# Mathematics Major, Statistics Concentration (B.S.) - Undergraduate - 2011 University Catalog

You are viewing the 2011 University Catalog. Please see the newest version of the University Catalog for the most current version of this program's requirements.

A minimum of 120 semester hours of coursework is required for the baccalaureate degree with a minimum 2.0 overall GPA, and a minimum 2.0 major GPA. However, more than 120 semester hours may be required depending upon the major field of study. In addition to the major requirement outlined below, all university students must fulfill the set of General Education requirements applicable to their degree (for further information, see General Education Requirements).

# STATISTICS CONCENTRATION

Complete 57 semester hours including the following 4 requirement(s):

1. ## MATHEMATICS CORE

Complete the following 5 courses:

 MATH 122 Calculus I 4 MATH 221 Calculus II 4 MATH 222 Calculus III 4 MATH 335 Linear Algebra 4 MATH 340 Probability 3
2. ## STATISTICS CONCENTRATION

Complete the following 2 requirements:

1. Complete the following 3 courses:

 MATH 469 Mathematical Modeling 3 STAT 330 Fundamentals of Modern Statistics I 3 STAT 443 Introduction to Mathematical Statistics 3
2. Complete 1 course from the following:

 STAT 441 Statistical Computing 3 STAT 442 Fundamentals of Modern Statistics II 3
3. ## MATHEMATICS ELECTIVES

Complete 15 semester hours from the following:

 MATH 320 Transitions to Advanced Mathematics 3 MATH 398 Vector Calculus 3 MATH 420 Ordinary Differential Equations 4 MATH 421 Partial Differential Equations 3 MATH 423 Complex Variables 3 MATH 425 Advanced Calculus I 3 MATH 426 Advanced Calculus II 3 MATH 431 Foundations of Modern Algebra 3 MATH 433 Theory of Numbers 3 MATH 436 Elements of Logic 3 MATH 450 Foundations of Geometry 3 MATH 451 Topology 3 MATH 460 Introduction to Applied Mathematics 3 MATH 463 Numerical Analysis 3 MATH 464 Operations Research I 3 MATH 465 Operations Research II 3 MATH 466 Mathematics of Finance I 3 MATH 467 Mathematics of Finance II 3 MATH 468 Fluid Mechanics 3 MATH 485 Applied Combinatorics and Graph Theory 3 MATH 487 Introduction to Mathematical Cryptography 3 MATH 490 Honors Seminar 3 MATH 495 Topics for Undergraduates 1-3 MATH 497 Research I 1-3 MATH 498 Research II 1-3 STAT 401 Applied Statistics for the Sciences 3 STAT 403 Techniques and Applications of Statistics 3 STAT 481 Introduction to Statistical Data Mining 3 STAT 487 Statistical Genomics 3 STAT 495 Topics in Statistical Science 1-3 STAT 497 Undergraduate Research in Statistical Science 1-3
4. ## COLLATERAL REQUIREMENTS

Complete the following 2 requirements:

1. Complete the following 2 courses:

 CMPT 183 Foundations of Computer Science I 3 CMPT 184 Foundations of Computer Science II 3
2. Complete 1 of the following sequences:

1. Complete 2 courses:

 PHYS 191 University Physics I 4 PHYS 192 University Physics II 4
2. Complete 2 courses:

 CHEM 120 General Chemistry I 4 CHEM 121 General Chemistry II 4
3. Complete 2 courses:

 BIOL 112 Principles of Biology I 4 BIOL 113 Principles of Biology II 4
4. Complete 2 courses:

5. Complete 3 courses:

 ECON 101 Principles of Economics: Macro 3 ECON 102 Principles of Economics: Micro 3 MGMT 231 Management Processes 3
6. Complete 3 courses:

 ACCT 201 Fundamentals of Financial Accounting 3 ACCT 202 Fundamentals of Managerial Accounting 3 MGMT 231 Management Processes 3

## Course Descriptions:

### ACCT201: Fundamentals of Financial Accounting

This is an introductory course in financial accounting from a user's perspective. The theoretical foundation and basic accounting terminology are addressed. The basic financial statements consisting of the balance sheet, income statement, statement of stockholder's equity and the statement of cash flows are presented and discussed. Financial statement analysis including ratios analysis will help students to make sound decisions as investors, creditors, and managers. (3 hours lecture.) 3 sh.

Prerequisites: ENWR 105 or HONP 100.

