Math (MATH)

see Math Department

Major Requirements

B.S.

To receive a B.S. degree a student must complete the following requirements:

  1. A total of thirty-seven (37) semester hours of mathematics in courses numbered 200 or higher, including MATH 201, MATH
    203, MATH 204, MATH 303, MATH 306, MATH 403 or MATH 407, MATH 404 or 405, MATH 462, and MATH 472.
  2. CSC 207. Supportive Courses: PHYS 104, 114, 105, 115.

B.A.

To receive a B.A. degree a student must complete the following requirements:

  1. A total of thirty-one (31) semester hours of mathematics in courses numbered 201 or higher, including MATH 201, MATH 203, MATH 204, MATH 303, MATH 306, MATH 462, and MATH 472.
  2. Of these twenty-seven hours seven (7) hours must be in courses numbered 401 or higher.
  3. CSC 207. Supportive courses: PHYS 104, 114, 105, 115.

Minor Requirements

A minor in mathematics consists of the following courses: MATH 115, MATH 201, MATH 203, MATH 303, and an additional 6 hours of mathematics with three of those hours being at the 300 level and the other three at the 400 level.

Students may be admitted to the Honors Program of the Mathematics Department if they have attained junior standing and meet the other requirements. For details consult the department chairman.

102. Mathematics and the Visual Arts (3)
A study of the mathematical aspects of the visual arts organized around the concept of dimension. Topics of study will include pointillism, parametric curves, analytical geometry, fractal curves and dimension, tiling and symmetry, the mathematics of perspective, polyhedra, and artistic representations of the fourth dimension. Alternate spring.

103. Algebra for Teachers (3)
(Open for credit only to elementary education majors or students certifying in secondary education.) Topics from number theory, geometry, algebra, and the history of mathematics. Offered yearly.

104. College Algebra (3)
A study of elementary mathematical models using linear functions, exponential functions, and logarithms. Data analysis including the study of regression lines. (Students may not earn credit for Math 104 after earning credit for Math 107 or higher.) Offered each fall.

105. Introduction to Finite Mathematics (3)
A study of the relations and properties of finite sets within mathematics. Topics include elementary set theory, probability, combinations, permutations, and propositional logic, with a focus on practical applications. Advanced topics may be selected from matrices, linear programming, Markov chains and game theory. Spring of even years.

106. Geometry for Teachers (3)
A study of geometry to include: proofs and congruent triangles; parallel lines; ratio and similarity; right triangles and the Pythagoren Theorem; circles; and solids. (Open for credit only to elementary education majors or students certifying in secondary education.) Offered alternate years.

107. Precalcus: A Study of Functions (3)
A unified study of elementary functions in preparation for Calculus. Algebraic, exponential, logarithmic, and trigonometric functions and their applications. (Students may not earn credit for Math 107 after earning credit for Math 109 or higher.) Offered each semester.

109. Calculus for Business and Economics (3)
Prerequisite: MATH 107. (Students will not be allowed credit for both MATH 115 and MATH 109; further MATH 109 will not satisfy the prerequisite requirement for MATH 201.) An Introduction to differential calculus; and application to business and economics. Offered each semester.

115. Calculus I (4)
Functions: straight lines, exponential, logarithmic and trigonometric. Derivatives and their applications. Introduction to definite integrals. Offered each semester. (3-1)

201. Calculus II (4)
Prerequisite: MATH 115. Integrals, definite and indefinite. Applications of the integral. Sequences and infinite series. Introduction to differential equations. Offered each spring. (3-1)

203. Linear Algebra (3)
Prerequisite: MATH 201. Systems of linear equations, vector spaces, linear dependence, bases, dimensions, linear mappings, matrices, determinants, applications. Offered each spring.

204. Transition to Advanced Concepts (3)
Prerequisite or corequisite: MATH 201. An examination of the introductory concepts which pervade most upper level mathematics courses with an emphasis on proving techniques. Topics include logic and proving, sets, functions, cardinality and the properties of integers. Offered each fall.

220. Theory of Computation (3)
Prerequisite: CSC 207. Two main questions arise with computational problem solving: can a problem be solved at all, and if so, how efficiently? Topics include computability and complexity theory as related to Turing machines, finite state automata, regular and context-free grammars, and the complexity classes of P and NP. Alternate years in the fall.

303. Multivariable Calculus (5)
Prerequisite: MATH 201. Three-dimensional analytic geometry. Calculus of several variables. Multiple integration. Line and surface integrals. Every fall.

