Rutgers, The State University of New Jersey
Undergraduate–Newark
 
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About the University
Undergraduate Education in Newark
Liberal Arts Colleges
Admission to the Liberal Arts Colleges
Newark College of Arts and Sciences
University College–Newark
Academic Programs and Courses
Availablity of Courses, Majors, and Minor Programs
Course Notation Information
Academic Foundations 003
African American and African Studies 014
Allied Health Technologies 045
American Studies 050
Ancient and Medieval Civilizations 060
Anthropology 070
Arabic 074
Art, Design, and Art History (080; 081; 082; 083; 085)
Biological Sciences
Chemistry 160
Chinese 165
Clinical Laboratory Sciences 191
Computer Science 198
Earth and Environmental Sciences (Geology 460)
Economics 220
Urban Education 300
English (350 and 352)
English: Composition and Writing 355
Environmental Sciences 375
French 420
Geoscience Engineering 465
Greek 490
History (History 510, American 512)
Honors 525
International Affairs
Italian 560
Japanese 565
Journalism and Media Studies 086
Korean 574
Latin 580
Legal Studies
Linguistics 615
Mathematics 640
Major Requirements: Mathematics Major (NCAS)
Major Requirements: Applied Mathematics
Minor Requirements: Mathematics
Teacher Certification
Courses (Mathematics 640)
Medical Technology 660
Microbiology
Music 087
Persian 685
Philosophy (Philosophy 730, Applied Ethics 733)
Physics 750
Political Science 790
Portuguese and Lusophone World Studies 812
Psychology 830
Religious Studies
Russian 860
Slavic Literature 861
Social Work 910
Sociology 920
Spanish 940
Theater 088
Urban Studies 975
Video Production 089
Women's Studies 988
Administration and Faculty
Consortium with New Jersey Institute of Technology
College of Nursing
Rutgers Business School: Undergraduate–Newark
School of Criminal Justice
School of Public Affairs and Administration
General Information
Divisions of the University
Camden Newark New Brunswick/Piscataway
Catalogs
  Newark Undergraduate Catalog 2011–2013 Liberal Arts Colleges Academic Programs and Courses Mathematics 640 Courses (Mathematics 640)  

Courses (Mathematics 640)

21:640:038 Intermediate Algebra Intensive (Noncredit) Prerequisite: Placement by examination. Corequisite: 21:640:104.
21:640:104 Intermediate Algebra Intensive (3) This course is intended to give students the necessary numerical and algebraic skills to allow for success in subsequent courses requiring a solid foundation in quantitative reasoning. The topics contained in this course include numerical systems such as the integers and the rational numbers (fractions), variable expressions, equations and applications, graphing simple equations, polynomials, and factoring. Prerequisite: Placement by examination. Corequisite: 21:640:038.
21:640:105 Intermediate Algebra (3) This course is intended to give students the necessary numerical and algebraic skills to allow for success in subsequent courses requiring a solid foundation in quantitative reasoning. The topics contained in this course include numerical systems such as the integers and the rational numbers (fractions), variable expressions, equations and applications, graphing simple equations, polynomials, and factoring. Prerequisite: Placement by examination.
21:640:106 Mathematics for the Liberal Arts (3) Fundamental ideas of mathematics, selected from graph theory, game theory, mathematical logic, number theory, geometry, probability, and statistics. Prerequisites: 21:003:102 or 21:300:102 or 21:640:102 or 21:640:104 or placement by examination. Intended for students in a liberal arts major who do not plan to enroll in additional courses in mathematics. Students who have passed college algebra (107, 108, or 109), or any other higher level math course cannot receive degree credit for this course.
21:640:107 College Algebra for Humanities (3) This course has been designed for students who intend to major or minor in one of the following subjects: humanities, social sciences, criminal justice, nursing, or public administration. The course covers functions and operations of functions, operations on polynomials, fractions, solution of linear and quadratic equations and inequalities, graphing of linear and quadratic functions, solution of word problems, elementary probability, and statistics. Prerequisites: 21:003:102 or 21:300:102 or 21:640:102 or 21:640:104 or 21:640:105 or placement by examination.
21:640:108 College Algebra for Business (3) This course has been designed for students who intend to major or minor in business. The course covers functions and operations of function, operations on polynomials, fractions, solution of linear and quadratic equations and inequalities, graphing of linear and quadratic functions, solution of word problems, functions, inverse functions, systems of equations, algebra of matrices. Prerequisites: 21:003:102 or 21:300:102 or 21:640:102 or 21:640:104 or 21:640:105 or placement by examination.
