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The program has been designed with great flexibility so that a student, after consultation with a mathematics faculty member, may choose the appropriate elective(s) to satisfy the requirements for the minor and to prepare her for the career or post-graduate program of her choice. When designing the program, we paid close attention to the standards set by and recommendations of the Society of Actuaries and the American Statistical Association in the development of new courses and in the construction of the minor requirements.

Even those not interested in pursuing a minor in statistics may find one or more of the courses below gives them an advantage when applying to graduate school, for internships, for summer research programs, or employment.

Overview **Your Program**

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.

Major/Minor

Courses ## Mathematics Courses (MATH)

**MATH 020. College Algebra (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.

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

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

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

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

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

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

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

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

**MATH 110. Introductory Linear Algebra (4 hrs) **Vector methods in geometry, real vector spaces, systems of linear equations, linear trans-formations and matrices, equivalence of matrices and determinants. Prerequisite: MATH 101.

**MATH 122. Probability (4 hrs) **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.

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

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

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

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

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

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

**MATH 221. Modern Algebra (4 hrs) **Elementary theory of groups, rings, integral domains and fields; properties of number systems; polynomials; and the algebraic theory of fields. Prerequisite: MATH 110.

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

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

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

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

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

**MATH 321. Real Analysis (4 hrs)** A rigorous treatment of the real number system, limits, continuity, sequences, series, differentiation and Riemann integration. Prerequisite: MA TH 103.

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

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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.

**MATH 020. College Algebra (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.

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

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

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

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

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

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

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

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

**MATH 110. Introductory Linear Algebra (4 hrs) **Vector methods in geometry, real vector spaces, systems of linear equations, linear trans-formations and matrices, equivalence of matrices and determinants. Prerequisite: MATH 101.

**MATH 122. Probability (4 hrs) **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.

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

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

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

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

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

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

**MATH 221. Modern Algebra (4 hrs) **Elementary theory of groups, rings, integral domains and fields; properties of number systems; polynomials; and the algebraic theory of fields. Prerequisite: MATH 110.

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

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

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

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

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

**MATH 321. Real Analysis (4 hrs)** A rigorous treatment of the real number system, limits, continuity, sequences, series, differentiation and Riemann integration. Prerequisite: MA TH 103.

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