*Note: *Some upper-level courses may be given in alternate years. Check with department advisers.

*New: * Changes to Remedial Math Policy at Rutgers University-Camden (3/29/2021).

## Foundational Courses

**( NO LONGER OFFERED AS OF FALL 2021) 50:640:041. Elementary Algebra (non-credited)**

*For students who do not have the usual background in mathematics for college admission.*

This course is designed to prepare students for 50:640:042 as part of a two semester sequence in pre-college algebra. Topics include: operations with real numbers, arithmetic and algebraic expressions and equations, coordinate geometry, systems of linear equations, inequalities, polynomials, and applications.

**( NO LONGER OFFERED AS OF FALL 2021) 50:640:042. Intermediate Algebra (non-credited)**

*Prerequisite: 50:640:041 or placement by Basic Skills Test.*

A review of pre-college algebra designed to prepare students for introductory courses in mathematics such as 50:640:106, 50:640:113, or 50:640:115. Topics include: arithmetic and algebraic expressions and equations, coordinate geometry, systems of linear equations, inequalities, polynomials, radicals, rational expressions and equations, quadratic equations, parabolas, and applications.

**( NO LONGER OFFERED AS OF FALL 2021) 50:640:043. Accelerated Elementary and Intermediate Algebra (non-credited)
**This course is a combination of both 50:640:041 and 50:640:042 into a single accelerated semester. All material from 50:640:042 is covered as well as a review of material from 50:640:041. This course satisfies the same prerequisites as 50:640:042 and is designed to prepare students for introductory courses in mathematics such as 50:640:106, 50:640:113, or 50:640:115. Topics include: operations with real numbers, arithmetic and algebraic expressions and equations, coordinate geometry, systems of linear equations, inequalities, polynomials, radicals, rational expressions and equations, quadratic equations, parabolas, and applications.

**50:640:103. Introduction to Mathematics for Liberal Arts (R) (4)**

*Prerequisite*: Mathematics Placement Examination.

This course introduces students to topics in mathematics and statistics, including: mathematics of elections, power, appointment, touring, networks, and scheduling; growth models; financial math; surveys and polls; graphs and charts; probability; and statistics. It incorporates lab sessions for arithmetic. This course satisfies the LQR, MAT, and QNT requirements. This course is a terminal course and is intended for students who do not need to take any further math courses as part of their program requirements. Students who plan to take additional courses in mathematics should take 640:104, 640:113, or 640:115 instead.

NOTE: Students interested in applying for the business school should NOT take this course if they anticipate taking Precalculus for Business and Economics (640:113). This course (640:103) does NOT count as a prerequisite for ANY further math course.

**50:640:104. Introduction to College Algebra for Business and Science (R) (4)***
Prerequisite*: Mathematics Placement Examination.

A review of algebra intended to prepare the student for Pre-Calculus. Topics include: solving linear equations and inequalities, equations and graphs of lines and conic sections, polynomials, exponents, factoring, rational expressions and equations, completing the square, quadratic equations, and radicals. This course satisfies the LQR, MAT, and QNT requirements. It is intended for students majoring or planning to major in business or the sciences who will need to take at least 640:113 or 640:115.

**50:640:106. An Introduction to Mathematical Thought (R) (3)
**

*Prerequisite: 50:640:042, 50:640:043, or proper placement.*

**A survey of mathematical concepts. This course satisfies the Logical and Quantitative Reasoning General Education requirement. Topics include: logic, set theory, numeration systems, number theory, operations with real numbers, functions, geometry, and graph theory.**

**50:640:108. Numbers and Beyond (R) (3)
**

*Prerequisite: 50:640:042, 50:640:043, or proper placement.*

A survey of mathematical concepts. This course satisfies the Logical and Quantitative Reasoning General Education requirement. Topics include: logic, set theory, numeration systems, number theory, operations with real numbers, functions, probability, and graph theory.

**50:640:110. The Joy of Math (R) (3)
**

*Prerequisite: 50:640:042, 50:640:043, or proper placement.*

**This course aims to explain mathematical ideas gently, clearly and with abundance of examples, hands-on activities, images and clips to attract the attention of a big audience. The course satisfies Gen Ed requirement for Logic and Quantitative Reasoning and has an Engaged Civic Learning component.**

**50:640:113. Precalculus for Business and Economics (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 non-required preparatory course for those students who must take 50:640:118.*

A study of real numbers with regard to algebraic operations and order properties. Introduction to complex numbers and logarithmic and exponential functions.

