760 COURSE DESCRIPTIONS

760-041 BEGINNING ALGEBRA                     3 cr

A course for students who need a review of basic mathematics or who lack the computational skills required for success in algebra and other University courses. Topics include fractions, decimals, percent, descriptive statistics, English and metric units of measure, and measures of geometric figures. Emphasis is on applications. A brief introduction to algebra is included at the end of the course. This course does count toward the semester credit load and will be computed into the grade point average. It will not be included in the 120 credits required for graduation. It may be taken for a conventional grade or on a satisfactory/no credit basis. Not available to students who have satisfied the University Proficiency requirement in mathematics.
Unreq: 760-140 or 760-141

760-041 BEGINNING ALGEBRA MATHEMATICAL & COMPUTER SCIENCES                 4 cr
A course for those who have a sound background in basic arithmetic, but who have not been exposed to algebra, or who need to strengthen their basic algebra skills. Topics include properties of the real numbers, linear and quadratic equations, linear inequalities, exponents, polynomials, rational expressions, the straight line, and systems of linear equations. The course counts towards the semester credit load and will be computed into the grade point average. It will not, however, be included in the credits necessary for graduation. It may be taken for a conventional grade or on a satisfactory/no credit basis.
Prereq: 760-040 or equivalent demonstration of capability. Students cannot receive credit for 760-041 if they have been waived from the Mathematics Proficiency Requirement. Not available to students who have satisfied the University Proficiency requirement in mathematics.
Unreq: 760-140 or 760 141.

760-140 MATHEMATICAL IDEAS                 (Proficiency)                         3 cr
Designed to give students a broad understanding and appreciation of mathematics. Includes topics not usually covered in a traditional algebra course. Topics encompass some algebra, problem solving, counting principles, probability, statistics, and consumer mathematics. This course is designed to meet the University Proficiency Requirement in mathematics for those students who do not wish to take any course which has 760-141 as a prerequisite.
Prereq: Satisfactory completion of 760-041, with a grade of C or better, or demonstration of equivalent capability. This course cannot be taken for credit after completing any mathematics course above 141.

760-141 INTERMEDIATE ALGEBRA             (Proficiency)                         4 cr
Introduction to college algebra. Topics and concepts extend beyond those taught in a beginning algebra course. A proficiency course for those who have not had sufficient preparation in high school to allow them to take 760-143 or 760-152.
Prereq: Satisfactory completion, with a grade of C or better, of 760-041 or demonstration of equivalent capability. A student cannot receive credit for both 760-141 and 760-141B. A student cannot receive credit for either 760-141 or 760-141B if they have been waived from the Mathematics Proficiency Requirement. (See University Proficiency Requirements in the Bulletin). Students may not take for credit any course for which they have received a waiver, nor may they take for credit any course in the same department that is a prerequisite for a course that has been waived (e.g., if a student has been waived from Math 143, he may not take Math 141 for credit).

760-143 FINITE MATHEMATICS FOR BUSINESS AND SOCIAL SCIENCES GM                 3 cr
Mathematical preparation for the understanding of various quantitative methods in modern management and social sciences. Topics included are sets, relations, linear functions, interest, annuities, matrix theory, the solution of linear systems by the graphical, algebraic, Gauss-Jordan, and inverse methods, linear programming by graphical and simplex methods, counting and probability, and decision theory. College of Business and Economics majors must take this course on a conventional grade basis.
Prereq: Waiver of or a grade of C or better in 760-141.

MATH 148 MATHEMATICS FOR THE ELEMENTARY TEACHER I GM                     3 u
A study of sets, whole numbers, fundamental operations of arithmetic, fundamental algorithms and structural properties of arithmetic, fractions, problem solving and introduction to inductive and deductive logic stressing the structure of mathematics. All students will prepare a mathematics based activity and present it at an area elementary school. For elementary education prekindergarten-6 and elementary education elementary/middle school emphasis students.
Prereq: A grade of C or better in 760-141 or 760-141B or a waiver from the university mathematics proficiency requirement.

