#### Mathematics 100 Level Courses

##### Math 110

MATH 110. Mathematical Literacy: An Introduction to College Mathematics. 3 hr.; 3 cr. (Syllabus)

Mathematical literacy necessary for success in today’s highly technological society. Students will gain hands-on experience in solving real world problems in such diverse areas as law, medicine, and politics. Applications include analysis of election results and voting schemes, interpretation of medical data, and study of the nature of fair political representation. Mathematical topics covered will include an introduction to probability and statistics through normal curves and confidence intervals; exponential and logistic growth models; and the algebraic skills necessary for all the applications covered. Extensive use will also be made of today’s sophisticated graphing calculators. Successful completion of the course satisfies the Basic Skills Requirement in Mathematics and prepares students for MATH 113, 114, 116, and 119. Not open to students who are taking or have received credit, including transfer credit or advanced placement credit, for any precalculus or calculus course.

##### Math 113

Prereq.: Two and one-half years of high school mathematics including intermediate algebra.

A liberal arts mathematics course for nonmathematics, nonscience majors. Will explore several areas of mathematics to give the student an appreciation of the significance of mathematics, both in terms of its applications and of its place in the history of civilization. Subject matter drawn from virtually the entire spectrum of modern mathematics, including such areas as calculus, probability, game theory, number theory, set theory, logic, non-Euclidean geometry, topology, and group theory. Not open to students who have received credit for MATH 201 (unless permission of the chair is obtained).

##### Math 114

Prereq.: Two and one-half years of high school mathematics including intermediate algebra.

An introduction to mathematical probability and statistics for the general student. Not open to mathematics, physics, or chemistry majors, or to students receiving credit for MATH 114W, 241, 611, 621, or 633.

##### Math 114W

Prereq.: ENGL 110.

An introduction to mathematical probability and statistics for the general student with a writing-intensive component. Includes the material in MATH 114, as well as additional topics such as sampling methods, research design, and composing and conducting surveys, explored through student research and writing assignments. Not open to mathematics, physics, or chemistry majors, or to students who are taking or have passed MATH 114, 241, 611, 621, 633, BIOL 230, ECON 249, PSYCH 107, SOC 205, 206, 207. Not open to students who will be receiving transfer credit or advanced placement credit for MATH 114.

##### Math 115

MATH 115. College Algebra for Precalculus. 3 hr.; 3 cr. (Syllabus)

Prereq.: Knowledge of elementary algebra. Topics include linear, polynomial, rational, and radical expressions as mathematical models; solving equations and systems of equations that arise through the application of these models. Not open to students who are taking or have received credit, including transfer credit or advanced placement credit, for any precalculus or calculus course. Students who fail or withdraw from this course multiple times may be prohibited from majoring in the sciences or mathematics; see the bulletin language for your major.

##### Math 116

Prereq.: Knowledge of intermediate algebra.

Topics include simple interest, compound interest, mortgages, bonds, depreciation, annuities, and life insurance.

##### Math 119

MATH 119. Mathematics for Elementary School Teachers. 3 hr.; 3 cr. (Syllabus)

This course is designed to make prospective elementary schoolteachers aware of the beauty, meaning, and relevance of mathematics. Topics are taken from those areas of mathematics that are related to the elementary school curriculum, and emphasis is placed on clearing up common misunderstandings of mathematical concepts and results.

##### Math 120

MATH 120. Discrete Mathematics for Computer Science. 3 hr.; 3 cr. (Syllabus)

Prereq.: MATH 122 or the equivalent.

This course lays the groundwork for further courses in discrete mathematics and theoretical computer science. Topics include sets, functions, relations, formal logic (propositional and predicate calculus); elementary number theory; elementary combinatorics and discrete probability; introductory abstract algebra, monoids, and groups. Not open to students who have received credit for MATH 220.

##### Math 122

MATH 122. Precalculus. 4 hr.; 4 cr. (Syllabus)

Prereq.: MATH 115 or the equivalent

This course offers a thorough introduction to the topics required for calculus. Topics include real and complex numbers, algebra of functions, the fundamental theorem of algebra, trigonometry, logarithms and exponential functions, conic sections, and the use of graphic calculators. Students unsure of their preparation for calculus are advised to take the Queens College mathematics placement test.