304. Foundations of Geometry (3)
Prerequisite: Consent of the department. An advanced proof-based course covering the history and theory of Euclidean and Non-Euclidean Geometry. Topics may include: Axioms of Euclid and Hilbert, contributions of Pythagoras, Plato and Descartes, the parallel postulate, projective geometry, hyperbolic geometry. Every third year.

305. Mathematical Statistics (3)
Prerequisite: MATH 303. Probability, sample spaces. Mathematical models, testing hypotheses. Empirical and theoretical frequency functions. Correlation and regression. Testing goodness of fit. Offered each spring.

306. Modern Algebra (3)
Prerequisites: MATH 203 and 204. A theoretical treatment of groups. Topics normally include: equivalence relations, permutations, symmetry groups, group homomorphisms and isomorphisms, Cayley’s Theorem, cosets, Lagrange’s Theorem, normal subgroups, factor groups and the isomorphism theorems. Additional topics may include group actions and an introduction to rings and fields. Offered each fall.

307. Differential Equations (3)
Prerequisite: MATH 303. Formulation of first and second order differential equations and interpretation of their solutions by qualitative, numerical, and analytical techniques, as well as their applications. Laplace transforms. Offered each spring.

310. Discrete Mathematics (3)
Prerequisite: MATH 201. An introduction to the mathematics of discrete objects. Topics include: combinatorics, recurrence relations and the analysis of algorithms, and an introduction to graph theory. Every third year.

311. Mathematical Models (3)
Prerequisite: MATH 303. Model Constructions and applications to the Social and Natural Sciences. Growth processes. Dimensional Analysis, linear optimization, stability, chains, networks. Every third year.

323. Mathematical Methods of Physics and Engineering (3)
Prerequisite: PHYS 105 and MATH 303 and 307. An Introduction to basic mathematical methods and techniques used in the solution of physical problems with emphasis on applications rather than theory. Topics include solutions of differential equations, vector analysis, Laplace transforms, Fourier series, an Introduction to methods of solving partial differential equations. (Same as PHYS 323 and ENGR 323)

395,396. Selected Topics (3-3)
Prerequisite: Consent of the instructor. A study of an area of mathematics not normally covered in the regular mathematics courses. Offered on demand.

398. Colloquium, Oak Ridge Semester (1)
Prerequisites: Junior standing and admission by ACS Selection Committee. A program of speakers on a variety of scientific and social issues presented by staff at Oak Ridge National Laboratory under supervision of resident ACS faculty. (Same as PHYS 398)

399. Research, Oak Ridge Semester (1-6)
Prerequisites: Junior standing and admission to the program by the ACS Selection Committee. Research performed through participation in the ACS-Oak Ridge Semester Program under supervision of senior staff at Oak Ridge National Laboratory. (Same as PHYS 399)

400. Internship in Mathematics (1-3)
(For mathematics majors only—not included in the required nine courses for the major.) Credit is given for on-the-job training in certain vocational areas of mathematics.

403. Topology (3)
Prerequisite: MATH 204. A survey of fundamental properties of topological spaces with particular emphasis on the real number system. Connectedness, compactness, continuous mapping, homeomorphism, metric spaces. Alternate spring.

404. Vector Analysis (3)
Prerequisite: MATH 303. A basic course in vectors. Topics included vector and scalar products, vector equations, and vector calculus. Applications from differential geometry and physics. Curvature, torsion, and Gaussian curvature. Alternate fall.

405. Numerical Analysis (3)
Prerequisites: MATH 203, MATH 303, and CSC 207. Selected numerical methods dealing with the solution of algebraic and transcendental equations, finite differences and interpolation, integration, and differential equations. Alternate fall.

407. Introductory Real Variable Theory (3)
Prerequisite: MATH 204. A proof-based study of the foundations of calculus. Topics include: sequences – monotone, convergent and Cauchy; limits and continuity; the derivative of a function; the Mean Value Theorem; the Riemann integral and the Fundamental Theorem of Calculus. Spring of even years.

462S. Seminar in Mathematical Investigation (2)
Prerequisite: Senior level standing as a mathematics major. An Introduction to mathematical research, oriented about a field chosen by the instructor. Students will conduct group investigations into the field and give presentations throughout the semester.

