Mathematics Minor  Undergraduate  2015 University Catalog
MATHEMATICS MINOR

Complete the following 2 requirement(s) for 19 semester hours:

Complete the following 4 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 
Complete 3 semester hours from the following:


MATH MINOR RESIDENCY REQUIREMENT
Residency requirement: 9 semester hours must be earned at Montclair.
Course Descriptions:
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 with grade of C or better.
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 with a grade of C or better.
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 with a grade of C or better.
MATH323: 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. Previous course MATH 423 effective through Spring 2014. 3 sh.
Prerequisites: MATH 222 with a grade of C or better.
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 with a grade of C or better.
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 with a grade of C or better.
MATH350: College Geometry (3 hours lecture)
The study of a wide range of advanced concepts in Euclidean geometry suitable for teaching foundations of axiomatic systems at the high school or middle school level. Topics involving triangle congruence, parallel line postulate, properties of polygons and circles, area, volume, Pythagorean Theorem, similarity, transformations and geometric constructions will be studied from an advanced, proofbased perspective. Basics of Non Euclidian geometries will be introduced. Geometers' Sketchpad and other software will be utilized. 3 sh.
Prerequisites: MATH 320 with a grade of C or better.
MATH360: Mathematical Modeling in Biology (3 hours lecture)
The course introduces students to the study of mathematical modeling in the biological and medical sciences. Continuous and discrete dynamical systems will be used to describe topics such as interacting and structured populations, biological control, population genetics and evolution, biological oscillators and switches, pattern formation, and the dynamics of infectious diseases. Each topic will be presented in its historical context, leading to questions of current research interest and providing a comprehensive overview of the field and a solid foundation for interdisciplinary research in the biological sciences. Emphasis is on applications and mathematical techniques for finding solutions. 3 sh.
Prerequisites: MATH 221 (or MATH 116 and BIOL 213 for Biology Majors).
MATH368: 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 environmental problems. Cross listed with PHYS 368. Previous course MATH 468 effective through Spring 2014. 3 sh.
Prerequisites: MATH 222 with a grade of C or better.
MATH370: Mathematics for Teaching (3 hours lecture)
This course will focus on the Common Core State Standards Mathematics (CCSSM) aligned with the content areas of number and quantity, prealgebra and algebra, and statistics and probability. These topics will be presented with the goal of fostering preservice mathematics teachers' (PSMT's) understanding of and commitment to teaching mathematics that promotes student understanding. PSMTs will explore mathematical content deeply while also discussing related pedagogical tools, including teaching methods, curricula, lesson planning, technology resources, and assessment practices. 3 sh.
Prerequisites: MATH 350 with a grade of C or better and admission into the Teacher Education program.
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 335 with a grade of C or better.
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 with a grade of C or better.
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 with a grade of C or better.
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 with a grade of C or better.
MATH426: Advanced Calculus II (3 hours lecture)
This course is a continuation of MATH 425. Topics include functions of several variables, partial derivatives, Green's theorem, Stoke's theorem, divergence theorem, implicit function theorem, inverse function theorem, infinite series and uniform convergence. 3 sh.
Prerequisites: MATH 425 with a grade of C or better.
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 with a grade of C or better.
MATH433: Theory of Numbers (3 hours lecture)
This course presents the principal ideas of classical elementary number theory, emphasizing the historical development of these results and the important figures who worked on them. Topics studied include the following: divisibility, primes, and the Euclidean Algorithm; numbertheoretic functions, linear congruencies, the Chinese Remainder Theorem, the Theorems of Fermat, Euler, and Wilson; quadratic congruencies and the Law of Quadratic Reciprocity; Diophantine equations and Fermat's Last Theorem; continued fractions; Pell's equation and the sum of two squares. 3 sh.
Prerequisites: MATH 335 with a grade of C or better.
MATH450: Foundations of Geometry (3 hours lecture)
The course deals with the fundamental ideas common to Euclidean and NonEuclidean geometries; projective, affine, and metric geometries. 3 sh.
Prerequisites: MATH 335 with a grade of C or better.
MATH451: Topology (3 hours lecture)
Point set topology including topics such as, metric spaces, limit points, derived sets, closure, continuity, compact sets and connected sets. 3 sh.
Prerequisites: MATH 425 with a grade of C or better.
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 420 with a grade of C or better.
MATH463: Numerical Analysis (3 hours lecture)
Finite differences, approximation theory, linear and nonlinear equations, error analysis. 3 sh.
Prerequisites: MATH 335 with a grade of C or better.
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 with a grade of C or better.
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 MATH 340 both with a grade of C or better.
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 and MATH 340 both with a grade of C or better.
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 with a grade of C or better.
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 420 and MATH 340; and MATH 464 or STAT 330 all with a grade of C or better.
MATH470: Teaching of Mathematics (4 hours lecture)
Selection, organization, and presentation of secondary mathematics, classroom activities, lesson planning, techniques of motivation, evaluation, multisensory aids, principles of learning, and applications of the microcomputer to classroom teaching. 4 sh.
Prerequisites: MATH 335 with a grade of C or better and admission into the Teacher Education Program.
MATH471: Selected Topics in Modern Mathematics (3 hours lecture)
Professionalized view of junior and senior high school mathematics topics: functions, real and complex numbers, analytic geometry, absolute value and inequalities, sets and logic, flow charting, linear programming. 3 sh.
Prerequisites: MATH 335 with a grade of C or better and admission into the Teacher Education Program.
MATH475: History of Mathematics (3 hours lecture)
This course surveys the origins and evolution of mathematical ideas from the antiquity to the present. Emphasis will be on the role of mathematics as an integral part of our cultural heritage and its relationship to areas such as science, art, religion, philosophy and literature. Classical mathematical methods will be examined by reading selected original works by great mathematicians. 3 sh.
Prerequisites: MATH 335 with a grade of C or better.
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 with a grade of C or better.
MATH487: Introduction to Mathematical Cryptography (3 hours lecture)
A modern introduction to the application of number theory, combinatorics and abstract algebra to cryptography. Specifically, this includes modular arithmetic, generating polynomials and matrix algebra over rings and fields. A discussion of a broad range of applications of mathematics to the security of credit cards, cell phones and codes among numerous other current examples will be covered. Current industry protocols will be explored. 3 sh.
Prerequisites: MATH 335 with a grade of C or better.
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 with a grade of C or better; and departmental approval.
MATH491: Research in Mathematics Education (3 hours seminar)
Research in Mathematics Education Research in an area of mathematics education agreed upon by the student and the instructor. The results of the research will be the basis of a seminar, colloquium, or conference presentation to be given by the student. May be repeated for a maximum of 6 credits with either a new research topic or continued research on the current topic. 3 sh.
Prerequisites: MATH 350 and departmental approval.
MATH495: Topics for Undergraduates (1 hour lecture)
Study of advanced topics in undergraduate mathematics. May be repeated for a maximum of 6.0 credits as long as the topic is different. 1  3 sh.
Prerequisites: MATH 335 and MATH 340 both with a grade of C or better; and departmental approval.
MATH497: Mathematics 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 with a grade of C or better; and departmental approval.
MATH498: Mathematics 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 with a grade of C or better; and departmental approval.
STAT330: Fundamentals of Modern Statistics I (3 hours lecture)
Displaying, describing and modeling data; arrangements for producing 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 with a grade of C or better.
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 with a grade of C or better.
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 with a grade of C or better; and STAT 330 or STAT 401 with a grade of C or better.