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Mathematics Courses

Mathematics General Course Listings

Sub CRSE Title
CSC 220 Discrete Structures (= MAT 220)
Prerequisites & Notes

MAT 140, MAT 150, or MAT 160, and the ability to program in a high-level language such as Python, C++, or Java at the level expected in CSC 121 or an equivalent course.

Instructor
Staff

(Cross-listed as MAT 220) An introduction to proof techniques, with a focus on topics relevant to computer science. Topics include: fundamental proof techniques, boolean logic, sequences and summations, set theory, algorithm analysis, recursion, mathematical induction, recurrence relations, an introduction to number theory, combinatorics, discrete probability, and graph theory. The class will be adequate preparation for students choosing to continue on the pure math track (Real Analysis, Abstract Algebra, etc.) or the theoretical computer science track (Analysis of Algorithms, Theory of Computation, etc.).

Satisfies the Mathematical and Quantitative Thought distribution requirement.
Counts towards the Mathematics major and minor.
Counts towards the Computer Science major and minor.

 

 

CSC 221 Data Structures
Prerequisites & Notes

Computer Science 121, 200, 209, or permission of instructor.

Instructor
Staff

A study of abstract data types, including lists, stacks, queues, and search tables, and their supporting data structures, including arrays, linked lists, binary search trees, and hash tables.  Implications of the choice of data structure on the efficiency of the implementation of an algorithm.  Efficient methods of sorting and searching.

Counts towards the Mathematics major and minor.
Counts towards the Computer Science major and minor.
Counts as an elective in the Data Science interdisciplinary minor.
Satisfies the Mathematical and Quantitative Thought distribution requirement.

CSC 315 Numerical Analysis (= MAT 315)
Prerequisites & Notes

MAT 150 and MAT 235, and proficiency in some programming language. (Spring)

Instructor
Staff
(Cross-listed as Mathematics 315.) Survey of methods to approximate numerical solutions of problems in root-finding, differentiation, integration, curve-fitting, differential equations, and systems of equations. Derivations, limitations, and efficiency of different algorithms are considered.

Counts towards the Mathematics major and minor.
Counts towards the Computer Science major and minor.

CSC 324 Theory of Computation
Prerequisites & Notes

One of Mathematics 220, 230, or 255. (Offered Spring of odd-numbered years.)

Instructor
Staff

Mathematical models of computation, and the fundamental capabilities and limitations of computers.  Topics include regular languages, finite automata, context-free languages, grammars, Turing machines, the Chomsky hierarchy, the halting problem, algorithms, decidable and undecidable problems, algorithmic reductions, complexity theory, the classes P, NP, and PSPACE, and NP-complete problems.

Counts towards the Mathematics major and minor.
Counts towards the Computer Science major and minor.

CSC 361 Computer Graphics
Prerequisites & Notes

MAT 140 or MAT 150 and CSC 221

Instructor
Peck

Overview of 2D and 3D computer graphics techniques: line drawing routines, antialiasing, 3D object representation, culling, z-buffers, a-buffers, illumination and shading models, ray tracing, color models, the graphics pipeline, levels of detail, and image processing. Emphasis on understanding and implementing computer graphics algorithms and creating computer generated images using OpenGL and C++.

Counts towards the Mathematics major and minor.
Counts towards the Computer Science major and minor.

CSC 370 Artificial Intelligence
Prerequisites & Notes

CSC 221 and one of MAT 220, 230, or 255; or permission of the instructor.

Instructor
Ramanujan

An introduction to the theory, principles, and techniques of Artificial Intelligence. Topics include search, game playing, constraint satisfaction problems, planning, reinforcement learning, knowledge representation, logic, and natural language processing.

Counts towards the Mathematics major and minor.
Counts towards the Computer Science major and minor.

CSC 371 Machine Learning
Prerequisites & Notes

Proficiency in a high-level programming language and data structures, at the level expected in CSC 221, and MAT/CSC 220 (or permission of the instructor). 

