Mathematics Courses

MAT 105 FUNDAMENTALS OF MATHEMATICS IN TODAY’S WORLD

Campus: St. Joseph's College,Brooklyn Campus St. Joseph's College, Long Island Campus

This course, recommended for liberal arts students of varying mathematical backgrounds, stresses critical thinking and reasoning. The course includes the study of patterns, set theory, logic, inductive and deductive reasoning, the real number system and topics in geometry. 3 hours a week, 1 semester, 3 credits. Fall, spring and summer.

MAT 106 EXCURSIONS IN CONTEMPORARY MATHEMATICS

Campus: St. Joseph's College,Brooklyn Campus St. Joseph's College, Long Island Campus

This course presents an overview of various topics in mathematics with a focus on recent developments and their applications. Designed for those students for whom the profundity of mathematics has often been obscured by its techniques, this course proposes to illustrate and explore the ubiquitous nature of mathematics in the world around us and thereby promote an appreciation for the significance, power and beauty of the discipline. Many topics are considered. They range from some modern applications of graphs to the mathematics of social choices. Not open to students who have credit for any 200-level math course. 3 hours a week, 1 semester, 3 credits. Spring.

MAT 107 INTRODUCTION TO PROBABILITY AND STATISTICS

Campus: St. Joseph's College,Brooklyn Campus St. Joseph's College, Long Island Campus

This course offers an introduction to probability and statistics. It is designed to provide a common foundation for the more specialized material presented in the various statistics courses offered in other quantitative departments. Material covered includes: probability models, random variables and probability distributions (both discrete and continuous), descriptive statistics, inference, sampling and hypothesis testing. 3 hours a week, 1 semester, 3 credits. Fall and spring.

MAT 111 COLLEGE ALGEBRA

Campus: St. Joseph's College, Long Island Campus

Properties of numbers and expressions; linear and quadratic equations; systems of equations; exponents and logarithms; functions; linear, quadratic, polynomial, exponential and logarithmic. Not open to students who have completed MAT 113 or students with credit for any 200-level math course. 3 hours a week, 1 semester, 3 credits. Fall, spring and summer.

MAT 113 ELEMENTARY FUNCTIONS: PRECALCULUS

Campus: St. Joseph's College,Brooklyn Campus St. Joseph's College, Long Island Campus

Introduction to the concept of functions: their graphs, elementary properties, geometric transformations, inverses and algebra of functions. Introduction to the elementary functions and their properties: linear, polynomial, rational, exponential, logarithmic and trigonometric functions. Designed for those who intend to go on to a calculus course. Prerequisite: 11th-year mathematics or equivalent. Not available to students with credit for any 200-level math course. Students will not receive credit for both MAT 111 and MAT 113. 3 hours a week, 1 semester, 3 credits. Fall and spring.

MAT 200 MATHEMATICS FOR BUSINESS AND ECONOMICS

Campus: St. Joseph's College,Brooklyn Campus St. Joseph's College, Long Island Campus

This course includes the study of matrices, linear programming, the simplex method and the mathematics of finance. Basic business applications of precalculus mathematics will be discussed. Prerequisite: MAT 111. 3 hours a week, 1 semester, 3 credits. Fall and spring.

MAT 203 MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE

Campus: St. Joseph's College,Brooklyn Campus St. Joseph's College, Long Island Campus

The emphasis will be on algorithmic problem solving and discrete mathematical concepts including logic, sets, Boolean algebra, relations, functions, induction and recursion, counting principles and combinatorics, graphs and trees. Use of the computer as a problem-solving tool will be integrated with the theory. Fundamental algorithms including sorting, searching and tree traversal will be introduced. Prerequisite: MAT 113 or equivalent. 4 hours a week, 1 semester, 4 credits. Fall and spring.

MAT 204 ANALYTIC TRIGONOMETRY AND GEOMETRY

Campus: St. Joseph's College,Brooklyn Campus St. Joseph's College, Long Island Campus

This course will focus on analytical geometry and the trigonometric functions and their properties. Amongst the topics considered under analytic geometry are the conic sections and the general quadratic equation along with polar and parametric equations. The topics covered under trigonometric functions include the inverse functions, trigonometric identities and the trigonometric representation of the complex numbers. Prerequisite: MAT 113 or equivalent. 3 hours a week, 1 semester, 3 credits. Fall and spring.

