MTH 009 Arithmetic and Basic Algebra: Math I
0 credits; 4 class hours
This course is designed to provide a foundation in the principles and methods of arithmetic and an introduction to basic algebra. Topics include number line concepts and diagrams, the arithmetic of whole numbers, integers, common fractions, decimals and percents, applications of integers, common factors, basic geometry, formulas, evaluation, ratio and proportions and solving simple equations in one variable. Furthermore, applications of fractions and percents to everyday problems as well as introduction to word problems are included. Computer aided instruction and calculators will be integrated into the classes; however, no calculators are used during exams. Pre-requisites: Incoming Student and Placement by CUNY/COMPASS Assessment Test
MTH 010 Elementary Algebra: Math II
0 credits; 4 class hours
The course is designed to provide students with a solid background in real number algebra. Topics include elementary properties of the real number system and number line diagrams, exponents, polynomials, coordinate systems, graphs, factoring and algebraic fractions, linear and quadratic equations and their applications. Computer aided instruction and calculators will be integrated into the classes. Pre-requisite: MTHP 009 or Exemption by CUNY/COMPASS Assessment Test
MTH 115 Nature of Mathematics I
3 credits; 3 class hours, 1 conference hour
This course is designed to provide the students in the liberal arts with an introduction to some of the major concepts of modern mathematics. Topics include why and how numbers were invented, history of mathematics; set theory and Venn diagrams, comparative study of algebra of sets, and algebra of numbers, applications to logic circuits; selected topics from number theory; counting and elementary probability; compound interest, discrete and continuous. Calculators and computers will be used to do experiments and illustrate mathematical concepts. Writing assignments will be given culminating in a term paper. Pre-requisite: MTH 010 or Placement by CUNY COMPASS Assessment Tests for Incoming Students
MTH 136 Intermediate Algebra and Trigonometry
3 credits; 4 class hours
This course is designed to provide students in general with the knowledge and skills needed for further studies in the mathematical and physical sciences as well as in such fields as accounting and finance, marketing and management. The topics to be discussed in this course include rational and polynomial expressions, graphical methods, solving equations and systems of equations by Cramer's Rule, principles of analytic trigonometry, exponentials and logarithms, induction, the binomial theorem, progressions, conic sections. Applications to various fields will be emphasized. Electronic calculators will be used throughout the course to perform detailed numerical calculations. Pre-requisite: Exit from Initial Placement by CUNY COMPASS Assessment Tests
MTH 138 College Algebra And Trigonometry
3 credits; 5 class hours
This course is designed to provide initial preparation in mathematics for students who are majoring in, or who intend to major in, the mathematical sciences, computer science, or environmental science. It is also for those in other science programs whose course of study requires advanced mathematical skills and training. A thorough understanding of the topics to be studied in this course will form the essential background for further studies in the mathematical and physical sciences and related fields. The topics to be discussed include solutions of compound statements including absolute value equations and inequalities, rational and radical equations and inequalities, the algebra of functions, modeling with exponential and logarithmic functions, systems of linear equations by the Gaussian and Gauss-Jordan elimination methods, nonlinear systems of equations and inequalities, conic sections and parametric equations, modeling with exponentials and logarithms, sequence and series, the binomial theorem, and mathematical induction. Topics from trigonometry include trigonometric functions and their inverses, graphs, identities and equations, the laws of sines and cosines with applications, polar coordinates and De Moivre's theorem. Electronic calculators and computers (based on availability) will be used throughout the course to perform detailed numerical calculations, and graphical presentations. Pre-requisite: Initial Placement by CUNY COMPASS Assessment Tests
MTH 141 Finite Mathematics
4 credits; 4 class hours
This course is designed to provide non-science majors with the mathematical background required for the applications of elementary quantitative methods to problems in business and the social sciences. The topics covered include basic probability theory and its applications, introductory statistics, matrices and linear programming, as well as concepts from precalculus and calculus such as set relations and functions, introduction to limits, and the rule for differentiating simple algebraic functions. Whenever appropriate, computers and calculators will be integrated into the course. Prerequisite: MTH 136 or MTH 138
MTH 151 Pre-Calculus
4 credits; 4 class hours; 1 lab hour
