Requirements & Courses

Major Requirements
Thirtysix credits which must include:
 MTH121, 122, 210, 223, 310, and 421 or 431.
 Twelve other upperlevel Mathematics credits.
 Cognates:CSC120 and one course other than a Mathematics course, approved by the Department, with a Mathematics prerequisite numbered 113 or higher.
 The senior comprehensive examination includes three parts: successful completion of the Major Field Test in Mathematics, submission of an approved writing sample and an approved oral presentation.
 At least one statistics course is recommended.
 Students interested in graduate school in mathematics should complete both MTH421 and 431 and an honors project. Students interested in business and industrial careers should consider additional courses in Applied Mathematics, Computer Science and fields which apply mathematics in significant ways.

Minor Requirements
Twentyfour credits which must include:
 MTH121, 122, 210
 At least two other upperlevel Mathematics courses.
Note: MTH100 and 202 do not count toward the Minor.

Secondary Teaching Major Requirements
Same as for the Mathematics major except that the program must include MTH341, 411, and 421.

Secondary Teaching Minor Requirements
At least twentysix credits which must include: MTH120, 121, 122, 223, 411; 117 or 310; and 116 or 341.

Elementary Teaching Major Requirements
Thirtysix credits which must include:
 MTH110, 117, 121, 122, 202, 203, 210, 223, 341
 Four other upperlevel credits in Mathematics
 Cognate: CSC118 or 120
 The senior comprehensive, which includes 1) submission of an approved writing sample, and 2) an approved oral presentation.

Elementary Teaching Minor Requirements
Twentyfour credits which must include:
 MTH110; 113 or 121; MTH116 or 341; MTH120 or 223; MTH202
 Four additional credits at MTH110 or above
 Required Cognate: CSC118 or 120

Mathematical Sciences Major Requirements
Fiftytwo credits which must include:
 MTH121, 122, 210, 223, 310, 336, 341, and 421 or 431
 Computer Science 120 and 121
 Twelve additional credits in upperlevel Mathematics or Computer Science courses, at least four credits of which must be Computer Science. Courses which combine applications and theory are encouraged (e.g. MTH211, 342, 391, 399 or 499; and CSC240, 310, 420, 430, 440, or 499).
 The senior comprehensive examination includes three parts: successful completion of the Major Field Test in Mathematics, submission of an approved writing sample and an approved oral presentation.

Restrictions
The following combinations of double majors are not permitted: Mathematical Sciences and Mathematics; and Mathematical Sciences and Computer Science.

Four credits from MTH 110 or higher, with the exception of practicum or independent study courses, count towards the Distributive Requirements in the Natural Sciences — Mathematics/Computation.
Courses

MTH100.Applied Algebra4 creditsDevelops mathematical skills with an emphasis on increasing the students’ ability to interpret and reason with quantitative information. Focuses on mathematical critical thinking and problem solving. Topics include variables and functions, linear, quadratic, exponential and other models, each presented in the context of applications from social and natural sciences, business, and everyday life.

MTH110.Liberal Arts Mathematics4 creditsPrerequisite: MTH100 or PlacementExploration of the beauty, extent and power of mathematics. Specific topics to be selected by the instructor.

MTH112.PreCalculus4 creditsPrerequisite: MTH100 or PlacementDesigned for students with strong high school mathematics backgrounds who plan to include a calculus course (Mathematics 113 or 121) in their programs. Investigates polynomial, rational, exponential, logarithmic and trigonometric functions. Explores the ideas of functions and graphs, with emphasis on concepts and skills central to calculus. Requires placement. May not be taken for credit by students who have successfully completed MTH121, 122 or 210.

MTH113.Applied Calculus4 creditsPrerequisite: MTH112 or PreCalculus in High SchoolIntroduction to differential and integral calculus. Focuses on applications; theory held to a minimum. Examples from business and the natural and social sciences. Background in trigonometry not needed.