MATH 149 MATHEMATICS FOR THE ELEMENTARY TEACHER II                         3 u
Selected topics in logic. The computer as a useful tool in mathematical explorations is introduced and applied throughout the course. Topics in probability and statistics, with emphasis on descriptive techniques. Investigations in geometric figures, measurement, construction, congruent and similar geometric figures. An introduction to coordinate geometry. Problem solving, discovery, and student projects are emphasized throughout. All students will prepare a mathematics based activity and present it at an area elementary school.
Prereq: Satisfactory completion of 760-111 with a grade of C or better.

760-152 ELEMENTARY FUNCTIONS                      GM                         5 cr
Review of algebraic functions, inequalities, mathematical induction, theory of equations, exponential and logarithmic functions, circular functions, trigonometric identities and equations, inverse trigonometric functions, solution of triangles.
Prereq: Waiver of or a grade of C or better in 760-141.

760-177 THE LOGIC OF CHESS 1 cr
A study of logic particularly as it is used in the game of chess and, most particularly, in chess strategy and the end game of chess. The rules are taught to those who are not already acquainted with the game.
Prereq: Fulfillment of University Proficiency requirement in mathematics.

760-230 INTRODUCTORY STATISTICS                          GM                       3 cr
A pre-calculus course in statistics. Descriptive statistics, probability distributions, prediction, hypothesis testing, correlation, and regression. This course does not count towards a mathematics major or minor in either liberal arts or secondary education or towards a mathematics minor in elementary education. This course may not be taken for credit if credit has been or is being earned in any other statistics course.
Prereq: Waiver or a grade of C or better in 760-141. Unreq: Any other statistics course.

760-231 UNDERSTANDING PROBABILITY AND STATISTICS   GM         3 cr
A pre-calculus course in probability and statistics. Descriptive statistics, classical probability, probability distributions, prediction, parametric and nonparametric hypothesis testing, correlation, regression, and use of some statistical software. This course does not count towards a mathematics major or minor in liberal arts or towards a mathematics major in secondary education. This course may not be taken for credit if credit has been or is being earned in any other statistics course.
Prereq: Completion, with a grade of C or better, of either 760-143 or 760-152. Unreq: Any other statistics course.

760-243 SHORT CALCULUS FOR BUSINESS AND SOCIAL SCIENCES      GM         3 cr
A general survey of the Calculus. Topics covered include limits, differentiation, max-min theory, exponential and logarithmic functions, integration and functions of several variables. As in 760-143, business and social science applications are stressed. College of Business and Economics majors must take this course on a conventional grade basis.
Prereq: Completion with a grade of C or better in either of the courses 760-143 or 760-152.
Unreq: 760-250. Students should check with their major department for advice on whether to take 760-243 or 760-250.

760-250 APPLIED CALCULUS SURVEY FOR BUSINESS AND THE SOCIAL SCIENCES  GM     5 cr
An applied calculus course covering elementary analytic geometry, limits, differentiation, max-min theory, transcendental functions, integration, functions of several variables, and elementary differential equations. Some computer topics may be included. College of Business and Economics majors must take this course on a conventional grade basis.
Prerequisite: 760-143, with a grade of C or better, or equivalent preparation as determined by the Mathematics Department. Unreq: 760-243, 760-253.

760-253 CALCULUS AND ANALYTIC GEOMETRY I          GM             5 cr
Review of algebraic and trigonometric functions, study of the derivative, techniques of differentiation, continuity, applications of the derivative, the Riemann integral, applications of the integral. Conventional grade basis only if course is required in the College of Business for major.
Prereq: 760-152 or equivalent high school preparation as determined by the Mathematics Department.
Unreq: 760-243 and 760-250.