This course is designed to provide students with the mathematical preparation necessary for a successful study of calculus. It also gives students in general education an opportunity to fulfill their desire for a mature investigation and understanding of the level of mathematics beyond the Algebra sequence through the study of real functions. In the study of the properties of real functions, both analytical and graphical methods will be used. Whenever possible, an effort will be made to apply mathematics to problems in the sciences and other disciplines. Topics include absolute value equations and inequalities; polynomial, rational, trigonometric, exponential and logarithmic functions and composite and inverse functions. Computers and calculators will be utilized throughout the course to enhance understanding of mathematics concepts. Prerequisite: MTH 136 or MTH 138 or Initial Placement by CUNY COMPASS Assessment Tests
MTH 202 Calculus I
4 credits; 4 class hours; 2 lab hours
The analysis of functions numerically, graphically, and algebraically, aided by technology; velocity and distance; Riemann sums; the integral assigned area; Fundamental Theorem of Calculus; antiderivatives and the indefinite integral; basic properties of integrals; integrals tables; techniques of closed form integration; numerical integrations; Taylor series; applications of integrals to problems in geometry and the sciences. Pre-requisite: MTH 151 with a Grade of "C" or Better
MTH 203 Calculus II
4 credits; 4 class hours; 2 lab hours
The analysis of functions numerically, graphically, and algebraically, aided by technology; velocity and distance; Riemann sums; the integral assigned area; Fundamental Theorem of Calculus; antiderivatives and the indefinite integral; basic properties of integrals; integrals tables; techniques of closed form integration; numerical integrations; Taylor series; applications of integrals to problems in geometry and the sciences. Pre-requisite: MTH 202 with a Grade of "C" or Better
MTH 204 Calculus III
4 credits; 4 class hours; 2 lab hours
This course generalizes the concepts and applications of the differential and integral calculus of functions of one variable to higher dimensions. The analysis of multivariable functions numerically, graphically, and algebraically aided by technology; partial derivatives, directional derivative; Taylor approximations; optimization, the quadric surfaces, polar, cylindrical, spherical coordinates; vector fields, line and surface integrals; multiple integrals. Pre-requisite: MTH 203 with a Grade of "C" or Better
MTH 205 Elementary Differential Equations
3 credits; 3 class hours; 1 lab hour
This course is designed to introduce students to the idea and nature of ordinary differential equations. Computers will be integrated in teaching the theory and applications in gaining insight into the solution of both linear and nonlinear differential equations. Topics covered include direction fields, phase planes and phase portraits; first order equations, higher order equations, systems of first order differential equations, the Laplace transform; and series solutions. Pre-requisite: MTH 203 with a grade of "C" or better.
MTH 206 Introduction to Mathematical Proof
4 credits; 4 class hours
This course is designed to provide students in the mathematical sciences degree program with a general introduction to the formal language and methods of proof and argument that are universally applied in the mathematical sciences. The close relationship between language (both natural and symbolic) and mathematical abstractions will be discussed in detail. The roles of undefined terms and defined terms in mathematics as well as the distinctions between them will be presented and illustrated. The basic mathematical terminology and standard notational systems will be presented, and students will be shown how to devise acceptable and efficient descriptive notation and symbols that may be required for specific mathematical tasks. The concepts of logical truth and consistency, along with the qualifiers and their use will be analyzed in detail. The construction method, the choose method, and the first and second principles of mathematical induction will be discussed in detail as will the indirect methods of proof by contradiction and proof by contrapositives. Proofs based on arguments by the method of exhaustion along with arguments based on the exhibition of a counterexample will be presented and illustrated. The distinction between general proofs and specific illustrations (examples) will be emphasized. Existence and uniqueness arguments from various branches of mathematics will be presented. Writing original proofs and detailed analyses will be emphasized throughout the course. When appropriate, computers will be used to test specific cases of general principles. Pre-requisite: MTH 202
MTH 207 Linear Algebra I
3 credits; 3 class hours; 1 lab hour
The course is designed to introduce students to elements of finite dimensional vector spaces over real numbers; linear transformations and applications; system of matrices; independence of vectors, bases, dimension; dot product; projections; linear transformations, matrix representation; eigenvalues and eigenvectors, diagonalization. Pre-requisite: MTH 202
MTH 209 Elementary Statistics
4 credits; 4 class hours
This course is designed to provide students with the basic statistical techniques commonly used in data collection, analysis and interpretation. Familiarity with such techniques is essential for any program of study and is vital for the nursing program. Topics include tabulation and presentation of data by charts and graphs; description of data using numerical measures: mean, median, mode, percentiles, variance and standard deviation; description of bi-variate data by scatter diagram, correlation co-efficient and regression line; intuitive development of probability for studying binomial and normal distributions; and applications to statistical inference such as estimation and tests of hypotheses. Required for nursing students. Whenever appropriate, computers and calculators will be integrated into the course. Not open to Science and Business students. Prerequisite: MTH 136 or MTH 138