MTH116.Elementary Statistics4 creditsPrerequisite: MTH100 or PlacementIntroduction to modern elementary statistics and applications. Focuses on statistical reasoning and data analysis. Includes statistical design of experiments, estimation, hypothesis testing, regression, correlation and other selected topics.

MTH117.Intro to Matrices and Linear Methods2 creditsPrerequisite: MTH112 or PreCalculus in High SchoolIntroduction to solving systems of linear equations, linear programming, elementary matrix theory, and the modeling of situations which are linear. Applications from business and natural and social sciences. Note: The content of this course is necessary background for MTH310. Requires placement in MTH112 or 4 years of high school math.

MTH118.Biostatistics4 creditsPrerequisite: MTH100 or PlacementIntroduction to statistical methods used in biomedical science and public health research. Focuses on experimental design, descriptive methods, hypothesis tests, analysis of variance, regression, and other selected topics.

MTH120.Discrete Mathematics4 creditsPrerequisite: MTH112 or PreCalculus in High SchoolIntroductory survey of propositional logic, functions, relations, counting methods and graph theory. Discussion of applications to computer science.

MTH121.Calculus I4 creditsPrerequisite: MTH112 or PreCalculus in High SchoolIntroduction to the calculus of one variable. Includes limits and continuity, the derivative and applications, the integral and applications, infinite series and sequences. (Part I of II)

MTH122.Calculus II4 creditsPrerequisite: MTH121Introduction to the calculus of one variable. Includes limits and continuity, the derivative and applications, the integral and applications, infinite series and sequences. (Part II of II)

MTH180.Topics in Mathematics24 creditsSelected topics of current or historic importance. Prerequisites vary with topics selected.

MTH192.Mathematical Modeling4 creditsPrerequisite: MTH113 or MTH121Development of various mathematical models used in business, social sciences and biological sciences; uses and limitations of models in practical situations. Some models use calculus and/or the computer. Computer programming not a prerequisite.

MTH202.Mathematics for the Elementary Teacher4 creditsPrerequisite: MTH100 or placement, Sophomore Standing, and Education MajorOverview and examination of the mathematical topics in the K8 curriculum. Includes arithmetic of integers, decimals and fractions; numeration systems; set theory; problem solving; elementary logic, elementary concepts in probability and statistics; elementary concepts in geometry; and an introduction to computing.

MTH203.Math  Middle and HS Teachers2 creditsPrerequisite: MTH121This course will provide an overview and examination of the mathematical topics and pedagogical approaches in the middle and high school curriculum. Topics include problem solving, number theory, algebraic thinking, geometry, probability and statistics, and mathematics software applications for teaching (e.g., Geometer’s Sketchpad and Tinkerplots).

MTH210.Multivariable Calculus4 creditsPrerequisite: MTH122Continuation of Math 122. Includes functions of several variables, vectors, vectorvalued functions, threedimensional analytic geometry, partial differentiation and multiple integration.

MTH211.Differential Equations4 creditsPrerequisite: MTH210Techniques and theory of solving ordinary differential equations. Includes series solutions, numerical methods and applications.

MTH220.Math Foundations of Computer Science4 creditsPrerequisite: MTH120Topics in the mathematical foundations of computer science. Includes graph theory, logic, Boolean algebras, languages and automata, and the analysis of algorithms.

MTH221.Introduction to Cryptography4 creditsPrerequisite: MTH122Introduction to the mathematics from several different branches of the subject including number theory, matrix algebra, probability, and statistics, all of which play a role in enciphering and deciphering secret messages.

MTH223.Mathematical Structures4 creditsPrerequisite: MTH120 and CSC121, or MTH122Study of predicate logic, proof techniques, set theory, relations, functions, cardinality and various discrete structures.

MTH241.Financial Mathematics4 creditsPrerequisite: MTH122Introduction of fundamental concepts of interest theory. Applications of those concepts in calculating present and accumulated values for various streams of cash flows. Topics include reserving valuations, pricing, asset/liability management, investment income, and capital budgeting. Financial instruments such as derivatives will also be introduced.