760-254 CALCULUS AND ANALYTIC GEOMETRY II                 5 cr
Transcendental functions, techniques of integration, improper integrals, L'Hospital's Rule and indeterminate forms, infinite series, polar coordinates and conic sections. This course includes a writing component.
Prereq: 760-250 with a grade of B or better, or 760-253.

760-255 CALCULUS AND ANALYTIC GEOMETRY III                 3 cr
Solid analytic geometry, vectors and vector functions, functions of several variables, multiple integrals and their applications.
Prereq: 760-254.

760-280 DISCRETE MATHEMATICS                                             3 cr
This course will supply a thorough grounding in the mathematical topics which are central to the study of computer science, and which form the basis for many modern applications of mathematics to the social sciences. Topics covered will include sets, logic, Boolean algebra and switching circuits, combinatorics, probability, graphs, trees, recursion, and algorithm analysis. Expressing mathematical ideas and writing proofs will be emphasized.
Prereq: 760-250 with a grade of C or better, or 760-253.

760-290 SPATIAL ANALYSIS                                                         3 cr
Presentation and interpretation of data, use descriptive statistics and measures of spatial patterns, introduction to statistical inference and measures of association, with particular reference to geographic examples. Students will become proficient in using computers to achieve these skills.
Prereq: 760-143

760-301 INTRODUCTION TO ANALYSIS                                 3 cr
The main emphasis of this course is to introduce students to mathematical proofs. Students will learn to read and write proofs in mathematics by writing proofs of theorems about limits, sets of real numbers, and continuous functions. If time permits, other topics may include derivative and integration theorems, theory of open and closed sets, and cardinality of sets.
Prereq: 760-255 and 760-280

760-342/542 APPLIED STATISTICS                                             3 cr
This course will cover the basics of statistical testing, regression analysis, experimental design, analysis of variance, and the use of computers to analyze statistical problems.
Prereq: 760-253 or 760-250 or cons instr.
Unreq: 230-245.

760-353 COLLEGE GEOMETRY                                                 5 cr
The topics included in this course are foundations of Euclidean geometry, Euclidean transformational geometry, modern synthetic geometry that builds on Euclidean geometry, selected finite geometries, and an introduction to non-Euclidean and projective geometry, including their relationship to Euclidean geometry. Although the course is adapted to the prospective teacher of geometry, it will also meet the needs of those in other majors needing a background in geometry. Standards and guidelines of appropriate national and local bodies will be implemented.
Prereq: 760-253 and 760-280 or consent of instructor.

760-355/555 MATRICES AND LINEAR ALGEBRA                     3 cr
Systems of linear equations, matrices and determinants, finite dimensional vector spaces, linear dependence, bases, dimension, linear mappings, orthogonal bases, and eigenvector theory. Applications stressed throughout.
Prereq: 760-250 or 760-253.

760-359 MATHEMATICAL MODELING & STATISTICS             3 cr
An introduction to mathematical modeling and descriptive statistics. Students will develop the basic skills of formulation, simplification, and analysis of mathematical models for describing and predicting physical phenomena. The basic tools of descriptive statistics will also be introduced; the use of descriptive statistics in formulating and interpreting mathematical models will be emphasized.
Prereq: 760-255 or consent of instructor.

760-361 DIFFERENTIAL EQUATIONS                                         3 cr
Ordinary differential equations: general theory of linear equations, special methods for nonlinear equations including qualitative analysis and stability, power series and numerical methods, and systems of equations. Additional topics may include transformation methods and boundary value problems. Applications stressed throughout.
Prereq: 760-255.

760-365/565 LINEAR PROGRAMMING                                     3 cr
A study of the vector-matrix theory and computational techniques of the simplex method, duality theorem, degeneracy problem, transportation problems and their applications to engineering and economics. Machine solution of large linear programming problems.
Prereq: 765-171 and 760-355.

760-375/575 DEVELOPMENT OF MATHEMATICS                    3 cr
A study of the development of mathematical notation and ideas from prehistoric times to the present. The development and historic background of the new math will be included.
Prereq: 760-152 or cons instr.