MAT 205 CALCULUS AND ANALYTIC GEOMETRY I

Campus: St. Joseph's College,Brooklyn Campus St. Joseph's College, Long Island Campus

Limits, continuity, differentiation, elementary integration and other topics. The study of calculus is enhanced through the use of computer software such as Maple and graphing calculators. Prerequisite: MAT 113 or equivalent. 3 lecture hours, 1 recitation hour, 1 lab hour, 1 semester, 4 credits. Fall and spring.

MAT 206 CALCULUS AND ANALYTIC GEOMETRY II

Campus: St. Joseph's College,Brooklyn Campus St. Joseph's College, Long Island Campus

Differentiation and integration of logarithmic and exponential functions. Techniques for computing integrals are developed and applications of integration such as volumes of various solids are explored. Differentiation and integration of inverse functions, including trigonometric functions, is examined. Maple software will be used in the laboratory component. Prerequisite: MAT 205 with a minimum grade of C-. 3 lecture hours, 1 recitation hour and 1 lab hour a week, 1 semester, 4 credits. Fall and spring.

MAT 207 CALCULUS AND ANALYTIC GEOMETRY III

Campus: St. Joseph's College,Brooklyn Campus St. Joseph's College, Long Island Campus

Infinite series and their convergence are explored and the Taylor series expansion for differentiable functions is developed. Parametric equations and polar functions are considered. Vectors in two and three dimensions along with their algebras are explored. Lines, planes and various families of surfaces in three-dimensional space are considered. Maple software will be used in the laboratory component. Prerequisite: MAT 206 with a minimum grade of C-. 3 lecture hours, 1 recitation hour and 1 lab hour a week, 1 semester, 4 credits. Fall and spring.

MAT 208 ADVANCED CALCULUS

Campus: St. Joseph's College,Brooklyn Campus St. Joseph's College, Long Island Campus

Functions of several variables are introduced and studied. The calculus is redeveloped in this context. Gradients, directional derivatives, tangent planes and normal lines along with relative and absolute extrema are considered. Line, contour and multiple integration are explored. Vector fields and their calculus are studied. Material is illustrated and enhanced by the use of software packages such as Maple. Prerequisite: MAT 207 with a minimum grade of C-. 4 hours a week, 1 semester, 4 credits. Fall and spring.

MAT 241 (HIS 240) HISTORY OF MATHEMATICS

Campus: St. Joseph's College,Brooklyn Campus St. Joseph's College, Long Island Campus

This course presents the development of mathematics from the ancient times to the present. Major advances in the field are examined in some depth and how these advances contributed to the growth of the discipline as a whole. Topics include the birth of the axiomatic system as exemplified by Euclidean geometry, the prescience of Archimedes, the study of roots of polynomials, the development of the calculus and many other breakthrough topics. Prerequisite: MAT 205. Recommended for prospective teachers. 3 hours a week, 1 semester, 3 credits. Spring and summer.

MAT 246 PROBABILITY AND STATISTICS

Campus: St. Joseph's College,Brooklyn Campus St. Joseph's College, Long Island Campus

A calculus based course in the basic concepts of probability and statistics. Topics include: descriptive and inferential statistics, measures of central tendency and dispersion, sample spaces and events, probability axioms, counting techniques, conditional probability and independence. Also included are Bayes’ Theorem, expected value, discrete and continuous random variables, probability density functions, various distribution functions and moments, Chebyshev’s Theorem and the Central Limit Theorem. Prerequisite: MAT 206 or departmental permission. 3 hours a week, 1 semester, 3 credits. Fall, spring and summer.

MAT 250 THEORY OF INTEREST

Campus: St. Joseph's College,Brooklyn Campus St. Joseph's College, Long Island Campus

This course deals with the mathematical aspects of investment. Topics treated include: interest rates, discount rates, present value, accumulated value, annuities, yield rates, amortization schedules and sinking funds. Applications to be treated include: bonds, real estate mortgages, methods of depreciation and insurance. Prerequisties: MAT 206, BUS 315 or BUS 219, or departmental approval. 3 hours a week, 1 semester, 3 credits. Fall.

