Mathematics Minor - Undergraduate - 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.


MATHEMATICS MINOR

Complete 19 semester hours, including the following 3 requirement(s):

  1. Complete the following 4 courses:

    MATH 122 Calculus I 4
    MATH 221 Calculus II 4
    MATH 222 Calculus III 4
    MATH 335 Linear Algebra 4
  2. Complete 3 semester hours from the following:

    MATH 340 Probability 3
    MATH 350 College Geometry 3
    MATH 398 Vector Calculus 3
    MATH 420 Ordinary Differential Equations 4
    MATH 423 Complex Variables 3
    MATH 425 Advanced Calculus I 3
    MATH 426 Advanced Calculus II 3
    MATH 431 Foundations of Modern Algebra 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 469 Mathematical Modeling 3
    MATH 471 Selected Topics in Modern Mathematics 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 330 Fundamentals of Modern Statistics I 3
    STAT 441 Statistical Computing 3
    STAT 443 Introduction to Mathematical Statistics 3
  3. MATH MINOR RESIDENCY REQUIREMENT

    Residency requirement: 9 semester hours must be earned at Montclair.

    MATH 122 Calculus I 4
    MATH 221 Calculus II 4
    MATH 222 Calculus III 4
    MATH 320 Transitions to Advanced Mathematics 3
    MATH 335 Linear Algebra 4
    MATH 340 Probability 3
    MATH 350 College Geometry 3
    MATH 398 Vector Calculus 3
    MATH 420 Ordinary Differential Equations 4
    MATH 421 Partial Differential Equations 3
    MATH 423 Complex Variables 3
    MATH 425 Advanced Calculus I 3
    MATH 426 Advanced Calculus II 3
    MATH 431 Foundations of Modern Algebra 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 470 Teaching of Mathematics 4
    MATH 471 Selected Topics in Modern Mathematics 3
    MATH 475 History of Mathematics 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 330 Fundamentals of Modern Statistics I 3

Course Descriptions:

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.

MATH350: College Geometry

Study of Euclidean and other geometries from an axiomatic point of view. (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.

MATH470: Teaching of Mathematics

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 hours lecture.) 4 sh.

Prerequisites: Admission to Teacher Education Program and MATH 335.

MATH471: Selected Topics in Modern Mathematics

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 hours lecture.) 3 sh.

Prerequisites: Admission to Teacher Education Program and MATH 335.

MATH475: History of Mathematics

Histories of geometry, number theory, algebra, calculus and infinite processes. (3 hours lecture.) 3 sh.

Prerequisites: MATH 335.

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.

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.

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.