# Graduate Courses

The Master’s program in mathematics provides both pure and applied tracks of study, with a variety of elective courses from which student can choose topics that interest them most. Students completing this program earn a strong background in both applications and theory, making our students highly qualified for employment in industry, the business world, and academia. Many MA Mathematics courses are offered on weekday evenings, giving those students with employment or other time constraints maximum flexibility.

**Apply Now!**

Contact **Graduate Advisor Prof. Dan Lee** if you have any questions about the Master’s Program in Mathematics.

Use the tabs at the top of the menu to switch amongst 500-, 600-, and 700-level courses.

Click here for more information about the requirements for a Masters Degree in Mathematics at Queens College.

Click here for the undergraduate course descriptions.

Click here for the official Queens College Graduate Bulletin.

**Important:** 500-level courses are for Education students.

They do not count towards the MA degree in mathematics.

They do not count towards the Pure, Applied, or Data Science and Statistics math majors.

### MATH 503. Mathematics from an Algorithmic Standpoint.

**3 hr. 3 cr. Prereq.: One year of calculus.**

An algorithmic approach to a variety of problems in high school and college mathematics. Experience in programming is not necessary. Topics may include problems from number theory, geometry, calculus and numerical analysis, combinatorics and probability, and games and puzzles. This course aims at a better understanding of mathematics by means of concrete, constructive examples of mathematical concepts and theorems. This course may not be credited toward the degree of Master of Arts in Mathematics, except with the special permission of the Chair of the Mathematics Department.

### MATH 505. Mathematical Problem-Solving.

**3 hr.; 3 cr.Prereq. or coreq.: One year of college mathematics.**

Not open to students who are taking or who have received credit for MATH205. 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. This course may not be credited toward the Master of Arts degree in Mathematics.

### MATH 509. Set Theory and Logic.

**3 hr.; 3 cr. Prereq.: One year of calculus or permission of instructor.**

Propositional logic and truth tables. Basic intuitive ideas of set theory: cardinals, order types, and ordinals. May not be credited toward the Master of Arts degree in Mathematics.

### MATH 518. College Geometry.

**3 hr.; 3 cr. Prereq.: One course in linear algebra.**

Advanced topics in plane geometry, transformation geometry. Not open to candidates for the Master of Arts degree in Mathematics.

### MATH 524. History of Mathematics.

**3 hr.; 3 cr. Prereq. or coreq.: Mathematics 201.**

Not open to candidates for the Master of Arts degree in Mathematics.

### MATH 525. History of Modern Mathematics.

**3 hr.; 3 cr. Prereq.: Mathematics 524 or permission of instructor.**

Selected topics from the history of nineteenth- and twentieth-century mathematics, e.g., topology, measure theory, paradoxes and mathematical logic, modern algebra, non-Euclidean geometries, foundations of analysis. May not be credited toward the Master of Arts degree in Mathematics.

### MATH 555. Mathematics of Games and Puzzles.

**3 hr.; 3 cr. Prereq.: Two years of calculus or permission of instructor.**

Elements of game theory. Analysis of puzzles such as weighing problems, mazes, Instant Insanity, magic squares, paradoxes, etc. May not be credited toward the Master of Arts degree in Mathematics.

### MATH 590. Studies in Mathematics.

**Prereq.: Permission of the Mathematics Department.**

Topics will be announced in advance. May be repeated once for credit if topic is not the same. Not open to candidates for the Master of Arts degree in Mathematics.

### MATH 601. Abstract Algebra I.

**4 hr.; 4 cr. Prereq.: MATH 231.**

Not open to students who are taking or who have received credit for MATH 301 or 702. 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.

### MATH 602. Abstract Algebra II.

**3 hr.; 3 cr. Prereq.: MATH 301 (or 601).**

This is a continuation of MATH 601. Not open to students who are taking or who have received credit for MATH 302 or 702. Advanced topics in group and ring theory. Fields and field extensions.

