Indiana University of Pennsylvania

1999-2000 Undergraduate Catalog
Indiana, Pennsylvania 15705

Mathematics

Department of Mathematics
College of Natural Sciences and Mathematics

Credit designation below title is expressed in (c) class hours per week, (l) lab or (d) discussion section hours per week, and (sh) semester hours of credit per semester.

MA100 MA101 MA105 MA110 MA117 MA121 MA122 MA123 MA124 MA127 MA128 MA151 MA152 MA171 MA214 MA216 MA217 MA219 MA227 MA241 MA271 MA272 MA281 MA317 MA320 MA342 MA350 MA353 MA355 MA363 MA364 MA366 MA371 MA417 MA418 MA420 MA421 MA422 MA423 MA424 MA425 MA427 MA445 MA446 MA447 MA451 MA452 MA453 MA454 MA456 MA457 MA458 MA459 MA460 MA465 MA471 MA476 MA477 MA480 MA481 MA482 MA490 MA493

MA100 Intermediate Algebra
3c-0l-3sh
Note: A student may not take MA100 after successfully completing MA105 or MA110 or a calculus course without the written approval of the mathematics department chairperson.
Basic course in algebra including factoring, exponents and radicals, systems of linear equations, complex fractions, and inequalities. Designed for those students who lack the basic algebraic skills required in MA105 or MA110. This course will not meet Liberal Studies math requirements.

MA101 Foundations of Mathematics
3c-0l-3sh
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.

MA105 College Algebra
3c-0l-3sh
Prerequisite: MA100 or equivalent high school preparation
Note: A student may not take MA105 after successfully completing a calculus course or MA110 without the written approval of the mathematics department chairperson.
Prepares students for the study of calculus for business, natural, and social sciences. Topics include a detailed study of polynomial, exponential, and logarithmic functions. This course is designed primarily for students planning to take MA121 Calculus for Business, Natural, and Social Sciences.

MA110 Elementary Functions
3c-0l-3sh
Note: A student may not take MA110 after successfully completing a calculus course without the written approval of the mathematics department chairperson. For students not prepared to begin the study of calculus; topics include polynomial, exponential, logarithmic, and trigonometric functions.

MA117 Principles of Mathematics
3c-0l-3sh
This course is 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.

MA121 Calculus I for Business, Natural, and Social Sciences
4c-0l-4sh
Note: A student may not take MA121 after successfully completing another calculus course without the written permission of the mathematics department chairperson.
Prerequisite: MA105 or MA110 or equivalent high school preparation
Introduces non-Math major to analytic geometry, elementary functions (including logarithmic and exponential functions), central ideas of the calculus (limit, derivative, and integral), applications of derivatives to business, social, and natural sciences.

MA122 Calculus II for Business, Natural, and Social Sciences
4c-0l-4sh
Applications of integrals to business, natural, and social sciences, functions of several variables, trigonometric functions, sequences and series, numerical methods, differential equations.

MA123 Calculus I for Physics, Chemistry, and Mathematics
4c-0l-4sh
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.)

MA124 Calculus II for Physics, Chemistry, and Mathematics
4c-0l-4sh
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.

MA127 Calculus I
4c-0l-4sh
Prerequisite: Permission of the mathematics department
The first in a three-course series of courses which stresses the theory of the calculus as well as the application in problem solving. Topics to be included are real numbers, an introduction to analytic geometry, functions, limits and continuity, derivatives and applications, the differential and antidifferentiation.

MA128 Calculus II
4c-0l-4sh
Prerequisite: Permission of the mathematics department
The second in a three-course series of courses stresses the theory of calculus as well as the application in problem solving. Topics to be included are definite integrals and applications, logarithmic and exponential functions, trigonometric and inverse trigonometric functions, polar coordinates, hyperbolic functions, indeterminate forms, improper integrals, and Taylor’s formula.

MA151 Elements of Mathematics I
3c-0l-3sh
Topics included are sets, concepts of logic, mathematical systems, systems of numeration, developing the set of integers, rational numbers, and real numbers.

MA152 Elements of Mathematics II
3c-0l-3sh
Prerequisite: MA151
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.

MA171 Introduction to Linear Algebra
3c-0l-3sh
Introduction to vector spaces, linear transformations, determinants, and matrix algebra. Topics are presented in a direct and intuitive approach.

MA214 Probability and Statistics for Business Majors
3c-0l-3sh
Designed to introduce the study of probability theory, discrete random variables and probability distributions, empirical frequency distributions, theoretical frequency distributions, statistical investigations and sampling, and sampling distributions.

MA216 Probability and Statistics for Natural Sciences
4c-0l-4sh
Prerequisite: MA121
Frequency distributions, measures of central tendency and variation, probability, probability distributions, sampling distributions. Hypothesis testing for means, variances, proportions. Correlation and prediction, regression, analysis of variance, and nonparametric statistics. Emphasis on applications.

