Mathematics Major (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.
MATHEMATICS MAJOR
Complete 54 semester hours including the following 4 requirement(s):
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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 -
MATHEMATICS SPECIALIZATION
Complete the following 3 courses:
MATH 320 Transitions to Advanced Mathematics (3 hours lecture) 3 MATH 425 Advanced Calculus I (3 hours lecture) 3 MATH 431 Foundations of Modern Algebra (3 hours lecture) 3 -
MATHEMATICS ELECTIVES
Complete 15 semester hours from the following:
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MATHEMATICS COLLATERAL REQUIREMENT
Complete the following 3 courses:
Course Descriptions:
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.
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 proof-writing skills and introduce students to the explore-conjecture-proof 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, 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 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, existence-uniqueness 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, Cauchy-Riemann 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 (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 sh.
Prerequisites: MATH 335.
MATH463: Numerical Analysis (3 hours lecture)
Finite differences, approximation theory, linear and non-linear 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, put-call 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, 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 sh.
Prerequisites: MATH 466.
MATH468: Fluid Mechanics (3 hours lecture)
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 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, inclusion-exclusion, 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.
PHYS191: University Physics I (3 hours lecture, 2 hours lab)
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. 4 sh.
Prerequisites: MATH 122 is prerequisite or co-requisite.
PHYS192: University Physics II (3 hours lecture, 2 hours lab)
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. 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, 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 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, non-parametric 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 two-way 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 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 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.
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