MTH 213 Introduction to Statistics
3 credits; 3 class hours; 1 lab hour
This course is designed to provide students with an introduction to basic statistical techniques commonly used in data analysis and business operations. This course focuses on the use of statistics as a tool to navigate and make sensible decisions in an increasingly quantitative world. Topics include tabulation and presentation of data; descriptive statistics; elementary probability theory; binomial and normal distributions with applications to sampling theory; the Central Limit Theorem; confidence intervals; hypothesis testing; correlation; linear regression. Statistical computer programs will be integrated into the course and will be used extensively. Not open to Science and Nursing students. Pre-requisites: MTH 136 or MTH 138
MTH 215 Nature of Mathematics II
4 credits; 4 class hours
This course is a continuation of MTH 115 and is designed to provide the students in the liberal arts with additional major concepts of modern mathematics including the design of mathematical models that describe real world situations and how these models can be used to obtain solutions to a wide variety of practical problems. Topics include interest, annuities and amortization, inferential statistics, application of symbolic logic and predicate calculus to switching circuits, graph theory and its applications. Pre-requisite: MTH 115
MTH 220 Introduction to College Geometry
3 credits ; 3 class hours
This course is designed to provide students with a survey of geometry and geometric methods. Students will be introduced to axiomatic systems and will be shown how different systems result in different geometries. The relationship between algebra and geometry will be examined in terms of coordinates in the plane and space. The perimeter, area and volume formulas for elementary plane and solid figures will be derived and applied to practical problems. The nature of proofs and their development from basic principles will be emphasized as will computational methods and compass and straightedge constructions. Non-Euclidean geometry will be investigated. Pre-requisite: MTH 136 or MTH 138
MTH 222 Introduction to Probability and Statistics
4 credits; 4 class hours
This course is designed to provide students with an introduction to statistical techniques commonly used in scientific research and business operations. The course will provide a strong foundation of statistical concepts for science and business majors. Topics include tabulation and presentation of data; numerical descriptions by measures of central tendency, measures of variability and measures of position; elementary probability theory leading to probability distributions and applications in statistics; binomial and normal distribution with applications to sampling theory and statistical inference such as estimation and test of hypotheses based on small and large samples; bi-variate data and correlation analysis; contingency tables and tests based on chi-square distribution; and introduction to analysis of variance. Whenever appropriate, computers and calculators will be integrated into the course. Not open to students majoring in Mathematics. Pre-requisite: MTH 136 or MTH 138
MTH 231 Mathematics for Elementary Educators
3 credits; 3 class hours
This course is designed to help prospective teachers of elementary school mathematics to view elementary mathematics from a higher standpoint. Students will be provided with an enriched background in a broad selection of topics from advanced mathematics through exploration, conjecture and reasoning. The topics covered include numeration system, number theory, decimals, ratios, and percents, intuitive plane and solid geometry and mensuration, construction, magic square and modular arithmetic, probability and statistics.
Whenever appropriate, computers and calculators will be integrated into the course. Pre-requisite: MTH 136 or MTH 138
MTH 237 Probability and Statistics
3 credits; 3 class hours
This course will provide a calculus-based introduction of probability theory and applications to statistical inference. Topics will include discrete and continuous probability distributions, moment generating functions, laws of large numbers, limit theorems, sampling distributions, and statistical inference using z, t, f and c2 distributions. Pre-requisite: MTH 203
MTH 241 Calculus for Business and Social Sciences
4 credits; 4 class hours
This course is designed to provide non-science majors with a mathematical background required for the application of elementary quantitative methods to problems in business and the social sciences. This course is also designed to provide students with a solid background in those topics from calculus that have applications in the study of business and economics. Topics to be studied include the derivative, graphing and optimization, and the chain rule. Integration techniques will be developed and then applied to business and economic problems. Topics from multivariable calculus include the use of the Lagrange multiplier in maxima and minima problems. The method of solving initial-value problems involving firstorder linear differential equations and their applications to business, economics, and social sciences will be presented. Pre-requisite: MTH 141
MTH 305 Number Theory
4 credits; 4 class hours
This course is intended to introduce students to classical number theory, including its proof techniques and history. Topics include divisibility, primes and their distribution, congruence, quadratic residues, Diophantine equations, continued fractions, and numbertheoretic functions. Pre-requisite: MTH 206
