Mathematics Major (B.S.) - Undergraduate (Combined B.S./M.A.T. with Teacher Certification in Mathematics (Preschool-Grade 12) and Teacher of Students with Disabilities) - 2010 University Catalog
You are viewing the 2010 University Catalog. Please see the newest version of the University Catalog for the most current version of this program's requirements.
MATHEMATICS MAJOR
Complete 48 semester hours including the following 3 requirement(s):
-
MATH TEACHER EDUCATION REQUIREMENTS
Complete the following 7 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 MATH 350 College Geometry 3 MATH 431 Foundations of Modern Algebra 3 -
MATH TEACHER EDUCATION ELECTIVES
Complete at least 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 425 Advanced Calculus I 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 471 Selected Topics in Modern 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 STAT 495 Topics in Statistical Science 1-3 STAT 497 Undergraduate Research in Statistical Science 1-3 -
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
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. Meets the 1983 General Education Requirement (GER) - Mathematics, Computer Science. 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. Meets the 1983 General Education Requirement (GER) - Mathematics, Mathematics. 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. Meets the 1983 General Education Requirement (GER) - Mathematics, Mathematics. 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 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 Mathematics majors. 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 sh.
Prerequisites: MATH 221.
MATH350: College Geometry
Study of Euclidean and other geometries from an axiomatic point of view. 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 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 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 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 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 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 sh.
Prerequisites: MATH 425.
MATH431: Foundations of Modern Algebra
Fundamental concepts of algebra including groups, rings, integral domains and fields, with important examples. 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 sh.
Prerequisites: MATH 335.
MATH436: Elements of Logic
Deduction, propositional functions, quantifiers, consistency, decision problems and Goedel's theorem. 3 sh.
Prerequisites: MATH 335.
MATH450: Foundations of Geometry
Groups of transformations, an introduction to projective geometry. 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 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 sh.
Prerequisites: 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 sh.
Prerequisites: Admission to Teacher Education Program and 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 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 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 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. Meets the 1983 General Education Requirement (GER) - Natural/Physical Science, Laboratory or Non-Laboratory Science. 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. Meets the 1983 General Education Requirement (GER) - Natural/Physical Science, Laboratory or Non-Laboratory Science. 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 sh.
Prerequisites: MATH 221.
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.
Output generated in 0.00009 seconds.