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# Mathematics

## ENGM 101 INTRODUCTORY MATHEMATICS FOR ENGINEERING APPLICATIONS

*Fall/Spring, 3 credits*

This course provides an overview of the salient math topics most heavily used in the core sophomore-level engineering and engineering technology course. These include algebraic manipulation of engineering equations, trigonometry, vectors and complex numbers, and system of equations. All topics are presented within the context of engineering application, and reinforced through extensive examples of their use in the core engineering or technology courses.

**Prerequisite:** Intermediate Algebra (MATH 106) or permission of instructor

## MATH 099 FUNDAMENTALS OF APPLIED MATHEMATICS

*Fall, 3 imputed credits*

The course connects mathematical concepts and procedures to real-life applications relevant to a variety of technical trade fields. Topics include: a review of fundamental arithmetic concepts, order of operations, measurement and conversions, ratio and proportion, signed numbers, exponents and radicals, estimation, and an introduction to algebra. For students with no algebra background or for those receiving less than 75 on the New York State Math A or Integrated Algebra Regents or equivalent examination, or permission of instructor. Three hours lecture per week.

## MATH 100 BEGINNING ALGEBRA

*Fall/Spring, 3 credit credits*

This course is designed to prepare the student for Intermediate Algebra (MATH106). It assumes a limited algebra background at the secondary level. Topics include: a review of arithmetic operations, signed numbers, exponents, basic geometry concepts (such as angle measure, area and volume formulas), operations with polynomials, solving linear equations, introduction to graphing, and elementary word problems. For students with a limited algebra background or for those receiving less than 75 on the New York State Math A or Integrated Algebra Regents or equivalent examination, or permission of instructor. Three hours lecture per week.

## MATH 101 APPLIED COLLEGE MATHEMATICS

*Fall, 4 credit credits*

This course is designed to prepare students for success in technical and pre-engineering technology programs. It assumes an algebraic background at an introductory level. The course connects mathematical concepts and procedures to real-life applications relevant to a variety of technical trade fields. Applications using algebra concepts are stressed in this course.

## MATH 106 INTERMEDIATE ALGEBRA

*Fall/Spring, 3 credit hours* *GER 1*

This developmental course reviews and builds on the basic, fundamental concepts of algebra, which are required in many other courses and areas of study. Topics include: a review of fundamental concepts, first degree equations and inequalities, graphing and systems of equations, products and factoring, rational expressions, exponents and radicals, quadratic equations.

**Prerequisite:** Beginning Algebra (MATH 100) with a grade of C or better, or New York State Math A or Integrated Math Regents or equivalent examination with a grade of 70 or above, or permission of instructor.

## MATH 111 SURVEY OF MATHEMATICS

*Fall/Spring, 3 credit hours GER 1*

A study of various mathematical topics including an introduction to quantitative reasoning skills, truth table logic, sets, probability, and geometry. This course is designed for non-technical oriented students. It is appropriate for students in liberal arts. Three hour lecture per week.

**Prerequisite:** Intermediate Algebra (MATH 106) with a grade of C or better, or 2 NYS high school regents math courses with a grade of 75 or above on the second New York State Regents mathematics examination, or permission of instructor.

## MATH 115 MATHEMATICS FOR ELEMENTARY TEACHERS I

*Fall/Spring, 3 credit hours GER 1*

The study of the development, meaning, and representations of numeration systems, operations on whole numbers, number theory and the real number system. The focus of the course will be on mathematical representations for K-8 topics via problem solving. This course is only open to students enrolled in the elementary education transfer program. The majority of the course will be activity-based (exploration of topics through problem solving activities). Three hours lecture per week.

**Prerequisite:** Intermediate Algebra (MATH 106) with a grade of C or better, or two (2) high school regents math courses with a grade of 75 or above on the second New York State Regents mathematics examinations, or permission of instructor.

## MATH 116 MATHEMATICS FOR ELEMENTARY TEACHERS II

*Fall/Spring, 3 credit hours*

The study of the development, meaning, and representations of statistics, patterns and functions, concepts of geometry, and measurement of two-and three-dimensional figures. The focus of the course will be on the construction of mathematical representations for K-8 topics via problem solving. This course is only open to students enrolled in the elementary education transfer program. The majority of the course will be activity-based (exploration of topics through problem solving activities.) Three hours per week.

**Prerequisite:** Mathematics for Elementary Teachers I (Math 115) with a grade of C or better, or permission of instructor.

