2007-08 Undergraduate Catalog
Indiana, Pennsylvania 15705
Mathematics (MATH)
Department of Mathematics
College of Natural Sciences and Mathematics
Credit designation below each title is expressed in (c) class hours per week, (l) lab or (d) discussion section hours per week, and (cr) credits per semester.
3c-0l-3cr
Note: May not be taken after successfully completing MATH 105 or 110 or a calculus course without written Mathematics Department chairperson approval
Basic course in algebra including factoring, exponents and radicals, systems of linear equations, complex fractions, and inequalities. For those students who lack the basic algebraic skills required in MATH 105 or 110. Will not meet Liberal Studies math requirements.
MATH 101 Foundations of Mathematics
3c-0l-3cr
Introduces logic and mathematical way of analyzing problems; develops an appreciation for nature, breadth, and power of mathematics and its role in a technological society; introduces useful mathematics or mathematics related to student interest. Possible topics include logic, problem solving, number theory, linear programming, probability, statistics, intuitive calculus, introduction to computers, mathematics of finance, game theory.
3c-0l-3cr
Prerequisite: MATH 100 or appropriate Placement Test Score or permission of the Mathematics Department chairperson
Note: May not be taken after successfully completing either a calculus course or MATH 110 without written Mathematics Department chairperson approval
Prepares students for the study of calculus for business, natural, and social sciences. Topics include detailed study of polynomial, exponential, and logarithmic functions.
3c-0l-3cr
Prerequisite: MATH 100 or appropriate Placement Test Score or permission of the Mathematics Department chairperson
Note: May not be taken after successfully completing a calculus course without written Mathematics Department chairperson approval
Prepares mathematics and science students for the study of calculus. Topics include detailed study of polynomial, exponential, logarithmic, and trigonometric functions.
MATH 115 Applied Mathematics for Business
4c-0l-4cr
Prerequisites: MATH 105 or appropriate Placement Test score or permission of the Mathematics Department chairperson
Note: May not be taken after successfully completing a calculus course without written Mathematics Department chairperson approval
Offers a review of elementary functions including logarithmic and exponential functions. Business majors are introduced to the mathematics of finance and central ideas of the calculus, including limit, derivative, and integral. Applications to business and economics are emphasized.
MATH 117 Principles of Mathematics
3c-0l-3cr
An introduction to the nature of mathematics, designed specifically as a first course for Mathematics Education majors to experience several facets of mathematics including deduction, induction, problem solving, discrete mathematics, and theory of equations. Enrollment open to Secondary Mathematics Education majors only.
MATH 121 Calculus I for Natural and Social Sciences
4c-0l-4cr
Prerequisite: MATH 105 or 110 or appropriate Placement Test Score or permission of the Mathematics Department chairperson
Note: May not be taken after successfully completing a calculus course without written Mathematics Department chairperson approval
Offers a review of elementary functions, including logarithmic and exponential functions. Natural and Social Science majors are introduced to the central ideas of calculus, including limit, derivative, and integral. Applications to natural and social sciences are emphasized.
MATH 122 Calculus II for Natural and Social Sciences
4c-0l-4cr
Prerequisite: MATH 121
Applications of integrals to natural and social sciences, functions of several variables, trigonometric functions, sequences and series, numerical methods, and differential equations.
MATH 123 Calculus I for Physics, Chemistry, and Mathematics
4c-0l-4cr
Prerequisites: High school algebra, geometry, and trigonometry
Functions, limits, continuity, derivatives, application of the derivative, integral, and applications of the integral. (Trigonometric and inverse trigonometric functions are included throughout the course.)
MATH 124 Calculus II for Physics, Chemistry, and Mathematics
4c-0l-4cr
Logarithmic and exponential functions, techniques of integration, sequences and series, differential calculus of functions of several variables, multiple integrals, line integrals, surface integrals, differential equations with application to physical problems.
MATH 125 Calculus I/Physics, Chemistry, Mathematics
3c-0l-3cr
Prerequisite: MATH 110 or equivalent placement (algebra, geometry, and trigonometry)
The first of a three-semester sequence for math and science majors covering the theory of calculus and its application in problem solving. Topics include functions, limits, continuity, derivatives, applications of derivative, integrals, and applications of the integral. (Trigonometric, exponential, and logarithmic functions are included throughout the course.)
