 Centre College Mathematics Program

## Courses

Below you will find a description of our regular long-term courses. For information on past CentreTerm offerings, special topics courses, course scheduling, and math placement, please use the links on the right.

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. Not open to students who have established basic skills in math.

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 145 Mathematical Modeling and Applied Calculus
An introduction to the process of mathematically modeling biological, economic, physical, and sociological phenomena. The course first explores common functions used in modeling, and then develops methods to analyze these models using single and multivariable calculus and linear algebra. The course includes the study of parameterized families of functions, dimensional analysis, matrix and vector algebra, differentiation, optimization, and integration. Scientific computing skills are developed. Prerequisite: Basic skills in mathematics.

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 200 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 170 or permission of the instructor.

MAT 205 Statistical Modeling
An introduction to multivariate statistical analysis, emphasizing fundamental statistical concepts, as well as application and interpretations. The course includes frequent data analysis using statistical software. Examples are drawn from economics, psychology, sociology, political science, biology, and medicine. Topics include simple/multiple regression, one-way/two-way ANOVA, and logistic regression. Additional topics may include time series, analysis of covariance, factor analysis, and cluster analysis. Prerequisite: MAT 145 or 170 or equivalent.

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 300 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 305 Combinatorics and Graph Theory
An introduction to the fundamental ideas of combinatorics and graph theory.  Topics include counting methods, generating functions, partitions, recurrence relations, trees, coloring, connectivity, planarity, and Ramsey Theory. Prerequisite: MAT 300 or permission of instructor.

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 300.

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 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 300.

MAT 4XX Special Topics Course
Currently offered every spring.

MAT 420 Putnam Seminar (one credit hour)
The Putnam Exam is a notoriously challenging annual mathematical competition. This is a course on problem-solving focusing on Putnam-style problems. Students learn strategies for tackling such problems and become familiar with the style by working out problems from past Putnam exams, discussions, and presentations to the group. The semester culminates in taking the Putnam exam. Prerequisite: MAT 230.