Basic Mathematics (0 credit)

Prerequisite: Must have failed Part 2 of Competency Test with a score below 9.

A course which provides the necessary mathematical background needed to pass the algebra section of the College Proficiency Examination in mathematics; covers polynomials, rational expressions, exponents and roots, solving equations and inequalities.

MAT 098

Basic Mathematics (0 credit)

Prerequisite: Must have failed Part 2 of Competency Test with score 9-13.

This is a fully computer-based instruction presentation. The instructor interacts with the program by evaluating pretests and placing the student appropriately in the course continuum. Primarily the computer program with instructor intervention presents information. Students are encouraged to complete the entire course of study, but may exit the course when they achieve a score at or above the minimum competency exam. One hour per week attendance is required.

MAT 103

Introduction to Contemporary Mathematics(3 credits)

Prerequisite: None

Some of the greatest achievements of mathematical thought, highlighting the beauty and creativity of these ideas.  Topics include: Fibonacci numbers; the golden rectangle; estimation; comparing infinities; fractals; the Pythagorean Theorem; the five platonic solids; and selected topics from probability and statistics. Designed for liberal arts majors who do not plan on taking further math courses.

MAT 107

Casino Gambling(3 credits)

Prerequisite: 3 years of Regents high school mathematics or equivalent.

An intensive encounter with the phenomenon of chance and the theory of probability, which governs it through a critical examination of various casino gambling games including roulette, craps, and blackjack.

MAT 110

Intermediate College Algebra and Trigonometry (3 credits)

Prerequisite: 3 years of Regents high school mathematics or equivalent.

A course which provides concepts and skills in intermediate algebra and right triangle trigonometry.

MAT 114

Functions and Modeling (3 credits)

Prerequisite: 3 years high school mathematics or equivalent.

Describe and explore real-world functions, data and phenomena through graphic, numeric, symbolic, and verbal representations. Use elementary functions (linear, polynomial, power, and exponential) to investigate and analyze applied problems (supported by the use of appropriate technology)

MAT 119

Finite Mathematics (3 credits)

Prerequisite: MAT 110 or 3 years of Regents high school math.

Logic, sets, partitions, probability, vectors, matrices; linear programming.

MAT 121

Elementary Mathematics From an Advanced Standpoint I(4 credits)

MAT 122

Elementary Mathematics From an Advanced Standpoint II(4 credits)

Prerequisite: MAT 121.

Second course of a two-semester sequence on the fundamental concepts of elementary mathematics: 2- and 3-dimensional geometry, measurement, probability, statistics, linear and non-linear functions. Emphasis on problem solving, understanding the concepts and procedures of elementary mathematics, mathematical modeling, the use of manipulatives, and effective communication of mathematical ideas.

MAT 124

Functions and Modeling II(3 credits)

Prerequisite: : MAT 114 with a minimum grade of C, or equivalent.

A pre-calculus course designed for students who have completed a minimum of 3 years of New York State Regents high school mathematics or the equivalent. Topics include analysis of polynomial, rational, exponential, logarithmic, and trigonometric functions from graphical, symbolic, numerical, and verbal perspectives with an emphasis on modeling and applications of those functions in real-world contexts. No credit given to students who have previously completed MAT 126 or MAT 161 or equivalent.

MAT 126

Applied Calculus I(4 credits)

Prerequisite: MAT 124 with a minimum grade of C, or equivalent.

Intuitive introduction to differential and integral calculus. Topics include analysis of functions; derivatives of algebraic, exponential, and logarithmic functions; applications of the derivative; antiderivatives of simple algebraic, exponential, and logarithmic functions; area and the fundamental theorem of calculus. Graphical, symbolic, numerical, and verbal representations are used for all topics. Designed for students majoring in disciplines which use calculus as a tool. Credit issued for either MAT 126 or MAT 161 (or equivalents), but not for both. Prerequisite: MAT 124 with a minimum grade of C, or equivalent. Functions; limits; continuity; techniques for differentiation and applications; summations; anti-derivatives; definite integrals; fundamental theorem of calculus, techniques of integration and applications. Credit may not be earned for both MAT 126 and MAT 161 or equivalents.

