Computer and Computational Mathematics

See College of Engineering and Computer Science for a major in Computer and Information Science.

Minor or BGS/LIBS Concentration Only

The courses in Computer and Computational Mathematics (CCM) develop skills in applying mathematical algorithms in ways useful in real world situations. A minor or concentration consists of 12 hours of upper-level credit in courses specifically selected as CCM courses.

CCM 150     Computer Science I     4 Credit Hours

An introduction to structured computer programming covering problem formulation, algorithm development, the C++ programming language, program testing and debugging, capabilities and elements of computer organization, and object-oriented software methodologies.

Prerequisite(s): MATH 115*

Corequisite(s): CCM 150L

CCM 172     Computing Environ for Math     3 Credit Hours

This course covers introductory programming techniques for Mathematics majors. Students will learn to program in sage and python. Topics include data types, variables and assignments, decisions, loops, functions, recursion, arrays and objects. Programming assignments focus on problems that are mathematical in nature, giving students an opportunity to use simulations to understand and verify familiar mathematical results. This course, or CIS/CCM 150, satisfies the programming requirement for the Mathematics concentration.

Prerequisite(s): MATH 115

Restriction(s):
Can enroll if Class is Freshman or Sophomore or Junior or Senior
Can enroll if College is Arts, Sciences, and Letters

CCM 305     The Theory of Computation     3 Credit Hours

An introduction to the foundations of computer science including the theory of computability, Turing machines, automata, and formal languages.

Prerequisite(s): CIS 175 and (CIS 200 or IMSE 200)

CCM 315     Applied Combinatorics     3 Credit Hours

An introduction to methods and applications of enumerative and configural combinatorics. Students study several elegant and useful techniques for counting and/or generating the elements in large and unwieldy finite sets. Students also study topics in graph theory that are applicable to real world problems. Topics include basic counting principles, the principle of inclusion-exclusion, generating functions and recurrence relations. Topics from graph theory include graph models, paths, circuits, cycles, and connectedness; additional topics include the theory and applications of planarity, coloring, directed graphs, networks and network flows.

Prerequisite(s): MATH 300)(MATH 200 and (MATH 217 or MATH 227)

CCM 372     Computing with Mathematica     3 Credit Hours

The course explores a variety of topics from different areas of undergraduate mathematics including calculus, matrix algebra, number theory, geometry, and discrete mathematics. Students learn to design customized Mathematica functions to solve specific problems in these areas using the symbolic, computational, graphics, and programming tools provided within Mathematica.

Prerequisite(s): MATH 217 or MATH 227

CCM 390     Topics in Computational Math     1 to 3 Credit Hours

A course designed to offer selected topics in different areas of applied mathematics. The specific topics will be announced together with the prerequisites for each separate offering. Course may be repeated when the topics covered differ.

CCM 399     Independent Studies     1 to 3 Credit Hours

Readings or analytical assignments in Computers and Computational Mathematics in accordance with the needs and interests of those enrolled and agreed upon by the student and advising instructor.

CCM 404     Dynamical Systems     3 Credit Hours

The aim of this course is to survey the standard types of differential equations. This includes systems of differential equations, and partial differential equations, including for each type, a discussion of the basic theory, examples of applications, and classical techniques of solutions with remarks about their numerical aspects. Also included are autonomous and periodic solutions, phase space, stability, perturbation techniques and Method of Liapunov. (AY).

Prerequisite(s): MATH 216 and (MATH 217 or MATH 227)

CCM 451     Computer Graphics     3 Credit Hours

Basic geometrical concepts: graphics output primitives, two-dimensional transformations, windowing and clipping, three-dimensional viewing, visible surface detection methods, graphical user interfaces.

Prerequisite(s): (CCM 350 or CIS 350 or IMSE 350) or (ECE 370 and MATH 276) and (MATH 215 or MATH 205) and (MATH 217 or MATH 227)

Restriction(s):
Can enroll if Class is Graduate

CCM 458     Introduction to Wavelets     3 Credit Hours

This course will introduce the students to theory and application of wavelets using linear algebra. Topics will include the discrete Fourier transform, the fast Fourier transform, linear transformations, orthogonal decomposition, discrete wavelet analysis, the filter bank, Haar Wavelet family, Daubechies's Wavelet family, and applications. Students cannot receive credit for both MATH 458 and MATH 558. (OC)

Prerequisite(s): MATH 216 and (MATH 217 or MATH 227)

Restriction(s):
Can enroll if Class is Sophomore or Junior or Senior

CCM 472     Intro to Numerical Analysis     3 Credit Hours

Solution of linear systems by Gaussian elimination, solution of nonlinear equations by iterative methods, numerical solutions of ordinary differential equations, data fitting with spline functions, numerical integration, optimization. (F).

Prerequisite(s): MATH 217 or MATH 227

CCM 473     Matrix Computation     3 Credit Hours

A study of the most effective methods for finding the numerical solution of problems which can be expressed in terms of matrices, including simultaneous linear equations, orthogonal projections and least squares, eigenvalues and eigenvectors, positive definite matrices, and difference and differential equations. (AY).

Prerequisite(s): MATH 217 or MATH 227

 
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An asterisk denotes that a course may be taken concurrently.

Frequency of Offering

The following abbreviations are used to denote the frequency of offering: (F) fall term; (W) winter term; (S) summer term; (F, W) fall and winter terms; (YR) once a year; (AY) alternating years; (OC) offered occasionally