##### Math 128

MATH 128. Mathematical Design. 3 hr.; 3 cr. (Syllabus)

Students will program computers to create digital art based on mathematical exploration of two dimensional geometry. Topics include transformations of the plane, trigonometric functions, polar coordinates, parametric functions, and Mobius transformations. No prior experience in programming is necessary.

##### Math 131

MATH 131. Calculus with Applications to the Social Sciences I. 3 hr.; 3 cr. (Syllabus)

Prereq.: MATH 122, or have a grade of A- or better in MATH 115.

Introduction of the fundamental ideas and techniques of calculus to nonscience students. Special emphasis is given to applications. Topics include functions and graphs; derivatives and differentiation techniques; the marginal concept in economics; optimization methods; compound interest; exponential and logarithmic functions. Not open to students who are taking any other calculus course or have received credit, including transfer credit or advanced placement credit, for any calculus course. Students who fail or withdraw from this course multiple times may be prohibited from majoring in the sciences or mathematics; see the bulletin language for your major.

##### Math 132

MATH 132. Calculus with Applications to the Social Sciences II. 3 hr.; 3 cr. (Syllabus)

Prereq.: MATH 131.

A continuation of MATH 131. Topics include limits and continuity; mean value theorem; antiderivatives; integrals and integration techniques; applications of the definite integral; the calculus of logarithmic, exponential, and trigonometric functions. This course prepares students who have taken MATH 131 to continue into MATH 143. Students who fail or withdraw from this course multiple times may be prohibited from majoring in the sciences or mathematics; seethe bulletin language for your major.

##### Math 141

MATH 141. Calculus/Differentiation. 3 hr.; 3 cr. (Syllabus)

Prereq.: MATH 122, or placement by departmental exam, or permission of the department.

The first part of a three-semester sequence (MATH 141, 142, 143) covering the same material as MATH 151 and 152. Credit is given for each course satisfactorily completed; a student need not take the entire sequence. Not open to students who are taking any other calculus course or have received credit, including transfer credit or advanced placement credit, for any calculus course. Students who fail or withdraw from this course multiple times may be prohibited from majoring in the sciences or mathematics; see the bulletin language for your major.

##### Math 142

MATH 142. Calculus/Integration. 3 hr.; 3 cr. (Syllabus)

Prereq.: MATH 141.

A continuation of MATH 141. Not open to students who are taking any other calculus course or have received credit, including transfer credit or advanced placement credit, for any calculus course other than MATH 141 or MATH 151. Students who fail or withdraw from this course multiple times may be prohibited from majoring in the sciences or mathematics; see the bulletin language for your major.

##### Math 143

MATH 143. Calculus/Infinite Series. 3 hr.; 3 cr. (Syllabus)

Prereq.: MATH 132 or 142. MATH 151 does not satisfy the prerequisite.

A continuation of MATH 142. Not open to students who are taking any other calculus course or have received credit, including transfer credit or advanced placement credit, for any calculus course other than MATH 131, MATH 132, MATH 141, MATH 142 or MATH 151. Students who fail or withdraw from this course multiple times may be prohibited from majoring in the sciences or mathematics; see the bulletin language for your major.

##### Math 151

MATH 151. Calculus/Differentiation & Integration. 4 hr.; 4 cr. (Syllabus)

Prereq.: MATH 122, or placement by departmental exam, or permission of the department.

The first part of a two-semester sequence (MATH 151 and 152) intended for students who want to study mathematics, physics, chemistry, or engineering. Credit is given for each course satisfactorily completed; a student need not take the entire sequence. Students who want a less rapid introduction to calculus should take MATH 141. Topics include sets, inequalities, straight lines, circles, functions, limits, continuity, the derivative, formulas of differentiation, implicit differentiation, velocity, acceleration, maxima and minima, Rolle?s theorem, the mean value theorem, points of inflection, curve sketching, and antiderivatives. Not open to students who are taking any other calculus course or have received credit, including transfer credit or advanced placement credit, for any calculus course. Not open to students who have received either a D or F in MATH 141. Students who fail or withdraw from this course multiple times may be prohibited from majoring in the sciences or mathematics; see the bulletin language for your major.

