CU Math Dept. -- List of Courses

• Ma 110 -- Introduction to Linear Algebra

Vectors in two- and three-dimensions, vector algebra, inner product, cross product and applications. Analytic geometry in three dimensions: lines, planes, spheres. Matrix algebra; solution of system of linear equations, determinants, inverses. 2 credits. Prerequisites: none

• Ma 111 -- Calculus I

Functions; limit of functions, continuity. The derivative and its applications: curve sketching, maxima and minima, related rates, velocity and acceleration in one dimension; trigonometric, exponential, logarithmic and hyperbolic functions. Definite and indefinite integrals; area, the fundamental theorem, techniques of integration. 4 credits. Prerequisites: none
course syllabus

• Ma 113 -- Calculus II

Applications of definite integrals: area, volume, improper integrals, work, arc length, surface area, centroid. Polar coordinates. Parametric curves in two and three dimensions: velocity, speed and accelerations. Partial derivatives and the chain rule, properties of the gradient. Maxima and minima. Sequences and series: convergence of sequences and series, Taylor and Maclaurin series, power series. 4 credits. Prerequisite: Ma 111; prerequisite or corequisite: Ma 110
course syllabus for Fall semester
course syllabus for Spring semester

• Ma 223 -- Vector Calculus

Double and triple integrals and their applications. Vector fields. Gradient, divergence and curl. Line and surface integrals. Theorems of Green, Gauss and Stokes. Path independence of line integrals. 2 credits. Prerequisites: Ma 110 and Ma 113. Usually given in fall and spring semesters

• Ma 224 -- Probability

Sample spaces. Random variables. Probability. Distribution and density functions. Expectation. Mean and variance. Moments and generating function. Central limit theorem. 2 credits. Prerequisite: Ma 113; corequisite: Ma 223. Usually given in both fall and spring semesters

• Ma 240 -- Ordinary and Partial Differential Equations

Equations Ordinary differential equations of the first order. Linear equations of higher order with constant coefficients. Power series solutions. Laplace transformation. Fourier series. Partial differential equations: method of separations of variables, applications to vibration and heat flow. 3 credits. Prerequisite: Ma 113

• Ma 151.1 -- Mathematics in Art

This course deals with the period beginning with Pythagoras in ancient Greece and goes up to the present day. Topics include: Goedel's incompleteness theorem. Euclidean and non-Euclidean geometries, infinity, paradoxes, soap film experiments. Also discussed are black holes, the Big-Bang theory, relativity, and quantum theory. The course is open to all Cooper Union students but is primarily oriented toward making the above-mentioned concepts comprehensive to those with very little mathematics in their background. Engineering students should see the Mathematics faculty and their adviser(s) for permission to take this course. The relatedness of seemingly distant fields (science, art, mathematics, music) is a central theme of the course. 3 credits. Prerequisites: none

• Ma 163-164 -- Calculus and Analytic Geometry I, II

Second year mathematics course for architecture students. Emphasis is on topics that involve the mathematical approach to geometrical and physical relationships and on basic concepts and applications of calculus of functions of one and two variables. 3 credits each semester. Cannot be used to satisfy any degree requirement in the School of Engineering. Prerequisites: none

Electives

• Ma 224.1 -- Probability and Statistics

This course deals with sample spaces, random variables, probability. Distribution and density functions. Expectation. Mean and variance. Moments and generating function. Central limit theorem. Point estimation. Confidence intervals. Hypothesis tests. Chi-square. ANOA. Estimations, sampling theory. 3 credits. Prerequisite: Ma 113; corequisite Ma 223

• Ma 326 -- Linear Algebra

Finite-dimensional vector spaces. Linear independence. Dimension. Basis. Subspaces. Inner product. Matrices. Rank. Determinant. Systems of linear equations. Matrix algebra. Coordinate transformation. Orthogonal matrices. Linear transformation. Eigenvalues and eigenvectors. Quadratic forms. Canonical form. 3 credits. Prerequisite: Ma 223

• Ma 336 -- Statistics

Statistical central limit theorem. Decision theory. Estimation: properties of estimators, point estimation, confidence intervals. Hypothesis testing: simple and composite hypothesis, Neyman-Pearson lemma, sequential methods, relationship to estimation. Normal distribution tests: t-test, chi-square, F-test. Introduction to non-parametric methods, regression and analysis of variance. 3 credits. Prerequisites: Ma 223 and Ma 224

• Ma 337 -- Operations Research

Linear programming, simplex method, graphs and network theory, dynamic programming, game theory, queues, variational techniques, duality, Markov chains, Monte Carlo simulation, decision theory. Special topics depending on student interest, possibly including language questions, integer programming, nonlinear programming and topics from mathematical biology, econometrics and other applications of mathematics to the sciences and social sciences. 3 credits. Prerequisite: Ma 224

