Mathematics Major, Discrete Applied Mathematics Concentration (B.S.)  Undergraduate  2012 University Catalog
You are viewing the 2012 University Catalog. Please see the newest version of the University Catalog for the most current version of this program's requirements.
DISCRETE APPLIED MATH CONCENTRATION
Complete 57 semester hours including the following 4 requirement(s):

MATHEMATICS CORE
Complete the following 5 courses:
MATH 122 Calculus I (4 hours lecture) 4 MATH 221 Calculus II (4 hours lecture) 4 MATH 222 Calculus III (4 hours lecture) 4 MATH 335 Linear Algebra (4 hours lecture) 4 MATH 340 Probability (3 hours lecture) 3 
DISCRETE APPLIED MATH CONCENTRATION
Complete the following 5 courses:
MATH 320 Transitions to Advanced Mathematics (3 hours lecture) 3 MATH 464 Operations Research I (3 hours lecture) 3 MATH 465 Operations Research II (3 hours lecture) 3 MATH 469 Mathematical Modeling (3 hours lecture) 3 MATH 485 Applied Combinatorics and Graph Theory (3 hours lecture) 3 
MATHEMATICS ELECTIVES
Complete 15 semester hours from the following:

COLLATERAL REQUIREMENTS
Complete the following 2 requirements:

Complete the following 2 courses:
CMPT 183 Foundations of Computer Science I (2 hours lecture, 2 hours lab) 3 CMPT 184 Foundations of Computer Science II (3 hours lecture) 3 
Complete 1 of the following sequences:

Complete 2 courses:
PHYS 191 University Physics I (3 hours lecture, 2 hours lab) 4 PHYS 192 University Physics II (3 hours lecture, 2 hours lab) 4 
Complete 2 courses:
CHEM 120 General Chemistry I (3 hours lecture, 3 hours lab) 4 CHEM 121 General Chemistry II (3 hours lecture, 3 hours lab) 4 
Complete 2 courses:
BIOL 112 Principles of Biology I (3 hours lecture, 3 hours laboratory) 4 BIOL 113 Principles of Biology II (3 hours lecture, 3 hours laboratory) 4 
Complete 2 courses:
EAES 105 Physical Geology (3 hours lecture, 2 hours lab) 4 EAES 240 Historical Geology (3 hours lecture, 2 hours lab) 4 
Complete 3 courses:
ECON 101 Principles of Economics: Macro (3 hours lecture) 3 ECON 102 Principles of Economics: Micro (3 hours lecture) 3 MGMT 231 Management Processes (3 hours lecture) 3 
Complete 3 courses:
ACCT 201 Fundamentals of Financial Accounting (3 hours lecture) 3 ACCT 202 Fundamentals of Managerial Accounting (3 hours lecture) 3 MGMT 231 Management Processes (3 hours lecture) 3


