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Mathematics
Bachelor of Science
Combined Undergraduate/Graduate Degree
Minor
Mathematics
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FYMA 100 First Year Seminar (Mathematics) 3 Credit(s) FYS
This course will introduce student to the experience of academic exploration that is at the heart of a liberal arts education. Through study of one or more compelling questions or topics in a small seminar setting, students will practice creative and critical thinking and will learn to express themselves effectively and appropriately in a college setting. They will develop relationships and practices that allow them to effectively utilize college resources and become members of a community of learners. The specific topic of the seminar will be developed by individual faculty and will be announced in advance. First year seminars are required for first-year students and transfer students with fewer than 15 credits. Not open to students who have received credit for IDS 189 or another first year seminar course.
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MAT 090 Basic Algebra 3 Credit(s)
This course is intended to develop those ideas, computational techniques, and methods of reasoning used in college mathematics, with an emphasis on algebra needed to formulate and solve first and second degree equations, constructing models using linear and quadratic functions, and concepts of coordinate geometry. Only for students entering Fall 1999 or later who have not passed either the Accuplacer Elementary Algebra Test or the College Level Math Test or for those students who entered before Fall 1999 who have not satisfied the Basic Mathematics Competency Requirement. Does not give degree credit. Three lecture hours per week.
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MAT 103 Mathematics for the Liberal Arts 3 Credit(s) DII QR
This course is designed to give the liberal arts student, as well as other interested students, an introduction to some mathematical topics which broadly reflect the nature of the discipline. Topics are selected to highlight mathematical problem solving, the use of mathematical models and/or analysis of quantitative data. Topics may include probability and descriptive statistics, voting theory, graph theory, cryptography, game theory, chaos, and problems relating to the environment. Classroom lectures and discussions cover the basic theories. These are followed by writing assignments which form an essential component of the course. Not open to math majors without the permission of the Department Chairperson. Three lecture hours per week. This course satisfies the Quantitative Reasoning category.
Prerequisite: Completion of the Basic College Mathematics Competency Requirement.
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MAT 108 Finite Mathematics 3 Credit(s) DII
This course will include sets, real numbers, inequalities, the straight line, functions, operations on matrices, systems of equations, inverse of a matrix, linear programming, the Simplex method, counting, permutations and combinations, sample spaces, and probability. Three lecture hours per week. Prerequisite: Completion of the Basic College Mathematics Competency Requirement.
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MAT 123 Mathematics for the Elementary Teacher I 3 Credit(s) DII
This course is the first in a sequence designed for prospective elementary teachers. Topics include numeration systems, algorithms and estimation for the arithmetic operations, number theory, patterns, and properties of basic functions. Use of manipulatives and relevant technology may be integrated into the course. Three lecture hours per week. Not open to students who have received credit for MAT123A.
Prerequisite: Satisfation of the Basic Mathematics Competency Requirement.
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MAT 124 Mathematics for Elementary Teachers II 3 Credit(s) DII Q QR
This course is a continuation of Mathematics for Elementary Teachers I. Topics will include geometric figures and solids, congruence, similarity, constructions, measurement including perimeter, area, surface area and volume, geometric transformations, descriptive statistics and basic probability theory. Use of manipulatives and relevant technology may be integrated into the course. Not open to students who have received credit for MAT223A. Three lecture hours per week.
Prerequisite: Satisfaction of the Basic Mathematics Competency Requirement.
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MAT 128 Quantitative Methods for Business and Finance 3 Credit(s) QR
This course is an introduction to the mathematics used in business. Topics may include graphing linear equations and inequalities, solving systems of linear equations and inequalities, linear programming, simple and compound interest, annuities, descriptive statistics, and rates of change. Three lecture hours per week. Not open to student who have received credit for MAT 108.
Prerequisite: Satisfaction of the Basic Mathematics Competency Requirement.
