MATH 105
BEGINNING ALGEBRA
Basic concepts and techniques of algebra including a review of real numbers, fractions, equations, inequalities, problem solving, graphs, functions, solving systems of linear equations, exponents, polynomials and factoring polynomials. College credit given only to students with deficiencies in the mathematics admission requirement. Not open to students who have credit for any higher-numbered mathematics course.
fall only

MATH 106
INTERMEDIATE ALGEBRA
Basic concepts and techniques of algebra, rational functions and expressions, problem solving, radicals, rational exponents, complex numbers, quadratic equations and functions, exponential and logarithmic functions, sequences and series. College credit given only to students with deficiencies in the mathematics admission requirement. Not open to students who have credit for any higher-numbered mathematics course.
every sem.

MATH 107
BASIC INTEGRATED MATHEMATICS
Development of basic algebraic skills with some geometry. The course is designed as a bridge between high school mathematics and elementary statistics. It is not adequate preparation for calculus. Prerequisites: grade of C or higher in MATH 104 or two years of high school math.
every sem.

MATH 108
ALGEBRA AND TRIGONOMETRY
Topics essential for the study of calculus, including elements of trigonometry, complex numbers, logarithms and basic algebra. Skill development in algebraic and trigonometric manipulations.
every sem.

MATH 130
MATHEMATICS IN ACTION
Emphasizes the real-world significance of mathematics and applications of several areas of mathematics. Topics covered include design of street networks, planning and scheduling, weighted voting systems, fair division and apportionment, measuring populations and the universe, symmetries, fractals and statistics. Provides students with an experience in quantitative reasoning and data analysis through mathematical modeling of some real-life problems including a hands-on approach. Further emphasis is on illustrating the importance, relevance and currency of mathematics in the modern world.
every sem.

MATH 147
ELEMENTARY STATISTICS
Classification of data, frequency distributions, probability and the normal curve, elementary sampling theory. Not open to students who have credit for any other course in statistics. Prerequisites: MATH 107 or equivalent with a grade of C or better.
every sem.

MATH 220
CALCULUS FOR BUSINESS AND MANAGEMENT
Elements of calculus; emphasis on maximum and minimum problems. Primarily for School of Management students, who may satisfy their mathematics requirement with either MATH 220 or 221, and for economics majors in the BS specialization in financial economics. Not equivalent to MATH 221 as prerequisite for MATH 222. Prerequisites: MATH 108 or equivalent with a grade of C or better.
every sem.

MATH 221
CALCULUS I
Differentiation and integration of elementary functions. Prerequisites: MATH 108 or equivalent with a grade of C or better.
every sem.

MATH 222
CALCULUS II
Techniques and application of integration. Sequences and series. Prerequisites: MATH 221 with a grade of C or better.
every sem.

MATH 304
LINEAR ALGEBRA
Vector spaces, linear transformations, determinants, characteristic values. Prerequisites: MATH 221 with a grade of C or better.
every sem.

MATH 314
DISCRETE MATHEMATICS
Logic, sets, relations, functions. Induction, recursion, counting methods. Graphs, trees. Some abstract algebra. Prerequisites: MATH 221 with a grade of C or better.
every sem.

MATH 323
CALCULUS III
Calculus of functions of several variables. Prerequisites: MATH 222 with a grade of C or better.
every sem.

MATH 324
SEMINAR IN ACTUARIAL SCIENCE
spring only, 2 cr.

MATH 327
PROBABILITY WITH STATISTICAL METHODS
Development of probabilistic concepts in discrete and absolutely continuous cases. Classical combinatorial methods, independence, random variables, distributions, moments, transformations, conditioning, confidence intervals, estimation. Open to Watson School students only. Does not serve as a prerequisite for MATH 448 or for any actuarial science courses. Prerequisites: MATH 222 with a grade of C or better, or consent of department.
fall only

MATH 330
NUMBER SYSTEMS
Careful discussion of the real numbers, the rational numbers and the integers, including a thorough study of induction and recursion. Countable and uncountable sets. The methodology of mathematics: basic logic, the use of quantifiers, equivalence relations, sets and functions. Methods of proof in mathematics. Training in how to discover and write proofs. Prerequisites: MATH 222 with a grade of C or better.
every sem.

MATH 335
MATHEMATICAL LOGIC
Development of predicate calculus. Introduction to metatheory of propositional and predicate calculus: completeness, consistency, decidability. Axiomatics. Prerequisites: MATH 314 or 330 with grades of C or better, or consent of department.

MATH 339
PROBLEM-SOLVING SEMINAR
fall only, 1 cr.

MATH 357
OPERATIONS RESEARCH
Theory and applications of operations research, including linear programming, mathematical programming and queueing theory. Prerequisites: MATH 222 and 304 with grades of C or better. No computer programming experience is required.

MATH 358
NUMERICAL ANALYSIS
Floating-point arithmetic, error analysis, root finding, interpolation and approximation by polynomials, numerical integration and differentiation, numerical differential equation methods, solutions of linear systems by Gaussian elimination with pivoting, direct factorization of matrices. Prerequisites: MATH 222 and 304 with grades of C or better, and CS 140 or equivalent.