### MATH 605. Number Theory. (Previously MATH 619.)

**3 hr.; 3 cr. Prereq.: MATH 231 or 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 305.

### MATH 609. Introduction to Set Theory.

**3 hr.; 3 cr. Prereq.: Mathematics 201 or permission of instructor.**

Axiomatic development of set theory; relations, functions, ordinal and cardinal numbers, axiom of choice. Zorns lemma, continuum hypothesis.

### MATH 612. Projective Geometry.

**3 hr.; 3 cr. Prereq.: A course in linear algebra.**

Study of the projective plane.

### MATH 614. Functions of Real Variables.

**3 hr.; 3 cr. Prereq.: Course in Elementary Real Analysis or Point Set Topology (equivalent of Mathematics 310 or 320), or permission of instructor.**

Provides a foundation for further study in mathematical analysis. Topics include: basic topology in metric spaces, continuity, uniform convergence and equicontinuity, introduction to Lebesgue theory of integration.

### MATH 615. Algebraic Number Theory.

**3 hr.; 3 cr. Prereq.: Mathematics 333 or 613 or permission of instructor.**

Modern theory of algebraic integers (generalization of integers), the problem of prime factorization, p-adic numbers, the Riemann zeta function, L-functions, theorem on primes in arithmetic progression.

### MATH 616. Complex Analysis. (Previously MATH 628.)

**3 hr.; 3 cr. Prereq.: One year of multivariable calculus (MATH 202) or the equivalent.**

Not open to students who are taking or have received credit for MATH 316. Topics covered include analytic functions, Cauchy’s Integral Theorem, Taylor?s theorem and Laurent series, the calculus of residues, singularities, meromorphic functions.

### MATH 617. Number Systems.

**3 hr.; 3 cr. Prereq.: Three semesters of undergraduate analytic geometry and calculus including infinite series.**

Axiomatic development of the integers, rational numbers, real numbers, and complex numbers. Not open to students who have received undergraduate credit for Mathematics 317 at Queens College.

### MATH 618. Foundations of Geometry.

**3 hr.; 3 cr. Prereq.: MATH 201. Not open to students who are taking or have received credit for MATH 318. **

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.

### MATH 620. Point-Set Topology.

**3 hr.; 3 cr. Coreq.: MATH 201. Not open to students who are taking or who have received credit for MATH 320. **

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.

### MATH 621. Probability.

**3 hr.; 3 cr. Prereq.: A semester of intermediate calculus (the equivalent of Mathematics 201) and an introductory course in probability, or permission of Chair.**

Binomial, Poisson, normal, and other distributions. Random variables. Laws of large numbers. Generating functions. Markov chains. Central limit theorem.

### MATH 623. Operations Research (Probability Methods).

**3 hr.; 3 cr. Prereq.: Course in probability theory (such as Mathematics 241).**

An introduction to probabilistic methods of operations research. Topics include the general problem of decision making under uncertainty, project scheduling, probabilistic dynamic programming, inventory models, queuing theory, simulation models, and Monte Carlo methods. The stress is on applications.

### MATH 624. Numerical Analysis I.

**3 hr.; 3 cr. Prereq.: A course in Linear Algebra (231 or 237) and either Mathematics 171 or knowledge of a programming language; Coreq.: Mathematics 201 (Calculus). **

Numerical solution of nonlinear equations by iteration. Interpolation and polynomial approximation. Numerical differentiation and integration.

### MATH 625. Numerical Analysis II.

**3 hr.; 3 cr. Prereq.: Mathematics 624 or its equivalent, including knowledge of a programming language.**

Numerical solution of systems of linear equations. Iterative techniques in linear algebra. Numerical solution of systems of nonlinear equations. Orthogonal polynomials. Least square approximation. Gaussian quadrature. Numerical solution of differential equations.