Offered Spring of even-numbered years.

A survey of the field of machine learning, with an introduction to the fundamental algorithms in the field and the theory underpinning them. Topics include techniques for regression, classification, ensemble methods, and dimensionality reduction.

Counts towards the Mathematics major and minor.
Counts towards the Computer Science major and minor.
Counts as an elective in the Data Science interdisciplinary minor.

CSC 379 Cryptology
Prerequisites & Notes

Math 150 (Linear Algebra), and an introductory proof course (one of CSC 220 Discrete Structures, MAT 230 Sets and Proofs, or MAT 255 Number Theory).

Instructor
Mossinghoff

The study of making and breaking secret codes, including classical ciphers and their cryptanalysis, modern symmetric ciphers, and public-key systems, and their application in cryptographic protocols for secrecy, key exchange, information assurance, and authentication. Analysis of the security of cryptosystems using tools from mathematics and computer science.

Fulfills an elective requirement in the Applications area of the Computer Science major.
Counts as an elective in the Computer Science minor.
Counts as an elective in the Mathematics major and minor.
Counts as an elective in the Social Science track of the Applied Mathemetics interdisciplinary minor.

MAT 108 Exploring Mathematical Ideas
Prerequisites & Notes

Not open to students with credit for, or enrolled in, Mathematics 220, 230, or 255.

Instructor
Staff

Survey of abstract mathematical ideas that deepen understanding of patterns from mathematics, art, and the physical world. Topics may include the nature of number, infinity, dimension, symmetries, alternate geometries, topology, chaos, fractals, probability and social choice. While techniques and concepts have much in common with advanced theoretical mathematics, little background is assumed and the course is not practical preparation for later courses in mathematics. The course title is occasionally changed to reflect a special emphasis.

Satisfies the Mathematical and Quantitative Thought distribution requirement.

MAT 110 Finite Mathematics
Prerequisites & Notes

Not open to students with credit for Mathematics 150, 220, or 340.

Instructor
Staff

Mathematical techniques that have been used, productively and extensively, during the last thirty years and that do not involve the use of calculus. Probability, linear programming, matrix algebra, Markov chains, game theory, and graph theory are representative topics. Students learn to use computer software, including a spreadsheet, to solve problems.

Satisfies the Mathematical and Quantitative Thought distribution requirement.

MAT 111 Calculus I (for those with no previous exposure)
Prerequisites & Notes

Not open to students with one semester of a high school or college course about calculus. (Spring)

Instructor
Staff

An introduction to the differential and integral calculus of algebraic, trigonometric, exponential, and inverse trigonometric functions with applications including graphical analysis, optimization and numerical methods. 

Satisfies the Mathematical and Quantitative Thought distribution requirement.

MAT 112 Calculus I and Modeling
Prerequisites & Notes

Assumes previous exposure to (not proficiency in) some calculus concepts.

Instructor
Staff
 
An introduction to the differential and integral calculus of algebraic, trigonometric, exponential, and inverse trigonometric functions with applications including graphical analysis, optimization, and numerical methods. An emphasis on investigating mathematical approaches to describing and understanding change in the context of problems in the life sciences. 

Satisfies the Mathematical and Quantitative Thought distribution requirement.

MAT 113 Calculus II
Prerequisites & Notes

Mathematics 111 or 112 or one year of high school calculus.

Instructor
Staff

An introduction to techniques and applications of integration; infinite series including convergence tests and Taylor series; calculus on parametric and polar curves; and concepts in 3-space including vectors, lines, planes, and vector-valued functions. Satisfies a major requirement in Mathematics.

Satisfies the Mathematical and Quantitative Thought distribution requirement.