##### Math 152

MATH 152. Calculus/Integration & Infinite Series. 4 hr.; 4 cr. (Syllabus)

Prereq.: MATH 151.

Deals with several aspects of differential and integral calculus. Among the topics studied are the definite integral, applications of the definite integral, the differentiation of logarithmic, exponential, and inverse trigonometric functions, integration, indeterminate forms, improper integrals, infinite series, and expansions of functions. Applications to problems of geometry and physics. Not open to students who are taking any other calculus course or have received credit, including transfer credit or advanced placement credit, for any calculus course other than MATH 151. Students who fail or withdraw from this course multiple times may be prohibited from majoring in the sciences or mathematics; see the bulletin language for your major.

##### Math 157, 158

MATH 157, 158. Honors Calculus I, II. 4 hr.; 4 cr. each semester.

Prereq.: Permission of the chair.

Intensive courses that are the first year of a two-year sequence (MATH 157, 158, 207, 208) that will cover elementary and advanced calculus. A rigorous treatment of calculus from a modern point of view is given. The best mathematics students are urged to take this course. Students taking this course can receive advanced placement credit for calculus courses taken in high school. Not open, without permission of the department chair, to students who have passed MATH 141 or 151.

##### Math 171

MATH 171. Computer Solutions of Mathematical Problems. 2 hr.; 2 cr.

req. orcoreq.: MATH 143 or 152.

Solution of problems arising in calculus, using BASIC or another suitable programming language. No prior computer experience or knowledge of a computer language is necessary. Not open to students who are taking or who have received credit for MATH 624 or CSCI 361.

##### Math 190

MATH 190. Studies in Mathematics.

Prereq.: Permission of the chair.

Topic announced in advance. May be repeated for credit if topic is different.

#### Mathematics 200 Level Courses

##### Math 201

MATH 201. Calculus. 4 hr.; 4 cr. (Syllabus)

Prereq.: MATH 143 or 152.

A continuation of the work of MATH 143 or 152. The topics include polar coordinates, vectors, solid analytic geometry, vector valued functions, double and triple integrals, functions of several variables, partial derivatives. Wherever possible, applications are made to problems of geometry and physics. Students who fail or withdraw from this course multiple times may be prohibited from majoring in the sciences or mathematics; see the bulletin language for your major.

##### Math 202

MATH 202. Advanced Calculus. 4 hr.; 4 cr. (Syllabus)

Prereq.: MATH 201 and either MATH 231 or 237, or permission of the chair.

Vector-valued functions, higher-order derivatives, maxima and minima of functions of several variables, integrals over paths and surfaces, vector analysis.

##### Math 205

MATH 205. Mathematical Problem Solving. 3 hr.; 3 cr. (Syllabus)

Prereq. or coreq.: one year of college mathematics.

This course presents techniques and develops skills for analyzing and solving problems mathematically and for proving mathematical theorems. Students will learn to organize, extend, and apply the mathematics they know and, as necessary, will be exposed to new ideas in areas such as geometry, number theory, algebra, combinatorics, and graph theory. Not open to students who are taking or who have received credit for MATH 505.

##### Math 207, 208

MATH 207, 208. Honors Calculus III, IV. 4 lec. hr., 1 conf. hr. and independent work; 5 cr. each sem.

Prereq.: MATH 158 or 201 and permission of the chair.

Continuation of Honors Calculus I and II (MATH 157, 158), including topics of advanced calculus.

##### Math 209

MATH 209. Elementary Set Theory. 3 hr.; 3 cr.

Prereq.: MATH 122 or the equivalent.

Basic axioms of set theory, algebra of sets, relations and functions, orders, countable and uncountable sets, and additional topics at the discretion of the instructor. The course will introduce some basic proof techniques, with no background in proof-writing assumed. Not open to students who are taking or have received credit for MATH 509 or 609.

##### Math 213W

Prereq.: One semester of calculus.

Students will learn to program in Mathematica, a high-level programming language, and use this capability to explore a number of interesting problems taken from number theory, combinatorics, probability, game theory, and calculus. They will learn how to conduct research in mathematics, using Mathematica, and also how to write up their research effort in a final project. No prior experience in programming is necessary. Students may not receive credit for both this course and MATH 503.