### ACCT202: Fundamentals of Managerial Accounting

This course introduces basic concepts of management accounting including cost classifications, product costing, cost-volume profit analysis, variable costing, operating budgeting, standards and performance evaluation, balance score card and non-routine decisions. The course will illustrate the use of accounting information by managers for internal decision-making purposes. (3 hours lecture.) 3 sh.

Prerequisites: ACCT 201.

### BIOL112: Principles of Biology I

Principles of Biology I involves the study of life from molecule to multicellular organism with focus on structure and function of cells, mechanisms of heredity and change, and the ways in which these processes shape higher levels of biological organization. This course is designed to fulfill the first core course requirement of the biology major. (3 hours lecture, 3 hours laboratory.) 4 sh.

Prerequisites: MATH 100 or a satisfactory score on the Math department's precalculus readiness test.

### BIOL113: Principles of Biology II

Principles of Biology II will provide an introductory level study of biodiversity and the origins of life, phylogenetic relationships among organisms, genetics, developmental biology, reproduction, the biology of populations and communities, and ecosystem processes. Meets Gen Ed 2002 - Interdisciplinary Core, Scientific Issues. (3 hours lecture, 3 hours laboratory.) 4 sh.

Prerequisites: MATH 100 or a satisfactory score on the Math department's precalculus readiness test.

### CHEM120: General Chemistry I

Introductory lecture and laboratory course for science majors, prerequisite for all advanced chemistry courses. Introduction to atomic and molecular structure, bonding, stoichiometry, states of matter, solutions, and selected topics in descriptive inorganic chemistry. Laboratory stresses techniques and data treatment and their use in examining chemical systems. (3 hours lecture, 3 hours lab.) 4 sh.

Prerequisites: One year of high school chemistry.

### CHEM121: General Chemistry II

Introductory lecture and laboratory course for science majors, prerequisite for all advanced chemistry courses. Introduction to thermochemistry, kinetics; general acid base, precipitation, redox equilibria, electrochemistry and selected topics in descriptive inorganic chemistry. Laboratory stresses techniques and data treatment and their use in examining chemical systems. (3 hours lecture, 3 hours lab.) 4 sh.

Prerequisites: CHEM 120 with a grade of C- or better.

### CMPT183: Foundations of Computer Science I

Basic theory of digital computers. Syntax and semantics of a programming language. Algorithms: logic, design, testing and documentation. (2 hours lecture, 2 hours lab.) 3 sh.

Prerequisites: MATH 100, MATH 112, MATH 114, MATH 116, MATH 122 or MATH 221.

### CMPT184: Foundations of Computer Science II

Continuation of CMPT 183. Algorithm development involving user functions; subroutines, recursions, structures file manipulation. (3 hours lecture.) 3 sh.

Prerequisites: CMPT 183.

### ECON101: Principles of Economics: Macro

A study of the American economy, analytically and institutionally; the achievement of an optimal allocation of resources, price stability, full employment level of national income and long term growth. Meets Gen Ed 2002 - Social Science, Social Science. (3 hours lecture.) 3 sh.

### ECON102: Principles of Economics: Micro

Organization and operation of the American economy for the production and distribution of goods and services. Pricing of products and factors of production in market situations varying from competition to monopoly. Resource allocation, price determination and behavior of the firm in the determination of quantity of output and the hiring of factors of production. Meets Gen Ed 2002 - Social Science, Social Science. (3 hours lecture.) 3 sh.

### MATH122: Calculus I

Limits, continuity; derivative and differentiation; applications of the derivative, maxima, minima, and extreme considerations; antiderivatives; Riemann integral. (4 hours lecture.) 4 sh.

Prerequisites: MATH 111 or MATH 112 or placement through the Montclair State University Placement Test (MSUPT) or a satisfactory score on department's Calculus Readiness Test. (Students who did not satisfy the course prerequisite at MSU and students who received a grade of D-, D, or D+ in the prerequisite course taken at MSU are required to demonstrate competency on the department's Calculus Readiness Test.)

### MATH221: Calculus II

Riemann integral applications, transcendental functions, techniques of integration, improper integrals, L'Hospital's rule, infinite series. (4 hours lecture.) 4 sh.

Prerequisites: MATH 122.

### MATH222: Calculus III

Vector algebra; partial differentiation, and extreme considerations; polar, cylindrical, and spherical coordinates, multiple integration; introduction to line integrals. (4 hours lecture.) 4 sh.

Prerequisites: MATH 221.

### MATH320: Transitions to Advanced Mathematics

This course will help students explore mathematics and make conjectures using technology. Students will enhance their understanding of mathematical models and to develop communication skills through the use of written reports and oral presentations of projects. The course content introduces students to difference equations, elementary linear algebra and ordinary differential equations. Further, the course will develop proof-writing skills and introduce students to the explore-conjecture-proof strategy. (3 hours lecture.) 3 sh.

