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Mathematical Sciences - Undergraduate Courses

Mathematics   MA 090 Pre-Calculus Close Partial fractions, polynomials, Remainder Theorem, Fundamental Theorem of Algebra, Descartes' Rule, exponential and log functions, trigonometric functions, trigonometry of triangles, right triangles, laws of sines and cosines, and conic sections. MA 115 Calculus I Close Functions of one variable, limits, continuity, derivatives, chain rule, maxima and minima, exponential functions and logarithms, inverse functions, antiderivatives, elementary differential equations, Riemann sums, the Fundamental Theorem of Calculus, vectors and determinants. MA 116 Calculus II Close Techniques of integration, infinite series and Taylor series, polar coordinates, double integrals, improper integrals, parametric curves, arc length, functions of several variables, partial derivatives, gradients and directional derivatives. MA 117 Calculus for Business and Liberal Arts Close This course is designed for undergraduate students in Business and Liberal Arts majors. It includes the following basic topics in calculus: the definition of functions, their graphs, limits and continuity; derivatives and differentiation of functions; applications of derivatives; and definite and indefinite integrals. Properties of some elementary functions, such as the power functions, exponential functions, and logarithmic functions, will be discussed as examples. The course also covers methods of solving the first-order linear differential equations and separable equations, and some basic concepts in multi-variable calculus, such as partial derivatives, double integrals, and optimization of functions. MA 118 Probability for Business and Liberal Arts Close This course is designed only for undergraduate students in Business and Liberal Arts majors. It introduces basic concepts and methods in probability. Topics includes the definition of sample spaces, events, and their probabilities; elementary combinatorics and counting techniques; and conditional probability, the total probability, and Bayes' Theorem. The course also deals with concepts of discrete and continuous random variables and probability distributions; multi-random variables and their joint distributions; the mean, variance, and covariance of random variables; and the Central Limit Theorem and t-distributions. MA 134  / MA 503  Discrete Mathematics Close This course provides the background necessary for advanced study of mathematics or computer science. Topics include propositional calculus, predicates and quantifiers, elementary set theory, countability, functions, relations, proof by induction, elementary combinatorics, elements of graph theory, mends, and elements of complexity theory. MA 182 Honors Mathematical Analysis II Close Covers the same material as MA 116, but with more breadth and depth. Additional topics discussed. By invitation or permission only. MA 188 Seminar in Mathematical Sciences Close Introduction to the modern applications of mathematics. The applications chosen demonstrate the power, beauty, and effectiveness of mathematics in establishing a rigorous understanding and treatment of scientific phenomena. Typical topics include optimization, chaotic dynamical systems, probability, information theory and coding, and computational mathematics. Permission of the instructor is required. This course may be taken more than once. If a student takes MA 188 at least three times, the student may earn three credits and count the course as an elective for the degree requirement. MA 221 Differential Equations Close Ordinary differential equations of first and second order, homogeneous and non-homogeneous equations; improper integrals, Laplace transforms; review of infinite series, series solutions of ordinary differential equations near an ordinary point; boundary-value problems; orthogonal functions; Fourier series; separation of variables for partial differential equations. MA 222 Probability and Statistics Close Introduces the essentials of probability theory and elementary statistics. Lectures and assignments greatly stress the manifold applications of probability and statistics to computer science, production management, quality control, and reliability. A statistical computer package is used throughout the course for teaching and for assignments. Contents include: descriptive statistics, pictorial and tabular methods, and measures of location and of variability; sample space and events, probability axioms, and counting techniques; conditional probability and independence, and Bayes' formula; discrete random variables, distribution functions and moments, and binomial and Poisson distributions; continuous random variables, densities and moments, normal, gamma, and exponential and Weibull distributions unions; distribution of the sum and average of random samples; the Central Limit Theorem; confidence intervals for the mean and the variance; hypothesis testing and p-values, and applications for the mean; simple linear regression, and estimation of and inference about the parameters; and correlation and prediction in a regression model. MA 227  / PEP 679  Multivariate Calculus Close Review of matrix operations, Cramer’s rule, row reduction of matrices; inverse of a matrix, eigenvalues and