MAT 307 REAL ANALYSIS

Campus: St. Joseph's College,Brooklyn Campus St. Joseph's College, Long Island Campus

This course provides a closer and more rigorous look at material covered in Calculus I, II and III. It reviews content from single variable calculus and goes further into the theoretical foundations of the subject. Topics covered include the real number system, sequences, limits, continuity, differentiation, Riemann integration and infinite series of numbers and of functions. Prerequisties: MAT 207 or equivalent with a minimum grade of C. 3 hours a week, 1 semester, 3 credits. Offered when there is sufficient demand.

MAT 346 ADVANCED TOPICS IN PROBABILITY AND STATISTICS

Campus: St. Joseph's College,Brooklyn Campus St. Joseph's College, Long Island Campus

A second course in probability and statistics. Topics studied include moment generating functions, jointly distributed random variables, marginal and conditional distributions, hypothesis testing, confidence intervals, minimum variance unbiased estimators, uniformly most powerful tests and an introduction to stochastic processes. Prerequisite: MAT 246 (with a minimum grade of C-) Co-requisite: MAT 208 or departmental approval. 3 hours a week, 1 semester, 3 credits. Spring.

MAT 350 DIFFERENTIAL EQUATIONS

Campus: St. Joseph's College,Brooklyn Campus St. Joseph's College, Long Island Campus

The topics of this course include ordinary differential equations of first and second order, homogeneous and non-homogeneous equations, numerical methods involving first order equations, linear differential equations, selected higher order equations and Laplace Transforms. Prerequisite: MAT 206 or equivalent. 3 hours a week, 1 semester, 3 credits. Fall.

MAT 352 ELEMENTARY NUMBER THEORY

Campus: St. Joseph's College,Brooklyn Campus St. Joseph's College, Long Island Campus

Prime and composite integers, number theoretic functions, Diophantine Equations, congruences: linear and higher order degree. Gaussian integers and algebraic number theory. Prerequisite: MAT 206 or equivalent. 3 hours a week, 1 semester, 3 credits. Fall.

MAT 354 MODERN ALGEBRA

Campus: St. Joseph's College,Brooklyn Campus St. Joseph's College, Long Island Campus

Groups, rings, fields and other algebraic structures. Prerequisite: MAT 206 or equivalent. 3 hours a week, 1 semester, 3 credits. Fall.

MAT 356 LINEAR ALGEBRA

Campus: St. Joseph's College,Brooklyn Campus St. Joseph's College, Long Island Campus

Vectors and vector spaces, matrices and their algebra, systems of linear equations, linear transformations in a vector space. Prerequisite: MAT 206 or departmental permission. 3 hours a week, 1 semester, 3 credits. Fall and spring.

MAT 362 MODERN GEOMETRY

Campus: St. Joseph's College,Brooklyn Campus St. Joseph's College, Long Island Campus

Axiomatic systems, Euclidean and non-Euclidean geometries: elliptic, hyperbolic and projective. Prerequisite: MAT 206 or equivalent. 3 hours a week, 1 semester, 3 credits. Spring.

MAT 364 TOPOLOGY

Campus: St. Joseph's College,Brooklyn Campus St. Joseph's College, Long Island Campus

Sets and functions, metric spaces, topological spaces, compactness, separation, connectedness and other topics. Prerequisite: MAT 206. 3 hours a week, 1 semester, 3 credits. Fall.

MAT 368 FUNCTIONS OF A COMPLEX VARIABLE

Campus: St. Joseph's College,Brooklyn Campus St. Joseph's College, Long Island Campus

Analytic functions, differentiation and integration theorems, elementary functions, conformal mapping, Riemann surfaces, infinite series. Prerequisite: MAT 208 or departmental approval. 3 hours a week, 1 semester, 3 credits. Fall.

MAT 470 DIRECTED READING

Campus: St. Joseph's College,Brooklyn Campus St. Joseph's College, Long Island Campus

Assigned reading in the mathematical literature. Normally the student is required to demonstrate progress in a paper of significant depth. Approval of associate chair is necessary. 1 semester, 1, 2, or 3 credits.

MAT 471 SEMINAR

Campus: St. Joseph's College,Brooklyn Campus St. Joseph's College, Long Island Campus

Special topics in the field of modern mathematics; preparation of written reports. Required of mathematics majors in their last semester. 2 hours a week, 1 semester, 3 credits. Fall and spring.

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