21:640:109 College Algebra for Physical Sciences (3) This course has been designed for students who intend to major or minor in one of the physical sciences, mathematics, or economics. The course covers functions and operations of functions, operations on polynomials, fractions, solution of linear and quadratic equations and inequalities, graphing of linear and quadratic functions, solution of word problems, functions, polynomial and rational functions, inverse functions, systems of linear equations, algebra of matrices, and series. Prerequisites: 21:003:102 or 21:300:102 or 21:640:102 or 21:640:104 or 21:640:105 or by placement by examination.
21:640:114 Precalculus (3) Algebraic, rational, trigonometric, logarithmic, and exponential functions; functions and inverse functions; solutions of nonlinear inequalities; advanced factoring techniques. Prerequisite: 21:640:112 or 113, or placement by examination. Intended for students who plan to enroll in additional courses in mathematics.
21:640:119 Basic Calculus (3) Intuitive approach to calculus, with emphasis on applications, differential and integral calculus, and multivariable calculus. Prerequisite: 21:640:112 or 113, or placement by examination. Credit not given for both 21:640:119 and 135. Intended for students majoring in information systems, business, social science, or the liberal arts.
21:640:135 Calculus I (4) Functions, limits, continuity, the derivative, rules of differentiation, exponential, log, trigonometric, and inverse trigonometric functions, applications, definite and indefinite integration, the fundamental theorems of calculus, and simple substitution. Prerequisite: 21:640:114 or placement by examination. Credit not given for both 21:640:119 and 135.
21:640:136 Calculus II (4) Applications of the integral, volumes and arc length, exponential and trig functions revisited, techniques of integration, L'Hospital's Rule, numerical integration, improper integrals, sequences and series, Taylor's Theorem, and polar coordinates. Prerequisite: 21:640:135 or 155.
21:640:155-156 Honors Calculus (4,4) These courses will rigorously cover the theory and applications of differential and integral calculus. Substantially more material with deeper applications will be covered than in the regular calculus sequence 21:640:135-136. Prerequisite: Invitation by department based on placement exam. Open to all majors.
21:640:211     Statistics (3) Principles, methods, and application of statistical methodology; includes frequency distributions, measures of central tendency and dispersion, simple probability, sampling, regression and correlation analysis, curve fitting, and tests of significance. Applications to natural and social sciences. Prerequisite: Placement by examination or successful completion, with a grade of C or better, of one of the following courses: 21:640:103, 112 and 113, 107, 108, 109, or any other higher level mathematics course.
21:640:219 Basic Linear Algebra (3) Solving linear systems and Gauss-Jordan elimination; matrix algebra, determinants; vectors, affine transformations in the plane; applications to linear programming, economics, and computer graphics; eigenvalues and eigenvectors. Prerequisite: 21:640:119 or 135 or 155, or permission of instructor. Credit not given for both 21:640:219 and 350. Intended for students majoring in business, social science, information systems, or the liberal arts. Mathematics majors and minors cannot get credit for 21:640:219.
21:640:235 Calculus III (4) Introduction to vectors in the plane, solid analytic geometry, vectors in three dimensions, partial differentiation, multiple integrals, and applications. Prerequisite: 21:640:136 or 156.
21:640:237 Discrete Structures (3) Sets, relations, functions, graphs, trees, formal expressions, mathematical induction, and some algebraic structures; applications to probability and computer science; and enumerative problems in combinatorial analysis. Prerequisite: 21:640:119 or 135 or 155.
21:640:238 Foundations of Modern Mathematics (3) Basic concepts on which modern mathematics is founded; language and logical structure of mathematics; elementary set theory, including set operations, relations, and mappings; the structure of the real number system and elements of real analysis. Proof techniques are stressed. Prerequisite: 21:640:136 or 156, or permission of instructor.
21:640:311-312 Advanced Calculus I,II (3,3) A rigorous development of the calculus of functions of one or more real variables: topology of Euclidean space, limits and continuity, the derivative, the Riemann integral, the Lebesgue integral, and selected topics from Fourier series, transformations and implicit functions, and line and surface integrals. Prerequisites: 21:640:235, 238, and 350, or permission of instructor.
21:640:314 Elementary Differential Equations (3) Ordinary differential equations, including solution by series and their applications; emphasis on linear equations. Prerequisite: 21:640:136 or 156.
21:640:327 Probability and Statistics (3) Modern probability, statistics, and statistical inference; discrete and continuous distributions of random variables, statistical inference, hypothesis testing, linear regression, and correlation. Prerequisite: 21:640:119 or 135 or 155, or permission of instructor.