### MATH 626. Mathematics and Logic.

**3 hr.; 3 cr. Prereq.: Intermediate calculus or permission of department.**

Propositional calculus, quantification theory, recursive functions, Godels incompleteness theorem.

### MATH 630. Differential Topology.

**3 hr.; 3 cr. Prereq.: Advanced calculus.**

Differentiable manifolds and properties invariant under differentiable homeomorphisms; differential structures; maps; immersions, imbeddings, diffeomorphisms; implicit function theorem; partitions of unity; manifolds with boundary; smoothing of manifolds.

### MATH 631. Differential Geometry.

**3 hr.; 3 cr. Prereq.: Advanced calculus.**

Theory of curves and surfaces and an introduction to Riemannian geometry.

### MATH 632. Differential Forms.

**3 hr.; 3 cr. Prereq.: Advanced calculus.**

A study in a coordinate-free fashion of exterior differential forms: the types of integrands which appear in the advanced calculus.

### MATH 633. Statistical Inference.

**3 hr.; 3 cr. Prereq.: A semester of intermediate calculus (the equivalent of Mathematics 201) and either an undergraduate probability course which includes mathematical derivations or Mathematics 611 or 621.**

Basic concepts and procedures of statistical inference.

### MATH 634. Theory of Graphs.

**3 hr.; 3 cr. Prereq.: One semester of advanced calculus.**

An introduction to the theory of directed and undirected graphs. The Four-Color Theorem. Applications to other fields.

### MATH 635. Stochastic Processes.

**3 hr.; 3 cr. Prereq.: Mathematics 611 or 621.**

A study of families of random variables.

### MATH 636. Combinatorial Theory.

**3 hr.; 3 cr. Prereq.: A course in linear algebra.**

This course will be concerned with techniques of enumeration.

### MATH 640. Probability Theory for Data Science.

**4 hr.; 4 cr. Prereq.: A course in probability. Coreq.: A course in multivariable calculus and linear algebra. Not open to students who are taking or who have received credit for MATH 340.**

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.

### MATH 641. Statistical Theory for Data Science.

**4 hr.; 4 cr. Coreq.: MATH 640 or the equivalent. Not open to students who are taking or who have received credit for MATH 341. **

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.

### MATH 642. Data Science Fundamentals and Machine Learning.

**4 hr.; 4 cr. Prereq: A course in linear algebra, and course in probability, and a course in programming (CSCI 111 or the equivalent) Not open to students who are taking or who have received credit for MATH 342W. Recommended corequisites include ECON 382, 387, MATH 341, MATH 343 or their equivalents. **

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.

### MATH 643. Computational Statistics for Data Science.

**3 hr.; 3 cr. Prereq.: MATH 641 or the equivalent. Coreq.: MATH 642 or the equivalent Not open to students who are taking or who have received credit for MATH 343.**

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.

### MATH 690. Studies in Mathematics.

**Prereq.: Permission of department.**

The topic will be announced in advance. This course may be repeated for credit provided the topic is not the same.

### MATH 701. Theory of the Integral.

**3 hr.; 4 1/2 cr. Prereq.: MATH 614.**

The Lebesgue integral in one dimension and in n dimensions, the abstract case.

### MATH 702. Modern Abstract Algebra I.

**3 hr.; 4 1/2 cr. Prereq.: MATH 301 (or 601).**

A course in the fundamental concepts, techniques, and results of modern abstract algebra. Concepts and topics studied are semi-groups, groups, rings, fields, modules, vector spaces, algebras, linear algebras, matrices, field extensions, and ideals.

### MATH 703. Point Set Topology.

**3 hr.; 4 1/2 cr. Prereq.: Advanced calculus.**

Topological spaces, mappings, connectedness, compactness, separation axioms, product spaces, function spaces.

### MATH 790. Independent Research.

May be repeated for credit if the topic is changed.

### MATH 791. Tutorial.

May be repeated for credit if the topic is changed.

### MATH 792. Seminar.

May be repeated for credit if the topic is changed.