MATH 126 Calculus II/Physics, Chemistry, Mathematics
3c-0l-3cr
Prerequisite: MATH 125 or the equivalent
The second of a three-semester sequence for math and science majors. Topics include techniques and applications of integration, sequences and series, convergence tests, Taylor polynomials, separable differential equations, vectors, and three-dimensional coordinates. (Trigonometric, exponential, and logarithmic functions are included throughout the course.)
MATH 151 Elements of Mathematics I
3c-0l-3cr
Topics included are sets, concepts of logic, mathematical systems, systems of numeration, developing the set of integers, rational numbers, and real numbers.
MATH 152 Elements of Mathematics II
3c-0l-3cr
Prerequisite: MATH 151
Topics included are sentences in one variable, sentences in two variables, nonmetric geometry, metric geometry, coordinate geometry, introduction to statistics and probability, computers, and calculators.
MATH 171 Introduction to Linear Algebra
3c-0l-3cr
An introduction to vector spaces, linear transformations, determinants, and matrix algebra. Topics are presented in a direct and intuitive approach.
MATH 214 Probability and Statistics for Business Majors
3c-0l-3cr
Studies the methods of describing data, probability theory, discrete and continuous random variables, sampling distributions, estimation and tests of hypothesis for means, proportions and variance, and simple linear regression and correlation.
MATH 216 Probability and Statistics for Natural Sciences
3c-0l-3cr
Frequency distributions, graphical representations of data, measures of central tendency and variation, correlation and regression, probability, probability distributions, and sampling distributions. Inferential statistics including confidence intervals and parametric and nonparametric tests of hypotheses. Emphasis will be on applications in the natural sciences using graphing calculators and statistical software.
MATH 217 Probability and Statistics
3c-0l-3cr
(For non-Math majors) Frequency distributions, measures of central tendency, variation, elementary probability, sampling, estimation, testing hypotheses, correlation, and regression; emphasis on applications as opposed to theoretical development of topics.
3c-0l-3cr
Prerequisite: COSC 110 and MATH 122 or 125
Topics include set algebra, mappings, relations, semigroups, groups, directed and undirected graphs, Boolean algebra, and propositional logic, with examples and applications of these to various areas of computer science. Emphasizes developing an intuitive understanding of basic structures rather than formal theories and influence of these topics on theory and practice of computing.
MATH 225 Calculus III/Physics, Chemistry, Mathematics
3c-0l-3cr
Prerequisite: MATH 126 or the equivalent
The third of a three-semester sequence for math and science majors. Topics covering the calculus of functions of several variables include vector functions and space curves, arc length, curvature, partial derivatives, gradients, areas and volumes in various coordinate systems, Lagrange multipliers, line integrals, Green’s Theorem, and applications of multiple integrals. (Trigonometric, exponential, and logarithmic functions are included throughout the course.)
MATH 241 Differential Equations
3c-0l-3cr
Prerequisites: MATH 122 or 126
Emphasizes techniques of solution and applications of differential equations. Topics include first order equations, second order linear equations, systems of linear equations, and series solutions of differential equations.
MATH 271 Introduction to Mathematical Proofs I
3c-0l-3cr
Prerequisites: MATH 121 or 125; 171
Gives basic ideas necessary to prove results in mathematics. Includes but is not limited to logic of mathematics, basic methods of proof, algebra of sets, equivalence relations and partitions of sets, functions, and mathematical induction.
MATH 272 Introduction to Mathematical Proofs II
3c-0l-3cr
Prerequisites: MATH 126 and 271 with a grade of C or better
A further study of the basic ideas of contemporary mathematics. Topics include but are not limited to mathematical induction, cardinality of sets, relations, methods of proof in number theory, analysis, and algebra.
var-1-3cr
Prerequisite: As appropriate to course content
Offered on an experimental or temporary basis to explore topics not included in the established curriculum. A given topic may be offered under any special topic identity no more than three times. Special topics numbered 281 are offered primarily for lower-level undergraduate students.
MATH 317 Probability and Statistics for Elementary and Middle School Teachers
3c-0l-3cr
Prerequisites: MATH 152, Elementary Education concentration
Introduces students to elementary concepts of probability and statistics, enabling them to analyze data, make predictions, and determine which concepts may be used with children.
