Mathematics [MAT] Courses
Students wishing to major in Biology or Mathematics must take a placement test to determine if MAT 107 is required prior to MAT 202. Liberal arts students and others wishing to take MAT 103, MAT 104, or MAT 301 must take a placement test (elementary algebra) to determine the student’s eligibility totake any of these courses, or whether MAT 050 is first required. All students required to complete MAT 050 as prerequisite to other courses must do so before
the completion of 60 credits. For accounting, business, economics, management, or science students, and others wishing to take MAT 107 or MAT 109, aplacement test (intermediate algebra) will be administered to determine if MAT 105 or MAT 070 is first required. For specific course information, contact theMathematics department in room 3204 or call (718) 489-5396.

MAT 050 Elementary Algebra

MAT 070 Intermediate Algebra

A remedial course designed to develop and/or strengthen basic
topics in algebra that a student should master before taking a firstcourse in mathematics. Prerequisite: Placement by examination. 3
lecture hours per week. No credits. Every semester; day andevening.

A review of topics in elementary algebra and an extended treatment of some topics such as equations and inequalities in one
and two variables as well as linear systems. Other topics include
relations, functions, exponents, logarithms, exponentials, quadratic equations, and applications. Prerequisite: Placement byexamination or MAT 050. 3 lecture hours per week. No credits.
Every semester; day and evening.

148 Courses of Instruction

St. Francis College

MAT 103 Foundations of Mathematics
A liberal arts mathematics course for non-mathematics and nonscience majors. Explores several ideas of mathematics to give thestudent an appreciation of the significance of mathematics. The
course covers mathematical patterns and problem solving, numeration and mathematical systems, other number bases, thebinary number system, modular arithmetic, the Fibonacci sequence and the Golden ration, and real numbers and their representation. Prerequisite: Placement by examination or MAT 050. 3credits. Every semester; day and evening.

MAT 104 Discrete Mathematics
Basic concepts of set theory, symbolic logic, counting methods,
permutations and combinations, discrete probability and elementary statistics, graphs, graph theory, Euler circuits, and trees.
Prerequisite: Placement by examination or MAT 050. 3 credits.
Every semester; day.

MAT 105 College Algebra
A review of topics in intermediate algebra and an extended
treatment of some topics such as relations, functions, and graphs
to include polynomial, rational, algebraic, exponential, and logarithmic functions and graphs. Additional topics include linear
systems of equations and inequalities in two variables, determinants, and matrices with applications to business and economics.
This course is recommended for students with a weak to moderate knowledge of intermediate algebra. Prerequisite: Placementby examination or MAT 070. 3 credits. Every semester; day andevening.

MAT 107 Algebra and Trigonometry forScience Majors
A course for mathematics and science majors designed to develop and strengthen those topics in algebra and trigonometrythat a student should master before taking a first standard course
in calculus. Prerequisite: Placement by examination or MAT 105.
Graphing calculator is optional. 4 credits. Every semester; day.

MAT 109 Mathematics for Managerial
Science Iplacement by examination. Students may purchase a graphingcalculator. 4 credits. Every semester; day.

MAT 203 Calculus II
Applications of integration, logarithmic, exponential, inverse,hyperbolic, and trigonometric functions. Methods of integration,
including integration by parts, trigonometric substitutions, conic
sections, rotation of axes and the general second degree equation,polar coordinates, improper integrals, L’Hôpital’s rules, sequences and infinite series. Prerequisite: MAT 202. 4 credits.
Every semester; day.

MAT 301 Statistics
Organization, description, and interpretation of data. Probabilityand probability distributions. Sampling distributions and estimation of population parameters. Testing hypotheses, linear regression, correlation analysis, and index numbers. Prerequisite:
Placement by examination or MAT 104 or higher. 3 credits.
Every semester; day and evening.

MAT 304 Calculus III
Vectors and vector functions. Functions of several variables.
Double and triple integrals, partial derivatives, chain-rule, cylindrical and spherical coordinates and change of variable, applications. Prerequisite: MAT 203. 4 credits. Every semester; day.