## MATH 121 COLLEGE ALGEBRA

*Fall/Spring, 4 credit hours GER 1*

This course provides basic algebraic concepts and an introduction to trigonometric and logarithmic functions. Emphasis is placed on equations and inequalities; polynomials, rational, exponential and logarithmic functions; and graphing and data analysis including modeling and linear regression. Additional topics include complex numbers; radical functions; right triangle trigonometry; systems of equations; and elementary transcendental functions. Four hours lecture per week.

**Prerequisite:** Intermediate Algebra (MATH 106) with a grade of C or better, or two (2) high school regents math courses with a grade of 75 or above on the second New York State Regents mathematics examinations, or permission of instructor. Cannot be taken for credit by students with credit in Pre-Calculus Algebra (MATH 123).

## MATH 123 PRE-CALCULUS

*Fall/Spring, 4 credit hours GER 1*

This course provides an intense study of topics which are fundamental to the study of Calculus. Emphasis is placed on functions and their graphs with special attention to polynomial, rational, exponential, logarithmic and trigonometric functions, and analytic trigonometry. Additional topics include complex numbers; systems of equations and inequalities; trigonometric identities; and trigonometric applications. Four hours lecture per week.

**Prerequisite:** Intermediate Algebra (MATH 106) with a grade of C or better, or 3 NYS high school regents math courses with a grade of 75 or above on the third New York State Regents mathematics examination, or permission of instructor. Cannot be taken for credit by students with credit in College Algebra (MATH 121)

## MATH 131 COLLEGE TRIGONOMETRY

*Spring, 3 credit hours GER 1*

This course is designed for those students who lack the trigonometry skills needed to perform successfully in Calculus I. Topics include: angle measurement; right triangle trigonometry; trigonometric identities; trigonometric equations; graphs of trigonometric functions; inverse trigonometric functions; oblique triangles; and exponential and logarithmic functions. Three hours lecture per week.

**Prerequisite:** College Algebra (MATH121) with a grade of C or better, or 3 years of high school mathematics with a grade of 75 or above on the third New York State Regents mathematics examination, or permission of instructor.

## MATH 141 STATISTICS

*Fall/Spring, 3 credit hours GER 1*

This course is an introduction to the standard methods of descriptive statistics, probability, and inferential statistics. Topics include: organization and presentation of data, descriptive measures of data, linear correlation and regression analysis, probability, probability distributions including binomial distributions, normal distributions, Students t-distributions, and Chi-square distributions, estimation of parameters and hypothesis testing. Three hours lecture per week.

**Prerequisite:** College Algebra (MATH 121), Pre-Calculus Algebra (MATH 123), Survey of Mathematics (MATH 111), or Mathematics for Elementary Teachers II (MATH 116) with a grade of C or better, or 3 years of high school mathematics with a grade of 75 or above on the third New York State Regents mathematics examination, or permission of instructor.

## MATH 150 BUSINESS CALCULUS

*Fall/Spring, 4 credit hours GER 1*

This course is an intuitive introduction to the Calculus. Topics include: Review of functions; analytical geometry of the line, properties of limits; the derivative with applications; transcendental functions; and integrals with applications. Selected additional topics will be offered, as time permits, at the discretion of instructor. Four hours lecture per week.

**Prerequisite:** College Algebra (MATH 121) or Pre-Calculus Algebra (MATH 123) with a grade of C or better, or for students who have taken 3 NYS high school regents math courses with a grade of 75 or above on the third New York State Regents mathematics examination, or permission of instructor.

## MATH 161 CALCULUS I

*Fall, 4 credit hours GER 1*

This course is the first of a three-semester sequence of Calculus courses developed for students in Engineering Science who expect to transfer to a four-year engineering college upon completion of the program. Other qualified students may also take this sequence. Topics include: quick review of functions and graphs, limit and continuity; the derivative and its properties, differentiation of algebraic and transcendental functions, curve sketching; related rates, applied extrema problems; other applications of differentiation, numerical methods, and antidifferentiation. Four hours lecture per week.

**Prerequisite: **College Algebra (MATH 121), Pre-Calculus Algebra (MATH 123) or College Trigonometry (MATH 131) with a grade of C or better, or for students who have taken 3 NYS high school regents math courses with a grade of 75 or above on the third New York State Regents mathematics examination, or permission of instructor.

## MATH 162 CALCULUS II

*Spring, 4 credit hours*

This course is the second of a three-semester sequence in Calculus which has been designed for students in Engineering Science. Other qualified students may also take this course. Topics include: differentials; definite integrals and their applications; integration of exponential, logarithmic, trigonometric, and inverse trigonometric functions; techniques of integration; series; parametric equations and polar coordinates. Four hours lecture per week.