MATH 320 Mathematics for Early Childhood
3c-0l-3cr
Prerequisites: MATH 151, Early Childhood Education/PreK-Grade 6 major
Studies child-centered, activity-oriented mathematics programs for early childhood education. Focuses on helping children develop understanding and insight into basic concepts of mathematics through the use of manipulative materials. Topics include pre-number activities, number activities, numeration, operations on whole numbers, estimation, rational numbers, geometry, measurement, probability, statistics, and problem solving.
MATH 340 Principles of Secondary School Mathematics
3c-0l-3cr
Prerequisite: MATH 271
Provides the mathematics content needed to teach in secondary schools. Connections are made between advanced and secondary school mathematics. Open to secondary mathematics education majors only.
MATH 342 Advanced Mathematics for Applications
4c-0l-4cr
Prerequisites: MATH 122 or 225; 241
Deals with the application of mathematics to problems of science. Emphasizes the three phases of such an application and the development of skills necessary to carry out each step: 1) translation of the given physical information to a mathematical model; 2) treatment of the model by mathematical methods; 3) interpretation of the mathematical result in physical terms. Topics include vector calculus, integral theorems, Fourier series, partial differential equations, and the Laplace transformation.
MATH 350 History of Mathematics
3c-0l-3cr
Prerequisite: MATH 122 or 126 or instructor permission
Development of the central concepts of mathematics from ancient times up to the development of calculus in the seventeenth century. Mathematical concepts are placed in historical perspective. The use of the history of mathematics as a pedagogical tool and its relationship to other sciences will be addressed.
3c-0l-3cr
Prerequisite: MATH 271 with a grade of C or better
Divisibility, congruences, primitive roots, number theoretic functions, Diophantine equations, continued fractions, quadratic residues.
MATH 355 Foundations of Geometry I
3c-0l-3cr
Prerequisites: MATH 171, 271 with a grade of C or better
Studies various groups of transformations and geometries associated with these groups in the Euclidean plane. The Euclidean Similarity and affine and projective groups of transformations are studied.
MATH 363 Mathematical Statistics I
3c-0l-3cr
Prerequisites: MATH 216; 225 (may be taken concurrently)
Probability theory necessary for an understanding of mathematical statistics is developed. Applications of set theory to models, combinations and permutations, binomial, Poisson and normal distributions, expected values, and moment generating functions.
MATH 364 Mathematical Statistics II
3c-0l-3cr
Prerequisite: MATH 363
Multivariate distributions, change of variable technique, chi-square distribution, estimation, confidence intervals, hypothesis testing, contingency tables, goodness of fit. Practical applications are used to aid in the development.
MATH 366 Preparation for Actuarial Examinations
1c-0l-1cr
Prerequisites: MATH 171 and calculus sequence
An introduction to the actuarial profession which also helps the student prepare for the first actuarial examinations. The examination preparation consists of studying sample actuarial examinations and related material. Student is required to take the actuarial examination. Student should be aware that for most students, considerable study beyond the requirements of this 1cr course is required in order to pass the actuarial examinations.
3c-0l-3cr
Prerequisites: MATH 171, 271 with a C or better grade
Vector spaces and linear transformations are studied in a theoretical setting. Also, canonical forms and multilinear algebra are studied.
MATH 417 Statistical Applications
3c-0l-3cr
Prerequisites: MATH 214, 216, or 217 (for non-Math majors)
Using computer programs, a wide array of statistical procedures for educational research workers will be explored. Basic concepts of statistical inference and prediction are reviewed, including regression analysis and prediction, hypothesis testing, analysis of variance and covariance, and partial and multiple correlation. Emphasizes use of the computer and interpretation of computer printouts, along with understanding techniques employed. No computer knowledge is necessary.
MATH 418 Sampling Survey Theory and Its Application
3c-0l-3cr
Prerequisites: (For non-Math majors) MATH 214, 216, or 217
Directed to the student who is or will be doing quantitative research, commissioning large-scale surveys, and evaluating the results. Sampling techniques and statistical principles underlying their use are introduced. Consideration to the practical problems associated with implementation.