Course Descriptions:
ACCT201: Fundamentals of Financial Accounting (3 hours lecture)
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 sh.
Prerequisites: ENWR 105 or HONP 100.
ACCT202: Fundamentals of Managerial Accounting (3 hours lecture)
This course introduces basic concepts of management accounting including cost classifications, product costing, costvolume profit analysis, variable costing, operating budgeting, standards and performance evaluation, balance score card and nonroutine decisions. The course will illustrate the use of accounting information by managers for internal decisionmaking purposes. 3 sh.
Prerequisites: ACCT 201.
BIOL112: Principles of Biology I (3 hours lecture, 3 hours laboratory)
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. 4 sh.
Prerequisites: MATH 100 or a satisfactory score on the Math department's precalculus readiness test.
BIOL113: Principles of Biology II (3 hours lecture, 3 hours laboratory)
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. 4 sh.
Prerequisites: MATH 100 or a satisfactory score on the Math department's precalculus readiness test.
CHEM120: General Chemistry I (3 hours lecture, 3 hours lab)
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. 4 sh.
Prerequisites: Satisfactory score on the Mathematics readiness test OR MATH 100 with a grade of C or better. Satisfactory score on the Chemistry/Biochemistry Department readiness test OR CHEM 113 with a grade of C or better.
CHEM121: General Chemistry II (3 hours lecture, 3 hours lab)
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. 4 sh.
Prerequisites: CHEM 120 with a grade of C or better.
CMPT183: Foundations of Computer Science I (2 hours lecture, 2 hours lab)
Basic theory of digital computers. Syntax and semantics of a programming language. Algorithms: logic, design, testing and documentation. 3 sh.
Prerequisites: MATH 100, MATH 112, MATH 114, MATH 116, MATH 122 or MATH 221.
CMPT184: Foundations of Computer Science II (3 hours lecture)
Continuation of CMPT 183. Algorithm development involving user functions; subroutines, recursions, structures file manipulation. 3 sh.
Prerequisites: CMPT 183.
EAES105: Physical Geology (3 hours lecture, 2 hours lab)
Materials of the earth; landforms and structures; the processes and agents responsible for their formation and modification. Modern tectonic concepts. Topographic and geologic maps. Required field trips. Not open to students who have had Principles of Geology. Meets Gen Ed 2002  Natural/Physical Science Laboratory. Previous course GEOS 112 effective through Spring 2012. 4 sh.
EAES240: Historical Geology (3 hours lecture, 2 hours lab)
Geological history of the earth; the evolution of North America in terms of the changing geography, climate, and plant and animal life as interpreted from the rock and fossil record. Required field trips. Meets Gen Ed 2002  Natural/Physical Science Laboratory. Previous course GEOS 114 effective through Spring 2012. 4 sh.
Prerequisites: EAES 101, EAES 105, EAES 107 or EAES 250.
ECON101: Principles of Economics: Macro (3 hours lecture)
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 sh.
ECON102: Principles of Economics: Micro (3 hours lecture)
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 sh.
MATH122: Calculus I (4 hours lecture)
Limits, continuity; derivative and differentiation; applications of the derivative, maxima, minima, and extreme considerations; antiderivatives; Riemann integral. 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 (4 hours lecture)
Riemann integral applications, transcendental functions, techniques of integration, improper integrals, L'Hospital's rule, infinite series. 4 sh.
Prerequisites: MATH 122.
MATH222: Calculus III (4 hours lecture)
Vector algebra; partial differentiation, and extreme considerations; polar, cylindrical, and spherical coordinates, multiple integration; introduction to line integrals. 4 sh.
Prerequisites: MATH 221.
MATH320: Transitions to Advanced Mathematics (3 hours lecture)
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 proofwriting skills and introduce students to the exploreconjectureproof strategy. 3 sh.
Prerequisites: MATH 221.
MATH335: Linear Algebra (4 hours lecture)
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, GramSchmidt 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 sh.
Prerequisites: MATH 222 or equivalent.
MATH340: Probability (3 hours lecture)
Chance and variability, elements of combinatorics, Bayes' theorem, random variables, binomial, poisson and normal distributions, applications to statistics. 3 sh.
Prerequisites: MATH 221.
MATH398: Vector Calculus (3 hours lecture)
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 sh.
Prerequisites: MATH 222.
MATH420: Ordinary Differential Equations (4 hours lecture)
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, existenceuniqueness theory, bifurcation analysis, and advanced topics. Prerequisite: MATH 335. 4 sh.
Prerequisites: MATH 335.
MATH421: Partial Differential Equations (3 hours lecture)
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 sh.
Prerequisites: MATH 420.
MATH423: Complex Variables (3 hours lecture)
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, CauchyRiemann equations, and contour integrals. 3 sh.
Prerequisites: MATH 335.
MATH425: Advanced Calculus I (3 hours lecture)
Properties of the real number system, limits, continuous functions, intermediate value theorem, derivative, mean value theorem, Riemann integral. 3 sh.
Prerequisites: MATH 335.
MATH426: Advanced Calculus II (3 hours lecture)
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 sh.
Prerequisites: MATH 425.
MATH431: Foundations of Modern Algebra (3 hours lecture)
Fundamental concepts of algebra including groups, rings, integral domains and fields, with important examples. 3 sh.
Prerequisites: MATH 335.
MATH433: Theory of Numbers (3 hours lecture)
Properties of integers, congruences, quadratic reciprocity law, primitive roots, diophantine equations, continued fractions, algebraic numbers, lattice points and partitions. 3 sh.
Prerequisites: MATH 335.
MATH436: Elements of Logic (3 hours lecture)