MA217 Probability and Statistics
3c-0l-3sh
(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.

MA219 Discrete Mathematics
3c-0l-3sh
Prerequisites: CO110, and MA123, 127, or MA122
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. Emphasis placed on developing an intuitive understanding of basic structures rather than formal theories and influence of these topics on theory and practice of computing.

MA227 Calculus III
4c-0l-4sh
Prerequisite: Permission of the mathematics department
The third in a three-course series of courses which stresses the theory of calculus as well as the application in problem solving. Topics to be included are vectors in the plane, parametric equations, vectors in three-dimensional space, solid analytic geometry, differential calculus of functions of several variables, directional derivatives, gradients, applications of partial derivatives, and infinite series.

MA241 Differential Equations
3c-0l-3sh
Prerequisites: MA122, MA124, or MA227
Emphasis is placed on techniques of solution and elementary physical applications. A thorough study is made of differential equations classified as order one-degree one, linear, and nonhomogeneous. Solution techniques involving reduction of order techniques, the differential operator, and infinite series are introduced.

MA271 Introduction to Mathematical Proofs I
3c-0l-3sh
Prerequisites: MA123 and MA171
Gives student basic ideas of 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.

MA272 Introduction to Mathematical Proofs II
3c-0l-3sh
Prerequisites: MA124 and MA271 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.

MA281 Special Topics
var-1-3sh
Prerequisite: As appropriate to course content
Special topics are offered on an experimental or temporary basis to explore topics that are 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.

MA317 Introduction to Probability and Statistics
3c-0l-3sh
Prerequisites: MA152, Elementary Education concentration
Introduces students to elementary concepts of probability and statistics which will enable them to analyze data, make predictions, and determine which concepts may be used with children.

MA320 Mathematics for Early Childhood
3c-0l-3sh
Prerequisites: MA151, Early Childhood major
This course studies child-centered, activity-oriented mathematics programs for early childhood education. The course 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. (Offered as MA450 prior to 1994)

MA342 Advanced Mathematics for Applications
4c-0l-4sh
Prerequisite: MA241
Deals with the application of mathematics to problems of science. Emphasis is placed on the three phases of such an application and on the development of skills necessary to carry out each step: (a) translation of the given physical information to a mathematical model; (b) treatment of the model by mathematical methods; (c) interpretation of the mathematical result in physical terms. Topics included are vector calculus, integral theorems, Fourier series, partial differential equations, and the Laplace transformation.

MA350 History of Mathematics
3c-0l-3sh
Prerequisite: MA122 or MA124 or permission of instructor
Development of the central concepts of mathematics from ancient times up to the development of calculus in the seventeenth century. Mathematical concepts will be placed in historical perspective. The use of the history of mathematics as a pedagogical tool and its relationship to other sciences will be addressed.

MA353 Theory of Numbers
3c-0l-3sh
Prerequisite: MA271 with a C or better grade
Divisibility, congruences, primitive roots, number theoretic functions, diophantine equations, continued fractions, quadratic residues.

MA355 Foundations of Geometry I
3c-0l-3sh
Prerequisites: MA171, MA271 with a C or better grade
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.

MA363 Mathematical Statistics I
3c-0l-3sh
Prerequisites: MA122, MA124, or MA227
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.

MA364 Mathematical Statistics II
3c-0l-3sh
Prerequisite: MA363
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.

MA366 Preparation for Actuarial Examinations
1c-0l-1sh
Prerequisites: MA171 and calculus sequence
This course provides an introduction to the actuarial profession and helps the student prepare for the first actuarial examinations. The examination preparation consists of studying sample actuarial examinations and related material. The student is required to take the actuarial examination. The student should be aware that for most students, considerable study beyond the requirements of this one-credit course will be required in order to pass the actuarial examinations.

MA371 Linear Algebra
3c-0l-3sh
Prerequisites: MA171, MA271 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.

MA417 Statistical Applications
3c-0l-3sh
Prerequisites: MA214, MA216, or MA217 (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 will be reviewed, including regression analysis and prediction, hypothesis testing, analysis of variance and covariance, and partial and multiple correlation. Emphasis is on use of the computer and interpretation of computer printouts, along with understanding techniques employed. No computer knowledge is necessary.

MA418 Sampling Survey Theory and Its Application
3c-0l-3sh
Prerequisites: (For non-Math majors) MA214, MA216, or MA217
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 will be introduced. Consideration to the practical problems associated with implementation.

MA420 Pre-Calculus Mathematics I
3c-0l-3sh
Prerequisites: MA152; 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 logarithmic functions, and all other inverse functions. Students will examine curricular materials that develop function concepts in Grades K-8.

