| MAT 003 - Intermediate Algebra |
3 sh |
The topics include a review of the real number system, linear equations and applications, linear inequalities and absolute value, graphs and functions, exponents, polynomial functions, factoring, rational functions, root functions, exponential and logarithmic functions. Students who have previously received credit for a higher-numbered mathematics course may not receive credit for this course without permission of the instructor.
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| MAT 005 - Mathematics for Nurses |
1 sh |
This course is an introduction to computing techniques used by nurses in hospitals and other clinical situations. Topics include a review of arithmetic and basic computational techniques, standard and apothecary measurement systems, dimensional analysis, and one-factor and multi-factor medication problems. These topics will be examined in depth with a focus placed on understanding the underlying computational techniques. Prerequisite: None.
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| MAT 017 - Introduction to Mathematics |
3 sh |
This General Education introductory-level course is intended to acquaint the student with the nature and spirit of mathematics. Topics include set theory, logic, counting methods, probability, statistics, and algebra-based problem-solving with graphical and analytic solutions.
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| MAT 030 - Survey of Mathematics |
3 sh |
Sets and logic; number systems; relations and functions; introduction to matrices; linear systems; counting and probability; sequences and limits; introduction to differential and integral calculus.
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| MAT 040 - Geometry |
3 sh |
An informal, intuitive study of topics in geometry. Non-metric geometry of the plane and space; measurement; error in measuring; simple closed curves; area; congruence; similarity; graphing in the plane and space; modern geometries; groups of geometric transformations. Open to all majors.
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| MAT 045 - Women in Mathematics |
3 sh |
This course examines women who have made significant contributions to the field of mathematics. Both their lives and their work will be explored as well as the gender issues surrounding their endeavors. Furthermore, mathematical topics related to their contributions will be discussed. Prerequisite: 2 years of high school algebra.
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| MAT 103 - Fundamentals of Math I |
3 sh |
This is the first course in a two-course sequence that is required for all Elementary Education and Special Education majors. It is not open to other majors. Topics include problem-solving; logic; set theory; mathematical systems; systems of numeration; number theory; equations and inequalities; and properties of whole numbers, integers, rational numbers, and real numbers. MAT 103 is a prerequisite for MAT 104 and ELU 308.
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| MAT 104 - Fundamentals of Math II |
3 sh |
This is the second course in a two-course sequence that is required for all Elementary Education and Special Education majors. It is not open to other majors. Topics include informal geometry; measurement; probability; statistics; and computer applications. MAT 103 is a prerequisite for MAT 104. MAT 103 and MAT 104 are prerequisites for ELU 308.
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| MAT 105 - College Algebra |
3 sh |
This course is intended for students with an elementary knowledge of algebra who need more work in algebraic topics before taking more advanced mathematics courses. Topics include properties of the real numbers, problem-solving using equations and inequalities, algebraic functions, graphing, and systems of equations. A graphing calculator is required for this course. Prerequisite: Two years of algebra at the high school level.
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| MAT 106 - Trigonometry |
3 sh |
This course is intended for students with an elementary knowledge of algebra who need more work in trigonometric topics before taking more advanced mathematics courses. Topics include properties of and operations with functions, inverse functions, exponential and logarithmic functions, angle measurement, trigonometric functions and their inverses, graphing functions, and problem-solving with equations that use the functions covered in the course. A graphing calculator is required for this course. Prerequisite: MAT 105 or its equivalent.
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| MAT 115 - Precalculus Mathematics |
3 sh |
This course is designed to give students a thorough review of the mathematics background needed for calculus courses. The course covers all the topics listed in the descriptions of MAT 105 and MAT 106. A graphing calculator is required for this course. Prerequisite: Three years of high school mathematics in algebra and trigonometry.
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| MAT 121 - Mathematics for Business and Information Science |
3 sh |
This course focuses on the application of mathematical concepts and methods to problems that arise for students who major in Business or Computer Science. The topics include a review of algebraic concepts and problem solving, systems of linear equations, matrix algebra, linear programming with graphical and simplex method solutions, and probability.A graphing calculator is required for this course. Prerequisite: MAT 105 or two years of high school algebra.
