Mathematics Major (B.S.) - Undergraduate (Combined B.S./M.S. Statistics) - 2015 University Catalog

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.

Students interested in this combined program should consult the Undergraduate Advisor after completing MATH 335 Linear Algebra or STAT 330 Fund. of Modern Statistics I.


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 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
  2. 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
  3. MATHEMATICS ELECTIVES

    Complete the following 2 requirement(s):

    1. Complete the following 1 course:

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

      MATH 323 Complex Variables (3 hours lecture) 3
      MATH 368 Fluid Mechanics (3 hours lecture) 3
      MATH 398 Vector Calculus (3 hours lecture) 3
      MATH 420 Ordinary Differential Equations (4 hours lecture) 4
      MATH 421 Partial Differential Equations (3 hours lecture) 3
      MATH 426 Advanced Calculus II (3 hours lecture) 3
      MATH 433 Theory of Numbers (3 hours lecture) 3
      MATH 450 Foundations of Geometry (3 hours lecture) 3
      MATH 451 Topology (3 hours lecture) 3
      MATH 460 Introduction to Applied Mathematics (3 hours lecture) 3
      MATH 463 Numerical Analysis (3 hours lecture) 3
      MATH 464 Operations Research I (3 hours lecture) 3
      MATH 465 Operations Research II (3 hours lecture) 3
      MATH 466 Mathematics of Finance I (3 hours lecture) 3
      MATH 467 Mathematics of Finance II (3 hours lecture) 3
      MATH 469 Mathematical Modeling (3 hours lecture) 3
      MATH 485 Applied Combinatorics and Graph Theory (3 hours lecture) 3
      MATH 487 Introduction to Mathematical Cryptography (3 hours lecture) 3
      MATH 490 Honors Seminar (3 hours seminar) 3
      MATH 495 Topics for Undergraduates (1 hour lecture) 1-3
      MATH 497 Mathematics Research I 1-3
      MATH 498 Mathematics Research II 1-3
      STAT 441 Statistical Computing (3 hours lecture) 3
      STAT 442 Fundamentals of Modern Statistics II (3 hours lecture) 3
      STAT 443 Introduction to Mathematical Statistics (3 hours lecture) 3
      STAT 481 Introduction to Statistical Data Mining (3 hours lecture) 3
      STAT 487 Statistical Genomics (3 hours lecture) 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 11 semester hours:

    CSIT 111 Fundamentals of Programming I (3 hours lecture) 3
    PHYS 191 University Physics I (3 hours lecture, 2 hours lab) 4
    PHYS 192 University Physics II (3 hours lecture, 2 hours lab) 4
  5. GRADUATE REQUIRED COURSES

    As part of the combined BS Math/MS Stat program, complete the following 3 courses:

    STAT 542 Statistical Theory I (3 hours lecture) 3
    STAT 544 Statistical Computing (3 hours lecture) 3
    STAT 552 Intermediate Statistics Methods (3 hours lecture) 3

Course Descriptions:

CSIT111: Fundamentals of Programming I (3 hours lecture)

Basic theory of digital computers. Syntax and semantics of a programming language. Algorithms: logic, design, testing and documentation. Previous course CMPT 183 effective through Spring 2014. 3 sh.

Prerequisites: MATH 100. MATH 112 may be taken as a corequisite or prerequisite.

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 proof-writing skills and introduce students to the explore-conjecture-proof 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, Cauchy-Riemann 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, 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 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.

MATH368: 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 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.

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, existence-uniqueness 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; number-theoretic 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 Non-Euclidean 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 (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 420 with a grade of C- or better.

MATH463: Numerical Analysis (3 hours lecture)

Finite differences, approximation theory, linear and non-linear 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, put-call 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, 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 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.

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 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.

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.

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 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.

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 with a grade of C- or better 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.

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 442 with a grade of C- or better.

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 Biology 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 with a grade of C- or better or STAT 401 with a grade of C- or better.

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 with a grade of C- or better and departmental approval.

STAT542: Statistical Theory I (3 hours lecture)

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 sh.

Prerequisites: STAT 541 and permission of graduate program coordinator.

STAT544: Statistical Computing (3 hours lecture)

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

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

STAT552: Intermediate Statistics Methods (3 hours lecture)

Follow up 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 sh.

Prerequisites: STAT 330, permission of graduate program coordinator.