MAT 127

Applied Calculus II (4 credits)

Prerequisite: MAT 126

Continuation of MAT 126. Techniques of integration; applications of integration; introduction to differential equations including separation of variables, first order linear equations, and their applications; Taylor polynomials; Newton’s method; partial derivatives; and optimization of functions of two and three variables. Graphical, symbolic, numerical, and verbal representations are used for all topics. Designed for students majoring in disciplines which use calculus as a tool. No credit given to students who have previously completed MAT 162 or equivalent.

MAT 161

Calculus I (4 credits)

Prerequisite: MAT 124 with a minimum grade of C, or equivalent.No credit given to students who have previously completed MAT 161 or equivalent.
Corequisite: MAT 163

MAT 162

Calculus II(4 credits)

Prerequisite: MAT 161
Co-requisite: MAT 164

A continuation of MAT 161. Area accumulation functions; definition of the definite integral; fundamental theorem of calculus; integration techniques; applications of integrals; improper integrals; sequences and series; function approximation. Graphic, symbolic, and numeric representations are used throughout the course. Appropriate for math majors and students in partner disciplines requiring understanding of fundamental principles of calculus with emphasis on deductive reasoning and proof.

MAT 163

Using Technology to Explore Calculus I (1 credit)

Prerequisite: Students must be concurrently enrolled in, or have successfully completed MAT 161 or its equivalent.

Weekly class session in which students use a programmable graphing utility to explore the mathematics they are learning in MAT 161.

MAT 164

Using Technology to Explore Calculus II(1 credit)

Prerequisite: Students must be concurrently enrolled in, or have successfully completed MAT 162 or its equivalent.

Weekly class session in which students use programmable graphing utilities and Computer Algebra Systems to explore the mathematics they are learning in MAT 162.

MAT 183

Problem Solving In Mathematics (3 credits)

Prerequisiste: 4 years of Regents high school math.

An introduction to the basic techniques of problem solving, creative problem solving, the methods of Polya, Wickelgren, and others, and applications to the areas of algebra, geometry, analysis, and recreational mathematics. The emphasis is on process rather than on content.

MAT 202

Introduction to Linear Algebra (3 credits)

Prerequisite: MAT 126 or MAT 161.

Vector and vector spaces; linear dependence, basis and dimension; matrices and determinants; linear systems; linear transformations; eigenvectors and invariant subspaces.

MAT 241

Computer Mathematics I (3 Credits)

Prerequisite: MAT 161 and MAT 163 or equivalent, or instructor’s permission

MAT 263

Calculus III (3 Credits)

Prerequisite: MAT 162.
Co-requisite: MAT 264

Vectors, partial differentiation, multiple integrals, and infinite series. Applications studied through algorithmic techniques and/or computer usage.

MAT 264

Using Technology to Explore Calculus III (1 credit)

Prerequisite: MAT 164; Students must be concurrently enrolled in, or have successfully completed MAT 263 or its equivalent.

Weekly class session in which students use programmable graphing utilities and Computer Algebra Systems to explore the mathematics they are learning in MAT 263.

MAT 270

Discrete Mathematics (3 credits)

Prerequisite: 4 years of high school mathematics or equivalent.

Fundamental principles used in discrete mathematics. Topics include logic, mathematical induction, sets, relations, functions, permutations, combinations, recursion, and graph theory.

MAT 301W

Fundamentals of Abstract Algebra (3 credits)

Prerequisite: MAT 202 and MAT 270

An introduction to the fundamental concepts of abstract algebra, sets, mappings, binary operations, relations, and to algebraic structures of groups, rings, fields and applications.

MAT 302

Abstract Algebra II (3 credits)

Prerequisite: MAT 301

Quotient fields of integral domains, polynomial rings. Euclidean domains, ideals, and factorization. Finite fields, extension fields, splitting fields. Applications to geometric constructions and solvability, applications chosen from contemporary areas of coding theory, block designs, etc.

MAT 304

Games and Linear Programming (3 credits)

Prerequisite: 3 years of Regents high school math.

Elementary techniques for finding optimal choices among games strategies and in linear programming problems using the fundamental minimax theorem and the simplex method. Application in such areas as business, industry, economics, social sciences, and behavioral sciences. Not open to mathematics majors.

