Requirements & Courses

Major Requirements
 Thirtysix credits in Mathematics, which must include:
 MTH121, 122, 210, 223, 310, and 421 or 431.
 Twelve other upperlevel credits, at least four of which must be at the 300 or 400level.
 Cognates:
 A computer science course numbered CSC121 or higher. For students with no previous computer science experience, this will require a prerequisite course of CSC119 or
 One nonMTH course, approved by the Department, with a Mathematics prerequisite numbered MTH113 or higher.
 Successful completion of the Major Field Test in Mathematics.
 Thirtysix credits in Mathematics, which must include:

Minor Requirements
Twentyfour credits in Mathematics, which must include:
 MTH121, 122, 210
 At least eight other upperlevel credits in MTH.

Secondary Teaching Major Requirements
 MTH120, 121, 122, 210, 223, 242, 310, 411, 421.
 Cognates:
 Any 4credit CSC course. The recommended course is CSC118.
 One nonMTH course with a Mathematics prerequisite numbered MTH113 or higher.
 Successful completion of the Major Field Test in Mathematics.

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

Mathematics Teaching Major Requirements (PK6)
Thirtysix credits which must include:
 MTH110, 117, 121, 122, 202 or 204, 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.

PK6 Teaching Minor Requirements
Twentyfour credits which must include:
 MTH110; 113 or 121; MTH116 or 341; MTH120 or 223; 204
 Four additional credits at MTH110 or above, excluding 203, 205, and 206

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.

Requirements for Honors in Mathematics
 A strong program of mathematics courses: at least five courses at the 300 or 400level, including both MTH421 (Abstract Algebra) and MTH431 (Advanced Calculus).
 A grade point average of at least 3.5 in Mathematics major courses
 A project including both a paper and oral presentation of honors quality

Program Considerations
 MTH100, 202, 203, 204, 205, and 206 do not count toward the Mathematics minor.
 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.

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

MTH108.Introduction to College Math2 creditsStrengthen your mathematical skills in preparation for coursework requiring quantitative reasoning. Topics include algebraic and exponential expressions, polynomial and rational equations, and graphs in the coordinate system. Emphasis will be placed on the development of critical thinking and problem solving skills through applications.

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

MTH111.College Algebra With Applications4 CreditsEstablishes problemsolving and critical thinking skills through applications. Topics include number systems, algebraic expressions and equations, and a variety of functions including linear, quadratic, exponential, and logarithmic. Intended for students who will take MTH112 or will encounter quantitative reasoning in multiple courses.

MTH112.PreCalculus4 creditsPrerequisite: MTH100 or PlacementFoundational concepts for the study of calculus. Investigates polynomial, rational, exponential, logarithmic and trigonometric functions. Explores the ideas of functions and graphs, with emphasis on concepts and skills central to calculus. 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 SchoolIntroduction to formal logic, sets, functions and relations, counting methods, graphs and trees, and recursive structures and inductive reasoning.

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.

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).

MTH204.Number Systems for PK6 Teachers4 creditsIntroduction to number systems and operations, including early algebraic thinking, problem solving, set theory, and elementary logic. Analysis and construction of effective mathematical tasks in teaching number systems and operations at the PK6 level.

MTH205.Rational Numbers for PK6 Teachers4 creditsUnpacking mathematical content and identifying competence for rational numbers, with a focus on representations, learning trajectories, performing and supporting mathematical explanations, and interpreting and extending mathematical thinking.

MTH206.Geometry for PK6 Teachers4 creditsAn exploration of 2D and 3D geometry topics and spatial relations while exploring the high leverage teaching practice of assessment, noticing student thinking, and using representations.

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.

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 or MTH122Introduction to proof techniques. Theoretical analysis of discrete structures such as sets, graphs, functions, and relations.

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.

MTH242.Applied Statistical Methods4 creditsPrerequisite: A MTH course numbered 112 or above, or DAT115 or 116, or ECN217, or PSY220Applied study of inferential and descriptive statistics. Topics include data visualization, confidence intervals and hypothesis tests, linear regression, ANOVA, ANCOVA, categorical data analysis, resampling methods, and time series. Emphasizes written and oral communication of results. Uses statistical software, such as R.

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.