Rutgers University - Camden
Armitage Hall • 311 N. 5th Street • Camden, NJ 08102
Tel: (856)225-6076 • Fax: (856)225-6602
|
Rutgers University - Camden Armitage Hall • 311 N. 5th Street • Camden, NJ 08102 Tel: (856)225-6076 • Fax: (856)225-6602 |
Courses (Mathematics 640)
Note: Some
upper-level courses may be given in alternate years.
Please check with
department advisers.
50:
640: 041. ELEMENTARY ALGEBRA (NC)
For students who do
not have the usual background in mathematics forcollege admission.
The system of integers,
exponentiation, graphing, solution of equations, and basic notions of geometry.
50:
640: 042. INTERMEDIATE ALGEBRA (NC)
Prerequisite: 50:
640: 041 or placement by Basic Skills Test.
Study of algebraic
operations on polynomials, integral and rational exponents, linear and
quadratic equations, systems of equations, and the function concept.
50:
640: 103. FUNDAMENTAL MATHEMATICS SYSTEMS I (R) (3)
Particularly suitable
for students of elementary education.
Sets, logic, number
systems, and algebraic structures.
50:
640: 104. FUNDAMENTAL MATHEMATICS SYSTEMS II (R) (3)
Informal geometry,
measurement, coordinate geometry, transformational geometry, introduction
to computers.
50:
640: 105. FINITE MATHEMATICS (R) (3)
Particularly suitable
for business and economics majors.
Introduction to important
and fundamental areas of mathematics that do not require calculus. Topics
include set theory, functions and relations, and the algebra of vectors
and matrices with applications to systems of linear equations, linear programming,
and game theory.
50:
640: 106. AN INTRODUCTION TO MATHEMATICAL THOUGHT (R) (3)
For the student who
has serious interest in learning something about mathematical thought and
its applications, but who is not planning to major in mathematics.
An understanding of
the topics chosen for illustrating mathematical thinking within the reach
of the student with the usual high school background.
50:640:108.
NUMBERS AND BEYOND (R)(3)This course is designed
for students who are considering secondary certification. In addition,
it also satifies the 3-credit mathematics requirement for any other major.
A study of the properties
and qualities of number systems and spatial relationships in geometry.
Topics needed to explore the developmental beauty of mathematics will be
discussed. Some of these are logic and reasoning, set theory and number
theory, functions (not limited to linear), sequences, basic concepts from
calculus, group and field concepts, and spatial concepts such as rotations,
translations, and geometric objects.
50:
640: 113. COLLEGE ALGEBRA (R) (3)
Prerequisite: 50:
640: 042 or appropriate score on the Mathematics Placement Examination.
Credit not given for both this course and 50: 640: 115. A nonrequired preparatory
course for those students who must take 50: 640: 130.
A study of real numbers
with regard to algebraic operations and order properties. Introduction
to complex numbers and logarithmic and exponential functions.
50:
640: 114. TRIGONOMETRY AND ANALYTIC GEOMETRY (R) (3)
Elements of plane
trigonometry and trigonometric identities. Plane loci, properties of the
conic sections, and transformations of co-ordinates. The line, plane, and
quadric surface in three dimensions.
50:
640: 115. PRECALCULUS COLLEGE MATHEMATICS (R) (3)
Prerequisite: 50:
640: 042 or appropriate score on the Mathematics Placement Examination.
Credit not given for both this course and 50: 640: 113. A nonrequired preparatory
course for those students who must take 50: 640: 121-122.
Algebraic expressions,
algebraic equations, functions, graphing, and exponential, logarithmic,
and trigonometric functions.
50:
640: 116. ELEMENTS OF CALCULUS (R) (3)
Students who plan
to take more than one term of calculus should follow the sequence 50: 640:
121-122. Credit will not, in general, be given for more than one of the
courses 50: 640: 116, 121, or 130.
A one-term survey
of the elements of calculus, with emphasis on applications. Topics include
elementary functions and their derivatives, rate of change, curve tracing,
velocity, minimum and maximum, law of growth and decay, antiderivatives,
and definite integral.
50:
640: 121. UNIFIED CALCULUS I (R) (4)
Prerequisite: 50:
640: 115 or accepted score on the Mathematics Placement Examination.
Students who plan to take more than one term of calculus should follow
the sequence 50: 640: 121-122. Credit will not, in general, be given for
more than one of the courses 50: 640: 116, 121, or 130.