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| MAT 122 - Calculus for Business and Information Science |
3 sh |
This course focuses on the application of concepts and methods of calculus to problems that arise for students who major in Business or Computer Science. The topics include differential and integral calculus; applying derivatives, differentials, and integrals to problem-solving; and maximizing and minimizing functions. A graphing calculator is required for this course. Prerequisite: MAT 121.
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| MAT 140 - Applied Statistical Methods |
3 sh |
An introduction to quantitative methods in the behavioral sciences. Techniques for obtaining, analyzing and presenting data in numerical form; measures of central tendency and dispersion; normal distribution curve; standard scores; applicability of probability and sampling theory to research in the behavioral sciences; interpretation of confidence intervals; hypothesis testing; correlation; linear regression. A graphing calculator is required for this course. Prerequisite: MAT 105 or two years of high school algebra.
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| MAT 171 - Calculus I |
3 sh |
This course is one of a series intended for students who major in mathematics, the sciences, or engineering. The topics include the definition and calculation of limits, continuity and differentiability, differentials, derivatives of algebraic and trigonometric functions, the application of derivatives to graphing, antiderivatives, and the introduction of the definite integral. A graphing calculator is required for this course. Prerequisite: Three years of mathematics in algebra and trigonometry.
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| MAT 172 - Calculus II |
3 sh |
This course is one of a series intended for students who major in mathematics, the sciences, or engineering. The topics include the definition, properties, and applications of definite integrals, properties, derivatives, and integrals of exponential, logarithmic, trigonometric, inverse trigonometric, and hyperbolic functions with applications; and techniques of integration. A graphing calculator is required for this course. Prequisite: Completion of MAT 171 with a grade of C or higher.
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| MAT 175 - Mathematical Investigations |
3 sh |
This course is applicable in the Honors Program and is open to any student in the Honors Program as well as to any student having completed at least 15 s.h. of study at Kutztown University with a grade point average of 3.00 or greater. This course, divided into three to five segments, providesfor study of concepts, procedures and applications in several mathematical disciplines. Topics studied will be drawn from the following areas: mathematical thought processes, history of mathematics, mathematics of finance, statistics, operations research, number theory, graphs as mathematical models, and finite geometries. This course cannot be taken for credit by mathematics majors in Secondary Education or the College of Liberal Arts and Sciences. Credit for the course can be applied in Categories IV or V in General Education. PREREQUISITES: at least three years of high school academic mathematics, including trigonometry, or permission of the department chair.
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| MAT 220 - History of Mathematics |
3 sh |
A study of mathematics as it has developed through the centuries and the mathematicians who have contributed to its growth. Mathematics of early Babylonian and Egyptian civilizations; mathematics under Greek influence; Chinese, Hindu and Arabic contributions; the Renaissance period; Seventeenth and Eighteenth Century mathematics; the liberation of geometry and arithmetization of analysis of the Nineteenth Century; Twentieth Century mathematics. Not applicable toward the Arts and Sciences Mathematics major. Prerequisite: Completion of MAT 171 with a grade of C or higher.
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| MAT 224 - Foundations of Higher Mathematics |
3 sh |
This course is designed to prepare the student for the study of advanced mathematics. Topics include fundamentals of logic, proof strategies, the algebra of sets; relations, including equivalence relations; functions and their properties; countable sets and counting techniques; ordered and well-ordered sets. This course should be taken only after the student has taken at least two college-level mathematics courses. Prerequisite: Completion of MAT 171 with a grade of C or higher.
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| MAT 225 - Discrete Mathematics |
3 sh |
Review of set theory; functions, relations; Boolean algebras; lattices and propositional logic; abstract algebras, groups and semigroups; homo-morphisms and isomorphisms; phrase structure grammars; graphs and digraphs; applications to computer and information science. Prerequisite: MAT 125, MAT 224 and CIS 136.
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| MAT 240 - Synthetic Geometry |
3 sh |
This course is designed for students who have, in addition to an interest in geometry, some previous experience in this subject area, either on the high school or college level. Topics include Euclidean geometry using Hilbert's axioms; neutral geometry; the historical development of non-Euclidean geometries; and hyperbolic geometry. Prerequisite: Completion of MAT 224 with a grade of C or higher.