**Prerequisite:** Calculus I (MATH 161) with a grade of C or better recommended or permission of instructor.

## MATH 263 CALCULUS III

*Fall, 4 credits*

This course is the third of a three-semester sequence of Calculus courses developed for students in Engineering Science who expect to transfer to an engineering program at a four-year institution upon graduation. Other qualified students may also take this course. Included are topics from analytic geometry, plane curves and polar coordinates, vectors, vector valued functions, and topics from differential geometry, partial differentiation, multiple integrals, along with selected topics from vector calculus. Four hours lecture per week.

**Prerequisite:** Calculus II (MATH 162) with a grade of C or better or permission of instructor.

## MATH 341 STATISTICS II

*TBD, 3 credit hours*

Includes confidence intervals and hypothesis testing for population proportions, variance and standard deviation; hypothesis testing two samples for differences between means; correlation and regression, including multiple regression; finding prediction intervals and hypothesis tests for the linear correlation coefficient; Chi-square tests and the F-distribution; non-parametric tests. Three hours lecture per week.

**Prerequisites:** Statistics (MATH 141) with a grade of C or better, or permission of instructor

## MATH 351 DISCRETE MATHEMATICS

*Fall/Spring, 3 credit hours*

This course studies the basic tools and techniques of discrete mathematics and their applications. The topics include sets, logic, proofs, functions and relations, algorithms, elementary number theory, counting methods, discrete probability, pigeonhole principle, recurrence relations, introduction to graph theory and Boolean algebras. Three hours of lecture per week.

**Prerequisites:** College Algebra (MATH 121) or Pre- Calculus Algebra (MATH 123) with a grade of C or better, or permission of instructor.

## MATH 361 LINEAR ALGEBRA

*Spring/Fall, 3 credit hours*

This course is an introduction to the theory of finite dimensional abstract vector spaces and linear transformations. Topics include: systems of linear equations, matrices, matrix algebra, determinants and inverses, linear combinations and linear independence, abstract vector spaces, change of basis and coordinates, inner product spaces, orthonormal bases. We also consider linear transformations, isomorphisms, matrix representation of linear maps, eigenvalues and eigenvectors, diagonalization and similarity. The applications include computer graphics, Markov chains, chemistry, linear regression, network flow, electrical circuits, and differential equations. Three hours of lecture per week.

**Prerequisites:** Calculus II (MATH 162) with a grade of C or better or permission of the instructor.

## MATH 364 DIFFERENTIAL EQUATIONS

*Spring, 4 credit hours*

This course is an introduction to ordinary differential equations. Topics include: First-order, second-order, and higher-order differential equations with constant and variable coefficients, Laplace transforms, systems of linear differential equations and numerical methods, eigenvalues, and applications of first and second-order linear equations intended for engineering, mathematics, and physical science students requiring a working knowledge of differential equations.

**Prerequisite:** Calculus II (MATH 162) with a grade of C or better or permission of the instructor.

## MATH 371 GRAPH THEORY

*Spring/Fall, 3 credit hours*

This course is an introduLon to the basic concepts of graph theory. Common classes of graphs such as paths, trees and cycles are analyzed. We will consider isomorphism, connectivity, and traversability. If time permits, planarity and graph colorings may be considered. Applications are given to chemistry, engineering and computer science.

**Prerequisites:** Calculus II (MATH 162) or permission of the instructor.

## MATH 461 ADVANCED CALCULUS

*Spring/Fall, 3 credit hours*

This course is sequel to Calculus III and serves as an introduction to topics in Advanced Calculus. Topics include line, surface and volume integrals in two and three dimensional space; investigations of the gradient of a scalar field, discussion of conservative fields and potential functions; the divergence and curl of vector fields; generalizations of the fundamental theorem of calculus to evaluate integrals; curvilinear coordinates, multiple integrals and transformation o f multiple integrals; implicit functions; Jacobians; partial derivatives; higher order partial derivatives; mean value theorems; infinite series;Taylor series and an introduction to Fourier series. Subject applications are given to fluid and solid mechanics, Electrostatics, and Electromagnetism.

**Prerequisites:** Calculus III (MATH 263) and Linear Algebra (MATH 361) with a grade of C or better or permission of the instructor.

## MATH 291-295, 391-395, OR 491-495 SPECIAL TOPICS IN MATHEMATICS

*Fall/Spring, 1-4 credit hours*

Individual courses of instruction of variable credit (1-4 credits) may be offered each semester. These courses are designed to expand on topics in specific areas of mathematics.