##### Math 220

MATH 220. Discrete Mathematics. 3 hr.; 3 cr.

rereq.: One semester of calculus.

Discrete structures including sets, relations, and functions. Enumeration. Propositional and predicate logic. Proof techniques. Graphs, trees, and networks. Not open to students who are taking or have received credit for MATH 120.

##### Math 223

MATH 223. Differential Equations with Numerical Methods I. 3 hr.; 3 cr.

rereq.: MATH 201 and 231.

First order linear, separable, and exact equations; second order linear equations; series solutions; existence and uniqueness theorem; numerical solutions; applications. Students receiving credit for this course may not receive credit for MATH 217.

##### Math 224

rereq.: MATH 223, and either MATH 231 or 237.

Linear systems of equations; stability of linear systems, orbits, phase portraits, periodic solutions, stability; boundary value problems; applications.

##### Math 231

MATH 231. Linear Algebra I. 4 hr.; 4 cr.

Prereq.: Math 141 or 151.

An introduction to linear algebra with emphasis on techniques and applications. Topics to be covered include solutions of systems of linear equations, vector spaces, bases and dimension, linear transformations, matrix algebra, determinants, eigenvalues, and inner products. Not open to students who are enrolled in or who have completed MATH 237. Students who fail or withdraw from this course multiple times may be prohibited from majoring in the sciences or mathematics; see the bulletin language for your major.

##### Math 232

rereq.: MATH 231.

A second course in linear algebra. Topics include a continuation of matrices and linear transformations, canonical forms, invariants, equivalence relations, similarity of matrices, eigenvalues and eigenvectors, orthogonal transformations and rigid motions, quadratic forms, bilinear maps, symmetric matrices, reduction of a real quadratic form and applications to conic sections and quadric surfaces. Not open except by permission of the chair to students who are enrolled in or who have completed MATH 237.

##### Math 237

MATH 237. Honors Linear Algebra. 4 hr.; 4 cr.

Prereq.: Permission of the chair.

An intensive course in linear algebra for superior mathematics students. Not open to students who are enrolled in or who have completed MATH 231.

##### Math 241

MATH 241. Introduction to Probability and Mathematical Statistics. 3 hr.; 3 cr.

Prereq.or coreq.: MATH 143 or 152.

An introduction to the basic concepts and techniques of probability and statistics with an emphasis on applications. Topics to be covered include the axioms of probability, combinatorial methods, conditional probability, discrete and continuous random variables and distributions, expectations, confidence interval estimations, and tests of hypotheses using the normal, t- and chi-square distributions. Students taking this course may not subsequently receive credit for MATH 114, except by permission of the chair. Not open to students who are taking or have received credit for MATH 611.

##### Math 242

MATH 242. Methods of Mathematical Statistics. 3 hr.; 3 cr. (Syllabus)

Prereq.: MATH 241.

A study of those methods of mathematical statistics that are most frequently used in the natural and social sciences, as well as actuarial science. Topics include estimation testing of statistical hypotheses, nonparametric tests, analysis of variance, correlation and regression analysis, and other methods of statistical analysis.

##### Math 245

Prereq.: MATH 132 or 142 or 152, and permission of the instructor.

Construction, analysis, and assessment of mathematical models as they arise in the physical, biological, and social sciences. Specific topics to be announced in advance. May be repeated for credit with permission of the chair.

##### Math 247

MATH 247. Linear Programming and Game Theory. 3 hr.; 3 cr. (Syllabus)

Prereq.: MATH 231 or 237.

Methods for handling optimization problems that arise in management, engineering, physical sciences, and social sciences. Topics include convex geometry, the simplex algorithm, duality theory, and the Von Neumann minimax theorem of game theory.

##### Math 248

MATH 248. Nonlinear Programming. 3 hr.; 3 cr.

Prereq.: MATH 201 and either MATH 231 or 237.

Iterative methods for solving nonlinear optimization problems; techniques for handling problems with and without constraints; termination criteria and convergence analysis.

##### Math 250

MATH 250. Mathematical Computing. 3 hr.; 3 cr.