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| MAT 260 - Linear Algebra |
3 sh |
This course gives the student an opportunity to make an in-depth investigation of a specialized area of mathematics which has wide-spread practical applications in the arts and sciences but still allows work with abstract concepts. A study of the properties of vector spaces; matrix theory with applications using systems or equations and determinants; linear transformations and invariants under such mappings. Prerequisite: Completion of MAT 224 with a grade of C or higher.
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| MAT 273 - Calculus III |
3 sh |
This course is one of a series intended for students who major in mathematics, the sciences, or engineering. The topics include indeterminate forms and improper integrals; sequences, series, and convergence tests; differentiation and integration of power series; conic sections; polar coordinates and polar integrals; vectors in two and three dimensions; operations on vectors; limits, derivatives and integrals of vector functions. A graphing calculator is required for this course. Prerequisite: MAT 172.
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| MAT 274 - Calculus IV |
3 sh |
This course is one of a series intended for students who major in mathematics, the sciences, or engineering. The topics include three-dimensional surfaces; the definition, properties, and partial differentiation of functions in more than one variable with applications; finding the extrema of functions in two variables; Lagrange multipliers; multiple integrals in various coordinate systems; Jacobians; line integrals in vector fields; and the application of Green's Theorem, the Divergence Theorem, and Stokes' Theorem. A graphing calculator is required for this course. Prerequisite: MAT 273.
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| MAT 280 - Cooperative Internship in Mathematics |
3-6 sh |
The internship consists of 6 to 12 weeks of full-time employment that provides students with a supervised industrial experience in mathematics. The internship is supervised by a member of the Mathematics Department. This internship is available only to Mathematics majors, and is taken on a pass/fail basis. PREREQUISITE: Substantial completion of the required and concomitant courses in the Mathematics major with an above-average grade-point average. Approval by the department chair is required. 3 to 6 credits
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| MAT 301 - Probability and Statistics I |
3 sh |
Elementary probability spaces; conditional probability; general probability spaces; random variables; expectation; variance; multivariant distributions; the algebra of expectation. Prerequisite: MAT 273 and MAT 224.
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| MAT 302 - Probability and Statistics II |
3 sh |
Probability distributions; sampling; estimation of parameters; Central Limit Theorem; confidence intervals; correlation and regression; sampling from a normal population; testing hypotheses; Markov chains. Prerequisite: MAT 301.
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| MAT 311 - Abstract Algebra I |
3 sh |
Sets, relations, and functions; groups; rings; integral domains; fields; elementary theory of groups. Prerequisite: Completion of MAT 224 with a grade of C or higher.
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| MAT 312 - Abstract Algebra II |
3 sh |
Extension of Abstract Algebra I topics; permutation groups; normal sub-groups and quotient groups; rings and ideals; ring homomorphisms; quotient rings, integral domains and their fields of quotients; fields; polynomial rings. Prerequisite: MAT 311.
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| MAT 332 - Numerical Analysis |
3 sh |
Numerical methods fundamental to scientific computing are developed. Topics include finite difference calculus; zeros of a function; matrix computations; solutions to systems of linear equations; approximation by polynomials; numerical differentiation and integration; numerical solutions of ordinary differential equations; rounding errors and other types of errors. Selected algorithms will be run on the computer. Prerequisite: MAT 260 and MAT 273.
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| MAT 340 - Differential Equations |
3 sh |
Theory and methods of solving ordinary differential equations are investigated - equations include first order, linear and systems; methods of solutions include exact, substitution, reduction, undetermined coefficients and variation of parameters. Consideration is given to application to the physical and natural sciences. Prerequisite: MAT 273.
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| MAT 351 - Advanced Calculus I |
3 sh |
Introduction to the structure of the real number system and its topology; metric space and its topology; basic theorems of real analysis; differentiable functions. Prerequisite: Completion of MAT 224 and 273 with a grade of C or higher.
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| MAT 352 - Advanced Calculus II |
3 sh |
Introduction to the theory of Reimann-Stieltjes integration; functions of bounded variation; Lebesgue measure and Lebesgue integrals; uniform convergence of sequences and series of functions. Prerequisite: MAT 351.