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MAT 147 Statistics 3 Credit(s) DII Q QR
This course is an introduction to elementary data analysis. Topics will include descriptive statistics. Normal distributions, sampling, interval estimation, testing of hypotheses, and linear regression. The emphasis is on practical and usable results, rather than on mathematical derivations. This course is intended to prepare students to use statistics in business, nursing, the social sciences, or education. Offered each semester. Three lecture hours per week.
Prerequisite: Completion of the Basic College Mathematics Competency Requirement.
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MAT 150 Precalculus 3 Credit(s) DII QR
This course is intended to prepare the student for the study of Calculus. Topics include: properties of the real number systems; absolute values, inequalities; detailed study of linear and quadratic equations; polynomial and rational functions and their graphs; exponential, logarithmic, and trigonometric functions. Three lecture hours per week. Not open to those students who received credit for MAT202N. Prerequisite: Completion of the Basic College Mathematics Competency Requirement.
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MAT 208 Business Calculus 3 Credit(s) DII Q
Introduction to calculus as applied to business. Differentiation, integration, and their applications are considered in conjunction with polynomial, algebraic, exponential, and logarithmic functions. Three lecture hours per week. Prerequisite: Completion of the Basic College Mathematics Competency Requirement.
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MAT 214A Discrete Structures 4 Credit(s) DII
A study of discrete mathematical structures of interest in computer science and other applied fields. Topics will be chosen from logic, proof techniques, sets, boolean algebra, functions, relations, basics of counting, recursion, graphs, trees, and discrete probability. Four lecture hours per week. Not open to students who have received credit for either MAT214 or MAT 314 .
Prerequisite: MAT 220 .
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MAT 218 Introduction to Mathematical Computing 1 Credit(s)
An introduction to a computer algebra system. Topics include the application of a computer algebra system to plotting functions, solving equations, simplifying expressions, and the creation of clear and attractive mathematical reports. One lecture hour per week. Prerequisite: MAT 220 .
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MAT 220 Calculus I 4 Credit(s) DII Q QR
An introduction to the differential calculus of real-valued functions of one real variable. Topics include limits and derivatives and their applications in a context that includes polynomial, rational, trigonometric, exponential, and logarithmic functions. Offered each semester. Four lecture hours per week. Required of all Mathematics majors. Prerequisites: Completion of the Basic College Mathematics Competency Requirement and either MAT 150 or a thorough knowledge of trigonometric and logarithmic functions.
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MAT 221 Calculus II 4 Credit(s) DII
An introduction to the integral calculus of real-valued functions of one real variable. Topics include infinite sequences and series of real numbers and integrals and their applications in a context that includes polynomial, rational, trigonometric, exponential, and logarithmic functions. Offered each semester. Four lecture hours per week. Required of all mathematics majors. Prerequisite: MAT 220 .
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MAT 234 Introduction to Mathematical Proof 3 Credit(s) W W-II
This course is an introduction to mathematical proof and the fundamental notions of higher mathematics. Topics include the basics of propositional logic, set theory, number theory, mathematical induction, functions, equivalence relations, and cardinality with an emphasis on writing proofs. Three lecture hours per week. Prerequisite: MAT 220 and a W-I course.
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MAT 240 Linear Algebra I 3 Credit(s) DII
This course is an introduction to vector spaces and linear transformations primarily in Euclidean spaces. Topics include the algebra of matrices, linear independence, determinants, eigenvalues, and eigenvectors. Three lecture hours per week. Required of all mathematics majors.
Prerequisite: MAT220.
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MAT 303A Abstract Algebra I 3 Credit(s) DII
This course is a proof-oriented introduction to groups. Topics will include examples and elementary properties of groups, subgroups, cyclic groups, symmetry groups, group isomorphisms and homomorphisms, normal subgroups and quotient groups, and direct products of groups. Three lecture hours per week. Required of all mathematics majors. Not open to students who have received credit for MAT303.
Prerequisites: MAT 234
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MAT 306 Theory of Numbers 3 Credit(s)
This course is a study of the arithmetic properties of numbers. Topics will included divisibility, prime numbers, congruences, Diophantine equations, number-theoretic functions, primitive roots and indices, and quadratic residues. Three lecture hours per week. Prerequisite: MAT 303A .