MTH 306 Set Theory
3 credits; 3 class hours
This course is designed to provide students with a thorough knowledge of notations, concepts, and language of set theory. The axiomatic basis of set theory will be presented, as will operations relations and functions, and composites. The Axiom of Choice, Zorn's Lemma, and the Well-Ordering Principle will be discussed. Ordinal and transfinite recursion and ordinal arithmetic will be explored. The Schroeder-Bernstein Theorem will be presented, as will countability, cardinality and cardinal arithmetic. Pre-requisite: MTH 206 or Permission of Chairperson
MTH 308 Abstract Algebra I
4 credits; 4 class hours
The course is designed to provide an introduction to modern, abstract algebra through concrete structures. Topics include congruence in integers; groups; rings; fields and field extensions; and applications. Pre-requisite: MTH 206
MTH 309 Abstract Algebra II
4 credits; 4 class hours
This course is designed to provide a deeper investigation of the structures and proof techniques introduced in MTH 308. Among the topics to be discussed will be the Sylow theorems, algebraic free abelian groups, group representations, factor rings and ideals, modules, field extensions, Galois Theory, and selected applications of abstract algebra. Pre-requisite: MTH 308
MTH 310 Matrices and Groups for the Sciences
3 credits; 3 class hours
This course is specifically designed to provide students in the space science program, the chemistry and the environmental science program, the physics program, and the computer science program with a survey of the basic tools from abstract and linear algebra that are used by physical scientists. The traditional topics on sets, basic counting principles and formulas, relations, mappings, linear transformations and matrixes as well as applications of these concepts to the sciences will be discussed in detail. Basic matrix algebra, inverses, transposes, adjoints and special matrices (such as unitary and hermitian matrices), along with systems of linear algebraic equations will be presented. Eigenvalues and eigenvectors, diagonalization of matrices and functions of matrices will be studied and applications of matrices to such areas in the physical and computer sciences as quantum mechanics, physical chemistry, advanced inorganic chemistry and networks, and computer graphics will be emphasized. Throughout the course the emphasis will be on the application(s) of abstract mathematical systems to the physical sciences. Use of the mathematical software MAPLE will be emphasized for all numerical and graphical work. Pre-requisite: Permission of chairperson
MTH 311 Advanced Calculus I
4 credits; 4 class hours
This course will offer an introduction to the rigorous analysis of functions of one and several variables that will provide students with the background needed for advanced study in pure and applied analysis. Topics will include properties of the real number system, limits, continuity, differentiability, vector analysis, and introductory differential geometry. Pre-requisite: MTH 203 and MTH 206
MTH 312 Advanced Calculus II
4 credits; 4 class hours
This course will offer a continuation of the rigorous analysis of functions begun in MTH 311. Topics will include multiple integrals, line and surface integrals, Green's Theorem, Stokes' Theorem, infinite series and improper integrals. Pre-requisite: MTH 311
MTH 315 Complex Variables I
4 credits; 4 class hours
The course is designed to provide a rigorous introduction to the theory and applications of functions of a complex variable. Among the topics to be discussed are complex numbers, complex functions, analytic and harmonic functions, the Cauchy-Riemann equations, complex integration, Cauchy's integral theorem, Liouville's Theorem, Taylor and Laurent series, singularities, residues, the Argument Principle, and Rouche's Theorem. Pre-requisite: MTH 203
MTH 316 Complex Variables II
4 credits; 4 class hours
After a review of selected results from MTH 315, the student will be introduced to more advanced topics in classical complex function theory. Topics to be discussed may include conformal mappings, the Riemann mapping theorem, analytic continuation, infinite products, the gamma function, asymptotic series, Jensen's theorem, the Phragmen-Lindelof theorems, and various applications of complex function theory. Pre-requisite: MTH 315
MTH 317 Linear Algebra II
4 credits; 4 class hours
This is a second course in linear algebra. It emphasizes abstract vector spaces and linear maps and provides a rigorous development of the fundamental theorems about them. Topics include vector spaces, linear maps, eigenvalues and eigenvectors, inner-product spaces and their operators, the polar and singular-value decompositions, the characteristic and minimal polynomials, the Jordan Normal Form. This course also covers applications of linear algebra to geometry, matrix analysis or data analysis. Pre-requisite: MTH 204, MTH 206 and MTH 207 with a Grade of "C" or Better
MTH 324 Introduction to Differential Geometry
4 credits; 4 class hours