An introduction to
analytic geometry, differentiation of algebraic and transcendental functions,
applications of differentiation, and a brief introduction to integration.
50:
640: 122. UNIFIED CALCULUS II (R) (4)
Prerequisite: 50:
640: 121 or equivalent.
An extensive introduction
to integration and the definite integral, transcendental functions, methods
of integration, applications, and infinite series.
50:
640: 129. LINEAR MATHEMATICS FOR BUSINESS AND ECONOMICS (R) (3) Prerequisite:
50: 640: 113 or accepted score on the Mathematics Placement Examination.
A mathematics foundations course for the student majoring in business and
economics.
Basic algebra, matrices,
and linear programming with applications to problems in business and economics.
50:
640: 130. CALCULUS FOR BUSINESS, ECONOMICS, AND LIFE SCIENCES (R) (3) Prerequisite:
50: 640: 113 or appropriate score on the Mathematics Placement Examination.
Students who plan to take more than one term of calculus should follow
the sequence 50: 640: 121-122. Credit will not, in general, be given for
more than one of the courses 50: 640: 116, 121, or 130.
A one-term survey
of the elements of calculus with emphasis on applications in business,
economics, and life sciences. Topics covered are basic algebra, derivatives,
maximum/ minimum problems, integration, and partial differentiation.
50:
640: 182. ELEMENTS OF PROBABILITY (R) (3)
A one-term survey
of the elements of the mathematical theory of probability with emphasis
on applications. Topics include sets, subsets, Venn diagrams, partitions,
independent events, sample spaces and weights, conditional probabilities,
the binomial theorem, methods in combinatorial probability, the binomial
distribution, and expected value.
50:
640: 190. INTRODUCTION TO HIGHER MATHEMATICS (R) (3)
Designed primarily
for mathematics majors.
An encyclopedic survey
of different branches of mathematics.
50:
640: 221. UNIFIED CALCULUS III (4)
Prerequisite: 50:
640: 122.
Solid analytic geometry,
partial differentiation, multiple integrals, series, and applications.
50:
640: 237. DISCRETE MATHEMATICS (3)
Prerequisite: 50:
640: 113 or placement.
Sets, relations, and
functions. Mathematical induction. Recursion. Propositional logic. Introduction
to first order logic. Boolean algebra. Elements of combinatorics. Introduction
to graphs and trees.
50:
640: 250. LINEAR ALGEBRA (3)
Prerequisite: 50:
640: 122 or permission of instructor.
Vector spaces, the
calculus of matrices, and the theory of determinants.
50:
640: 311-312. ADVANCED CALCULUS I, II (3,3)
Prerequisite: 50:
640: 221.
A study of convergence,
uniform convergence, and continuity, with applications to series expansions
in one and several variables; partial differentiation; multiple, line,
and surface integrals.
50:
640: 314. ELEMENTARY DIFFERENTIAL EQUATIONS (3)
Prerequisite: 50:
640: 221 or permission of instructor.
Theory of ordinary
differential equations. Power series methods and existence and uniqueness
theorems. Applications to problems in economics, biology, chemistry, physics,
and engineering.
50:
640: 331. INTRODUCTION TO ACTUARIAL MATHEMATICS (3)
Pre-or
corequisites: 50: 640: 221, 250. Preparation course for the first exam of
the college of actuaries.
Survey of calculus
and linear algebra, with particular emphasis on topics such as complex
exponents and logarithms.
50:
640: 351-352. INTRODUCTION TO MODERN ALGEBRA (3,3)
Prerequisite: 50:
640: 250 or permission of instructor.
The study of groups,
rings, field, and linear spaces.
50:
640: 356. THEORY OF NUMBERS (3)
Prerequisite: Permission
of instructor.
Properties of the
natural numbers, simple continued fractions, congruences, and elementary
arithmetical functions.
50:
640: 358. ADVANCED DISCRETE MATHEMATICS (3)
Prerequisite: 50:
640: 237.
Graphs and trees,
generating functions, recursion theory, and difference equations. Regular
and context-free languages. Finite and pushdown automata. Turing machines.
50:
640: 363-364. FOUNDATIONS OF APPLIED MATHEMATICS I, II (3,3)
Prerequisite: 50:
640: 314.
Covers integral theorems
of vector analysis, complex variables, series solutions to differential
equations, Laplace and Fourier transforms, and use of mathematical software
languages such as Maple and Mathematica.