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MAT 308 Linear Programming 3 Credit(s) DII
This course is a study of linear optimization with application to business and the sciences. Topics may include linear equations and inequalities, convex regions, the simplex algorithm, duality and minimax theorems, matrix games, transportation and assignment problems. Experience is provided in the computer solution of linear programming problems. Three lecture hours per week.
Prerequisite: MAT210 or MAT 220 .
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MAT 314 Discrete Mathematics 3 Credit(s)
This course is a further study of discrete mathematical structures. Topics may include finite-state machines, feedback, partially ordered sets, lattices, recursion and iteration, with applications to logic, circuit design, and computer systems. Three lecture hours per week.
Prerequisite: MAT 234
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MAT 316 Combinatorial Mathematics 3 Credit(s)
This course is a survey of combinatorial methods. Topics may include graphs, trees, networks, permutations and combinations, partitions, and enumeration theory. Three lecture hours per week.
Prerequisite: MAT 234 .
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MAT 320 Calculus III 4 Credit(s)
An introduction to two and three dimensional analytic geometry and an extension of the ideas of calculus to both real-valued functions of several variables and vector-valued functions. Topics include polar, cylindrical and spherical coordinates, vectors in two and three dimensions, limits, derivatives and integrals of functions of several variables and vector-valued functions. Offered each fall. Four lecture hours per week. Required of all mathematics majors. Prerequisite: MAT 221 .
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MAT 323 Numerical Analysis 3 Credit(s)
A study of numerical methods. Topics include root finding for nonlinear equations, polynomial interpolation, series methods, numerical integration, finite differences, and solutions of linear systems. Efficiency, accuracy and round off and truncation errors are considered. Computer implementation of selected methods is included. Three lecture hours per week. Prerequisite: MAT 221 .
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MAT 403 Abstract Algebra II 3 Credit(s)
Topics include normal subgroups, ideals, morphisms of groups and rings, fields and field extensions with examples and applications. Three lecture hours per week. Not open to students who have received credit for MAT404. Prerequisite: MAT 303A .
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MAT 406 Modern Geometry 3 Credit(s)
This course is a study of topics in advanced geometry from three perspectives: synthetic, analytic, and transformational. Topics include advanced results in Euclidean geometry, axiomatic development of Euclidean and non-Euclidean and non-Euclidean geometries, the use of coordinates, transformations, and symmetries. Writing, primarily in the form of mathematical proof, is an essential component of the course. Three lecture hours per week. Required of all Mathematics majors with a Secondary Education minor. Not open to students who have received credit for MAT405.
Prerequisite: MAT 234 and MAT 304A
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MAT 407 Probability and Mathematical Statistics I 3 Credit(s)
This course is an introduction to probability models and random variables. Topics may include simple counting methods, expectation, variance, moment and moment generating functions, the binomial, Poisson, exponential, and Normal distributions. Three lecture hours per week. Required of all Mathematics majors with a Secondary Education minor.
Prerequisite: MAT 221
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MAT 409 Complex Variables 3 Credit(s)
This course is a study of functions of a complex variable. Topics may include Cauchy-Riemann equations, Cauchy’s integral theorem and formula, the calculus of residues, series expansions of analytic functions, singularities, and contour integration. Three lecture hours per week.
Prerequisite: MAT 221 or MAT 234 .
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MAT 410 History of Mathematics 3 Credit(s)
This course is a survey of the fundamental developments in mathematics from ancient to modern times, with special attention to the historical and logical bases of geometry, algebra, and analysis. Three lecture hours per week.|
Prerequisite: MAT 221 .
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MAT 411 Real Analysis 3 Credit(s)
This course is a rigorous study of the fundamental ideas of calculus. Topics may include sequences, limits, continuity, derivatives, and integrals. Three lecture hours per week. Required of all mathematics majors.
Prerequisite: MAT 221 or MAT 234
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MAT 412 Topology 3 Credit(s)
This course is a study of abstract mathematical spaces. Topics may include topological spaces, metric spaces, connectedness, compactness, and product and quotient spaces. Three lecture hours per week.