MAT 306

Problem-Solving with Computers (3 credits)

Prerequisite: 3 years of Regents high school math.

An introduction to the mathematical uses of computers in today's society. Background; typical uses; writing programs to solve problems in number theory, geometry, finance and algebra; mathematical games; sorting. Does not satisfy Mathematics major requirements.

MAT 309

Discrete Mathematics II (3 credits)
 
Automata, modules, group codes, linear machines, polynomial rings, cyclic codes, minimum polynomials, context-free gramúmers, tree automata, polish notation, pushdown automata. Prerequisites: MAT 301 and MAT 270

MAT 311

Elementary Probability and Statistics (3 credits)

Prerequisite: MAT 110 or 3 years of Regents high school math.

Empirical frequency distributions; measures of central tendency and dispersion; theory of probability of a finite sample space; application of statistical distributions. Does not satisfy Mathematics major requirements.

MAT 315

Differential Equations (3 credits)

Prerequisite: MAT 263 and MAT 202, or permission of instructor.

Preliminary ideas of order, degree, and solutions; formation of differential equations; differential equations of first order linear equations with constant coefficients; special high order equations; simultaneous equations; linear equations of the second order, series solutions.

MAT 316

Intermediate Differential Equations (3 credits)

Prerequisite: MAT 315.

Laokacer transform; inverse Laplace transform and applications; partial differential equations; Fourier series; boundary value problems; transform methods application.

MAT 318

MATHEMATICAL MODELING (3 credits)

Prerequisites: MAT 162 and MAT 202.

Construction, interpretation and application of mathematical models; various modeling paradigms such as deterministic, probabilistic, discrete and continuous modeling. Models which provide valuable insights into contemporary topics from different fields that may include bio-medical applications, financial mathematics, cellular automata models, mathematical methods for data collection and analysis in geology, mathematical tools for GIS, and weather prediction.

MAT 319

Mathematical Biology(3 credits)

Prerequisites: MAT 161 with a minimum grade of C, or equivalent.

A project-oriented, introductory mathematical modeling course with an emphasis on the construction and analysis of mathematical models of biological events and phenomena. Mathematical topics include matrix algebra, difference and differential equations. Biological topics include population dynamics, dynamics of infectious disease and models of molecular evolution.

MAT 322W

Modern Geometry (3 credits)

Prerequisite: MAT 270

Euclidean constructions; theorems of Menelaus and Ceva; cross ratio; harmonic points; orthogonal circles; isometrics and similarites in the plane; introduction of projective geometry.

MAT 325

Probability and Statistics

Prerequisites: For 0721  majors:  MAT 270, MAT 162.  For 0520, 0521, 
0522, 0524, and 0299  majors:  (MAT 127 or MAT 162) and MAT 270 and 
MAT 311; or  permission of instructor.

Probability (graphic representations, descriptions of probabilistic events, combinatorics and combinatorial probability), discreteand continuous probability distributions,descriptive statistics, estimationand tests of hypotheses concerning means,proportions,variance and standard deviationand differences between means and proportions, Chi Square tests for goodness offit and independence, F-distribution and Analysis of
Variance, correlationand regression, non-parametric statistics.

MAT 351

Elementary Theory of Numbers (3 credits)

Prerequisite: MAT 124 or 4 years of high school math.
(MAT 270 is recommended.)

Divisibility, Euclid's Algorithm; numbers; prime factorization theorem; Euler's phi-function (totient); Diophantine analysis; congruence; theorems of Fermat, Euler, and Wilson.

MAT 366

Computer Mathematics II (3 credits)

Prerequisite: MAT 164, MAT 241 and Mat 270 or instructor's permission.

Structured programming, verification of program validity, data structures, combinatorial problems, flow network algorithms, random number generators, simulation of random and nonrandom processes.

MAT 370

Applied Networks (3 credits)

Prerequisite: MAT 202 and MAT 270.

Introduction to network and graph theoretic concepts. Consider properties with application in computational mathematics, social science decision making and physical science.

MAT 381

Probability (3 credits)

Prerequisite: MAT 270 and (MAT 127 or MAT 162).