eigenvectors; systems of linear algebraic equations; matrix methods for linear systems of differential equations, normal form, homogeneous constant coefficient systems, complex eigenvalues, nonhomogeneous systems, the matrix exponential; double and triple integrals; polar, cylindrical and spherical coordinates; surface and line integrals; integral theorems of Green, Gauss and Stokes. Engineering curriculum requirement. MA 230 Multivariable Calculus and Optimization Close Begins with a study of n-dimensional geometry (hyperplanes, hyperspheres, convex hulls, and convex polyhedra), and moves on to study the differential calculus of functions of several variables. In this context, classical optimization theory is studied - that is, the application of calculus to the basic problem of finding the maxima and minima of a continuous function of one or more variables, using Lagrange multipliers, and paying particular attention to convex and concave functions. The final major topic studied is linear programming through the simplex method. Computational methods are stressed throughout. Other topics, such as search techniques, are taken up as time permits. MA 232 Linear Algebra Close This course introduces basic concepts of linear algebra from a geometric point of view. Topics include the method of Gaussian elimination to solve systems of linear equations; linear spaces and dimension; independent and dependent vectors; norms, inner product, and bases in vector spaces; determinants, eigenvalues and eigenvectors of matrices; symmetric, unitary, and normal matrices; matrix representations of linear transformations and orthogonal projections; the fundamental theorems of linear algebra; and the least-squares method and LU-decomposition. MA 234 Complex Variables with Applications Close This course introduces basic concepts and methods in complex analysis. Topics include complex numbers and their properties, followed by limits, continuity, complex differentiation, analytic functions, the Cauchy-Riemann equations, complex integrations, Cauchy's integral formula, Taylor and Laurent series, Cauchy residue theorem, applications of contour integrals, conformal mappings, and applications in physics and engineering. MA 281 Honors Mathematical Analysis III Close Covers the same material as that dealt with in MA 221, but with more breadth and depth. By invitation only. MA 282 Honors Mathematical Analysis IV Close Covers the same material as that dealt with in MA 227, but with more breadth and depth. By invitation only. MA 293 Supplementary Topics of Differential Equations Close This course is designed for the completion of transferring credits for MA 221 Differential Equations. The transfer students, who need to learn some topics of MA 221 not included in the courses taken elsewhere, may enroll in this course only once with permission of an undergraduate adviser in the Math Department, and are required to complete this course under the guidance of the MA 221 course coordinator. The students who pass this course will receive the full transfer credits for MA 221. The students who fail will then be required to enroll in the full course of MA 221 at Stevens. Pass/Fail. MA 294 Supplementary Topics of Calculus IV Close This course is designed for the completion of transferring credits for MA 227 Multivariable Calculus. The transfer students, who need to learn some topics of MA 227 not included in the courses taken elsewhere, may enroll in this course only once with permission of an undergraduate adviser in the Math Department. The students are required to complete this course under the guidance of the MA 227 course coordinator. The students who pass this course will receive the full transfer credits for MA 227. The students who fail will then be required to enroll in the full course of MA 227 at Stevens. Pass/Fail. MA 331 Intermediate Statistics Close An introduction to statistical inference and to the use of basic statistical tools. Topics include descriptive and inferential statistics; review of point estimation, method of moments, and maximum likelihood; interval estimation and hypothesis testing; simple and multiple linear regression; analysis of variance and design of experiments; and nonparametric methods. Selected topics, such as quality control and time series analysis, may also be included. Statistical software is used throughout the course for exploratory data analysis and statistical inference based in examples and in real data relevant for applications. MA 335 Introduction to Number Theory Close This is an introductory course to number theory. Topics include divisibility, prime numbers and modular arithmetic, arithmetic functions, the sum of divisors and the number of divisors, rational approximation, linear Diophantine equations, congruences, the Chinese Remainder Theorem, quadratic residues, and continued fractions. MA 336 Modern Algebra Close A rigorous introduction to group theory and related areas with applications as time permits. Topics include proof by induction, greatest common divisor, and prime factorization; sets, functions, and relations; definition of groups and examples of other algebraic structures; and permutation groups, Lagrange's Theorem, and Sylow's Theorems. Typical application: error correcting group codes. Sample text: Numbers Groups and Codes, Humphries and Prest, Cambridge