**50:640:115. Precalculus College Mathematics (R) (4) **

*Prerequisite: 50:640:042 or appropriate score on the Mathematics Placement Examination. Credit not given for both this course and 50:640:113. A non-required preparatory course for those students who must take 50:640:121-122.*

This is a 4-credit preparatory course for the Calculus sequence. It provides a study of functions, with special emphasis on polynomial, rational, exponential, logarithmic, and trigonometric functions.

*Course objectives*: By the end of this course, students will be able to

- Quickly recall and apply basic algebra skills.
- Identify functions algebraically and graphically, using the definition of a function, basics of functions and their graphs, function operations, and function transformations.
- Understand the basics of limits to help with the beginning of the Calculus sequence.
- Recognize various types of functions, analyze their behavior, and use their properties to solve equations and application problems.
- Understand trigonometry through trigonometric functions, right triangle trigonometry, and the unit circle.

**50:640:116. Elements of Calculus (R) (3) **

*Prerequisite: 50:640:113 or 115. 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, 118, or 121.*

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.

**50:640:118. Calculus for Business and Economics (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, 118, or 121.*

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.

**50:640:120. Math and Music (R) (3)
**

*Prerequisite: 50:640:113, 50:640:115, or appropriate score on the Mathematics Placement Examination.*

This course introduces the students to the mathematics behind aspects of music theory, with focus on Fourier’s theory of harmonic analysis. Topics include: overview of Euclid’s Elements and Pythagoras’ theory of numbers and music; overview of Newton’s Principia; mathematical concepts such as groups, function, limit, and derivatives; and applications of these concepts in music theory. This course satisfies the general education LQR requirement.

**50:640:121. Calculus I (R) (4) **

*Prerequisite: 50:640:115 or accepted score on the Mathematics Placement Examination. Credit will not, in general, be given for more than one of the courses 50:640:118, 121, or 123.*

This 4-credit course covers differential calculus of elementary functions of a single real variable including rational, trigonometric, exponential functions, and their inverses, as well as an introduction to integral calculus. Topics include: limits, continuity, derivatives, antiderivatives, definite integrals, and applications.

**50:640:122. Calculus II (R) (4)**

*Prerequisite: 50:640:121 or 50:640:123. Credit will not, in general, be given for more than one of the courses 50:640:122 or 124.*

This 4-credit course continues to study integral calculus of elementary functions of a single real variable. Topics include: evaluating integrals, applications of definite integrals, differential equations, sequences, and series.

**50:640:123. Active Calculus I (4)**

*Prerequisite: 50:640:115 or accepted score on the Mathematics Placement Examination. Credit will not, in general, be given for more than one of the courses 50:640:118, 121, or 123.
*

This 4-credit course covers differential calculus of elementary functions of a single real variable including rational, trigonometric, exponential functions, and their inverses, as well as an introduction to integral calculus. Topics include: limits, continuity, derivatives, antiderivatives, definite integrals, and applications. This course is equivalent to Calculus I (640:121), but uses active learning, with an emphasis on participation, group work, and developing theory.

**50:640:124. Active Calculus II (4)
**

*Prerequisite: 50:640:123 or 50:640:121. Credit will not, in general, be given for more than one of the courses 50:640:122 or 124.*

This 4-credit course continues to study integral calculus of elementary functions of a single real variable. Topics include: evaluating integrals, applications of definite integrals, differential equations, sequences, and series. This course is equivalent to Calculus II (640:122), but uses active learning, with an emphasis on participation, group work, and developing theory.

**50:640:182. Elements of Probability (R) (3)
**

*Prerequisite: 50:640:113 or appropriate score on the Mathematics Placement Examination.*

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.

**50:640:199. Exploring Careers in Mathematical Sciences (1)
**

*Prerequisite: None.*

This one credit course provides students a platform to explore potential career paths in mathematics, including computer programming, data analytics, education, and financial services. Class meetings will include presentations from the career center, from alumni, and from researchers, and discussions on those presentations. Students will learn practical skills, such as how to build a resume, apply for graduate schools, and look for internships. Students will gather information on what careers will be available, and of interest, to them if they graduate with a degree in mathematics.

**50:640:221. 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 proper 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: 50:640:121 or permission of instructor.*

Vector spaces, the calculus of matrices, and the theory of determinants.

**50:640:253. Linear Algebra with Applications (3) **

*Prerequisite:50:640:121 or permission of instructor.*

The topics from 640:250 plus applications using MatLab. Students may not receive credits for this course and 640:250. This is a required course for the B.S. program.

## Upper-Level Courses

**50:640:300. Mathematical Reasoning with Proofs (3)
**

*Prerequisite: 50:640:121 and 122.*

Course develops two fundamental components of “writing mathematics”: reasoning (thinking about the proof) and writing (formulating and writing the ideas precisely using logical statements). Begins with illustrative examples and general guidelines.