• Ma 341 -- Differential Geometry

Theory of curves and surfaces, curvature, torsion, mean and Gaussian curvatures length, area, geodesics, 1st and 2nd quadratic forms, conformal mapping, minimal surfaces, tensor formulation and applications. 3 credits. Prerequisites: Ma 223 and permission of instructor

• Ma 344 -- Tensor Analysis

Tensor algebra, covariant and contravariant tensors, metric tensors, Christoffel symbols and applications. 3 credits. Prerequisite: Ma 326

• Ma 345 -- Functions of a Complex Variable

Topological properties of complex plane, complex analytic functions, Cauchy-Riemann equations, line integrals, Cauchy's integral theorem and formula. Taylor series, uniform convergence, residues, analytic continuation, conformal mappings and applications. 3 credits. Prerequisite: Ma 223

• Ma 347 -- Modern Algebra

Sets and mappings, the integers: well ordering, induction residue class arithmetic, Euler-Fermat theorems. Permutation groups: cyclic decompositions. transpositions, conjugate classes of permutations. Abstract groups: morphisms, subgroups, cyclic groups, coset decompositions. Factor and isomorphism theorems. Direct products of groups. Sylow's theorems. 3 credits. Prerequisite: Ma 326

• Ma 350 -- Advanced Calculus I

Sets and functions, topological properties of real line, continuity and uniform continuity, differentiability, mean value theorems, the Riemann-Stieltjes integral and Taylor's theorem. 4 credits. Prerequisite: Ma 223

• Ma 351 -- Advanced Calculus II

Uniform convergence. Differentitation of transformations, inverse and implicit function theorems. Applications to geometry and analysis. 4 credits. Prerequisite: Ma 350

• Ma 352 -- Discrete Mathematics

Relations. Mathematical structures. Number theory. Algorithms. Complexity of algorithms. Cryptology. Recurrence relations. Graph theory. A shortest-path algorithm. Planar graphs. Trees. A maximal flow algorithm. Finite-state automata. Languages and grammars. Turing machines. The Church-Turing thesis. Unsolvable problems. 3 credits. Prerequisite: Ma 110

• Ma 370 -- Selected Topics In Mathematics

This is a seminar course involving discussion of topics in pure or applied mathematics that will be chosen by mutual agreement between the students and the instructor. Students will work independently on projects that may be of special interest to them. 3 credits. Prerequisites: Ma 326 and permission of the mathematics faculty

• Ma 381 -- Seminar

Individual investigation of selected topics in pure or applied mathematics, centered on a subject to be agreed on between students and the faculty leader. Emphasis will be on training in independent reading of mathematical literature, oral presentations and group discussions of the theory and problems. Credits and class hours to be determined by faculty on individual basis. Prerequisite: Ma 223

• Ma 382 -- Seminar (continuation of Ma 381)

Credits to be determined by faculty on individual basis. Prerequisite: Ma 381

• Ma 391 -- Research Problem 1

An elective course available to qualified upper division students. Students may approach a faculty member and apply to carry out independent research on problems of mutual interest in pure or applied mathematics. Each student is encouraged to do independent creative work with faculty guidance. 3 credits. Prerequisites: Ma 240 and permission of research adviser

• Ma 392 -- Research Problem 2

Continuation of Ma 391. This is intended to allow students to continue ongoing research. 3 credits. Prerequisites: Ma 391 and permission of research adviser

Graduate Courses

• Ma 401 -- Boundary Value Problems

Orthogonal polynomials, Fourier series; properties of Legendre polynomials and Bessel functions. Applications to the wave equation and the differential equations of heat transfer in several dimensions. 3 credits. Prerequisites:Ma 223 and Ma 240

• Ma 402 -- Numerical Analysis

Techniques for the solutions of ordinary and partial differential equations, the classical problems of linear algebra, integration and systems of nonlinear equations. Error analysis, convergence and stability theory. Course assignments will include use of computing facilities. 3 credits. Prerequisites: Ma 223 and Ma 240

• Ma 403 -- Special Topics in Applied Mathematics

Introduction to the general theory of partial differential equations; existence and uniqueness of solutions; integral equations; computational techniques using finite-element and probabilistic methods. Other current topics in engineering may be included also. 3 credits. Prerequisites: Ma 223 and Ma 240

• Ma 415 -- Wavelets and Multiresolution Imaging (same as ECE 415)

3 credits. Prerequisite: permission of instructors. Taught by the faculties of mathematics and electrical engineering

• Ma 417 -- Mathematics of Medical Imaging

Mathematical basis for various medical imaging methods including CT, MRI, PET. Radon transform, tomography (recovery from projections), inverse problems, artifacts and noise. Mathematical physics of related topics such as wave propagation, signal generation and detection, quantum mechanics. 3 credits. Prerequisites: Ma 240, Ma 326 or permission of instructor

• Ma 470 -- Selected Advanced Topics in Mathematics

Selected topics in Mathematics treated at an advanced level. Credits to be determined by Mathematics faculty. Prerequisites: Ma 326 and permission of faculty member

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