MAT 140 Multivariable Calculus and Modeling
Prerequisites & Notes

Mathematics 112 (Calculus I and Modeling). (Spring)

Instructor
Staff

Continued study of calculus and other mathematical methods for modeling change and uncertainty. Topics include multivariable calculus; systems of linear equations, difference equations and differential equations; and probability models such as Bayes' rule and random walks. Students will be guided in the discovery and mastery of mathematical techniques in the context of problems in the life sciences.

Satisfies the Mathematical and Quantitative Thought distribution requirement.

MAT 150 Linear Algebra
Prerequisites & Notes

Mathematics 113 or permission of instructor.

Instructor
Staff

An introduction to systems of linear equations, matrices, determinants, vector spaces, and eigenvectors in an interactive learning environment provided by the computer algebra system Mathematica. Applications are chosen from linear programming, least squares approximation, graph theory, cryptography, computer graphics, and other topics. 

Satisfies the Mathematical and Quantitative Thought distribution requirement.

MAT 160 Calculus III
Prerequisites & Notes

Mathematics 113.

Instructor
Staff

A study of the differential and integral calculus of functions of several variables together with an introduction to vector calculus.  Topics include partial derivatives, directional derivatives, gradients, tangent planes to surfaces, double and triple integrals, change of variables in multiple integrals, vector fields, line integrals, Green's Theorem, and surface integrals.

Satisfies the Mathematical and Quantitative Thought distribution requirement.

MAT 210 Mathematical Modeling
Prerequisites & Notes

Mathematics 140 or 150 or permission of the instructor. (Spring)

Instructor
Staff

A survey of discrete mathematical modeling techniques and their application to the natural and social sciences. Mathematical tools are selected from Monte Carlo simulation, queuing theory, Markov Chains, optimization, discrete dynamical systems, artificial intelligence, and game theory. Emphasis is on formulating models, investigating them analytically and computationally, and communicating the results.

Counts as an elective in the Data Science interdisciplinary minor.
Satisfies the Mathematical and Quantitative Thought distribution requirement.

MAT 220 Discrete Structures (= CSC 220)
Prerequisites & Notes

MAT 140, MAT 150, or MAT 160, and the ability to program in a high-level language such as Python, C++, or Java at the level expected in CSC 121 or an equivalent course.

An introduction to proof techniques, with a focus on topics relevant to computer science.  Topics include: fundamental proof techniques, boolean logic, sequences and summations, set theory, algorithm analysis, recursion, mathematical induction, recurrence relations, an introduction to number theory, combinatorics, discrete probability, and graph theory.  The class will be adequate preparation for students choosing to continue on the pure math track (Real Analysis, Abstract Algebra, etc) or the theoretical computer science track (Analysis of Algorithms, Theory of Computation, etc.).

Satisfies the Mathematical and Quantitative Thought distribution requirement.
Counts towards the Mathematics major and minor.
Counts towards the Computer Science major and minor.

MAT 230 Sets and Proofs
Prerequisites & Notes

Mathematics 150 or Mathematics 160  or permission of the instructor.

Instructor
Staff

An introduction to proof techniques (including quantifiers and induction), elementary set theory, abstract functions, infinite cardinalities, and properties of sets of real numbers; followed by an introduction to topics chosen from topology, analysis, dynamical systems, or set theory, among others.  Emphasis throughout is on developing abilities in writing proofs.

Satisfies the Mathematical and Quantitative Thought distribution requirement.

MAT 235 Differential Equations
Prerequisites & Notes

Mathematics 150. (Fall)

Instructor
Staff

A study of solution techniques and models in ordinary differential equations including first order equations, linear differential equations, series solutions, Laplace transform methods, and concepts of numerical and graphical techniques applied to equations and systems. 

Satisfies the Mathematical and Quantitative Thought distribution requirement.

MAT 255 Number Theory
Prerequisites & Notes

Mathematics 150 or Mathematics 160 or permission of the instructor. (Spring)

Instructor
Staff

Mathematical properties of the integers and related sets, including divisibility properties, prime numbers and their distribution, congruences, diophantine equations, arithmetic functions, primitive roots, and quadratic residues.