760-380/580 PATTERNS OF PROBLEM SOLVING                     3 cr
This course will expose students to a variety of techniques useful in solving mathematics problems. The experiences gained from this course can be applied to problems arising in all fields of mathematics. The student will have the chance to see how some general techniques can be used as tools in many areas. Homework for this course will consist mostly of solving a large number of mathematics problems. Consent will be given to students with substantial interest in problem solving, and adequate preparation.
Prereq: 760-280 or cons instr.

760-415/615 MODERN ALGEBRA AND NUMBER THEORY FOR THE ELEMENTARY TEACHER     3 cr
An introduction to modern algebra with special emphasis on the number systems and algorithms which underlie the mathematics curriculum of the elementary school. Topics from logic, sets, algebraic structures, and number theory.
Prereq: 760-112 and 760-152. Unreq: 760-452.

760-416/616 GEOMETRY FOR THE ELEMENTARY TEACHER                 3 cr
A study of the intuitive, informal geometry of sets of points in space. Topics include elementary constructions, coordinates and graphs, tesselations, transformations, problem solving, symmetries of polygons and polyhedra, and use of geometry computer software.
Prereq: 760-112 and 760-152

760-417/617 THEORY OF NUMBERS                             3 cr
A study of the properties of integers, representation of integers in a given base, properties of primes, arithmetic functions, module arithmetic. Diophantine equations and quadratic residues. Consideration is also given to some famous problems in number theory.
Prereq: 760-280 or 760-415 or cons instr.

760-431/631 TOPOLOGY                                 3 cr
An introduction to point-set topology, including such topics as topological spaces, mappings, connectedness, compactness, separation axioms, metric spaces, complete spaces, product spaces and function spaces.
Prereq: 760-255 and either 760-280 or cons instr.

760-441/641 PROBABILITY THEORY                             3 cr
Probability spaces, discrete and continuous random variables, mathematical exceptation, discrete and continuous distributions.
Prereq: 760-255 and either 760-280 or cons instr.

760-442/642 MATHEMATICAL STATISTICS                 4 cr
This course will cover moment generating functions, moments of linear combinations of random variables, conditional expection, functions of random variables, sampling distributions, the theory of estimation, Bayesian estimation, hypothesis testing, nonparametric tests, and linear models.
Prereq: 760-441 and either 760-355 or cons instr.

760-446/646 ACTUARIAL MATHEMATICS                     3 cr
This course will discuss the actuarial profession and the insurance industry, provide direction to students wishing to take the first few actuarial examinations, thoroughly cover the theory of interest, and introduce the basic concepts of actuarial mathematics.
Prereq: 760-441 or concurrent registration

760-452/652 INTRODUCTION TO ABSTRACT ALGEBRA                     3 cr
An introductory survey of abstract algebra and number theory with emphasis on the development and study of the number systems of integers, integers mod n, rationals, reals, and complex numbers. These offer examples of and motivation for the study of the classical algebraic structures of groups, rings integral domains and fields. Applications to algebraic coding theory and crystallography will be developed if time allows.
Prereq: 760-280.
Unreq: 760-415.

760-453/653 ABSTRACT ALGEBRA                                 3 cr
This course is a continuation of 760-452/652 with emphasis on ring and field theory. Topics include a review of group theory, polynomial rings, divisibility in integral domains, vector spaces, extension fields, algebraic extension fields, finite fields, etc.
Prereq: 760-355 and 760-452.

760-458/658 APPLIED MATHEMATICAL ANALYSIS I                     3 cr
Selected topics in ordinary differential equations: series solutions, stability, transform methods, special functions, numerical methods, vector differential calculus, line and surface integrals.
Prereq: 760-361.

760-459/659 PARTIAL DIFFERENTIAL EQUATIONS                         3 cr
Fourier analysis, partial differential equations and boundary value problems, complex variables, and potential theory.
Prereq: 760-361.