Prerequisites: MATH 221.

### MATH335: Linear Algebra

The course content will cover the foundations of the algebra of vector spaces, matrix operations, matrix invertibility theorems, linear independence, span, basis, linear transformations, finite dimensional Hilbert Spaces, Gram-Schmidt process, projections, eigenvalues and eigenvectors, and applications. The focus of the course will be to develop advanced mathematical skills in reading and understanding abstract mathematical definitions, constructing examples, and developing mathematical proofs. Meets the University Writing Requirement for majors in Mathematics. (4 hours lecture.) 4 sh.

Prerequisites: MATH 222 or equivalent.

### MATH340: Probability

Chance and variability, elements of combinatorics, Bayes' theorem, random variables, binomial, poisson and normal distributions, applications to statistics. (3 hours lecture.) 3 sh.

Prerequisites: MATH 221.

### MATH398: Vector Calculus

Topics include the algebra of the differential and integral calculus; gradients, divergence and curl of a vector field, and integral theorems together with applications drawn from the physical sciences. (3 hours lecture.) 3 sh.

Prerequisites: MATH 222.

### MATH420: Ordinary Differential Equations

A course in the theory and applications of ordinary differential equations which emphasizes qualitative aspects of the subject. Topics include analytic and numerical solution techniques for linear and nonlinear systems, graphical analysis, existence-uniqueness theory, bifurcation analysis, and advanced topics. Prerequisite: MATH 335. (4 hours lecture.) 4 sh.

Prerequisites: MATH 335.

### MATH421: Partial Differential Equations

Partial differential equations arise in the mathematical modeling of many physical, chemical, and biological phenomena. They play a crucial role in diverse subject areas, such as fluid dynamics, electromagnetism, material science, astrophysics, financial modeling, and hydrogeology, for example. This course is an introduction to partial differential equations with emphasis on the wave, diffusion and Laplace equations. The focus will be on understanding the physical meaning and mathematical properties of solutions of partial differential equations. Methods of solutions include separation of variables using orthogonal series, transform methods, method of characteristics, and some numerical methods. (3 hours lecture.) 3 sh.

Prerequisites: MATH 420.

### MATH423: Complex Variables

This course is a study of the arithmetic and algebra of complex numbers, and an introduction to the differentiation and integration of complex functions. Topics include: rectangular and polar form of complex numbers, algebra of complex numbers, differentiation, Cauchy-Riemann equations, and contour integrals. (3 hours lecture.) 3 sh.

Prerequisites: MATH 335.

Properties of the real number system, limits, continuous functions, intermediate value theorem, derivative, mean value theorem, Riemann integral. (3 hours lecture.) 3 sh.

Prerequisites: MATH 335.

Functions of several variables, partial derivatives, Green's theorem, Stoke's theorem, divergence theorem, implicit function theorem, inverse function theorem, infinite series, uniform convergence. (3 hours lecture.) 3 sh.

Prerequisites: MATH 425.

### MATH431: Foundations of Modern Algebra

Fundamental concepts of algebra including groups, rings, integral domains and fields, with important examples. (3 hours lecture.) 3 sh.

Prerequisites: MATH 335.

### MATH433: Theory of Numbers

Properties of integers, congruences, quadratic reciprocity law, primitive roots, diophantine equations, continued fractions, algebraic numbers, lattice points and partitions. (3 hours lecture.) 3 sh.

Prerequisites: MATH 335.

### MATH436: Elements of Logic

Deduction, propositional functions, quantifiers, consistency, decision problems and Goedel's theorem. (3 hours lecture.) 3 sh.

Prerequisites: MATH 335.

### MATH450: Foundations of Geometry

Groups of transformations, an introduction to projective geometry. (3 hours lecture.) 3 sh.

Prerequisites: MATH 335.

### MATH451: Topology

Topological spaces, metric spaces, continuity, compactness, connectedness, and separability properties; topological generalizations of basic continuity theorems of advanced calculus. (3 hours lecture.) 3 sh.

Prerequisites: MATH 425.

### MATH460: Introduction to Applied Mathematics

This course is a survey of applied mathematical techniques, including such topics as control theory (feedback control systems, Nyquist and Popov plots, pole shifting, Laplace transforms) and classical boundary value problems (Sturm-Liouville equations with solution techniques involving Fourier series). Applications will use the theory of calculus of variations which includes the variational derivative, the general variation of a functional, variation in parametric form, and the invariance of the Euler's equations. Prerequisite: MATH 335. (3 hours lecture.) 3 sh.