Probability models, discrete and continuous random variables, sampling distributions, estimation, tests of hypothesis and simple linear regression.

MAT 382

Topics In Mathematical Statistics(3 credits)

Prerequisite: MAT 381 and MAT 263.

Sampling distributions; the central limit theorem; point and interval estimation; tests of hypotheses.

MAT 383

Applied Statistics  (3 credits)

Prerequisite: MAT 382 or MAT 325 or (MAT 311 and MAT 381)

Categorical data analysis; simple linear regression and correlation; multiple linear regression; experimental design models (one, two or more factors); nonparametric statistics.

MAT 390 

Introduction to Operations Research

Prerequisites:  MAT 202 and  MAT 270

Optimization of real-world problems modeled by linear objective functions subject to systems of linear inequalities and solved by either the two-phase revised simplex method or by the network simplex method. Mathematics behind these methods. Applications in diverse areas such as business management, industry, economics, finance, game theory, geometry, and networks.

MAT 401

Introduction to Computability (former title -Introduction To Turing Machines)(3 credits)

Prerequisite: MAT 270 and either MAT 301 or MAT 351

An introduction to topics in finite automata and Turing machines; universal Turing machines; topics in abstract computability theory, and general unsolvability theory.

MAT 404

Applications Of Linear Algebra(3 credits)

Prerequisite: MAT 202, MAT 263 and MAT 264 .

Selected applications of linear algebra to diverse fields such as biology, economics and ecology, as well as to other areas of mathematics including curve fitting, geometry and numerical analysis. Theory of eigenvalues/eigenvectors developed and applied to areas such as genetics, population growth, demography, conic sections, differential equations and recursive sequences.

MAT 411

Complex Variables(3 credits)

Prerequisite: MAT 263 and MAT 270

Topics selected from the theory of functions of a real and/or complex variable; axioms of real numbers, geometry of complex numbers, point set topology differentiation, analytic functions, Cauchy-Riemann equations, power series, integration, special functions, power series, integration, special functions, and the calculus of residues.

MAT 417

Introduction To Real Analysis I (3 credits)

Prerequisite: MAT 263 and MAT 270

A rigorous treatment of elementary real analysis including: topology and Cartesian spaces, Heine-Borel theorem, sequences of numbers, sequences of functions, continuous functions, limits of functions, differentiation, mean-value theorem, Weierstrauss approximation theorem.

MAT 418

Introduction To Real Analysis II (3 credits)

Prerequisite: MAT 417 or equivalent

A continuation of MAT 417 with topics to be chosen from: Reimann-Stielties integration, improper integrals, infinite series, series of functions, partial differentiation, Jacobians, implicit function, multiple integrals, and Fubini's Theorem.

MAT 431

Mathematical Logic (3 credits)

Prerequisites:     MAT 202 and MAT 270

Validity, deducibility, and completeness in propositional and predicate logics; first order formal theories and informal theories in the context of set theory.
 

MAT 461

Numerical Analysis(3 credits)

Prerequisite: MAT 202, MAT 263 and MAT 264.

Fundamentals; finite differences; difference tables; tabulation of polynomials; difference operators; linear interpolation; classical polynomial formulas; inverse interpolation; Lagrange's formulas; numerical integration; Gauss' formula difference equations.

MAT 471

Introduction To Topology(3 credits)

Prerequisite: MAT 263 and MAT 270

An introduction to topology -- sets and functions; metric spaces; topological spaces; connectedness; compactness; separation.

MAT 490

Seminar(3 credits)

Prerequisite: Senior mathematics major or permission of instructor.

Investigation of some topics of current interest to mathematicians, such as group theory, game theory, differential geometry, measure theory, sampling theory, etc.. Emphasis is on oral presentations by the students and discussion.

MAT 491

Capstone Research in Mathematics (3 credits)
 
Prerequisites: MAT301, MAT417, and senior status; or instructor permission.

Independent research under the direction of the instructor. Composition of a research paper and presentation of results at a seminar for faculty and students. This course satisfies the Intellectual Foundations requirement for Oral Communication.

MAT 495

Project (3 credits)

MAT 499

Independent Study (3 credits)

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