U.P. MA 346 Numerical Methods Close This course begins with a brief introduction to writing programs in a higher level language, such as Matlab. Students are taught fundamental principles regarding machine representation of numbers, types of computational errors, and propagation of errors. The numerical methods include finding zeros of functions, solving systems of linear equations, interpolation and approximation of functions, numerical integration and differentiation, and solving initial value problems of ordinary differential equations. MA 360 Intermediate Differential Equations Close This course offers more in-depth coverage of differential equations. Topics include ordinary differential equations as finite-dimensional dynamical systems; vector fields and flows in phase space; existence/uniqueness theorems; invariant manifolds; stability of equilibrium points; bifurcation theory; Poincaré-Bendixson Theorem and chaos in both continuous and discrete dynamical systems; and applications to physics, biology, economics, and engineering. MA 361 Intermediate Partial Differential Equations Close This course offers a rigorous approach to classical partial differential equations. It begins with definitions, properties, and derivations of some basic equations of mathematical physics followed by the topics: solving of first order equations with the method of characteristics; classification of second order equations; the heat equation and wave equation; Fourier series and separation of variables; Green's functions and elliptic theory; examples of the first and second order nonlinear partial differential equations. MA 410 Differential Geometry Close This course is an introduction to the geometry of curves and surfaces. Topics include tangent vectors, tangent bundles, directional derivatives, differential forms, Euclidean geometry and calculus on surfaces, Gaussian curvatures, Riemannian geometry, and geodesics. MA 441 Introduction to Mathematical Analysis Close This course introduces students to the fundamentals of mathematical analysis at an adequate level of rigor. Topics include fundamental mathematical logic and set theory, the real number systems, sequences, limits and completeness, elements of topology, continuity, derivatives and related theorems, Taylor expansions, the Riemann integral, and the Fundamental Theorem of Calculus. MA 442 Real Variables Close This course introduces principles of real analysis and the modern treatment of functions of one and several variables. Topics include metric spaces, the Heine-Borel theorem in R-n, Lebesgue measure, measurable functions, Lebesgue and Stieltjes integrals, Fubini's theorem, abstract integration, L-p classes, metric and Banach space properties, and Hilbert space. MA 460 Chaotic Dynamics, with Computations and Applications Close This course introduces students to the concepts behind the modern theory of dynamical systems, particularly chaotic systems. Although the course is mathematical in nature, the emphasis is on the underpinning ideas and applications, rather than a systematic exposition of results. Topics include: standard examples and definitions, solutions of ODEs as dynamical systems, flows, and maps; fixed points of linear maps, periodic orbits, limit cycles, and asymptotic stability; rudiments of hyperbolicity; and symbolic dynamics and the Horse Shoe. Further topics may include: fundamentals of topological dynamics, fundamentals of ergodic theory, attractors, and fractals. A good part of the assigned work involves computer experimentation and computations. MA 461 Special Problems I Close Individual projects in pure and applied mathematics. Enrollment limited. Departmental approval required. MA 462 Special Problems II Close Individual projects in pure and applied mathematics. Enrollment limited. Departmental approval required. MA 463 Seminar in Mathematics I Close Seminar in selected topics, such as: combinatorial topology, differential geometry, finite groups, number theory, or statistical techniques. Enrollment limited. Instructor’s permission required. May be taken twice for credit. MA 464 Seminar in Mathematics II Close Seminar in selected topics such as: combinatorial topology, differential geometry, finite groups, number theory, or statistical techniques. Enrollment limited. Instructor’s permission required. May be taken twice for credit. MA 498 Senior Research Project I Close Students will do a research project under the guidance of a faculty advisor. Senior standing and prior approval are required. Topics may be selected from any area of mathematics with the instructor's approval. Each student will be required to present results in both a written and oral report. The written report may be in the form of a senior thesis.   MA 499 Senior Research Project II Close Students will do a research project under the guidance of a faculty advisor. Senior standing and prior approval are required. Topics may be selected from any area of mathematics with the instructor's approval. Each student will be required to present results in both a written and oral report. The written report may be in the form of a senior thesis.

Contact

Dr. Patrick Miller
Associate Dean of Science
McLean Hall
Room 515
Phone: 201.216.8072
Fax: 201.216.8196
pmiller@stevens.edu

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