Prerequisites: MATH 335.

### MATH463: Numerical Analysis

Finite differences, approximation theory, linear and non-linear equations, error analysis. (3 hours lecture.) 3 sh.

Prerequisites: MATH 222 and 335.

### MATH464: Operations Research I

Linear programming, transportation problem, assignment problem, duality, sensitivity analysis, network flows, dynamic programming, nonlinear programming, integer programming. (3 hours lecture.) 3 sh.

Prerequisites: MATH 335.

### MATH465: Operations Research II

Game theory, queuing models, inventory models, Markov processes, reliability theory and applications. (3 hours lecture.) 3 sh.

Prerequisites: MATH 335 and 340.

### MATH466: Mathematics of Finance I

Mathematical theory of interest rates, annuities, bond valuation, stock valuation, options, arbitrage, binomial trees, put-call parity, Black Scholes Model, Capital Asset Pricing Model (CAPM) and portfolio selection. (3 hours lecture.) 3 sh.

Prerequisites: FINC 321, MATH 340.

### MATH467: Mathematics of Finance II

Mathematical theory of forward/futures contract, hedging with futures, fixed income market analysis, duration, immunization, financial swaps, interest swaps, currency swaps, future options, Black Scholes Model, put-call parity, binomial trees, other options, and volatility. This course can be used as part of preparation for SOA/CASACT Actuarial Examinations, Course 2. (3 hours lecture.) 3 sh.

Prerequisites: MATH 466.

### MATH468: Fluid Mechanics

Mechanics of continuous media, liquids and gases; stress, viscosity, Navier-Stokes and Euler Equations, exact solutions, potential flow, circulation and vorticity, dimensional analysis and asymptotic models, boundary layers, stability theory and applications to industrial and environmental problems. Cross listed with PHYS 468. (3 hours lecture.) 3 sh.

Prerequisites: PHYS 210 or MATH 222.

### MATH469: Mathematical Modeling

The art of constructing mathematical models for "real world" problems, solving the model, and testing the accuracy of the model. Problems will be selected from business, science, computer science, and the social sciences. (3 hours lecture.) 3 sh.

Prerequisites: MATH 335, and MATH 340, and MATH 464 or STAT 330.

### MATH485: Applied Combinatorics and Graph Theory

Problem solving by counting, enumeration, and graph theory. Permutation, combinations, binomial coefficients, generating functions, and recurrence relations, partitions, inclusion-exclusion, Polya's formula, graph theoretic models, trees, circuits, networks, matching, and their applications to puzzles, games, tournaments, traffic patterns, transportation. (3 hours lecture.) 3 sh.

Prerequisites: MATH 340.

### MATH487: Introduction to Mathematical Cryptography

A modern introduction to the application of number theory, combinatorics and abstract algebra to cryptography. The mathematics of a broad range of current applications to security issues in industry and government will be covered. Use of Maple Computer Algebra System. (3 hours lecture.) 3 sh.

Prerequisites: MATH 335.

### MATH490: Honors Seminar

This course will concentrate on subject matter not usually covered within standard mathematics courses. A written and oral report are required. (3 hours seminar.) 3 sh.

Prerequisites: MATH 335 and departmental approval.

Study of advanced topics in undergraduate mathematics. May be repeated once for a maximum of 6.0 credits as long as the topic is different. () 1 - 3 sh.

Prerequisites: MATH 335 and departmental approval.

### MATH497: Research I

Individual research in a mathematical area agreed upon by the student and the instructor. The results of the research will be a basis of a seminar or colloquium to be given by the student. Students must not accumulate more than 6 credits total in courses MATH 497, 498. () 1 - 3 sh.

Prerequisites: MATH 335 and departmental approval.

### MATH498: Research II

Individual research in a mathematical area agreed upon by the student and the instructor. The results of the research will be a basis of a seminar or colloquium to be given by the student. Students must not accumulate more than 6 credits total in courses MATH 497, 498. () 1 - 3 sh.

Prerequisites: MATH 335 and departmental approval.

### MGMT231: Management Processes

To provide undergraduate students a review of classical and modern approaches to the managerial process as it relates to the manager's functions of planning, organizing, communication, motivation, leading, controlling, and managing change. Emphasizing new forces in the managerial environment such as workplace diversity and economic globalization, these reviews will be tied to the open-system model and the contingency approach as overall frameworks for understanding organizations and management. (3 hours lecture.) 3 sh.

