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.

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Contact Graduate Advisor Prof. Scott Wilson if you have any questions about the Master’s Program in Mathematics.

Requirements for Matriculation in the Master of Arts Programs

These requirements are in addition to the general requirements for admission.

  1. To be admitted to the program, a candidate must have at least 25 credits in advanced courses in mathematics and related fields (such as computer science and physics). At least 12 credits must be in mathematics, including advanced calculus and linear algebra, with an average of at least B in the mathematics courses. Applicants not meeting these requirements must secure special permission of the department, and may be required to take courses to remove the deficiencies without receiving graduate credit.
  2. At least two of the written recommendations must be from the applicant’s undergraduate instructors and must deal with the ability of the applicant to pursue graduate work in mathematics.
  3. The applicant must have the approval of the department’s Committee of the Graduate Program.
  4. The applicant’s plan of study must be approved by the department.
Master of Arts in Pure Mathematics

1. A candidate for this degree is required to complete MATH 621, 628, 701, 702, and 703. A total of 30 credits required for the degree must be in mathematics, except that, with the approval of the Mathematics Department, a limited number of appropriate courses in physics or computer science may be substituted for mathematics courses. It is required that the program be completed with an average of B or better.

2. Each candidate for the degree must pass an oral examination.

 

Master of Arts with a Concentration in Applied Mathematics

1. A candidate for this degree is required to complete 30 credits in an approved sequence of graduate-level courses in mathematics and related fields. All students must achieve a solid grounding in the three areas of probability and statistics, analytic methods, and numerical methods. This can be achieved by taking the following courses: MATH 621, 624, 625, 628, and 633; or by demonstrating competence in specific areas to the satisfaction of the department; or by taking an alternative program of courses selected with the advisement and approval of the Graduate Advisor. A list of current courses and suggested programs of study will be made available. Students may obtain permission to design programs tailored to their individual needs. It is required that the master’s program be completed with an average of B or better.

2. Each candidate will be required to pass a written examination in an area of specialization to be approved by the Mathematics Department.

 

PROGRAM FOR THE MASTER OF SCIENCE IN EDUCATION DEGREE

Requirements for Matriculation

These requirements are in addition to the general requirements for admission. To be admitted to the program a candidate must have:

1. A cumulative index and Mathematics index of at least B, as well as a B index in education are required for matriculated status. Students who do not meet the above requirements may be permitted to enter as probationary matriculants. Probationary status will be removed when the first 12 credits of approved coursework have been completed with a minimum average of B.

2. At least 21 credits in college-level mathematics courses. These courses must include intermediate calculus and linear algebra, with an average of at least B. Note that before taking the mathematics courses that go toward the master’s degree, students must have a total of 36 credits in college-level mathematics.

3. Two letters of recommendation.

Requirements for the Degree

1. Candidates in this program have two advisors, one in the Department of Secondary Education & Youth Services and one in the Department of Mathematics. The Education Advisor should be consulted first to plan out the required coursework.

2. Students must take 15 credits in mathematics and 15 credits in Secondary Education. Note that the coursework in mathematics usually includes study in the History of Mathematics, Probability and Statistics, and Geometry. Students must consult their advisor to plan an appropriate course of study.

3. Students are required to pass an oral examination in mathematics. This exam is given by two of the student’s professors and is based on the content of the two courses. The student may decide on the professors and submits a request to the Mathematics Advisor who then schedules the oral examination

 

Graduate Course Descriptions

Jump to Mathematics Level: 500 600700

Mathematics 500 Level Courses

Math 503
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
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
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

MATH 518. College Geometry. 3 hr.; 3 cr. (Syllabus)
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

MATH 524. History of Mathematics. 3 hr.; 3 cr. (Syllabus)
Prereq. or coreq.: Mathematics 201.
Not open to candidates for the Master of Arts degree in Mathematics.

Math 525

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
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

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.

