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COMPUTER SCIENCE (COMP)
1300C Introduction to Computer Science and Programming 4 creditsComponents of a computer system; machine, assembly, and high-level languages; the Python programming language; numerical systems and coding; representation of data and instructions; data types, constants, variables; arithmetic expressions; logical expressions; assignment statement; sequencing, alteration, and iteration; arrays, subprograms, and parameters; simple I/O; techniques of problem solving; flowcharting; stepwise refinement; simple numerical examples; basic search and sort algorithms. Principles of good programming style, expression, and documentation; control flow; invariant relation of a loop; stepwise refinement of statements and data structures, or top-down programming. (lecture: 3 hours; lab: 2 hours)Prerequisite: A passing grade in either high school or college pre-Calculus.
1320C Introduction to Data Structures 4 creditsString processing, concatenation, substrings, matching, internal searching and sorting, recursion, linked lists and linear allocation (stacks, queues, deques). Elementary data structures, file structures and algorithms, searching and sorting, trees and algorithms for their manipulation, notions of algorithm complexity, memory and data management systems. (lecture: 3 hours; lab: 2 hours) Prerequisite: COMP 1300C.
1504 Discrete Structures 3 creditsBoolean algebra and predicate calculus; proof methods; sets, functions, and relations; combinatorics; graph theory and algorithms; mathematical induction and recursion; probability and average case analysis of algorithms. Prerequisite: three years of high school mathematics.
1621 Theory of Computation 3 creditsDeterministic and nondeterministic finite state automata; regular grammars and regular expressions; languages generated by regular expressions; equivalence of regular expressions and finite automata; solvable problems concerning finite automata; context¬free grammars; languages generated by context-free grammars; derivation trees; simplification of context-free grammars; pushdown automata; properties of context-free languages; solvable and unsolvable problems concerning context-free languages; Turing machine model; Universal Turing machine; Halting problem; further examples of solvable and unsolvable problems about Turing machines, grammars, and sets. Prerequisite: COMP 1504.
2115C Computer Systems (replaces 2113C Computer Organization and Assembly Language Programming) 4 creditsThe course is devoted to exploring the interaction between a program, the operating system, and the hardware. Topics include: the C programming language emphasizing pointers, explicit dynamic memory allocation, and formatted I/O; machine-level representation of programs; processor architecture; program optimization; the memory hierarchy; processes; UNIX I/O; concurrent programming. The course will have both lecture and laboratory components. Prerequisite: COMP 1300C.
2314C Applied Linux Programming and Scripting 4 creditsIntroduces Linux, with a focus on the operating system features that are accessible from the command line and programming or scripting languages such as Python or Awk. Topics will include software development in a Linux environment, pipes, redirection, process management, and shell programming. Prerequisite: COMP 1300C.
2545 Algorithms 3 creditsAdvanced data structures and algorithms: tables, AVL and red-black trees, B and B+ trees, heaps, disjoint sets. Graph algorithms: minimum spanning trees, shortest path, and maximum flow algorithms. Selected algorithms in parallel computers, string matching, and computational geometry. (lecture: 3 hours; lab: 2 hours) Prerequisites: COMP 1320C, 1504, MATH 1412.
3610 Operating Systems 3 creditsReview of instruction sets. I/O and interrupts, addressing schemes, microprogramming; dynamic procedure activation; dynamic storage allocation; design methodology, monitors, kernels, networks of operating system modules; elementary queuing; memory management: virtual memory, paging, segmentation; memory protection; multiprogramming. Operating system concerns for internet and intranet operations, distributed computing, and the handling of critical security issues. Prerequisites: COMP 1320C, 2113C.
3640 Programming Languages 3 creditsFormal language concepts, including basic characteristics of syntax and grammars; regular, context-free, and ambiguous grammars; constructs for specifying and manipulating data types; language features affecting static and dynamic storage man¬agement; control structures and data flow; subroutines, procedures, block structures, interrupts, decision tables, recursion; relationship with good programming style; runtime considerations; interpretative languages, lexical analysis and parsing. Prerequisites: COMP 1320C
3760 Artificial Intelligence 3 creditsHeuristic versus algorithmic methods, cognitive processes, investigation of methods of making machines behave intelligently, problem solving, theorem probing, game playing, pattern recognition, question answering, learning self-organization, methods of programming such procedures, data structures and program organization; the mind-brain problem; the nature of intelligence. Advanced elective. Prerequisite: COMP 2545.
3780 Web Programming and Development 3 creditsThe world-wide web was originally a vehicle for delivering documents. It still does this, but its most demanding current uses are as a platform for sophisticated interactive applications, replacing traditional mechanisms for distributing and installing software. Creating web applications requires different approaches from traditional applications and involves the integration of numerous technologies. This course introduces web technologies and gives the student experience creating web applications. In the process, students learn about markup languages, scripting, network protocols, interactive graphics, event-driven programming, and databases. Students also explore the way web applications can be exploited by malicious hackers, and the defensive strategies to keep hackers at bay. Prerequisite: COMP 1300
4500 Topics: Computational Methods in Scientific Research 3 creditsUse of computers to solve real problems in biology, physical sciences and economics. Numerical methods and data analysis, and how to visualize results with plots and movies.Prerequisites: MATH 1413. Recommended PHYS 1032C or 1042C
4541 Numerical Analysis 3 creditsFinite difference calculus; numerical solution of differential equations and linear systems of equations; iterative methods; computation of eigenvalues and eigenvectors. Advanced elective. Prerequisite: MATH 1413
4901, 4902 Independent StudySee Academic Information and Policies section.