MATH  463  COMPLEX  VARIABLES                           3 cr
This course is a study of the algebra and geometry of complex numbers, the properties of analytic functions, contour integration, the calculus of residues, and the properties of power series.
Prereq: MATH 255

760-464/664 ADVANCED CALCULUS I                             3 cr
This course presents a rigorous treatment of the differential and integral calculus of single variable functions, convergence theory of numerical sequences and series, uniform convergence theory of sequences and series of functions, metric spaces, functions of several real variables, and the inverse function theorem. This course contains a writing component.
Prereq: 760-301.

760-471/671 NUMERICAL ANALYSIS I                             3 cr
Emphasis on numerical algebra. The problems of linear systems, matrix inversion, the complete and special eigenvalue problems, solutions by exact and iterative methods, orthogonalization, gradient methods. Consideration of stability and elementary error analysis. Extensive use of microcomputers and programs using a high level language, such as PASCAL.
Prereq: 765-171 and 760-355.

760-473 LIGHTNING RADIATIVE TRANSFER                 4 cr
This course will introduce the students to the field of Mathematical Lightning Radiative Transfer. It will provide the students with the background needed to analyze lightning events and to discriminate cloud to ground discharges from intra-cloud discharges. In addition, this course will introduce the students to the area of Ground Detection of Lightning.
Prereq: 760-361 and 800-174 or consent of instructor.

760-475 DATA INTERPRETATION OF SPACE SCIENCE                     3 cr
This course will continue the study of Mathematical Space Science. The course will teach and train students on how to read and interpret data from Space and ground instruments. Students will learn how to access and work with satellite data.
Prereq: 760-361 and 765-171 or consent of instructor.

MATH 477  MATHEMATICAL  SCATTERING                                    3 cr
 THEORY  AND  APPLICATIONS
This course will address the fundamental theory and applications of mathematical scattering. Students will be exposed to the scalar, vector, and tensor scattering. In addition, the course will introduce the students to diverse techniques of statistical and mathematical scattering inversion. Applications from earth system and space sciences will be studied throughout the course.
Prereq: MATH 458, MATH 459, MATH 463 AND PHYSCS 322 or consent of instructor.

MATH 483  MATHEMATICAL   WAVES                                             3 cr
 PROPAGATION  THEORY   AND   APPLICATIONS
This course will address the fundamental theory and applications of mathematical wave propagation. Students will be exposed to the scalar, vector, and tensor wave nature of matter. In addition, the course will introduce diverse techniques of linear and non-linear modeling of natural occurrences and their role in understanding mathematical inversion. Applications from earth system and space sciences will be studied throughout the course.
Prereq:  MATH 458, MATH 459, MATH 463 AND PHYSCS 322 or consent of instructor.

760-490/690 WORKSHOP                     1-3 cr
Repeatable.
Prereq: Consent of instructor.

760-492 FIELD STUDY                         1-3 cr
A study for which data is obtained or observations are made outside the regular classroom. Repeatable.
Prereq: Consent of instructor.

760-494/694 SEMINAR                         2 cr
Repeatable.
Prereq: Consent of instructor.

760-496/696 SPECIAL STUDIES                     1-3 cr
Repeatable three times maximum in 6 years.
Prereq: Consent of instructor.

760-498 INDEPENDENT STUDY                     1-3 cr
Repeatable.
Prereq: Consent of instructor and consent of department chairperson.

760-499 PROJECT FOR MAJORS                     1 cr
This course is designed to give students experience and to improve their skill in reading, writing, and understanding mathematics by requiring them to research one or more mathematical topics and then write a report about their activities and discoveries. The focus is on the learning and communication of mathematics: how to read with understanding, write with clarity and precision, and in the process discover how writing can aid in understanding.
Prereq: Jr st or cons dept chp

Registrar's Office - UW-Whitewater For comments: registrar@mail.uww.edu. Last revised on March 10, 2000 by WDT URL: http://www.uww.edu/catalog2000