Mathematics 600 Level Courses

Math 601
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
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 [Formerly 619]
MATH 605. Number Theory. 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 MATH305.
Math 609
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 611
MATH 611. Introduction to Mathematical Probability. 3 hr.; 3 cr.
Prereq.: A one-year course in differential and integral calculus (including improper integrals). A first course in probability at an advanced level.
Topics to be covered include axioms of probability, combinatorial analysis, conditional probability, random variables, binomial, Poisson, normal, and other distributions, mathematical expectation, and an introduction to statistical methods. Not open to students who have received credit for Mathematics 241 or 621. May not be counted toward the Master of Arts degree in Mathematics.
Math 616 [Formerly 628]
MATH 616. Complex Analysis. 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 612

MATH 612. Projective Geometry. 3 hr.; 3 cr. (Syllabus)
Prereq.: A course in linear algebra.
Study of the projective plane.

Math 614
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
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
MATH 616. Ordinary Differential Equations. 3 hr.; 3 cr.
Prereq.: Mathematics 614 or permission of Chair.
Existence and uniqueness of solutions, linear systems, Liapunov stability theory, eigenvalue and boundary value problems.
Math 617
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
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
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
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
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
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
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

MATH 626. Mathematics and Logic. 3 hr.; 3 cr. (Syllabus)
Prereq.: Intermediate calculus or permission of department.
Propositional calculus, quantification theory, recursive functions, Godels incompleteness theorem.

Math 630
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
MATH 631. Differential Geometry. 3 hr.; 3 cr.
Prereq.: Advanced calculus.
Theory of curves and surfaces and an introduction to Riemannian geometry.
Math 632
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
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
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
MATH 635. Stochastic Processes. 3 hr.; 3 cr.
Prereq.: Mathematics 611 or 621.
A study of families of random variables.
Math 636
MATH 636. Combinatorial Theory. 3 hr.; 3 cr.
Prereq.: A course in linear algebra.
This course will be concerned with techniques of enumeration.
Math 690

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.

Mathematics 700 Level Courses

Math 701
MATH 701. Theory of the Integral. 3 hr.; 4 1/2 cr.
Prereq.: Mathematics 614.
The Lebesgue integral in one dimension and in n dimensions, the abstract case.
Math 702
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
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 704
MATH 704. Functional Analysis. 3 hr.; 4 1/2 cr.
Prereq.: A course in linear algebra and Mathematics 614.
Abstract linear spaces, normed linear spaces, continuous linear transformations, dual spaces. Hahn-Banach theorem, closed graph theorem, uniform boundedness principle, Hilbert spaces, the weak-star-topology, Alaoglus theorem, topological linear spaces.
Math 705
MATH 705. Theory of Functions of a Complex Variable. 3 hr.; 4 1/2 cr.
Prereq.: Mathematics 701.
Math 706
MATH 706. Advanced Ordinary Differential Equations. 3 hr.; 4 1/2 cr.
Prereq.: Mathematics 616.
Math 707
MATH 707. Partial Differential Equations. 3 hr.; 4 1/2 cr.
Prereq.: Mathematics 706.
Math 708
MATH 708. Combinatorial Topology. 3 hr.; 4 1/2 cr.
Prereq.: Mathematics 703.
Math 709
MATH 709. Set Theory. 3 hr.; 4 1/2 cr.
Math 710
MATH 710. Mathematics and Logic: Advanced Course. 3 hr.; 4 1/2 cr.
Prereq.: Mathematics 626.
Math 711
MATH 711. The Mathematical Structure of Modern Statistics. 3 hr.; 4 1/2 cr.
Prereq.: A course in either probability or statistics.
Math 712
MATH 712. Higher Geometry. 3 hr.; 4 1/2 cr.
Math 713
MATH 713. Modern Abstract Algebra II. 3 hr.; 4 1/2 cr.
Prereq.: Mathematics 702.
Math 717
MATH 717. Theory of Approximation I. 3 hr.; 4 1/2 cr.
Prereq.: Mathematics 614 or permission of department.
Math 718
MATH 718. Theory of Approximation II. 3 hr.; 4 1/2 cr.
Prereq.: Mathematics 717.
Math 790
MATH 790. Independent Research.
May be repeated for credit if the topic is changed.
Math 791
MATH 791. Tutorial.
May be repeated for credit if the topic is changed.
Math 792
MATH 792. Seminar.
May be repeated for credit if the topic is changed.