Mathematics Program Requirements

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:

  1. Analyze and solve real-world problems using a variety of mathematical techniques,
  2. Convey mathematical information in effective ways,
  3. Choose and employ appropriate technology,
  4. Secure desired employment or gain admission to graduate or professional programs of study.

Complete the following courses (45 cr):

Code Course Credits

CIS 2031

C/C++ Programming I

This 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

3

MAT 1531

Calculus I

Topics 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 II

Continuation 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 III

Continuation 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 Algebra

This 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

Probability

This 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 Statistics

This 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 SPSS

Methods 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 Equations

This 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 Proofs

This 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 Calculus

This 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 Algebra

This 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

Geometry

This 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 Seminar

An 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

(Total credits required for the major: 45)

In addition, Foreign language proficiency is recommended (12 credits or equivalent)

And complete the University's Gen Ed requirements

Click here for General Education Requirements.