Deduction, propositional functions, quantifiers, consistency, decision problems and Goedel's theorem. 3 sh.
Prerequisites: MATH 335.
MATH450: Foundations of Geometry (3 hours lecture)
Groups of transformations, an introduction to projective geometry. 3 sh.
Prerequisites: MATH 335.
MATH451: Topology (3 hours lecture)
Topological spaces, metric spaces, continuity, compactness, connectedness, and separability properties; topological generalizations of basic continuity theorems of advanced calculus. 3 sh.
Prerequisites: MATH 425.
MATH460: Introduction to Applied Mathematics (3 hours lecture)
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 (SturmLiouville 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 sh.
Prerequisites: MATH 335.
MATH463: Numerical Analysis (3 hours lecture)
Finite differences, approximation theory, linear and nonlinear equations, error analysis. 3 sh.
Prerequisites: MATH 222 and 335.
MATH464: Operations Research I (3 hours lecture)
Linear programming, transportation problem, assignment problem, duality, sensitivity analysis, network flows, dynamic programming, nonlinear programming, integer programming. 3 sh.
Prerequisites: MATH 335.
MATH465: Operations Research II (3 hours lecture)
Game theory, queuing models, inventory models, Markov processes, reliability theory and applications. 3 sh.
Prerequisites: MATH 335 and 340.
MATH466: Mathematics of Finance I (3 hours lecture)
Mathematical theory of interest rates, annuities, bond valuation, stock valuation, options, arbitrage, binomial trees, putcall parity, Black Scholes Model, Capital Asset Pricing Model (CAPM) and portfolio selection. 3 sh.
Prerequisites: FINC 321, MATH 340.
MATH467: Mathematics of Finance II (3 hours lecture)
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, putcall parity, binomial trees, other options, and volatility. This course can be used as part of preparation for SOA/CASACT Actuarial Examinations, Course 2. 3 sh.
Prerequisites: MATH 466.
MATH468: Fluid Mechanics (3 hours lecture)
Mechanics of continuous media, liquids and gases; stress, viscosity, NavierStokes 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 sh.
Prerequisites: PHYS 210 or MATH 222.
MATH469: Mathematical Modeling (3 hours lecture)
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 sh.
Prerequisites: MATH 335, and MATH 340, and MATH 464 or STAT 330.
MATH485: Applied Combinatorics and Graph Theory (3 hours lecture)
Problem solving by counting, enumeration, and graph theory. Permutation, combinations, binomial coefficients, generating functions, and recurrence relations, partitions, inclusionexclusion, Polya's formula, graph theoretic models, trees, circuits, networks, matching, and their applications to puzzles, games, tournaments, traffic patterns, transportation. 3 sh.
Prerequisites: MATH 340.
MATH487: Introduction to Mathematical Cryptography (3 hours lecture)
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 sh.
Prerequisites: MATH 335.
MATH490: Honors Seminar (3 hours seminar)
This course will concentrate on subject matter not usually covered within standard mathematics courses. A written and oral report are required. 3 sh.
Prerequisites: MATH 335 and departmental approval.
MATH495: Topics for Undergraduates
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 (3 hours lecture)
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 opensystem model and the contingency approach as overall frameworks for understanding organizations and management. 3 sh.
Prerequisites: ENWR 105 or HONP 100.
PHYS191: University Physics I (3 hours lecture, 2 hours lab)
This onesemester calculusbased 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. 4 sh.
Prerequisites: MATH 122 is prerequisite or corequisite.
PHYS192: University Physics II (3 hours lecture, 2 hours lab)
Calculusbased 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. 4 sh.
Prerequisites: MATH 221 is prerequisite or corequisite.
STAT330: Fundamentals of Modern Statistics I (3 hours lecture)
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 sh.
Prerequisites: MATH 221.
STAT401: Applied Statistics for the Sciences (3 hours lecture)
Organizing, displaying, and describing data; designing experiments; methods for drawing conclusions from data; significance testing, confidence intervals, linear regression, analysis of variance, chisquare tests of independence. Examples from disciplines in the natural and physical sciences. Statistical software is used. Not for Mathematics and Computer Science majors. 3 sh.
Prerequisites: MATH 111 or Math 112.
STAT403: Techniques and Applications of Statistics (3 hours lecture)
Statistical techniques for the social and behavioral sciences including estimation, tests of hypothesis, nonparametric statistics, regression and correlation. May not be taken for credit by mathematic majors. 3 sh.
Prerequisites: MATH 112.
STAT441: Statistical Computing (3 hours lecture)
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 sh.
Prerequisites: STAT 330 or STAT 401 and computer experience.
STAT442: Fundamentals of Modern Statistics II (3 hours lecture)
Continuation of STAT 440. Principles of statistical inference, categorical data analysis, one and twoway anova, multiple linear regression, nonparametric methods, bootstrap methods. Examples from a wide variety of disciplines. Statistical software is used. 3 sh.
Prerequisites: STAT 330 or STAT 401 or equivalent.
STAT443: Introduction to Mathematical Statistics (3 hours lecture)
Develops statistical methods from probability theory. Topics discrete and continuous probability distributions, estimation, inference and hypothesis testing. 3 sh.
Prerequisites: MATH 340 and either STAT 330 or STAT 401.
STAT481: Introduction to Statistical Data Mining (3 hours lecture)
Introduction to the concepts and applications of a variety of datamining 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. Handson applications to data sets from diverse fields. Statistical software is used. 3 sh.
Prerequisites: STAT 330 or STAT 401 or equivalent.
STAT487: Statistical Genomics (3 hours lecture)
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 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.