Prerequisites: ENWR 105 or HONP 100.

### PHYS191: University Physics I

This one-semester calculus-based course including laboratory is a study of the principles of physics and some applications to society's problems. Topics covered include mechanics, thermodynamics, fluids, and harmonic motion. (3 hours lecture, 2 hours lab.) 4 sh.

Prerequisites: MATH 122 is prerequisite or co-requisite.

### PHYS192: University Physics II

Calculus-based course. Study of some principles of physics and some applications to society's problems. Topics include: wave motion, sound and noise pollution, optics, electricity, lasers, nuclear theory, radiation, nuclear reactors, waste disposal. (3 hours lecture, 2 hours lab.) 4 sh.

Prerequisites: MATH 221 is prerequisite or corequisite.

### STAT330: Fundamentals of Modern Statistics I

Displaying, describing and modeling data; arrangements for producting data; probability; methods for drawing conclusions from data: significance testing, confidence interval estimation, linear regression, analysis of variance. Examples from many disciplines including the social and natural sciences. Statistical software is used. (3 hours lecture.) 3 sh.

Prerequisites: MATH 221.

### STAT401: Applied Statistics for the Sciences

Organizing, displaying, and describing data; designing experiments; methods for drawing conclusions from data; significance testing, confidence intervals, linear regression, analysis of variance, chi-square tests of independence. Examples from disciplines in the natural and physical sciences. Statistical software is used. Not for Mathematics and Computer Science majors. (3 hours lecture.) 3 sh.

Prerequisites: MATH 111 or Math 112.

### STAT403: Techniques and Applications of Statistics

Statistical techniques for the social and behavioral sciences including estimation, tests of hypothesis, non-parametric statistics, regression and correlation. May not be taken for credit by mathematic majors. (3 hours lecture.) 3 sh.

Prerequisites: MATH 112.

### STAT441: Statistical Computing

This course is designed: (1) to acquaint students with the use of the computer in solving statistical problems, and (2) to develop intermediate level statistical methodology. Several statistical computing packages and the student's own programs will be utilized. (3 hours lecture.) 3 sh.

Prerequisites: STAT 330 or STAT 401 and computer experience.

### STAT442: Fundamentals of Modern Statistics II

Continuation of STAT 440. Principles of statistical inference, categorical data analysis, one and two-way anova, multiple linear regression, nonparametric methods, bootstrap methods. Examples from a wide variety of disciplines. Statistical software is used. (3 hours lecture.) 3 sh.

Prerequisites: STAT 330 or STAT 401 or equivalent.

### STAT443: Introduction to Mathematical Statistics

Develops statistical methods from probability theory. Topics discrete and continuous probability distributions, estimation, inference and hypothesis testing. (3 hours lecture.) 3 sh.

Prerequisites: MATH 340 and either STAT 330 or STAT 401.

### STAT481: Introduction to Statistical Data Mining

Introduction to the concepts and applications of a variety of data-mining methods. Data mining is the process of selecting, exploring, and modeling large amounts of data to uncover previously unknown patterns in the data. Statistical techniques covered include classification and regression trees, predictive modeling, and unsupervised learning. Hands-on applications to data sets from diverse fields. Statistical software is used. (3 hours lecture.) 3 sh.

Prerequisites: STAT 330 or STAT 401 or equivalent.

### STAT487: Statistical Genomics

Analysis of discrete data illustrated with genetic data on morphological characters, allozymes, restriction fragment length polymorphisms and DNA sequences. Maximum likelihood and Bayesian estimation including iterative procedures. Numerical resampling and bootstrapping. Development of statistical techniques for characterizing genetic disequilibrium and diversity. Locating genes with markers. Cross listed with Biology and Molecular Bioilogy BIOL 487. (3 hours lecture.) 3 sh.

Prerequisites: BIOL 380 and STAT 330 or STAT 401, or equivalent.

### STAT495: Topics in Statistical Science

Guided study of selected topics in statistical science such as exploratory data analysis, applied multivariate methods, statistical quality control, design of experiment. May be repeated once for a maximum of 6.0 credits. () 1 - 3 sh.

Prerequisites: STAT 330 or STAT 401 and department approval.

### STAT497: Undergraduate Research in Statistical Science

Individual research in an area of statistical science agreed upon by the student and instructor. The results of the research will be the basis of a seminar or colloquium to be given by the student. May be repeated five times for a total of six credits. Students must not accumulate more than six credits total in courses MATH 497, MATH 498, STAT 495, STAT 497. () 1 - 3 sh.

Prerequisites: STAT 442 and departmental approval.