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1010 Excursions in Mathematics 3 creditsThis course is intended for non-science majors and Education majors. Several topics will be taught in depth from the following list: Sets of numbers, geometry, elements of probability and statistics, consumer mathematics, linear programming.
1160 Introduction to Elementary Functions 4 creditsNumber systems, functions, equations, and inequalities; algebra of polynomials, exponentials, and logarithms; analytic geometry of lines and circles; vectors, trigonometry, and complex numbers. (lecture: 3 hours; recitation: 2 hours). Prerequisites: two years of high school mathematics and placement by examination.
1412, 1413 Calculus I, II 4 creditsFirst semester: limits, derivatives, and integrals; continuous and differentiable functions, mean value theorem, chain rule, implicit differentiation. Applications: curve sketching, maxima and minima, related rates, motion, area. Trigonometric, inverse trigonometric, logarithmic and exponential functions. Second semester: methods of integration, area, moments, volume. Indeterminate forms, improper integrals, sequences and series. Parametric equations, arc length and polar coordinates. (lecture: 3 hours; recitation: 2 hours).Prerequisites: three years of high school mathematics and placement by examination or MATH 1160.
1504 Discrete Structures 4 creditsBoolean algebra and predicate calculus; proof methods; sets, functions, and relations; combinatorics; graph theory and algorithms; mathematical induction and recursion; probability and average case analysis of algorithms. (lecture: 3 hours; recitation: 2 hours) Prerequisite: three years of high school mathematics.
1510 Multivariable Calculus 4 creditsLimits and continuity in Euclidean spaces; partial derivatives, gradient, and chain rule; maxima and minima with constraints; multiple integrals, cylindrical and spherical coordinates; vector calculus; theorems of Green, Gauss, and Stokes. Prerequisite: MATH 1413.
1520, 1521 Advanced Calculus I, II 3 creditsReal numbers; theorems on limits; continuous, differentiable, and integrable functions; sequences and series of functions; metric space methods, fixed points, existence theorems for differential equations; implicit function theorem. Prerequisites: MATH 1413 and permission of the instructor.
1523 Introduction to Analysis 3 creditsFamiliarizes students with analytic tools and ideas that are of practical significance for a variety of applications along with an awareness of the foundations, interrelations, and limitations of those methods. Prerequisites: MATH 1510, 2105.
1540 Functions of a Complex Variable 3 creditsAnalytic functions, Cauchy Riemann equations, Cauchy integral formula, residue theory, conformal mappings. Prerequisite: MATH 1520 or permission of the instructor.
2105 Linear Algebra 3 creditsSystems of linear equations, Gaussian elimination, matrices, matrix algebra; vector spaces, linear transformations, similarity; inner product spaces; determinants; eigenvalues and eigenvectors, diagonalization; quadratic forms; canonical forms; spectral theory; applications. Prerequisite: MAT 1412.
2168 Elementary Number Theory 3 creditsProperties of integers, Euclidean algorithm, unique factorization, arithmetic functions, perfect numbers, linear and quadratic congruences, public-key encryption.
2215 Modern Algebra 3 creditsBasic concepts of an algebraic system, a sub-system, a factor-system, an isomorphism and a homomorphism. Examples and initial results from the theory of groups, rings, and fields. The second semester will be devoted to advanced topics, including recent developments. Prerequisite: MATH 2105 or permission of the instructor.
2461 Probability Theory 3 creditsDiscrete and continuous sample spaces; combinatorial analysis; density and distribution functions of random variables; expectation and variance; independence and conditional probability; law of large numbers; central limit theorem; generating functions; random walk and ruin problems. Prerequisite: MATH 1510.
2462 Mathematical Statistics 3 creditsApplication of probability theory to the classical parametric models: moment-generating functions, chisquare and t distributions, central limit theorem, sampling distributions, maximum likelihood and interval estimation, confidence intervals, hypothesis testing; nonparametric models; the Bayesian controversy. Examples from natural science and social and behavioral research. Prerequisite: MATH 2461.
2601 Differential Equations 3 creditsClassification of differential equations; existence and uniqueness of solutions; initial-value problems, boundary-value problems; power series methods, integral transforms; numerical algorithms and error estimation; topological methods. Prerequisite: MAT 1413.
2651 Numerical Analysis 3 creditsFinite difference calculus; numerical solution of differential equations and linear systems of equations; iterative methods; computation of eigenvalues and eigenvectors. Advanced elective. Prerequisite: MATH 1413
2901 Mathematics of Finance 3 creditsDiscrete models for options, pricing derivatives,continuous stock price models, Brownian motion, the Black-Scholes formula, the Black-Scholes differential equation, hedging options, dynamic programming, bond price models, yield curves, forwards and futures, Keynes interest rate parity formula. Prerequisite: familiarity with differential equations.
3301, 3302, 3303, 3304 Topics in Modern Mathematics 3 credits.Selected subjects in analysis, algebra, geometry, actuarial, and applied mathematics. Students may register for up to four semesters with permission of the Department Chair. Prerequisites: junior status and permission of the instructor.
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New York, NY 10033
500 West 185th Street
New York, NY 10033
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