Prereq.: MATH 201 or MATH 231.

Introduction to a mathematical programming language such as Mathematica, Maple, MATLAB, or Sage. Students will learn algorithmic thinking and apply these ideas to explore problems arising in various areas of mathematics. No prior experience in programming is necessary.

##### Math 271

Prereq.: MATH 241 (or MATH 611).

Coreq.: MATH 201.

This course covers probability and probability-based actuarial mathematics required for the Exam P examination of the Society of Actuaries.

##### Math 272

Prereq.: MATH 241 (or MATH 611), and MATH 201.

Coreq.: At least one of MATH 242, 621, and 633, where MATH 633 is probably the most efficient.

This course covers probability and probability-based actuarial mathematics required for the Exam P examination of the Society of Actuaries. MATH 272 focuses on problems similar to those covered in MATH 271, but with an increased emphasis on MATH 201 topics, such as double integrals and functions of two or more variables.

##### Math 290

Prereq.: Permission of the chair.

Topic announced in advance. May be repeated for credit if topic is different.

#### Mathematics 300 Level Courses

##### Math 301 [Formerly Math 333]

Prereq.: MATH 231 or the equivalent.

Theory of groups, including cyclic and permutation groups, homomorphisms, normal subgroups and quotient groups. Theory of rings, including integral domains and polynomial rings. Additional topics may be discussed. Not open to students who are taking or who have received credit for MATH 601 or 702.

##### Math 302

Prereq.: MATH 301 (or 601).

This is a continuation of Math 301. Advanced topics in group and ring theory. Fields and field extensions. Not open to students who are taking or who have received credit for MATH 602 or 702.

##### Math 305

Prereq.: MATH 231 or MATH 237.

Prime numbers, the unique factorization property of integers, linear and non-linear Diophantine equations, congruences, modular arithmetic, quadratic reciprocity, contemporary applications in computing and cryptography. Not open to students who are taking or have received credit for MATH 605.

##### Math 310

MATH 310. Elementary Real Analysis. 3 hr.; 3 cr. (Syllabus)

Prereq.: MATH 201.

Rigorous introduction to functions of a real variable. Topics include real numbers and the completeness property; limits of sequences; elementary topological concepts; continuity and uniform continuity; sequences and series of functions, derivatives; Taylor’s theorem; the Riemann integral.

##### Math 316

MATH 316. Complex Analysis. 3 hr.; 3 cr.

Prereq.: MATH 202.

Topics covered include analytic functions, Cauchy?s Integral Theorem, Taylor?s theorem and Laurent series, the calculus of residues, singularities, meromorphic functions. Not open to students who are taking or have received credit for MATH 616.

##### Math 317

MATH 317. Foundations of Analysis. 3 hr.; 3 cr. (Syllabus)

Prereq.: MATH 201.

Language of logic and set theory; relations and functions; Peano systems; iterative processes; the natural numbers; integers and integral domains; rational numbers and fields; completeness and the real numbers; alternative characterizations of the real numbers; Archimedean order. Undergraduate students may elect MATH 617 in place of MATH 317. Students may not take both courses.

##### Math 310

MATH 318. Foundations of Geometry. 3 hr.; 3 cr.

Prereq.: MATH 201 and two proof-based courses in mathematics such as MATH 209, 220, 301, 302, 310, or 320.

The course is an exploration of Euclid?s fifth postulate, often referred to as the parallel postulate. Development of the basics of Euclidean geometry with a focus on understanding the role of the fifth postulate. Development and exploration of hyperbolic geometry, a non-Euclidean geometry. Not open to students who are taking or have received credit for MATH 618.

##### Math 320

MATH 320. Point-Set Topology. 3 hr.; 3 cr. (Syllabus)

coreq.: MATH 201.

The basic concepts and fundamental results of point-set topology. The course includes a review of sets and functions, as well as the study of topological spaces including metric spaces, continuous functions, connectedness, compactness, and elementary constructions of topological spaces. Not open to students who are taking or who have received credit for MATH 620.

##### Math 328

MATH 328. Introduction to Partial Differential Equations. 3 hr.; 3 cr.

Prereq.: MATH 223.