MAT 309 College Geometry
Topics of higher Euclidean geometry and geometric constructions. Geometrical transformations and different kinds of geometries. Projective and hyperbolic geometries. Prerequisite:
MAT 107. 3 credits. Offered as needed; day.

MAT 310 Vector Analysis
The algebra and calculus of vectors, scalar and vector product,
coordinate systems, space geometry, vector differential operators,
divergence and curl of vector fields, curvilinear coordinates, lineand surface integrals. Green’s theorem, Stokes’ theorem, anddivergence theorem. Prerequisite: MAT 304. 3 credits. Offered asneeded; day.

MAT 311 Introduction to Set Theory

The study of matrices and their application. Examples include
the Leontief model and solution of systems in linear equations,inequalities in linear programming (graphical and algebraic approach), dual problems, and economic interpretation. Prerequisite: Placement by examination or MAT 105. 3 credits. Fallsemester; day and evening. Spring semester; day.

The algebra of propositions and quantifiers; sets, relations, functions, equivalence relations, partial and total orders, and productsets; Cantor hypothesis, cardinal and ordinal numbers, and wellordered sets; Axiom of Choice, Zorn’s dilemma, and well ordering axiom. Prerequisite: MAT 203. 3 credits. Offered as needed;day.

MAT 110 Mathematics for Managerial
Science IIMAT 312 Linear Algebra

Introduces the basic concepts of functional relationships, thebasic skills of differentiation and integration, maxima and minimaproblems, and several other applications of calculus, especiallymodels in business and economics, exponential models, andmathematics of finance. Prerequisite: MAT 109. 3 credits. Springsemester; day and evening. Fall semester; day.

MAT 202 Calculus I
Emphasis given to calculus, including differentiation and integration of algebraic forms, areas, applications of the derivative,differentials, Rolle’s theorem, the mean value theorem, and thefundamental theorem of calculus. Prerequisite: MAT 107 orSt. Francis College

Systems of linear equations, vector spaces, linear independencebasis, and dimension; matrices and determinants, rank, andnullity; eigenvalues and eigenvectors; diagonalizable matrices;
linear transformations; and matrices. Prerequisite: MAT 203. 4credits. Fall semester; day.

MAT 401 Differential Equations IMethods of solving ordinary differential equations with applications. Linear differential equations of first-, second-, and higherorder applications. Systems of linear differential equations. Prerequisite: MAT 203. 3 credits. Fall semester; day.

Courses of Instruction 149

MAT 402 Differential Equations II
Fourier series and Laplace transformations: applications. Series
solution of differential equations. Lengendre’s and Bessel’sequations. Partial differential equations. Prerequisite: MAT 401. 3credits. Offered as needed; day.

MAT 403 Advanced Calculus I
Axiom of continuity, least upper bounds, and greatest lowerbounds; open and closed sets; continuity differentiation; maxima
and minima for functions of two or more variables; the methodof Lagrange; implicit function theorems; and general theorems ofpartial differentiation. Prerequisite: MAT 304. 4 credits. Fallsemester; day.

MAT 404 Advanced Calculus II
Transformations and mappings, point set theory, uniform continuity, and fundamental theorems of continuous functions, thetheory of integration, infinite series and uniform convergence,
power series, improper integrals, and a study of the gammafunctions. Prerequisite: MAT 403. 4 credits. Spring semester; day.

MAT 406 Theory of Numbers
An introductory course dealing with divisibility, number theorems, theory and congruences, quadratic residues, and Diophantine equations. Quadratic residues and quadratic reciprocity
law. Fermat’s theory, Chinese remainder theorem, Euler’s theorem, and Wilson’s theorem. Prerequisite: MAT 202. 3 credits.
Offered as needed; day.

