These requirements are from an excerpt from the University Academic Catalog, which outlines the requirements for a student to earn the distinction of being a Castleton University graduate. The complete catalog is available online.
Students who complete the Mathematics major are able to:
Upon successfully completing the major, graduates will be well equipped to secure desired employment in education, pure and applied mathematics, statistics, and actuarial science, as well as to pursue graduate studies in mathematics or math-related programs of study.
| Code | Course | Credits |
|---|---|---|
CIS 2031 |
C/C++ Programming IThis course introduces students to the concepts of programming with abstract data types and object-oriented programming. It uses C++ to cover classes, inheritance, and polymorphism. The course also builds on the prerequisites to provide students with more advanced exposure to software design, implementation, debugging, and documentation. This course fulfills the Scientific and Mathematical Understanding Frame of Reference. Fee Materials charge $20. Fall, odd years |
3 |
MAT 1531 |
Calculus ITopics include limits, differentiation, applications of derivatives, and an introduction to integration. This course may utilize graphing calculators on a regular basis. This course fulfills the Scientific and Mathematical Understanding Frame of Reference. Prerequisite: MAT 1360 or equivalent. Every semester |
4 |
MAT 2532 |
Calculus IIContinuation of Calculus I, with topics to include techniques of integration, applications of integration, improper integrals, sequences, series, and Taylor polynomials. Students in this course may be required to utilize graphing calculators. This course fulfills the Scientific and Mathematical Understanding Frame of Reference. Prerequisite: MAT 1531 Every semester |
4 |
MAT 3533 |
Calculus IIIContinuation of Calculus II, with topics including polar, spherical and cylindrical coordinates, partial derivatives, multiple integrals and vector calculus such as line integrals, surface integrals, and Gauss's, Green's, and Stoke's Theorems. Students in this course may be required to utilize graphing calculators. Prerequisite: MAT 2532 Spring |
4 |
MAT 3210 |
Linear AlgebraThis course introduces students to linear algebra including a study of vector spaces, linear transformations, determinants, inner products, and characteristic equations. Topics to be studied include mathematical structures, algebraic properties, and applications of matrices, determinants, vectors, vector spaces, and linear transformations. Students develop and solve mathematical models involving systems of linear algebraic equations and systems of linear differential equations. Students utilize graphing calculators and a computer algebra system. Prerequisite: MAT 2532 Fall |
3 |
MAT 3220 |
ProbabilityThis is a calculus-based course introducing probability theory including discrete and continuous random variables and their probability distributions, multivariate probability distributions, functions of random variables, and limit theorems. Prerequisite: MAT 3533 Fall |
3 |
MAT 3230 |
Mathematical StatisticsThis calculus-based course is a continuation of MAT 3220 including estimation theory, hypothesis testing, analysis of enumerative data, regression, analysis of variance, and nonparametric statistics. Prerequisite: MAT 3220. Spring |
3 |
MAT 3250 |
Applied Statistics with SPSSMethods of analyzing univariate and multivariate data using statistical packages including Minitab, SPSS, and SAS. Topics include descriptive statistics for univariate and bivariate data, basic properties of multivariate distributions, multivariate linear regression, principal component analysis for dimension reduction, factor analysis, canonical correlation analysis, discrimination and classification, and simple multiple series models. This course fulfills the Scientific and Mathematical Understanding Frame of Reference. Prerequisite: MAT 2022 or MAT 3230 Every Semester |
3 |
MAT 3310 |
Differential EquationsThis course is a study of first and higher order differential equations with many applications to science. Students explore analytical and numerical solution methods for ordinary and partial differential equations including series solutions and special functions for the solution of ODEs and the use of Fourier series to solve PDEs. Laplace transforms and numerical methods for solving ODEs and PDEs are introduced. Prerequisite: MAT 2532 and MAT 3210. Spring |
3 |
MAT 3410 |
Introduction to Mathematical ProofsThis course is an introduction to mathematical proof and serves as a bridge from elementary courses to more advanced mathematics. Students explore fundamental ideas in logic, sets, the theory of numbers, relations and functions. Prerequisite: MAT 1360 Fall |
3 |
MAT 4110 |
Advanced CalculusThis course is devoted to rigorous presentation of the basics of mathematical analysis of real valued functions of one (real) variable from the standpoint of contemporary/modern mathematics. It is a natural continuation of the sequence of calculus courses and will give proofs of important theorems used in those courses. Emphasis will be on the concepts and theoretical approach to calculus. Topics to be covered include theory of the real number system, theory of sequences and series of real numbers, theory of continuity, differentiability of real-valued functions, and theory of the Riemann integral of real valued functions. Prerequisite: MAT 3533 and MAT 3410 Periodically |
3 |
MAT 4130 |
Abstract AlgebraThis course is an introduction to the principles and concepts of modern abstract algebra. Topics will include groups, rings, and fields with applications to number theory, the theory of equations, and geometry. Prerequisite: MAT 3210 and MAT 3410, or consent of instructor. Periodically |
3 |
MAT 4140 |
GeometryThis course includes a review of Euclidean geometry and an introduction to non-Euclidean geometries including finite geometries and systems of axioms, classical theorems and elementary transformations. Prerequisite: MAT 3410 . Spring |
3 |
MAT 4720 |
Senior SeminarAn undergraduate research seminar. Students spend the first half of the semester studying and presenting undergraduate research in mathematics. In the second half, students investigate their own topic, prepare a written report, and present their research. Prerequisite: Math major, senior standing, or consent of the instructor. Fall |
3 |