Mathematics Major (B.S.)- Undergraduate (Combined B.S./M.S. Statistics) - 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).

MATHEMATICS MAJOR

Complete 63 semester hours including the following 5 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. MATHEMATICS SPECIALIZATION

    Complete the following 3 courses:

    MATH 320 Transitions to Advanced Mathematics 3
    MATH 425 Advanced Calculus I 3
    MATH 431 Foundations of Modern Algebra 3
  3. MATHEMATICS ELECTIVES

    Complete the following 2 requirement(s):

    1. Complete the following 1 course:

      STAT 330 Fundamentals of Modern Statistics I 3
    2. Complete 12 semester hours from the following:

      MATH 398 Vector Calculus 3
      MATH 420 Ordinary Differential Equations 4
      MATH 421 Partial Differential Equations 3
      MATH 423 Complex Variables 3
      MATH 426 Advanced Calculus II 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 469 Mathematical Modeling 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 441 Statistical Computing 3
      STAT 442 Fundamentals of Modern Statistics II 3
      STAT 443 Introduction to Mathematical 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. MATHEMATICS COLLATERAL REQUIREMENT

    Complete the following 3 courses:

    CMPT 183 Foundations of Computer Science I 3
    PHYS 191 University Physics I 4
    PHYS 192 University Physics II 4
  5. As part of the combined BS Math/MS Stat program, complete the following 3 courses:

    STAT 542 Statistical Theory I 3
    STAT 544 Statistical Computing 3
    STAT 552 Intermediate Statistics Methods 3

Course Descriptions:

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.

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.

MATH425: Advanced Calculus I

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.

MATH426: Advanced Calculus II

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.

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

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.

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.

STAT542: Statistical Theory I

Discrete and continuous probability distributions, multivariate distributions, sampling theory, transformations, Chi-squared, 'F' and 't' distributions. Point estimation, properties of estimators, sufficiency, exponential families, interval estimation, hypothesis testing, power, Neyman-Pearson Lemma, likelihood ratio tests. The impact of the above theory on areas such as regression analysis, analysis of variance and analysis of discrete data. (3 hours lecture.) 3 sh.

Prerequisites: STAT 541 and permission of graduate program coordinator.

STAT544: Statistical Computing

Computer systems for data analysis and data graphics, and intermediate level statistical methodology are investigated. Several statistical computing packages are utilized and evaluated. (3 hours lecture.) 3 sh.

Prerequisites: STAT 541 or STAT 548, and CMPT 183, and permission of graduate program coordinator.

STAT552: Intermediate Statistics Methods

Followup to introductory statistical methods course. 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, permission of graduate program coordinator.