50:
640: 368. MATHEMATICS FOR ECONOMIC AND BUSINESS ANALYSIS (3) Prerequisites:
50: 640: 129 and 130.
Emphasizes the mathematical
foundations of analysis in optimiza-tion of multivariate functions; differential
and difference equations; linear programming; problems with particular
consideration to business and economic interpretation.
50:
640: 375. FOURIER SERIES (3)
Prerequisite: 50:
640: 314.
Introduction to the
solution of boundary value problems in the partial differential equations
of mathematics, physics, and engineering by means of Fourier series, Fourier
transforms, and orthogonal functions.
50: 640: 396. HONORS PROGRAM IN MATHEMATICS (3)
50:
640: 401. FOUNDATIONS OF ANALYSIS (3)
Pre-or corequisite:
50: 640: 311.
Introduction to basic
concepts of topology and analysis, including point sets, uniform continuity,
uniform convergence, compactness, metric spaces, Jordan curves, and the
Riemann-Stieljes integral.
50:
640: 402. FOUNDATIONS OF ANALYSIS (3)
Prerequisite: 50:
640: 401.
Hilbert Space, Banach
Space, Lebesgue integral, elements of functional analysis.
50:
640: 403. INTRODUCTORY THEORY OF FUNCTIONS OF A COMPLEX VARIABLE (3) Prerequisite:
50: 640: 311 or permission of instructor.
Topological concepts,
analytic functions, elementary conformal mappings, line integrals, Cauchy's
theorem, Cauchy's integral formula, the calculus of residues. Taylor and
Laurent series, normal families, Riemann mapping theorem, and harmonic
functions.
50:
640: 410. VECTOR ANALYSIS (3)
Prerequisite: 50:
640: 221.
Vector calculus and
its application to physics. Gauss, Stokes, Green theorems. Potentials.
50:
640: 427. ADVANCED DIFFERENTIAL EQUATIONS (3)
Prerequisites: 50:
640: 250 and 314.
Autonomous and nonautonomous
systems of differential equations; phase plane analysis and stability of
critical points; the perturbation method applied to nonlinear equations;
modeling and analysis of environmental, biological, chemical, and economic
systems. An article that is interdisciplinary in nature is discussed in
detail.
50:
640: 432. INTRODUCTION TO DIFFERENTIAL GEOMETRY (3)
Prerequisite: Permission
of instructor.
Space, curves, curvature,
torsions, Frenet formulas, curvilinear coordinates, fundamental forms,
mean and Gaussian curvature, and the general theory of surfaces.
50:
640: 435. GEOMETRY (3)
Prerequisites: 50:
640: 121, 122, 221, or permission of instructor.
Euclidean and non-Euclidean
geometries, geometric transformations. Complex language in geometry. Moebius
transformations. Symme-tries and tessellations. Projective geometry. Regular
polytopes.
50:
640: 441. INTRODUCTORY TOPOLOGY (3)
Prerequisite: Permission
of instructor.
A study of the standard
topics of the set theoretic topology.
50:
640: 463-464. PARTIAL DIFFERENTIAL EQUATIONS AND BOUNDARY VALUE PROBLEMS
(3,3)
Prerequisites: 50:
640: 363-364.
An advanced course
in methods of applied mathematics. Covers differential equations, orthogonal
functions, Sturm-Liouville boundary value problems, Green's functions,
variational methods, and other topics.
50:
640: 465. INTRODUCTION TO THE FUNDAMENTALS OF MATHEMATICS (3) Prerequisite:
Permission of instructor.
Selected topics from
the different areas of mathematics.
50:
640: 472. SPECIAL FUNCTIONS (3)
Prerequisite: 50:
640: 314.
Theory and applications
of functions frequently used in modern analysis such as the gamma function,
delta function, Green's functions, Legendre functions, Bessel functions,
Schwarz distributions, and others.
50:
640: 477-478. MATHEMATICAL THEORY OF PROBABILITY (3,3)
Prerequisites: 50:
640: 121 and 50: 960: 336 or permission of instructor.
Mathematical theory
of discrete and continuous probabilities.
50:
640: 491,492. MATHEMATICS SEMINAR I, II (3,3)
Prerequisite: Permission
of instructor.
Members of the seminar
present individually developed reports on topics of mathematical interest.