MATH 420 Patterns and Functions for Elementary and Middle School Teachers
3c-0l-3cr
Prerequisites: MATH 152; Elementary Education concentration
Examines the function concept as applied to elementary real number functions and graphing techniques for these functions. Topics include real number functions such as absolute value, step, linear, quadratic, and other polynomial functions, trigonometric and other periodic functions, exponential and logarithmic functions, and all other inverse functions. Students examine curricular materials that develop function concepts in Grades K-8.
3c-0l-3cr
Prerequisite: MATH 272 with a grade of C or better
A study of set theory, real number system, functions, topology of Cartesian space, sequences, convergence and uniform convergence, continuity, and uniform continuity.
3c-0l-3cr
Prerequisite: MATH 421
Includes the study of convergence sequences in Rn, global properties of continuity, uniform continuity, differentiation of Rn, Riemann integrals, and infinite series.
3c-0l-3cr
Prerequisite: MATH 225
An introduction to the theory of functions of a complex variable: topics included are elementary functions, analytic functions, conformal mapping, integration, series, and application.
MATH 425 Applied Mathematical Analysis I
3c-0l-3cr
Prerequisites: Calculus sequence, introductory linear algebra, or instructor permission
Provides the necessary background for an understanding of mathematical programming, proofs of convergence of algorithms, convexity, and factorable functions. Also develops necessary concepts in matrix theory which are required to develop efficient algorithms to solve linear and nonlinear programming models.
MATH 427 Introduction to Topology
3c-0l-3cr
Prerequisite: MATH 272 with a grade of C or better
A study of sets, functions, continuity, compactness, the separation axioms, and metric spaces; application of topology to analysis is demonstrated.
MATH 430 Seminar in Teaching Secondary School Mathematics
3c-0l-3cr
Prerequisite: Junior standing
Provides insights into the teaching of general mathematics, algebra, geometry, probability, and statistics. Students become aware of and use the resources and methods of instruction for teaching mathematics at the secondary level. Open to secondary mathematics education majors only and must be taken within two semesters prior to student teaching.
MATH 445 Deterministic Models in Operations Research
3c-0l-3cr
Prerequisites: MATH 122 or 225; 171
An introduction to using the basic tools of solving deterministic models in operations research. Includes optimization techniques and applications such as linear programming, nonlinear and dynamic programming, transportation models, and network models. In addition, sensitivity analysis, duality, simplex methods, and integer programming are discussed. Uses technology to solve problems and interpret the results. (Titled Programming Models in Operations Research prior to 2005-06)
MATH 446 Probabilistic Models in Operations Research
3c-0l-3cr
Prerequisites: MATH 122 or 225; 171; 216
A survey of probabilistic methods for solving decision problems under uncertainty. Probability review, decision theory, queuing theory, inventory models, and Markov chains are covered. Uses technology to solve problems and interpret the results.
MATH 447 Modeling and Simulation
3c-0l-3cr
Prerequisites: MATH 122 or 126; 171; 216
Construction and solution of mathematical models. Emphasizes applications in areas such as logistics, natural and social sciences, and manufacturing. Discrete and continuous system models are analyzed using mathematical and computer-based methods. An introduction to computer simulation. An introductory course in differential equations is recommended but not required. (Titled Simulation Models prior to 2005-06)
MATH 451 Numerical Methods for Supercomputers
3c-0l-3cr
Prerequisites: MATH 121 or 125; 171, COSC 250/MATH 250
Supercomputers make use of special computer architectures–vector and parallel processors–in order to achieve the fastest processing speed currently available. Students are introduced to these features and learn how numerical algorithms can be constructed to exploit supercomputers’ capabilities. They gain practical experience in programming for the Cray, YMP, in incorporating existing scientific software packages into user-written programs, in submitting remote jobs to the Pittsburgh Supercomputer Center, and in producing animated graphical output to summarize the typically large volume of output data generated by large scientific programs. (Also offered as COSC 451; may not register for duplicate credit)
MATH 452 Seminar in Teaching Algebra
var-1-4cr
MATH 453 Seminar in Teaching Geometry
var-1-4cr
MATH 454 Seminar in Teaching General Mathematics
var-1-4cr
Designed for pre-student teachers, who gain insights into the problems in teaching each topic and become aware of the materials available and of methods of instruction geared to the special type of student. Education majors only.