MAT 408 Numerical Analysis
Numerical solutions of equations, difference tables, operator
methods; numerical differentiation and integration; numericalsolution of ordinary differential equations; systems of linearequations; solutions by iterative methods. Prerequisite: MAT 304
or MAT 401. 3 credits. Offered as needed; day.

MAT 409 Modern Algebra
Sets and mappings; theory of groups, rings, and fields; homomorphism, isomorphism, and the first isomorphism theorem; thefield of real numbers and the field of complex numbers. Prerequisite: MAT 304. 3 credits. Every semester; day.

MAT 410 Functions of a Complex Variable
Complex numbers and the topology of the complex plane; analytic and elementary functions, contour integrals, conformal
mappings, power series, Laurent series, Cauchy-Riemann partialdifferential equations; Cauchy-Goursat theorem. Prerequisite:
MAT 304. 3 credits. Offered as needed; day.

MAT 411 Introduction to Real Analysis
Families of sets, countable and uncountable sets, metric spaces,
the space of continuous functions on a compact set, the StoneWeirstrass theorem, measure and measurable functions, theLebesgue Integral, and dominated and monotone convergence
theorem, Lp spaces. Prerequisite: MAT 404. 3 credits. Offered asneeded; day.

MAT 413 Advanced Linear Algebra
Advanced course in linear algebra examining linear transformations and matrices, the characteristics and minimal polynomials,

150 Courses of Instruction

Caley-Hamilton theorem, diagonalization, unitary spaces, selfadjoint, normal matrices and the spectral theorem, Jordan canonical form, and quadratic form. Prerequisites: MAT 312. 3credits. Offered as needed; day.

MAT 414 General Topology
Set-theoretic preliminaries, metric spaces, topological spaces,continuity and homomorphism, compactness and connectedness,separation axioms, complete metric spaces, and covering spaces.
Prerequisite MAT 403. 3 credits. Offered as needed.

MAT 415 Probability Theory
Discrete and continuous random variables and their probabilitydistributions. Mathematical expectation and moments. Chebyshev’s Theorem, the Bernoulli, Poisson, Geometric, and Hypergeometric distributions; the Uniform, Exponential, Gamma, ChiSquare, and Normal distribution. Multivariate probability distributions. Functions of random variables. Central Limit theorems.
Prerequisite: MAT 304. 3 credits. Fall semester; day.

MAT 416 Mathematical Statistics
Sampling distributions, methods of estimation and hypothesis,
linear regression, and the method of least squares. Correlationand analysis of variance. Elements of decision theory, statisticalgames, and nonparametric tests. Prerequisite: MAT 415. 3 credits. Offered as needed; day.

MAT 418 Seminar in Actuarial Science
Advanced problem-solving seminar for students interested incareers as actuaries. This seminar covers material in calculus,advanced calculus, linear algebra, and probability theory. Examination given by the Society of Actuaries. Prerequisites: MAT 312,
MAT 403, and MAT 415. 2 credits. Offered as needed; day andevening.

MAT 420 Topics in Advanced Mathematics
One of two courses that provide ideal preparation for studentspursuing graduate studies in mathematics. Topic is announced inadvance. Prerequisite: Chairperson’s approval. 3 credits. Offered
as needed, Spring semester.
Topics in Algebra: Solvability by radicals, Galois groups, andpolynomial equations not solvable by radicals. The Sylow theorems and the fundamental theorem of Algebra. Prerequisite:MAT 409.
Topics in Analysis: Banach and Hilbert spaces, linear operatorsand special classes of operators, self-adjoint and normal operators. Elements of spectral theory. The Fourier transform. TheBanach fixed-point theorem. Applications to differential andintegral equations. Prerequisite: MAT 404.

MAT 500 Independent Study inMathematics
Independent study under the direction of a faculty member inthe Mathematics department. For students majoring in Mathematics Education, the independent study is on the history ofmathematics. Prerequisites: senior standing, major in mathematics or mathematics education, and departmental approval. 1-3credits. Every semester; day.

St. Francis College