Course Offerings | Mathematics

Division of Science and Mathematics

John Wilson (chair), Michael Bradshaw, Anne Collins, Ken Dutch, William Johnston, Alex McAllister, Christine Shannon, Andre Wehner; student: Josh Smith



The Mathematics Program seeks to give students an understanding and appreciation of the beauty and utility of mathematics. Quantitative and analytic skills are increasingly important in economics, biology, and the social sciences, as well as in the physical sciences and engineering. The study of mathematics at Centre provides the opportunity for the development of clear, logical, and creative thinking that may be applied to a wide variety of problems and interests. In addition to these important problem-solving skills, the mathematics major will learn to present concise, logical arguments in writing and orally. Emphasis is placed on mathematical thinking and precise communication of these thoughts.

Students completing the mathematics major at Centre have a broad range of interests. Many also complete a major in another field. For example, recent mathematics majors have second majors in chemistry, computer science, economics, English, history, physics, and Spanish. Some majors earn secondary teacher certification. Our graduates often decide to continue their academic studies, entering law school, medical school, engineering programs, and M.B.A. programs, as well as graduate school programs in a wide variety of disciplines. Others choose to join the workforce immediately, taking jobs with companies and agencies such as the Census Bureau, the military services, computer companies, public or private schools, and financial institutions. Our students find that the problem-solving and communication skills learned in the mathematics major serve them well in whatever career paths they follow.


Requirements for the Major

MAT 170 or both MAT 140 and 141, or equivalent;
MAT 171, or equivalent (this requirement should be completed by the end of the freshman year to complete the major in the normal four-year period);
MAT 230, 240, 290, 330, 380 ;

One of MAT 190, MAT 350, or PHY 330;
Four MAT courses numbered 300 or higher
, excluding MAT 350. A CentreTerm math course or CSC 117 may substitute for one of these courses.


Requirements for the Minor

MAT 170 or both MAT 140 and 141, or equivalent;
MAT 171, or equivalent;
MAT 230
;
MAT 240 or 290
;
Any three MAT courses numbered 300 or higher. CSC 117 may substitute for one of these.


Mathematics Courses

MAT 110 Mathematics in Our Society
An introduction to applied mathematics devoted to solving contemporary problems from diverse disciplines. This course helps students develop logical thinking skills and improve quantitative skills, particularly with linear equations (in the context of decision-making) and with exponential and logarithmic models (in the context of finance). Further topics will be chosen from graph theory, geometry, symmetry, coding, game theory, social issues, and logic.

MAT 130 Introduction to Statistics
An investigation into the mathematical techniques for analyzing and interpreting data with the goal of understanding our world and facilitating informed decision-making processes. The course includes the study of random variables, descriptive statistics, basic probability theory, and inferential statistics. Specific topics include frequency distributions, mean, median, variance, probability distributions, hypothesis testing, confidence intervals, correlation, and regression analysis. Prerequisite: Basic skills in mathematics or permission of the instructor.

MAT 140 Differential Calculus with Review
This is the first course in a two-course sequence that provides both an in-depth review of functions and an introduction to differential calculus. In particular, limits and derivatives are introduced as tools used to analyze the behavior of algebraic, exponential, and logarithmic functions. This course is not available to students with credit for MAT 160 or 170. Prerequisite: MAT 110 or placement.

MAT 141 Integral Calculus with Review
A continuation of MAT 140, this course begins with an in-depth review of trigonometric functions and their derivatives. The majority of the course focuses on the definition of the integral, the Fundamental Theorem of Calculus, and applications of the integral. Prerequisite: MAT 140.

MAT 170 Calculus-I
An introduction to single variable calculus reviewing the real number line, inequalities and absolute value, and discussing functions and graphing, limits, continuity, the derivative, rules of differentiation, the Mean Value Theorem, applications of the derivative, antiderivatives, Riemann sums and the definite integral, the Fundamental Theorem of Calculus, and applications of the integral. Prerequisite: placement. Note: This course is not available to students with credit for MAT 140.

MAT 171 Calculus-II
A continuation of MAT 170. The techniques of single variable calculus are applied to inverse trigonometric, exponential, and logarithmic functions. Also included are further techniques of integration, indeterminate forms, improper integrals, and infinite series. Prerequisite: MAT 141 or 170 or placement.

MAT 190 Discrete Mathematics
An introduction to the study of "discrete" mathematical objects and number systems, in contrast to the study of the continuous real number line. The course explores many topics at the analytical level of calculus: relations, logic, techniques of proof, counting techniques, algorithms, graph theory, number systems, Boolean algebra, and set theory. Prerequisite: MAT 141 or 170 or permission of the instructor.

MAT 210 Mathematics in the Elementary School
A study of the language and structure of mathematics including problem solving, set and number theory, integers, rational and real numbers, probability and statistics, and geometry. NOTE: This course is open to early elementary education majors only.

MAT 230 Calculus-III
An extension of the concepts of function, limit, derivative, and integral to three-dimensional space and vector spaces; the course describes many applications and their historical significance, such as planetary motion and magnetic fields. Topics include vector algebra, elementary differential geometry of curves and surfaces, limits, continuity, partial derivatives, directional derivatives, multiple integrals, line integrals, surface integrals, Green's Theorem, Stokes' Theorem, and the Divergence Theorem. Prerequisite: MAT 171 or placement.

MAT 240 Linear Algebra
The abstract study of systems of linear equations: the determination of whether a system has no, one, or infinitely many solutions and the techniques for obtaining such solutions. The topics include the algebra of matrices, Gaussian elimination, vector spaces, spanning, linear independence, basis, dimension, inner products, Gram-Schmidt orthogonalization, determinants, linear transformations and their matrix representations, eigenvalues and eigenvectors. Prerequisite: MAT 171.