MATH 455 Seminar in Teaching Probability and Statistics
1c-0l-1cr
Designed for pre-student teachers, who gain insights into the problems in teaching each topic and become aware of the materials available and methods of instruction geared to the secondary mathematics student. Education majors only.
MATH 456 Geometry for Elementary and Middle School Teachers
3c-0l-3cr
Prerequisites: MATH 152, Elementary Education concentration
Students become acquainted with an informal, intuitive approach to geometry. Activities and materials for teaching geometrical concepts to children are an integral part of the course.
MATH 457 Number Theory for Elementary and Middle School Teachers
3c-0l-3cr
Prerequisites: MATH 152, Elementary Education concentration
An introduction to topics of elementary number theory including divisibility, prime numbers, factorization, modular arithmetic, problem solving, and place of number theory in the elementary school curriculum. Examines many number theory activities which can help to strengthen skills with basic facts in an interesting, nonroutine setting.
MATH 458 Logic and Logical Games for Elementary and Middle School Teachers
3c-0l-3cr
Prerequisites: MATH 152, Elementary Education concentration
An introduction to some of the basic ideas, terminology, and notation of mathematical logic and Boolean algebra as well as games of strategy that involve logic. In addition, an investigation of how logic is taught and used in various programs for the elementary school.
MATH 459 Technology in Elementary and Middle School Mathematics Instruction
3c-0l-3cr
Prerequisites: MATH 152, Elementary Education concentration
Develops the knowledge, skills, and perspectives required for using educational technology in teaching mathematics at the elementary and middle school levels. Participants have hands-on experiences with technology.
MATH 460 Technology in Mathematics Instruction
3c-0l-3cr
Prerequisite: COSC 110, junior status
Laboratory based and designed to provide preservice mathematics teachers with expertise in instructional technology for teaching mathematics at the secondary level. A strong emphasis is placed upon the integration of pedagogy and subject matter knowledge. Open to secondary mathematics education majors only and must be taken within two semesters prior to student teaching.
3c-0l-3cr
Prerequisite: MATH 364
Correlation and regression from applied and theoretical points of view, bivariate and multivariate normal distribution, analysis of variance, nonparametric methods. Practical problems involving statistical techniques and use of computer statistical packages. Knowledge of computer programming is not required.
MATH 471 Basic Concepts of Algebra
3c-0l-3cr
Prerequisites: MATH 152, Elementary Education concentration
Concepts of basic algebraic structures such as group, ring, integral domain, field, and vector space are studied within the context of the mathematical maturity of the student. Other topics include relations and functions, polynomials and polynomial equations, systems of equations, and inequalities. Consideration given to development of these concepts in the mathematics curriculum.
3c-0l-3cr
Prerequisite: MATH 272 with a grade of C or better
Development of theory of integral domains, fields, rings, and groups; designed to develop student’s power to think for himself or herself and to improve ability to construct formal proofs.
3c-0l-3cr
Prerequisite: MATH 476
Continue study of algebra by use of axiomatic method; Euclidean domains; polynomial domains and extension fields included; interrelationships between these structures and simpler structures, particularly groups and rings, are developed as in study of Galois group of a polynomial and in an introduction to Galois theory.
1c-0l-1cr
Prerequisite: Senior standing in Mathematics major
To assess the effectiveness of the mathematics curriculum and to provide mathematics majors with a culminating mathematical experience.
var-1-3cr
Prerequisite: As appropriate to course content
Offered on an experimental or temporary basis to explore topics not included in the established curriculum. A given topic may be offered under any special topic identity no more than three times. Special topics numbered 481 are primarily for upper-level undergraduate students.
var-1-3cr
Prerequisite: Prior approval through advisor, faculty member, department chairperson, dean, and Provost’s Office
Students with interest in independent study of a topic not offered in the curriculum may propose a plan of study in conjunction with a faculty member. Approval is based on academic appropriateness and availability of resources.
var-1-3cr
MATH 493 Internship in Mathematics
var-3-12cr
Prerequisites: Completion of core curriculum, completion of application
Positions with participating companies or agencies provide students with experience in mathematics-related work under the supervision of the agencies and faculty. Requirements include one to three on-site consultations, two university consultations, completion of progress reports, and presentation of final cumulative paper. Internship credit may not be used in fulfilling math major course requirements.
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