This course is designed to provide students in the Mathematical Sciences Program with an introduction to the classical (local) differential geometry of curves and surfaces in R3 using vector methods. The concepts of arc length, curvature, torsion along with the fundamental systems of basic unit vectors and the associated lines and planes will be discussed. The Serret-Frenet formulas and their application and the moving trihedron will be investigated in detail. The representation problem in terms of the natural parameter (arc lengths) and the general theory of smooth space (twisted or gauche) curves will be emphasized, as will the representation problem and elementary theory of smooth surfaces embedded in Euclidean space. The First and Second Fundamental Forms will be presented and the various curves on embedded surfaces (such as lines of curvature, asymptotic lines, and directions) will be discussed, as will Meusnier’s theorem, Euler’s theorem and the Dupin indicatrix. Elementary principles and methods of the tensor calculus will be introduced as a means of investigating the Fundamental Theorem of Surface Theory, the Gauss-Weingarten equations, and the Mainardi-Codazzi equations. The Theorema Egrigium of Gauss will be discussed, as will the concepts of geodesics and geodesic coordinates. The course will conclude with an analysis of the classical Gauss-Bonnet Theorem and its implications. Pre-requisite: MTH 204 AND MTH 207
MTH 335 Discrete Mathematical Structures
4 credits; 4 class hours
An introductory course that introduces students to the major topics in elementary discrete mathematics and builds skills in mathematical reasoning and proof techniques. The course will cover such topics as sets, algorithms, mathematical induction, recursion, counting techniques, relations, graphs, trees, Boolean algebra, and applications. Pre-requisite: MTH 207
MTH 345 Mathematical Modeling
4 credits; 4 class hours
An introduction to the principles and techniques of mathematical modeling that builds upon the mathematics the students have already seen and enhances their abilities to apply mathematics to solve scientific and industrial problems. Topics will include the modeling process, graphs, proportionality, model fitting, optimization, experimental modeling, dimensional analysis and similitude, simulation modeling, dynamic systems, graph-theoretic models, game-theoretic models, and a summary of the modeling process emphasizing tools and the literature. Pre-requisite: MTH 203
MTH 353 General Topology
4 credits; 4 class hours
A rigorous introduction to the concepts of point-set and algebraic topology that will provide a foundation for further studies in advanced mathematics and enhance students' abilities to think abstractly. Topics will include set theory, pseudometric spaces, topological spaces, continuous functions, connected and compact spaces, product spaces, sequences, complete pseudometric spaces, Euclidean spaces, quotient spaces, hyperspaces and multi functions, dimension, and an introduction to algebraic topology. Pre-requisite: MTH 311
MTH 360 Numerical Analysis
4 credits; 4 class hours
This course will provide an introduction to numerical methods that provides the foundation for further work in pure and applied mathematics. The course includes a review of calculus, a survey of numerical software, solution of equations in one variable, interpolation and polynomial approximation, numerical differentiation and integration, initial value problems for ordinary differential equations, linear systems, iterative techniques in linear algebra, approximation theory, nonlinear systems of equations, and boundary value problems for ordinary differential equations. Pre-requisite: MTH 203
MTH 400 Special Topics in Mathematics
3 credits; 3 class hours
The content of this course will vary depending on the interests and needs of the students and the interests of the faculty. Selected topics in advanced mathematics will be discussed. The course will allow students to experience specialized areas of mathematics that are not a regular part of the curriculum. Pre-requisite: Permission of chairperson
MTH 405 Senior Seminar
1 credit; 3 class hours
This is a capstone course that builds upon the mathematical maturity developed in earlier courses. It will require the reading of current and classical articles in mathematics journals and will develop a student's ability to solve problems. The course will unify the students' previous course work and illustrate the power and usefulness of mathematics in the modern world. Pre-requisite: Permission of chairperson
MTH 411/412/413 Independent Research I, II, III 3
3 credits; 3 class hours
A minimum of 9 hours of conference and independent research per week will be required. Library and/or laboratory investigation of problems in mathematical science or related fields will be selected and pursued under the guidance of the faculty of the department. Regular meetings with advisor, presentation of findings at departmental seminars, and submission of a written report of research carried out will also be required. Pre-requisite: Completion of all required 300 Level Courses or Permission of chairperson. Only 3 of these credits may be applied to the Bachelors degree.
COMPASS Assessment Test
4 credits; 4 class hours; 1 lab hour
This course is designed to provide students with the mathematical preparation necessary for a successful study of calculus. It also gives students in general education an opportunity to fulfill their desire for a mature investigation and understanding of the level of mathematics beyond the Algebra sequence through the study of real functions. In the study of the properties of real functions, both analytical and graphical methods will be used. Whenever possible, an effort will be made to apply mathematics to problems in the sciences and other disciplines. Topics include absolute value equations and inequalities; polynomial, rational, trigonometric, exponential and logarithmic functions and composite and inverse functions. Computers and calculators will be utilized throughout the course to enhance understanding of mathematics concepts. Prerequisite: MTH 136 or MTH 138