50: 640: 493-494. INDIVIDUAL STUDY IN MATHEMATICS (BA, BA)
50: 640: 495-496. HONORS PROGRAM IN MATHEMATICS (3,3)
50:
640: 497. VISUALIZING MATHEMATICS BY COMPUTER (3)
Prerequisites: 50:
640: 121, 122, 221, or permission of instructor. Recommended also
for students majoring in computer science as an elective.
A comprehensive introduction
to symbolic computational packages and scientific visualization through
examples from calculus and geometry. Covers 2-D, 3-D, and animated computer
graphics using Maple, Mathematica, and Geomview. No programming knowledge
required.
50:
640: 498. COMPUTATIONAL MATHEMATICS (3)
Prerequisite: 50:
640: 250 or permission of instructor. Alternate substitute for 50:
640: 356. Recommended also for students majoring in computer science as
an elective.
Designed to emphasize
the computational aspect of number theory. The most important topics to
treat are the prime numbers, pseudo primes, and their applications, especially
cryptography; prime factorization of composite numbers via several different
methods explored. Computer simulation emphasized.
50:
640: 499. MATHEMATICS ON THE WEB (3)
Prerequisites: 50:
640: 121, 122, 221, 250, or permission of instructor. Recommended also
for students majoring in computer science as an elective.
Designed to get acquainted
with using the World Wide Web for finding mathematical information and
communicating mathematics.
Courses (Statistics 960)
50:
960: 183. ELEMENTARY APPLIED STATISTICS (R) (3)
No prerequisite beyond
the usual three years of high school mathematics. Credit will not be given
for both this course and 50: 830: 215.
Frequency distribution,
graphical representations, measures of central tendency and variability,
elements of probability, the normal curve and its applications, sample
versus population, estimating and testing hypotheses, regression and correlation
analysis, nonparametric tests. Emphasis on applications.
50:
960: 283. INTRODUCTION TO STATISTICS I (R) (3)
Prerequisite: 50:
640: 121 or 130. Intended primarily for business majors and information
systems/ computer science majors.
Elementary course
in the principles and methods of statistics. Topics include measures of
central tendency and dispersion, probability theory, random variables and
probability distribution, binomial and normal distributions, central limit
theorem, confidence intervals, and testing of hypotheses on mean( s) and
proportion( s).
50:
960: 284. INTRODUCTION TO STATISTICS II (R) (3)
Prerequisite: 50:
960: 283. Intended primarily for business majors and information systems/
computer science majors.
A second introductory
statistics course. Emphasizes the application of statistical techniques
to data analysis. Topics include analysis of variance, nonparametric statistics,
simple linear regression, correlation, multiple regression, time series,
and index numbers.
50:
960: 336. APPLIED STATISTICS (3)
Prerequisite: 50:
640: 122. Intended primarily for applied mathematics majors but open to
all qualified students. Descriptive statistics, probability,
random variables, probability distributions, estimation and tests of hypotheses,
regression and correlation analysis. Emphasis on applications of these
techniques to problems in the biological, physical, and social sciences.
50:
960: 337. MANAGERIAL STATISTICS (INTERMEDIATE) (3)
Prerequisite: 50:
960: 283 or permission of instructor.
An intermediate course
oriented to business and managerial decisions and research in social sciences.
Statistical decision making, a priori and a posteriori probabilities, quality
control sampling, power curve solutions, sequential decisions, and research
design. Design of sample surveys and study of replicated sampling plans.
50:960:340
SPECIAL TOPICS IN STATISTICS (3)
Prerequisite: 50:
960: 284.
Aimed at students
with any major who want to go beyond the first two statistics courses.
Instructor will provide proper description.
50:960:384
STATISTICAL DATA ANALYSIS (3)
Prerequisite: 50:
960: 284.
Aimed at students
who want to go beyond the first two statistics courses. Application of
statistical techniques to analyze data. Topics include correlation and
regression analysis, regression diagnostics, model building, design of
experiments, categorical data analysis. Use of computer packages for visual
analysis and interpretation of data.
50:960:390.
INTRODUCTORY COMPUTING FOR STATISTICS (1)
Prerequisite: 50:
960: 283 and Corequisite (or Prerequisite): 50: 960: 284.
Aimed at students
who want to learn statistical computing along with or after the second
statistics course. Purpose of the course is to introduce statistical computing
using packages (like Excel, SAS, etc.). It includes computing basic univariate
statistics, generating random numbers, computing point estimates and confidence
interval, testing of hypothesis, basic ANOVA and regression.