MTH280.Topics in Mathematics24 creditsPrerequisite: MTH122 or Permission.Selected topics of current or historic importance. Prerequisites vary with topics selected.

MTH280M.Topics in Mathematics24 creditsSelected topics of current or historic importance. Prerequisites vary with topics selected.

MTH310.Linear Algebra4 creditsPrerequisite: MTH210; MTH117 Strongly RecommendedStudy of finitedimensional real vector spaces; kernel, dimension, basis, linear transformations and their matrices, and eigenvalues.

MTH323.Complex Analysis4 creditsPrerequisite: MTH210Introduction to the theory of functions of a single complex variable. Analytic functions, complex series, Cauchy’s theorem and conformal mapping.

MTH336.Numerical Analysis4 creditsPrerequisite: MTH122 and CSC120Analysis and implementation of numerical algorithms for approximating functions, derivatives and integrals, and for solving nonlinear equations, ordinary differential equations and systems of linear equations. Discussion of standard software packages and techniques for writing efficient and reliable mathematical software in Pascal and/or FORTRAN.

MTH341.Probability and Statistics I4 creditsPrerequisite: MTH122Indepth examination of probability and introduction to mathematical statistics. Topics include axiomatic probability, discrete and continuous random variables, transformations of random variables, moment generating functions, limit theorems, and point estimation.

MTH342.Probability and Statistics II4 creditsPrerequisite: MTH341Continuation of MTH341, focusing on mathematical statistics. Selected topics may include maximum likelihood estimation, likelihood ratio tests, linear models, and Bayesian methods.

MTH345.Stochastic Processes4 creditsPrerequisite: MTH210Introduction to the theory and applications of stochastic processes, including Markov chains, Poisson processes, queuing theory, and Brownian motion. Example applications include models of random walks, DNA sequences, call centers, and the BlackScholes option pricing formula.

MTH351.Elementary Number Theory4 creditsPrerequisite: MTH223Study of integers, including divisibility, the theory of prime numbers, congruences and solutions of equations in integers.

MTH380.Topics in Mathematics4 creditsSelected topics of current or historic importance. Prerequisites vary with topics selected.

MTH390.Combinatorics4 creditsPrerequisite: MTH120 or 122Introduction to combinational theory. Topics include enumeration, recurrence, generating functions, graph theory and optimization.

MTH390M.Combinatorics4 creditsPrerequisite: MTH120 or 122Introduction to combinational theory. Topics include enumeration, recurrence, generating functions, graph theory and optimization.

MTH391M.Introduction to Graph Theory4 creditsPrerequisite: MTH122 or PermissionIntroductory survey of the major concepts and applications of graphs, digraphs and networks. Application areas include transportation, traffic flow, games and puzzles. Spring Term only.

MTH411.College Geometry4 creditsPrerequisite: MTH223Axiomatic systems, models, finite geometries, Hilbert’s axioms, independence of the parallel postulate, and introduction to nonEuclidean geometries with emphasis on hyperbolic geometry.

MTH413.Topology4 creditsPrerequisite: MTH223Introduction to pointset topology. Includes topological properties of Euclidean spaces, abstract spaces and metric spaces. Explores connectedness, compactness, continuity and homeomorphisms.

MTH421.Abstract Algebra4 creditsPrerequisite: MTH223 and 310Introduction to the theory of algebraic structures including elementary theory of groups, rings and fields.

MTH431.Advanced Calculus4 creditsPrerequisite: MTH210 and 223Indepth examination of the calculus of one variable, including topology of the real line, sequences and series of functions.

MTH491.Mathematical Methods of Physics4 creditsPrerequisite: MTH211; MTH310 recommendedSurvey of advanced mathematical topics for application in the physical sciences. Topics selected from Fourier series, transform calculus, partial differential equations, boundary value problems, complex variables and vector calculus. Highly recommended for students planning graduate study in the physical sciences or applied mathematics.

MTH499.Mathematics Independent Study1 creditRequires instructor permission.

MTH500.Senior Thesis4 creditsRequires instructor permission.