Satisfies the Mathematical and Quantitative Thought distribution requirement.

MAT 315 Numerical Analysis (= CSC 315)
Prerequisites & Notes

MAT 150 and MAT 235, and proficiency in some programming language. (Spring)

Instructor
Staff

Survey of methods to approximate numerical solutions of problems in root-finding, differentiation, integration, curve-fitting, differential equations, and systems of equations. Derivations, limitations, and efficiency of different algorithms are considered. 

Counts towards the Mathematics major and minor.
Counts towards the Computer Science major and minor.

MAT 320 Combinatorics
Prerequisites & Notes

The mathematics of arrangements of discrete sets, including binomial and multinomial coefficients, inclusion and exclusion, the pigeonhole principle, partitions and compositions, Stirling and Catalan numbers, occupancy problems, generating functions, recurrence relations, and selected modern topics. Prerequisite: CSC/MAT 220, MAT 230, or MAT 255.

 

Satisfies a major requirement in Mathematics

Satisfies a minor requirement in Mathematics

MAT 325 Graph Theory
Prerequisites & Notes

A rigorous introduction to graph theory including the study of trees, connectivity, graph distances, adjacency matrices, Euler tours, Hamiltonian cycles, matchings, graph colorings, planarity, Euler characteristic, directed graphs, network flows, algorithms and extremal problems. The prerequisite is one of the following: MAT/CSC 220, MAT 230, MAT 255

 

Satisfies a major requirement in Mathematics

Satisfies a minor requirement in Computer Science

Satisfies a distribution requirement in Mathematical and Quantitative Thought

MAT 330 Real Analysis I
Prerequisites & Notes

Mathematics 113 and one of Mathematics 220, 230, or 255.  (Fall)

Instructor
Staff

The theory of functions of a real variable. Topics include properties of the real numbers, sequences and series, continuity, differentiation, the Riemann integral, and sequences of functions.

MAT 331 Complex Analysis
Prerequisites & Notes

Mathematics 160 and one of Mathematics 220, 230, or 255. (Spring)

Instructor
Staff

The algebra and geometry of complex numbers, sequences and series of complex numbers, derivatives, and integrals of functions of a complex variable. The Cauchy-Goursat Theorem, the Cauchy Integral Formula and its consequences, Taylor series, classification of singularities, the Residue Theorem, Laurent series, harmonic functions, conformal mappings, and, if time permits, miscellaneous applications. 

MAT 340 Probability
Prerequisites & Notes

Mathematics 140 or 160. (Fall)

Instructor
Staff

A study of probability theory relative to both discrete and continuous probability laws. Topics include independence and dependence, mean, variance and expectation, random variables, jointly distributed probability laws, Chebysheff's Inequality and a version of the Central Limit Theorem. Applications of probability theory are approached through a variety of idealized problems.

MAT 341 Mathematical Statistics
Prerequisites & Notes

Mathematics 340. (Spring)
 


 

Instructor
Staff

A mathematical approach to statistical theory. Includes a study of distribution theory, important properties of estimators, interval estimation and hypothesis testing, regression and correlation, and selected topics from non-parametric statistics.

Satisfies a requirement in the Data Science interdisciplinary minor.

MAT 355 Abstract Algebra I
Prerequisites & Notes

Mathematics 150 and one of Mathematics 220, 230, or 255. (Fall)

Instructor
Staff

An introduction to the theory of groups, rings and fields. Topics include normal subgroups, quotient groups, homomorphisms, Cayley's theorem, permutation groups, ideals, the field of quotients of an integral domain, and polynomial rings.

MAT 360 Topology
Prerequisites & Notes

One of Mathematics 220, 230, or 255. (Offered Spring of even-numbered years.)