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| MAT 361 - Mathematical Methods in Operations Research |
3 sh |
Operations Research uses quantitative methods to determine the best decision for an operating system. A mathematical approach to studying methods as applied to the decision process in industry is taken. The methods studied are selected from among linear programming; game theory; mathematical programming; graph theory and network analysis; and queuing theory. Prerequisite: MAT 121 or MAT 260 or permission of the instructor.
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| MAT 370 - Selected Topics in Mathematics |
3 sh |
This course involves individual or small group independent study in some area of mathematics under the direction of a mathematics staff member. This study can be made in any area of mathematics or mathematical application. A student may register for this course more than once up to a maximum of six semester hours of credit. Prerequisite: The consent of the student's advisor, instructor and department head and their approval of the project.
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| MAT 372 - Independent Study and/or Projects in Mathematics |
6 sh |
This course involves individual or small group independent study in mathematics under the direction of a mathematics staff member. This study can be carried out in any area of mathematics or its application. A student may register for this course more than once up to a maximum of six semester hours of credit. Prerequisites: approval of the student's advisor, the instructor, and the department chairperson.
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| MAT 380 - Senior Seminar in Mathematics |
3 sh |
Readings and discussions in areas of student interest and background. The student reviews and structures the mathematics he/she has learned and also explores mathematical topics not covered in the usual course offerings. The comprehensive examination for Arts and Sciences Mathematics majors is given in conjunction with this course. Required of all arts and sciences mathematics majors.
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| MAT 431 - Topology I |
3 sh |
Topics covered for this course include set theory; functions; metric spaces; basic topological concepts; topologies and neighborhood systems; open and closed sets; accumulation points and closures; bases and subbases for a topology; separation and connectedness; nets; continuity and homeo-morphisms; compactness; product and quotient spaces. Prerequisite: MAT 272 and MAT 311 or their equivalents.
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| MAT 512 - Foundations of Mathematics |
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This course is intended to broaden and deepen the beginning graduate student's knowledge of the foundational concept of mathematics. Topics covered are: mathematical logic, theory of sets, algebra of sets, relations and functions, ordering, equivalence classes, real numbers, and ordinal and cardinal numbers and related topics. The implementation of proof strategies and procedures are emphasized. Required of all M.Ed. mathematics majors.
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| MAT 540 - Theory of Probability |
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The topics in this course include axiomatic probability, probability spaces, conditional probability, random variables and functions of random variables, probability distributions, sums of random variables, and the Central Limit Theorem are studied. Prerequisites: MAT512 or its equivalent.
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| MAT 545 - Statistical Inference and Sampling Theory |
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The topics in this course include the Weak Lay of Large Numbers, estimation of parameters, Central Limit Theorem, confidence intervals, regression analysis, sampling from a normal population, and testing hypotheses. Prerequisites: MAT540 or its equivalent.
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| MAT 550 - Foundations of Geometry |
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The topics in this course include foundational aspects of geometry, postulational systems and their properties, Euclidean geometry from both the metric and the synthetic viewpoints, finite geometries, non-Euclidean geometries, and geometric transformations are studied. Prerequisites: MAT512 or its equivalent.
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| MAT 561 - Abstract Algebra I |
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The topics in this course include sets, mappings and relations, basic properties of integers, concept of group, subgroups and LaGrange's Theorem, normal subgroups and quotient groups, homomorphisms, isomorphisms, Cayley's Theorem, permutation groups, Sylow's Theorems, direct products. Prerequisites: MAT512 or its equivalent.
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| MAT 562 - Abstract Algebra II |
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The topics in this course include rings, homomorphisms, ideals and quotient rings, field of quotients of an integral domain, Euclidean rings, polynomial rings, vector spaces, extension fields, constructability criteria, Galois Theory, solvability of radicals. Prerequisites: MAT561 or its equivalent.
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| MAT 580 - Special Topics in Mathematics |
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| This course is designed to enable the student to pursue interests in some area of mathematics. The function of this course is not to introduce the student to beginning concepts. Rather, it is to permit the student to pursue the study of topics encountered in courses already taken. Prerequisites: At least two graduate courses in Mathematics. Permission of the instructor, advisor, and department chairperson. |