**50:640:311-312. Introduction to Real Analysis 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; introduction to Lebesgue measure and integral.

**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. Probability and Stochastic Processes (3)**

*Pre- or co-requisites: 50:640:122, or permission of instructor.*

This course provides a mathematically precise introduction to the basic concepts and essential introductory results of probability: a branch of math aimed at the description and study of random phenomena. The basic principles of stochastic modelling are described. Properties and applications of some standard stochastic models are analyzed. The concepts of conditional probabilities and independence are presented. The expectation and variance of random variables and their properties are discussed. Two fundamental limit theorems for long-time averages of independent, identically distributed random variables are stated and proven. The course concludes with an introduction to Markov chains and their long-run behavior.

**50:640:351-352. Introduction to Modern Algebra (3,3) **

*Prerequisite: 50:640:250, 50:640:300, or permission of instructor.*

The study of groups, rings, field, and linear spaces.

**50:640:356. Theory of Numbers (3)**

*Prerequisite: 50:640:122, 50:640:250/50:640:253, or permission of instructor.*

Properties of the natural numbers, simple continued fractions, congruences, and Elementary arithmetical functions.

**50:640:357. Introduction to Computational Mathematics (3)
**

*Prerequisites: 50:640:221, 50:640:250/50:640:253, or permission of instructor.*

This course introduces students to numerical techniques for solving mathematical problems on a computer: the IEEE internal representation of floating point numbers, interpolation, root finding, numerical integration, numerical differentiation, optimization.

**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.*

This course 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.

**50:640:375. 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)**

**50:640:403. Introduction to Complex Analysis (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.

**50:640:427. 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: 50:640:221, or 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:50:640:300, 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: 50:640:300, or permission of instructor.*

A study of the standard topics of the set theoretic topology.

50:640:450 Advanced Linear Algebra (3)

Prerequisite: 50:640:250/253, 50:640:300, or permission of instructor

Continuation of 50:640:250/253. Abstract vector spaces, linear transformations, inner product spaces, diagonalization, singular value decomposition, Jordan canonical form, numerical techniques and applications.

50:640:463-464. Applied Partial Differential Equations (3,3)

*Prerequisites: 50:640:221, 50:640:314, or permission of instructor.*

An advanced course in methods of applied mathematics. It covers partial differential equations such as the heat equation, wave equation, and Laplace’s equation; Fourier and Laplace transforms; orthogonal systems; Sturm-Liouville boundary value problems; separation of variables; Green’s functions; variational methods; and applications to life and physical sciences.

**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. Advanced Computational Mathematics (3)
**

*Prerequisites: 50:640:221, 50:640:250/50:640:253, 50:640:314, 50:640:357, or permission of instructor.*

This course covers numerical techniques for solving scientific problems with aid of a computer. Topics include: Numerical linear algebra, in particular numerical solution of linear systems of equations and the algebraic eigenvalue problem, and numerical solution of initial and boundary value problems of differential equations.

**50:640:499. Data Visualization (3)**

*Prerequisite: 50:640:250/50:640:253, or permission of instructor.
*This is a one-semester introduction to data visualization techniques. Students will learn and work through the data science pipeline, focusing on how to effectively and efficiently transform and visualize their data. Techniques will be applied to produce publication quality graphics, as well as interactive tools for exploratory analysis. Mathematical techniques for transforming data to address common data problems in today’s industries will be covered. The Python programming language along with popular data science packages are used extensively.

## Statistics Courses

**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.

**50:960:185. Introduction to Data Science (R) (3) **

No prerequisite beyond the usual three years of high school mathematics. This course develops the students’ inferential thinking and computational abilities and enables them to communicate and collaborate with data scientists effectively. The class consists of five main components: data structures, data wrangling, data mining, inferential thinking and statistical computations.

**50:960:283. Introduction to Statistics I (R) (3) **

*Prerequisite: 50:640: 113 or 115. 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 applications 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 data sets 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 Resarch (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.

**50:960:489.** **Statistical Models (3)**

*Prerequisite: 50:640:331.*

Introduction to multiple linear regression and its diagnostics, estimation, and testing in regression. Analysis of variance models (ANOVA), regularized regression:ridge and lasso, and generalized linear models.

**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.

**50:960:491** **Time Series and Forecasting (3)**

*Prerequisite: 50:960:489.*

Introduction to time series models, stationary processes, measure of dependence, tests of randomness, forecasting, estimation, model selection, ARIMA and ARMA models, and bootstrapping and smoothing.

**50:960:492** **Actuarial Models (3)**

*Prerequisite: 50:960:489.*

Distribution theory and its convolution, application to loss models, failure times and censored data models, survival models:parametric and nonparametric, estimation, and model building.

**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.