MAT 250-289 Centre Term Special Topic Courses - 2004-2005 Topic:


MAT 254 Explorations in Advanced Mathematics
A course designed to enhance the ability of students to discover and prove results in advanced mathematics. Students use the computer to explore questions and look for patterns, leading to conjectures and eventually to the proofs of mathematical theorems. Examples are taken from areas like number theory, analysis, discrete mathematics, and geometry. Prerequisite: MAT 171; CSC 117 helpful but not required.

MAT 290 Foundations of Mathematics
This course develops the abstract thinking and the writing skills necessary for proof-oriented mathematics courses and surveys various areas of mathematics. Fundamental concepts and questions are studied from mathematical logic, abstract algebra, number theory, and real analysis. Further topics include complex analysis, statistics, graph theory, and/or other areas of mathematics according to the interests of instructor and students. Prerequisite: MAT 171.

MAT 310 Probability Theory
A mathematical study of chance, this course uses counting techniques and topics from calculus to develop a mathematical approach that describes the likelihood of events happening. Specific topics include an introduction to the theory of probability, random variables, discrete and continuous probability distributions, expected values, moments and moment-generating functions, distributions of functions of random variables, and multivariate distributions. Prerequisite: MAT 230 or permission of instructor.


MAT 311 Mathematical Statistics
A calculus-based course in statistics devoted to techniques for analyzing and interpreting data with the goal of understanding our world and facilitating informed decision-making processes. This course is a continuation of MAT 310 that studies applications of sampling distributions related to the normal distribution. These include estimation of parameters, confidence intervals, hypothesis testing, regression analysis and least-squares estimators, correlation, design of experiments, analysis of variance, chi-square tests, and nonparametric statistics. Prerequisite: MAT 310 or permission of the instructor.

MAT 330 Abstract Algebra-I
This course defines and investigates the key properties of the mathematical structure called an algebraic group, studying many examples, including groups of numbers, groups of functions, and groups of matrices, with the goal of determining the common properties of all of these mathematical systems. Topics include the basic properties of the integers, permutation groups, subgroups, Lagrange’s Theorem, quotient groups, isomorphisms and homomorphisms, and Cayley's Theorem. Prerequisite: MAT 240.

MAT 331 Abstract Algebra-II
A continuation of MAT 330, in which key properties from the integers and the real numbers are used as models for the algebraic structures known as rings and fields. Students construct and examine a rich collection of examples including rings of polynomials, Gaussian integers, and finite fields. Topics include prime factorization, integral domains, ideals, ring homomorphisms, and extension fields. Prerequisite: MAT 330.

MAT 340 Complex Variables
A study of functions of one complex variable, the course extends notions from the calculus of real-valued functions. Topics include complex numbers, limits, continuity, differentiability, Cauchy-Riemann equations, analytic functions, elementary transformations, complex integration, Cauchy's Theorem, the annulus theorem, Cauchy's Integral Formula, Morera's Theorem, complex power series, Laurent series, and the theory of residues. Prerequisite: MAT 230.

MAT 350 Mathematical M
ethods of Economics
An introduction to mathematical tools used for modeling in economics and other social and natural sciences. The tools studied include differential calculus, partial differentiation, integral calculus, game theory, and linear algebra. Applications focus on the use of marginal analysis and comparative statics to economic topics, but may include topics form other disciplines as appropriate. Prerequisite: MAT 140 or 170, and ECO 220.

MAT 360 Differential Equations
This course describes the many physical and social phenomena that involve a change in some quantity with respect to time and are described mathematically via differential equations. Topics include techniques for solving first-order differential equations (exact, separable, linear, integrating factors, homogeneous), solving higher order linear differential equations (constant coefficients, undetermined coefficients, variation of parameters), and the Laplace transform methods and series solutions of differential equations. Prerequisite: MAT 230 or permission of the instructor.

MAT 370 Numerical Methods
A study of how computers obtain numerical estimates of solutions when people apply mathematics to diverse disciplines (e.g. physics, economics, medicine, etc.). In this course we discuss and develop various algorithms that form the basis for computer applications including root finding, interpolation, differentiation and integration, differential equations, and systems of equations. Prerequisite: MAT 240 and CSC 117.

MAT 380 Introduction to Real Analysis
A systematic exploration of how calculus provides profound insights into explaining and understanding our world and its phenomena. The study of real analysis discusses the theoretical foundations of single variable calculus to arrive at a deep understanding of why calculus works. Topics include properties of the real numbers, limits, continuity, differentiation, and integration. Prerequisite: MAT 230 and MAT 240.

MAT 403 Partial Differential Equations
A study of linear partial differential equations of first and second order. Includes the introductory theory of linear partial differential equations. Also, explicit solutions of the wave equation, Laplace's equation, and heat equation are obtained using the method of separation of variables and Fourier series. Prerequisite: MAT 360 or 26.

MAT 404 Introduction to Topology
Topics include metric spaces, continuity, and homeomorphisms. Prerequisite: MAT 230 and 240.

MAT 405 Theory of Integration
A study of the theory of the integral, the course begins by describing Bernhard Riemann’s 1850s formulation of the integral (used in calculus courses to integrate continuous functions). It then explains Henri Lebesgue’s reformulation (developed in 1901), which mathematicians often consider the beginning point of a modern analysis of functions. The Lebesgue integral forms a “natural” mathematical venue for many fields such as probability theory and quantum mechanics. Discussion of the Riemann integral includes Upper and Lower Riemann Sums and finishes by characterizing Riemann integrable functions. The course then introduces the Lebesgue Integral (as a generalization of the Riemann integral) for the real line only. Prerequisite: MAT 230 and MAT 240.


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