### 100-level

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

This course will give students the 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.*

*MATH 113.* Ideas in Mathematics. 3 hr.; 3 cr.

*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.* Elementary Probability and Statistics. 3 hr.; 3 cr.

*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.* Elementary Probability and Statistics. 4 hr.; 4 cr.

*Prereq.:* ENGL 110.

An introduction to mathematical probability and statistics for the general student with writing-intensive component. Includes the material in MATH 114, as well additional topics such as sampling methods, research design, composing and conducting surveys, explored through student research and writing assignments.
*Not open to mathematics, physics, or chemistry majors, or to students receiving credit for MATH 114, 241, 611, 621, or 633.*

*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.

*MATH 116.* Mathematics of Finance. 3 hr.; 3 cr.

*Prereq.:* Knowledge of intermediate algebra.

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

*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.* Discrete Mathematics for Computer Science. 3 hr.; 3 cr.

*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.* Precalculus. 4 hr.; 4 cr.
(Syllabus)

*q**.:* Three years of high school math.

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

*r**eq**.:* MATH 122, or placement by departmental exam, or permission of the department.

This course is intended to introduce the fundamental ideas and techniques of calculus to nonscience students.
Special emphasis is given to applications. Credit is given for each course satisfactorily completed; a student need not take the entire sequence. 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 or who have passed MATH 141 or 151.*

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

*P**re**r**e**q.**:* MATH 131.

It is a transitional course, intended to prepare student who have taken Math 131 (Calculus for economics and social science) to continue in the regular calculus sequence. Special attention must be devoted to trigonometry, trig limits and derivatives, and continuity, and other topics of Math 141 not covered in Math 131. Further topics include integration, transcendental functions, and applications of integration, as in Math 142. Math 132 prepares students to take Math 143.

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

*P**re**r**e**q.**:* 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 or who have passed MATH 131 or 151.*

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

*P**re**r**e**q.**:* MATH 141.

A continuation of MATH 141.
*Not open to students who are taking or who have passed MATH 151.*

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

*P**re**r**e**q.**:* MATH 142. *MATH 151 does not satisfy the prerequisite.*

A continuation of MATH 142.
*Not open to students who are taking or who have passed MATH 152.*

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

*P**re**r**e**q.**:* 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, antiderivatives.
*Not open to students who are taking or who have passed MATH 131 or 141.*

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

*P**re**r**e**q.**:* 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 or who have passed MATH 142.*

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

*P**re**r**e**q.**:* 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.* Computer Solutions of Mathematical Problems. 2 hr.; 2 cr.

*r**eq. **o**r c**o**r**eq**.**:* 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.* Studies in Mathematics.

*P**r**e**r**e**q.**:* Permission of the chair.

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

### 200-level

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

*P**r**e**r**e**q.**:* 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.

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

*P**r**e**r**e**q.**:* 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 207, 208.* Honors Calculus III, IV. 4 lec. hr., 1 conf. hr. and independent work; 5 cr. each sem.

*P**r**e**r**e**q.**:* 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 213W.* Discovering Mathematics with Mathematica. 4 hr.; 4 cr.;

*P**r**e**r**e**q.**:* 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.* Discrete Mathematics. 3 hr.; 3 cr.
(Syllabus)

*Pr**e**r**eq**.:* One semester of calculus, or permission of the instructor.

Topics taken from the subjects of logic and switching circuits, set theory, combinatorics, graph theory, and their applications.
*Not open to students who have received credit for MATH 120.*

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

*Pr**e**r**eq**.:* 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.* Differential Equations with Numerical Methods II. 3 hr.; 3 cr.

*Pr**e**r**eq**.:* 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.* Linear Algebra I. 4 hr.; 4 cr.

*Pr**e**r**eq**.:* One semester of calculus.

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.*

*MATH 232.* Linear Algebra II. 3 hr.; 3 cr.

*Pr**e**r**eq**.:* 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.* Honors Linear Algebra. 4 hr.; 4 cr.

*Pr**er**eq**.:* 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.* Introduction to Probability and Mathematical Statistics. 3 hr.; 3 cr.

*Pr**ereq.**or **c**o**re**q**.:* 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 receive credit for MATH 114, except by permission of the chair. Not open to students who are taking or who have received credit for MATH 611.*

*MATH 242.* Methods of Mathematical Statistics. 3 hr.; 3 cr.

*Pr**er**eq**.:* 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.* Mathematical Models. 3 hr.; 3 cr.

*Pr**er**eq**.:* 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.* Linear Programming and Game Theory. 3 hr.; 3 cr.
(Syllabus)

*Pr**er**eq**.:* 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.* Nonlinear Programming. 3 hr.; 3 cr.

*P**r**e**re**q.**:* 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 271.* Actuarial Mathematics I: Preparation for Exam P, the Actuarial Society examination on Probability [First of two courses]. 1 hr.; 1 cr.

*P**r**e**re**q.**:* MATH 241 (or MATH 611).

*C**o**r**e**q.**:* MATH 201.

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

*MATH 272.* Actuarial Mathematics II: Preparation for Exam P, the Actuarial Society examination on Probability [Second of
two courses]. 1 hr.; 1 cr.

*P**r**e**re**q.**:* MATH 241 (or MATH 611), and MATH 201.

*C**o**r**e**q.**:* 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.* Studies in Mathematics.

*P**r**e**re**q.**:* Permission of the chair.

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

### 300-level

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

*P**r**e**re**q.**:* 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 317.* Foundations of Analysis. 3 hr.; 3 cr.
(Syllabus)

*P**r**e**re**q.**:* 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 320.* Introduction to Point Set Topology. 3 hr.; 3 cr.
(Syllabus)

*c**o**r**eq**.**:* MATH 201.

Presents the basic concepts and some of the fundamental results of point-set topology.

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

*P**r**e**req.**:* MATH 223.

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

*MATH 333.* Introduction to Algebraic Structures. 3 hr.; 3 cr.
(Syllabus)

*P**r**e**req.**:* MATH 231.

Theory of groups, including cyclic and permutation groups, homomorphisms, normal and factor groups. Theory of rings, integral domains, field of quotients, maximal and prime ideals, rings of polynomials, field extensions.
*Students may not take both MATH 333 and 613.*

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

*P**r**e**req.**:* 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 341.* Bayesian Modeling. 3 hr.; 3 cr.

*P**r**e**req.**:* MATH 241.

A review of frequentist methods followed by a survey of statistical modeling using the Bayesian framework: prior distribution design, including Jeffrey's priors; likelihood models; posterior probabilities; hypothesis tests; Bayesian linear regression; Gibbs sampling; basic computing. Emphasis on real-world applications, including those in finance and engineering.

*MATH 385, 385W.* Mathematical Foundations of the Secondary School Curriculum. 3 hr.; 3 cr.
(Syllabus)

*P**r**e**req.**:* MATH 201, or 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.

*MATH 390.* Studies in Mathematics.

*P**r**e**req.**:* Permission of the chair.

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

*MATH 391, 392.* Special Problems.

*P**r**e**req.**:* 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.* Honors Seminar I.

*P**r**e**req.**:* 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.* Honors Seminar II.

*P**r**e**req.**:* MATH 395.

Continuation of MATH 395.