Instructor
Staff

An introduction to metric and topological spaces. Topics include concepts of completeness, compactness, connectedness, fixed point theorems, knot theory, and classification of surfaces. 

MAT 380 Seminar in Problem Solving and History of Mathematics
Prerequisites & Notes

One of Mathematics 220, 230, 255 or permission of the instructor. (Fall)

 

Instructor
Staff

A seminar in the history of mathematics with an emphasis on problem solving techniques available during different historical periods. The chronological development of mathematics is studied from ancient Egypt and Babylon to the Renaissance, with occasional non-chronological forays into modern mathematics. 

MAT 381 Seminar
Prerequisites & Notes

Permission of the instructor.

Instructor
Staff

MAT 381-385
Study of topics of interest in Mathematics. 

MAT 386 Seminar
Prerequisites & Notes

Permission of the instructor.

Instructor
Staff

MAT 386-389
Study of topics of interest in Mathematics. 

MAT 395 Independent Study
Prerequisites & Notes

Open to qualified students with the permission of the department chair. Eligible for major credit by departmental approval.

 

Instructor
Staff

Independent study under the direction and supervision of a faculty member who reviews and approves the topic(s) of the independent study and who determines the basis for the evaluation of students' work.  

MAT 396 Independent Study
Prerequisites & Notes

Open to qualified students with the permission of the department chair. Eligible for major credit by departmental approval.

Instructor
Staff

Independent study under the direction and supervision of a faculty member who reviews and approves the topic(s) of the independent study and who determines the basis for the evaluation of students' work.  

MAT 430 Real Analysis II
Prerequisites & Notes

Mathematics 160 and 330. (Offered Spring of even-numbered years.)

Instructor
Staff

Further development of the theory of real functions, including such topics as functions of several variables, metric spaces, function spaces, Riemann-Stieltjes integrals, and Lebesgue measure.

MAT 437 Dynamical Systems
Prerequisites & Notes

Mathematics 150 and 330 or permission of the instructor. (Offered Spring of odd numbered years.)

Instructor
Staff

A study of the iteration of systems, typically arising from physical or biological models, and the resulting long term behavior. Periodic and chaotic dynamics as well as fractal graphics will be investigated.

MAT 450 Advanced Linear Algebra
Prerequisites & Notes

Mathematics 355 or permission of the instructor.

Instructor
Staff

A further study of vector spaces, dual spaces, inner product spaces, modules, linear transformations, characteristic roots, matrices, canonical forms, trace, transpose, determinants, normal transformations, and quadratic forms.

MAT 455 Abstract Algebra II
Prerequisites & Notes

Mathematics 355. (Offered Spring of even-numbered years.)

Instructor
Staff

A continuation of Mathematics 355, including additional topics in group theory and ring theory, extension fields, straight-edge and compass constructions, Galois Theory, and solvability by radicals.

MAT 481 Seminar
Prerequisites & Notes

Permission of the instructor.

Instructor
Staff

MAT 481-485
Study of topics of interest in Mathematics.
 

MAT 486 Seminar
Prerequisites & Notes

Permission of the instructor.

Instructor
Staff

MAT 487-489
Study of topics of interest in Mathematics.
 

MAT 491 Independent Study
Prerequisites & Notes

Independent study

MAT 492 Independent Study
Prerequisites & Notes

Independent Study

MAT 495 Independent Study
Prerequisites & Notes

Open to qualified students with the permission of the department chair. Eligible for major credit by departmental approval.

 

Instructor
Staff

Independent study under the direction and supervision of a faculty member who reviews and approves the topic(s) of the independent study and who determines the basis for the evaluation of students' work.

MAT 496 Independent Study
Prerequisites & Notes

Open to qualified students with the permission of the department chair. Eligible for major credit by departmental approval.

 

Instructor
Staff

Independent study under the direction and supervision of a faculty member who reviews and approves the topic(s) of the independent study and who determines the basis for the evaluation of students' work.