# Descriptions of and Information for MATH and CPSC Courses

**Mathematics and Computer Science Course Descriptions and Information**

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The information provided below is intended as a guide for students as they plan their time at Salem College. Please refer to the most current edition of the *Salem College Undergraduate Catalog* for the most accurate information regarding courses in mathematics and computer science.

**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.

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.

**MATH 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.

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

**MATH 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.

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.

**MATH 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.

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.

**MATH 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.

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 Biochemistry, 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.

**MATH 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.

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 Biochemistry, the BS in Chemistry, the BA in Teaching Schools and Society with the Mathematics Concentration, and the BA in Environmental Studies with the Computational Environmental Analysis concentration.

**MATH 102. Calculus III (1 course) **

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

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.

**MATH 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.

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

**MATH 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.

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

**MATH 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.

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

**MATH 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.

**MATH 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.

**MATH 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. Prerequisite: 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. This course also satisfies the requirements for the Computational Analysis Concentration and the Conservation Ecology Concentration of the Environmental Studies major.

**MATH 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. Prerequisite: MATH 102.

**MATH 200. Independent Study in Mathematics (0.5 – 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.

**MATH 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.

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

**MATH 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.

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.

**MATH 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.

**MATH 240. Topology (1 course) **

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

**MATH 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. Prerequisite: MATH 070 or 100 and either BIOL 205, BUAD 240, ECON 320, MATH 132, MATH 142, PSYC 101, or SOCI 215.

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

**MATH 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 19^{th} and 20^{th} 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 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 (1 course); admission by application only.

**MATH 280. Special Topics in Mathematics (1 course)**

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

**MATH 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.

**MATH 321. Real Analysis (1 course) **

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

**MATH 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.

**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.

Note: This course is required for both the BA and the BS in Mathematics. It also satisfies the requirements for the BA in Environmental Studies with the Computational Environmental Analysis concentration.

**CPSC 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.