472. Senior Seminar (2)
Senior standing. Each student will be responsible for at least three presentations. Each presentation topic will be chosen in consultation with the course instructor and may be in a current area of mathematics or a topic found in one of Centenary’s junior /senior level courses. A study sheet of background information will be included with each presentation topic and each presentation will include oral questioning on the material covered in the study sheet. The presentations will be made before the mathematics department faculty and interested students. Spring.

491-496. Independent Study in Mathematics (1-6)
(Open to advanced students in mathematics with departmental approval.) One hour conference per week. Library and research work pertinent to the area of study selected. A written thesis is required.

199. Module Studies (3)
Special topics offered during the Module.

Computer Science (CSC)

Computer science is the study of information and computation. The Department of Mathematics offers a minor in computer science focused on the central principles of problem solving and algorithms as they are applied to diverse fields such as bioinformatics, artificial intelligence, databases, security and computational mathematics. Courses in computer science will provide valuable programming experience relevant to many scientific endeavors, and the minor can be individually tailored to complement majors such as mathematics, biology, neuroscience, business, and economics.

It is recommended that students planning to minor in computer science take the introduction course CSC 207 in either the first or second year of their coursework. Those students interested in a computer science minor but with limited mathematical background are encouraged to first take CSC 107.

Requirements for a Minor in Computer Science

A minor in computer science consists of 18 credit hours of computer science and mathematics coursework. All computer science minors are required to take CSC 207 and CSC 234 and at least one course from CSC 310, CSC 340 or CSC 350. The remaining 9 credit hours must be selected from the following courses: MATH 220, CSC 277, MATH 310, CSC 310, CSC 340, CSC 350, CSC 400 (at least 3 credit hours), and MATH 405.

107. Explorations in Agent-Based Modeling (3)
This course explores how computers can be used to model complex phenomenon in the world through the simple behavior of agents and their interactions over time. Labs examine the mathematical properties that emerge from these agent interactions. Topics are drawn from a wide array of fields, including biology, ecology, sociology, economics, political science, mathematics, physics, and geology. (Students may not earn credit in CSC 107 after earning credit for CSC 207.) Alternate years in the spring.

207. Introduction to Computer Science (3)
Prerequisite: CSC 107 or MATH 104 or higher, or permission of instructor. This course covers the principles of problem solving, programming and algorithm development through an interdisciplinary approach. Topics include mathematical functions, string manipulation, logic and control structures, file input/output, elementary data structures, and object-oriented programming. Every fall.

234. Data Structures (3)
Prerequisite: CSC 207. This course studies different structures for storing and processing data implemented through object-oriented programming. These structures include stacks, queues, linked lists, graphs and trees. Also studied are techniques and algorithms for sorting, searching and simulation. Every spring.

277. Bioinformatics (3)
Prerequisite: CSC 207. This course explores computational methods for analyzing and understanding the large quantities of information now available in the growing fields of genomics, proteomics and systems biology. It complements practical experience of current bioinformatics systems with a deep understanding of their algorithmic underpinnings. Topics include aligning pairwise and multiple sequences, constructing phylogenies, searching strings, modeling motifs, clustering microarray data, inferring regulatory networks, and modeling biological systems. Alternate years in the spring.

310. Database Management (3)
Prerequisite: CSC 234. Real examples of database applications give students an opportunity to experience the entire database life cycle. Topics include the context, analysis, logical and physical design, and the implementation of a database management system. A database project will be required. Every third year in the fall.

340. Artificial Intelligence (3)
Prerequisite: CSC 234. This course provides an introduction to artificial intelligence, with a particular focus on the empirical approach: how can we have a computer act rationally? Topics include both local and global search techniques for problem solving, game theory, automated logical reasoning, statistical machine learning, and complex adaptive systems. Every third year in the fall.

350. Cryptology and Security (3)
Prerequisite: CSC 234. This course investigates both classical and modern methods for information security. Topics include classical alphabetic cryptographic and decryption techniques, RSA, private and public key encryption, visual cryptography, and data privacy. Every third year in the fall.

395,396. Selected Topics 3
A study of an area of computer science not normally covered in the regular computer science courses. On demand.

400. Internship in Computer Science (1-3)
Prerequisite: CSC 207. Credit is given for on-the-job training in certain vocational areas of computer science. On demand.

496. Independent Studies in Computer Science 1-6
(Open to advanced students in Computer Science with departmental approval). One hour conference per week. Library and research work pertinent to the area of study selected. A presentation of the work is required. On demand.

Last updated May 13, 2008.