with R (4 hrs)
- ECON 320. Econometrics (4 hrs)

The minor in statistics requires the completion of five courses.

Required courses:

- MATH 107. Statistical Methods with R (4 hrs)

- MATH 122. Probability (4 hrs)
- MATH 132. Mathematical Statistics (4 hrs)
- MATH 242. Nonparametric Statistical Methods (4 hrs)

Select one of the following:

- MATH 110. Linear Algebra (4 hrs)
- MATH 140. Numerical Analysis (4 hrs)
- MATH 162. Mathematics of Finance (3 hrs)

Two of the five classes must be taken at Salem.

Structure of algebraic properties of real numbers, polynomials and their roots, rational expressions, exponents and radical expressions, solution of equations and inequalities, properties of functions and graphing. The course is designed to prepare first-year students for MATH 025 and MATH 070. Some familiarity with basic algebra is expected. Not included in the major; does not satisfy any Salem Signature requirements. Prerequisite: placement.

Functions, including the trigonometric functions, exponential functions and logarithmic functions, will be studied in detail. Additional topics will be included at the discretion of the instructor, including systems of equations, conic sections, and limits of functions. This course is designed to prepare the student for calculus MATH 100. Not included in the major; does not satisfy any Salem Signature requirements. Prerequisite: MATH 020 or placement.

A course in mathematics that introduces students to useful quantitative topics and techniques that are beneficial to many areas of study. 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, game theory, logic, and Markov processes may be included at the discretion of the instructor. Prerequisite: placement.

An algebra-intensive introduction to calculus with emphasis on applications to business, accounting, life sciences, 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’s and consumer’s surplus. Other applications to physical sciences may be included at the discretion of the instructor. Not included in the mathematics major. Students may not receive credit for both MATH 070 and MATH 100. Prerequisite: A grade of C- or better in MATH 020 or placement. (QI)

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. (QI)

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: placement or grade of C- or better in MATH 100. (QI)

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. (QI)

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. (QI)

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. Prerequisite: successful completion of General Education Requirement in mathematics.

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

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 Prerequisite: MATH 101.

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.

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 may be taken from the physical, life, financial, social, or statistical sciences. Students will develop and utilize computer programming techniques throughout the course, using a programming language or mathematical computing software of the instructor’s choice. Prerequisite: MATH 102.

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.

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 maximum total of twelve semester hours, no more than seven semester hours in any term.

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. Prerequisite: MATH 101.

Basic theory of ordinary differential equations with applications; linear differential equations and linear systems; numerical methods, solutions in series, Laplace transforms, existence and uniqueness theorems. Prerequisite: MATH 101. (QI)

Elementary theory of groups, rings, integral domains, and fields; properties of number systems; polynomials; and the algebraic theory of fields. Prerequisite: MATH 110.

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. Prerequisite: One of the following: BIOL 205, BUAD 240, ECON 320, MATH 107, MATH 132, PSYC 101, or SOCI 215.

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 of the Western tradition. The birth of calculus and selected topics from the nineteenth and twentieth 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.

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 of four semester hours per term; admission by application only.

Investigation of a topic, issue application, or problem in mathematics. Topics might include: mathematical modeling, dynamical systems, graph theory, combinatorics, biomathematics, or another topic chosen by the instructor.

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 eight semester hours.

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

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.

I was quickly won over by the genius, yet down-to-earth professors in the Math Department. My advisor, Debbie Harrell, is one of many unforgettable professors in the department who will give you all of the individualized attention you need to succeed. In College Geometry, Dr. Paula Young encouraged me to explore my love for sports in a class project where I looked at the fascinating geometry of basketball. In addition to the awesome faculty, class sizes are small and intimate. Your peer cohort is sure to bond as you triumph together through the Calculus course sequence, all the way into Real Analysis. The power of numbers is so strong, and mastering these techniques and problem-solving skills will give you an unparalleled confidence and sense of accomplishment.
Salem and its Department of Mathematics filled me with confidence to pursue what I thought was the unthinkable—six more years of school! Because of the relationships I formed, I was able to get amazing recommendation letters and had the credentials to get into a really great program for my field. I now do applied research on student-athletes at the national headquarters for the NCAA. I get to study the coolest topics relating to the college athlete experience such as academic performance, mental health and well-being, retention, major choice, relationships with coaches, and life after sport retirement.

Tiese L. Roxbury

**Class Year: **2004

**Major: **Mathematics

**Graduate Studies: **MS, PhD in educational research methodology

**Career:** Educational research scientist, NCAA

*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

Aug 05

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Aug 06