50:
960: 452. INTRODUCTION TO BIOSTATISTICS (3)
No prerequisite beyond
the usual three years of high school mathematics.
Introduction to the
principles and methods of statistical inference for advanced undergraduate
and graduate students in biological science. Topics include discussion
of random variables, probability distributions, population, sample, measures
of central tendency and dispersion, point and interval estimation, testing
hypothesis, two-sample comparison, analysis of variance, linear regression
and correlation model, and nonparametric methods. Emphasizes appli-cations
of statistical principles and analyses for biological science.
50:960:467
INTRODUCTION TO APPLIED MULTIVARIATE ANALYSIS (3)
Prerequisite: 50:
960: 284.
Aimed at students with any
major who want to go beyond the first two statistics courses. Introduction
to applied multivariate analysis through multivariate normal distribution.
Topics include comparison of mean vector, multiple linear regression, discriminant
analysis, principal components, factor analysis, and other applied multivariate
topics. Use of statistical packages to perform all the multivariate computation
and its interpretation.
50:
960: 476. INTRODUCTION TO SAMPLING (3)
Prerequisite: 50:
960: 283 or 50: 960: 336 or permission of instructor.
Application of the
principles of sampling to economic procurement or assessment of data. Introduction
to various sampling procedures. Emphasis on the design and control phases
of investigation. Applications of the techniques to large-scale surveys,
accounting and auditing, and operations research.
50:
960: 481, 482. MATHEMATICAL THEORY OF STATISTICS (3,3)
Prerequisite: First
course in calculus or permission of instructor.
First term:
theory of probability, discrete and continuous probability distributions,
introduction to statistical inference.
Second term: further
study of distribution functions, correlation and regression, analysis of
variance and design of experiments, nonparametric methods, sequential sampling.
50:
960: 483. STATISTICAL QUALITY CONTROL (3)
Prerequisite: 50:
960: 283 or permission of instructor.
Basic course in modern
statistical quality control. Statistical measures, histogram analysis,
construction and analysis of control charts for variables and attributes,
use of Dodge-Roming and military standards acceptance sampling plans, statistical
aspects of tolerances.
50:960:484
STATISTICAL COMPUTING BY SAS (3)
Prerequisite: 50:
960: 283 and Corequisite (or Prerequisite): 50: 960: 284.
Aimed at students
who want to learn statistical computing along with or after the second
statistics course. Topics include introduction to SAS for reading data,
creating datasets and handling other data steps. Using SAS to perform basic
regression and model building techniques. Carrying out ANOVA procedures
for different design of experiments. Exposure to basic analysis of categorical,
time series and other types of data.
50:
960: 485-486. NUMBER PROBLEMS IN MATHEMATICAL THEORY OF STATISTICS (2,2)
To be used as laboratory
in conjunction with 50: 960: 481-482.
Numerical problems
applied to data in student's field of study where possible. Emphasis on
application of mathematical statistical distributions and methods.
50:
960: 487-488. INTRODUCTION TO OPERATIONS RESEARCH (3,3)
Prerequisites: 50:
960: 283,284 or permission of instructor.
A two-term introduction
to techniques of operations research involved in construction and solution
of models in inventory, linear programming, nonlinear programming, queuing,
sequencing, network, replacement, reliability, Markov chains, and competitive
problems.
50:
960: 490. EXPERIMENTAL DESIGN AND ANALYSIS (3)
Prerequisites: 50:
960: 283,284 or permission of instructor.
An advanced course
in statistics with applications in all fields of study. Analysis of variance
and covariance, experimental framework and layout, simple randomized designs,
randomized blocks. Latin squares, Graeco-Latin squares, factorials, balanced
and partially balanced designs, gains in precision and estimation.
50:
960: 495. INDEPENDENT STUDY IN STATISTICS (3)
Prerequisites: 50:
960: 283,284 and permission of instructor.
Intended for students
who want to concentrate on special methods of statistical analysis and
their applications to real world problems.
50:
960: 496. INDEPENDENT STUDY IN OPERATIONS RESEARCH (3)
Prerequisites: 50:
960: 487-488 and permission of instructor.
Intended to meet the
needs of students who wish to study special techniques of operations research
beyond the level of 50: 960: 487-488, or their applications to real world
problems.