MA421 Advanced Calculus I
3c-0l-3sh
Prerequisites: MA124 and MA272 with a C or better grade
Study of set theory, real number system, functions topology of Cartesian space, sequences, convergence and uniform convergence, continuity, and uniform continuity.

MA422 Advanced Calculus II
3c-0l-3sh
Prerequisite: MA421
Includes the study of convergence sequences in Rn, global properties of continuity, uniform continuity, differentiation of Rn, Riemann integrals, and infinite series.

MA423-424 Complex Variable I and II
each 3c-0l-3sh
Prerequisite: MA124 or MA227
Introduction to the theory of functions of a complex variable: topics included are elementary functions, analytic functions, conformal mapping, integration, series, and application.

MA425 Applied Mathematical Analysis I
3c-0l-3sh
Prerequisites: Calculus sequence, introductory linear algebra, or permission of instructor
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.

MA427 Introduction to Topology
3c-0l-3sh
Prerequisite: MA272 with a C or better grade
Study of sets, functions, continuity, compactness, the separation of axioms, and metric spaces; application of topology to analysis is demonstrated.

MA445 Programming Models in Operations Research
3c-0l-3sh
Prerequisites: Two-semester sequence of calculus and MA171 or permission of instructor
Development of deterministic mathematical models for managerial and social sciences with relevant computational techniques.

MA446 Probabilistic Models in Operations Research
3c-0l-3sh
Prerequisites: Two-semester sequence of calculus, MA363
Development of probabilistic mathematical models for managerial and social sciences with relevant computational techniques.

MA447 Simulation Models
3c-0l-3sh
Prerequisites: Completion of the calculus sequence; background in statistics and probability, and familiarity with concepts of programming (knowledge of a particular programming language not required)
Considers the types of models that are basic to any simulation and methods for building and using such models. It includes discrete and continuous system simulations, their applications, and an introduction to SLAM II (Simulation Language for Alternative Modeling).

MA451 Numerical Methods for Supercomputers
3c-0l-3sh
Prerequisites: MA121 and MA122, or MA123 or MA127, MA171, CO250
Supercomputers make use of special computer architectures—vector and parallel processors—in order to achieve the fastest processing speed currently available. Students will be introduced to these features and will learn how numerical algorithms can be constructed to exploit supercomputers’ capabilities. Students will 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 CO451; may not register for duplicate credit)

MA452 Seminar in Teaching Algebra
var-1-4sh
MA453 Seminar in Teaching Geometry
var-1-4sh
MA454 Seminar in Teaching General Mathematics
var-1-4sh
Seminars are designed for pre-student teacher. Students in each class will gain insights into the problems in teaching each topic and become aware of the materials available and methods of instruction geared to the special type of student. Education majors only.

MA456 Principles of Geometry I
3c-0l-3sh
Prerequisites: MA152, 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.

MA457 Introduction to Number Theory
3c-0l-3sh
Prerequisites: MA152, Elementary Education concentration
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. Students will examine many number theory activities which can help to strengthen skills with basic facts in an interesting, nonroutine setting.

MA458 Introduction to Logic and Logical Games
3c-0l-3sh
Prerequisites: MA152, Elementary Education concentration
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.

MA459 Computer-related Topics in the Elementary and Middle School
3c-0l-3sh
Prerequisites: MA152, Elementary Education concentration
Provides teachers with concepts and techniques necessary to teach computer-related topics to children. Participants will work with elementary school children throughout the semester.

MA460 Technology in Mathematics Instruction
3c-0l-3sh
Prerequisite: CO205
Designed to provide preservice mathematics teachers with expertise in instructional technology for teaching mathematics at the secondary level. Pedagogical and content knowledge are integrated within the context of technology and current reforms.

MA465 Topics in Statistics
3c-0l-3sh
Prerequisite: MA364
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.

MA471 Basic Concepts of Algebra
3c-0l-3sh
Prerequisites: MA152, 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.

MA476 Abstract Algebra I
3c-0l-3sh
Prerequisite: MA272 with a C or better grade
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.

MA477 Abstract Algebra II
3c-0l-3sh
Prerequisite: MA476
Designed to have student 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.

MA480 Senior Seminar
1c-0l-1sh
Prerequisites: Senior standing in mathematics major
To assess the effectiveness of the mathematics curriculum and to provide mathematics majors with a culminating mathematical experience.

MA481 Special Topics
var-1-3sh
Prerequisite: As appropriate to course content
Special topics courses are offered on an experimental or temporary basis to explore topics that are 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.

MA482 Independent Study
var-1-3sh
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.

MA490 Independent Study
var-1-3sh

MA493 Internship in Mathematics
var-3-12sh
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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This information is maintained by the Office of the Registrar, with approval from the University Senate. Last modified at 9:50 PM on 7/15/99.