Prerequisite: MAT 221 and MAT 234 .
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MAT 413 Ordinary Differential Equations 3 Credit(s)
This course is a study of the methods of solving linear and elementary nonlinear ordinary differential equations. Topics may include variation of parameters, series solutions, Laplace transforms and applications. Three lecture hours per week.
Prerequisite: MAT 304A .
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MAT 414 Linear Algebra II 3 Credit(s)
This course is a continuation of Linear Algebra I. Topics include diagonalization, similarity, orthogonality, quadradic forms, inner products, and the singular value decomposition. Applications of these topics will be highlighted. Three lecture hours per week. Prerequisite: MAT 240 .
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MAT 415 Geometric Structures 3 Credit(s)
An analysis of various geometric structures, especially projective geometry and its relation to certain algebraic structures. Three lecture hours per week. Prerequisite: MAT303.
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MAT 417 Probability and Mathematical Statistics II 3 Credit(s)
This course is an introduction to statistical inference. Topics may include sampling distributions, limit theorems, point and interval estimation, hypothesis testing, linear regression and correlation, analysis of variance, and nonparametric methods. Three lecture hours per week.. Prerequisite: MAT 407 .
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MAT 420 Special Problems Seminar 3 Credit(s)
This course is a study of field mathematics chosen by the instructor that is not covered in detail in other courses in the Mathematics Department. Topics chosen are determined by mathematical relevance and the perceived value that would be added to the mathematics curriculum.
Prerequisite: MAT 221 and MAT 234 .
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MAT 421 Advanced Calculus 3 Credit(s)
This course is a study of functions of several variables, implicit functions and Jacobian determinants, line and surface integrals, and the theorems of Green and Stokes. Three lecture hours per week.
Prerequisite: MAT 320 .
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MAT 490 Senior Seminar in Mathematics 3 Credit(s) W W-III
This course is a culminating experience for the mathematics major. Students will read mathematics journal articles, work problems and prove theorems derived from those articles, study topics independently, give oral presentations and write a mathematical paper. The paper may be expository or original in nature and students will hand in several drafts and make necessary revisions before the final product is completed. In the process, students will need to review and apply skills learned in previous courses as well as independently study new concepts. Students will be exposed to the “nuts and bolts” of doing mathematical research along the way, including using common databases for finding papers and typesetting a paper properly. Three lecture hours per week. Required of all mathematics majors. Prerequisites: successful completion of the calculus sequence (MAT 220 , MAT 221 and MAT 320 ) MAT 240 , and either MAT 411 or MAT 303A and a W-II course.
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MAT 500 Directed Study in Mathematics 3 Credit(s)
The purpose of this course is to provide the student with an opportunity to explore in depth an area of mathematics that would not ordinarily be encountered in the program of required courses. It is recommended that the student take as many of the required courses as possible before enrolling in Directed Study. Credit for this course may not be applied toward Major requirements. Prerequisites: At least one 400 level math course (with a grade of C or above), Junior or Senior standing, agreement of a Department faculty member to act as supervisor and permission of Mathematics Department Chairperson.
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MAT 520 Mathematics Internship 3-12 Credit(s)
An opportunity for students to gain practical or technical training in an industrial/commercial/research environment. The student makes the necessary arrangements with the chosen facility, in consultation with an appropriate faculty member. The internship must meet College Academic Policies (described elsewhere in this Catalog) and Mathematics Department Policy (available in the Mathematics Department). Open only to Junior/Senior Mathematics Majors who have obtained a faculty sponsor for this internship. Prerequisites: Permission of a faculty supervisor and permission of the Department Chairperson.
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MAT 572 Mathematics Research I 1-3 Credit(s)
This course provides qualified students with research direction and the opportunity to participate in independent work in any area of mathematics of special interest to them, provided that a faculty supervisor is available. A paper and poster presentation are required at the end of the course. This course may be repeated.
Prerequisites: Permission of the faculty supervisor and the Department Chairperson.
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