21:640:350 Linear Algebra (3) Row reduction, solving linear systems; vector spaces, subspaces, bases; linear transformations, images, and kernels; eigenvalues, eigenvectors, and diagonalization of matrices; applications to differential equations, computer graphics, and numerical calculation. Prerequisite: 21:640:136 or 156, or permission of instructor. Credit not given for both 21:640:219 and 350.
21:640:353 Theory of Equations (3) Algebraic equations, including methods of solving equations; introductory theory of solvability; tranformations; algebraic invariants; the fundamental theorem of algebra. Prerequisite: 21:640:350.
21:640:397,398 Mathematics Teaching Apprenticeship (3,3) Practice in the teaching of mathematics supervised by members of the faculty.
21:640:403 Introductory Theory of Functions of a Complex Variable (3) Analytic functions, Cauchy's integral theorem, contour integration, residues, series, and conformal mapping. Prerequisite: 21:640:311 or permission of instructor.
21:640:410 Vector Analysis (3) Vector algebra and vector calculus, including line and surface integrals and the theorems of Green, Gauss, and Stokes; applications to physics and geometry. Pre- or corequisite: 21:640:235 or permission of instructor.
21:640:423 Elementary Partial Differential Equations (3) Partial differential equations of science and engineering. Topics include initial and boundary value problems for parabolic, hyperbolic, and elliptic second-order equations. Stress on separation of variables, special functions, transform methods, and numerical techniques. Prerequisite: 21:640:314.
21:640:424 Operations Research (3) Major topics and techniques in operations research; topics chosen from transportation problems, scheduling problems, linear programming, dynamic programming, mathematical inventory theory, and game theory. Prerequisite: 21:640:235 or permission of instructor.
21:640:432 Introductory Differential Geometry (3) Differential geometry; curves in Euclidean 3-space; regular surfaces in space; parametrization of surfaces; first fundamental form for surfaces; Gauss map and second fundamental form; intrinsic geometry of surfaces; intrinsic geometry of manifolds. Prerequisites: 21:640:235, 238.
21:640:433 Projective Geometry (3) Projective and affine curves; polynomial rings; ideals; Hilbert's basis theorem; the nullstellungsatz; local rings; singularities. Prerequisite: 21:640:238.
21:640:435-436 Geometry I,II (3,3) Axiomatic systems, finite geometries, Euclidean geometry, and non-Euclidean geometry. Prerequisites: 21:640:235, 350.
21:640:441-442 Topology I,II (3,3) General topological spaces and continuous mappings; linear point set theory and plane point set theory; separation, connectedness, and compactness; localization; topological products and Tychonoff's theorem; metric spaces and isometrics. Prerequisite: 21:640:238 or permission of instructor.
21:640:451-452 Abstract Algebra I,II (3,3) Fundamental structures of algebra: groups, rings and ideals, fields, homomorphisms, isomorphisms, quotients, the fundamental theorem of finite abelian groups, group actions, the Sylow theorems, Euclidean and Unique Factorization Domains, splitting fields, ruler and compass constructions, and the fundamental theorem of Galois theory. Prerequisites: 21:640:238 and 350, or permission of the instructor.   
21:640:456 Theory of Numbers (3) Divisibility of integers; the series of primes; number-theoretic functions; continued fractions; congruences; diophantine equations; quadratic residues; the Pell equation. Prerequisite: 21:640:238 or permission of instructor.
21:640:473 Numerical Analysis (3) Error analysis; interpolation theory; numerical solution of equations; polynomial approximations; numerical differentiation and integration; solution of differential equations. Prerequisites: 21:198:101 and 21:640:136 or 156.
21:640:475-476 Applied Mathematics I,II (3,3) Fourier series and integrals; boundary value problems; matrices; finite differences; special functions; numerical methods. Prerequisites: 21:640:314 or permission of instructor.
21:640:477 Fundamental Mathematical Probability (3) Fundamentals of probability theory for discrete and continuous distributions; random variables and probability distributions; Bayes's theorem; the Bernoulli and Poisson distributions; central limit theorem; strong law of large numbers. Prerequisite: 21:640:136 or 156 or permission of instructor.
21:640:491,492 Mathematics Seminar (3,3) Selected topics in mathematics; individual study stressed. Prerequisite: Permission of instructor. Students may enroll multiple times.
21:640:493,494 Individual Studies in Mathematics (3,3) Individual studies of selected topics in mathematics. Prerequisite: Permission of instructor. Students may enroll multiple times.
 
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