MATH 371
ORDINARY DIFFERENTIAL EQUATIONS
Ordinary differential equations. Emphasis on applications to problems in physics, chemistry, biology, economics, etc. Prerequisites: MATH 222 with a grade of C or better.
fall only

MATH 375
COMPLEX VARIABLES
Analytic functions. Cauchy's integral theorem, power series. Prerequisites: MATH 323 with a grade of C or better.
spring only

MATH 381
GRAPH THEORY
Directed and undirected graphs, trees, connectivity, Eulerian and Hamiltonian graphs, planar graphs, coloring of graphs, graph parameters, optimization and graph algorithms. Prerequisites: MATH 304, and either MATH 314 or 330 with grades of C or better, or consent of department.
spring only

MATH 386
COMBINATORICS
Topics from among counting techniques, generating function and recurrence relations, pigeonhole principle, Ramsey's Theorem, Latin squares, combinatorial designs. Prerequisites: MATH 304 and either MATH 314 or 330 with grades of C or better, or consent of department.
fall only

MATH 391
PRACTICUM IN COLLEGE TEACHING
Independent study through teaching in particular mathematics course. Various assignments closely directed by instructor in course, including development of syllabi and other course materials; construction and reading of examinations; lecturing and/or discussion leadership; laboratory supervision; academic counseling of student. May be repeated for total of no more than eight credits. Credits may not be earned in conjunction with course in which student is currently enrolled. Does not satisfy major or Harpur College Distribution requirements. Prerequisites: consent of instructor. Pass/Fail only.
var. cr.

MATH 401
MODERN ALGEBRA I
Groups, rings, integral domains, fields. Prerequisites: MATH 304 and 330 with grades of C or better, or consent of department.
fall only

MATH 402
MODERN ALGEBRA II
Further study of topics in MATH 401. Vector spaces, modules, lattices, Galois theory. Prerequisites: MATH 401 with a grade of C or better.
spring only

MATH 404
ADVANCED LINEAR ALGEBRA
Modules, normal forms of linear transformations, quadratic forms. Prerequisites: MATH 304 and 330 with grades of C or better, or consent of department.
spring only

MATH 407
INTRODUCTION TO THE THEORY OF NUMBERS
Classical number theory. Divisibility, prime numbers, quadratic reciprocity, Diophantine equations. Prerequisites: MATH 330 with a grade of C or better, or consent of department.
offered as needed

MATH 447
INTRODUCTION TO PROBABILITY AND STATISTICS I
Development of probabilistic concepts, sampling distributions, estimation, confidence intervals, tests of hypotheses. Prerequisites: MATH 323 with a grade of C or better, or consent of department.
fall only

MATH 448
INTRODUCTION TO PROBABILITY AND STATISTICS II
Methods of probability applied to estimation and testing on hypotheses, both parametric and non-parametric; random variables, limit theorems, Markov chains, stochastic processes. Prerequisites: MATH 447 with a grade of C or better.
spring only

MATH 449
Actuarial Mathematics
Basic concepts of actuarial mathematics: theory of interest, annuities, bonds, life tables, utility theory and risk models, life tables and survival functions. Material focuses on the actuarial mathematics requirements for the actuarial examinations. Prerequisites: MATH 447 with a grade of C or better, or consent of department.
fall only

MATH 450
Applied Probability Models
Methods of probability applied to estimation and testing on hypotheses, both parametric and non-parametric; random variables, limit theorems, Markov chains, stochastic processes. Basic concepts of actuarial mathematics. The material closely follows the actuarial mathematics requirements as needed for the third actuarial examination. Prerequisites: MATH 447 with a grade of C or better.
spring only

MATH 461
TOPOLOGY
Study of topological spaces. Metric spaces, separation properties, connectivity, compactness. Prerequisites: MATH 304, 323 and 330 with grades of C or better, or consent of department.
fall only

MATH 465
FOUNDATIONS OF GEOMETRY
Postulational treatment of geometric systems, including projective, affine and non-Euclidean geometries. Prerequisites: MATH 304 and 330 with grades of C or better, or consent of department.
offered as needed

MATH 471
PARTIAL DIFFERENTIAL EQUATIONS
Vector calculus, Fourier series, partial differential equations, with emphasis on applications. Prerequisites: MATH 371 with a grade of C or better.
spring only

MATH 478
REAL ANALYSIS I
Geometry and topology of Rn, functions and limits, calculus of functions on Rn and higher dimensional spaces. Prerequisites: MATH 304, 323 and 330 with grades of C or better, or consent of department.
fall only

MATH 479
REAL ANALYSIS II
Sequences and series of functions, more advanced study of differentiation and integration. Prerequisites: MATH 478 with a grade of C or better.
spring only

MATH 480
SEMINAR IN ALGEBRA
spring only
var. cr.

MATH 488
TOPICS IN HIGHER
offered as needed

MATH 495
ACTUARIAL INTERNSHIP
Internship with a company in the actuarial field, off campus. A faculty member must approve the proposed work in advance. The student must write a proposal before approval, keep a log during work and submit a paper after the experience. Prerequisites: consent of the instructor and departmental approval required. Pass/Fail only.
var. cr.

MATH 497
INDEPENDENT WORK
Individual study under direct supervision of faculty member. Prerequisites: consent of department. May be repeated for credit with maximum of eight credit hours of MATH 497 allowed toward major requirements.
var. cr.

MATH 498
HONORS STUDY IN MATHEMATICS
Independent studies/research open only to students who have been accepted in the mathematics honors program. May be repeated for credit, with maximum of four credit hours of MATH 498 allowed toward major requirements. Prerequisites: consent of department.