Topics covered include partial differential equations, Fourier series, and boundary value problems.

##### Math 334

MATH 334. Graph Theory. 3 hr.; 3 cr.

Prereq.: MATH 231.

Families of graphs, graph statistics, graph isomorphism, coloring, cycles, connectivity, planarity, graph algorithms. Not open to students who are taking or have received credit for MATH 634.

##### Math 337

MATH 337. Honors Abstract Algebra I. 3 hr.; 3 cr.

Prereq.: Permission of the chair.

The first part of an intensive two-semester* sequence for students intending to do advanced work related to mathematics. Definitions, examples, and basic properties of groups, rings, fields, and vector spaces. (*Credit may be received for MATH 337 without completing MATH 338. Credit may not be received for both MATH 337 and either MATH 333 or 613. It is suggested that students needing a slower presentation of abstract algebra register for MATH 333 or 613 instead.)

##### Math 340

MATH 340. Probability Theory for Data Science. 4 hr.; 4 cr.

Prereq.: MATH 241. Coreq: Math 201 and Math 231

Topics include introducing common random variable models, the central limit theorem, law of large numbers, random variable convergence. Topics may also include order statistics, probability inequalities, Slutsky’s Theorem, Markov chains and stochastic gradient descent. Probability computation using modern software. Not open to students who are taking or who have received credit for MATH 640.

##### Math 341

MATH 341. Statistical Theory for Data Science. 4 hr.; 4 cr.

Coreq.: MATH 340.

Point estimation, confidence sets and hypothesis testing from both the Frequentist

and Bayesian perspectives. Topics may also include power calculations, multiple

comparisons, model selection and randomized experimentation. Not open to students who are taking or who have received credit for MATH 641

##### Math 342W

MATH 342W. Data Sci via Machine Learning. 6 hr.; 4 cr.

Prereq.: ENGL 110, MATH 231, MATH 241, CSCI 111 (or equivalent)

Philosophy of modeling with data. Prediction via linear models and machine learning including support vector machines and random forests. Probability estimation and asymmetric costs. Underfitting vs. overfitting and model validation.

Formal instruction of data manipulation, visualization and statistical computing in a

modern language. Not open to students who are taking or who have received credit for MATH 642. Writing Intensive (W). Recommended corequisites include ECON 382, 387, MATH 341, MATH 343 or their equivalents.

##### Math 343

MATH 343. Computation Stats for Data Sci. 3 hr.; 3 cr.

Prereq.: MATH 341. Coreq.: MATH 342W.

Topics may include the Score and generalized likelihood ratio tests, chi-squared

tests, Kolmogorov-Smirnov test, basic linear model theory, ridge and lasso, Metropolis-within-Gibbs sampling, permutation tests, the bootstrap and survival modeling. Special topics. Not open to students who are taking or who have received credit for MATH 643.

##### Math 385W

MATH 385W. Mathematical Foundations of the Secondary School Curriculum. 6 hr.; 4 cr. (Syllabus)

Prereq.: MATH 201, 231, 241, SEYS 201, 221, and minimum 2.67 mathematics GPA, and permission of the instructor.

Designed to give prospective secondary school mathematics teachers an understanding of the mathematics they will be teaching as well as the history of mathematics. An examination will be made of the thought underlying the secondary curriculum, from a consideration of the nature of mathematics and mathematical thought to the construction of simple mathematical models drawn from secondary school topics. Students will work in small groups to create and implement lessons.

##### Math 390

MATH 390. Studies in Mathematics.

Prereq.: Permission of the chair.

Topics announced in advance. May be repeated for credit if topic is different.

##### Math 391, 392

MATH 391, 392. Special Problems.

Prereq.: Junior or senior standing and permission of the chair.

Each student works on a minor research problem under the supervision of a member of the department. Only students of exceptional mathematical ability and promise are admitted to the course.

##### Math 395

MATH 395. Honors Seminar I.

Prereq.: Permission of the instructor.

A specific area of current research interest will be studied. As the specific material covered may vary from year to year, this course may be taken for credit more than once if the subject matter changes.

##### Math 396

MATH 396. Honors Seminar II.

Prereq.: MATH 395.

Continuation of MATH 395.