| source Georgetown (X) |
level |
department Mathematics (X) |
This course is designed to assist students whose high school mathematics background is insufficient for the standard first-year mathematics courses. It is primarily intended as a preparation for MATH-035. Topics include: algebraic operations, factoring, exponents and logarithms, polynomials, rational functions, trigonometric functions, and the logarithmic and exponential functions. Graphing and word problems will be stressed. This course is not intended to complete the math/science requirement in the College. Fall.
Score: 7.0963445 Details | Listing | Web page
Credits: 3
Score: 7.0963445 Details | Listing | Web page
The primary objective of this beginning course in statistics is to have students learn and understand statistical concepts without being overwhelmed by cumbersome formulae and computations. The emphasis will be on data exploration and graphical techniques. Topics to be covered will include descriptive statistics, measures of center and spread, linear regression, probability theory, sampling, random variables and probability distributions. Uniform, discrete, binomial, normal, t and chi-square distributions will be among those used to introduce statistical inference, including estimation and hypothesis testing. Considerable use will be made of video tapes and computers. All classes will be held in the computer lab where the statistical software MINITAB will be taught and used to simplify computation and enhance graphical presentations. A computer tutorial will also be used. Minimum computer ability is recommended (but not required). This course is regarded as a core course (or SONY core course, as appropriate) for completion of the math/science requirement in the College. Fall and Spring.
Score: 7.0963445 Details | Listing | Web page
This course if for students who want to see how the math they have previously learned can be applied to personal issues related to health and finance as well as in policy decisions from many different fields. In the first part of the course, personal issues, such as weight gain or loss, alcohol abuse, proper drug dosage, mortgages and annuities are primarily considered. In the second part of the course, we will consider more global models that give insight into sustainable management of the worlds resources or issues related to genetics and genetic engineering. Often the results will be counterintuitive, such as finding that an increase in the rate of wild-life harvesting may actually decrease the long-term harvest. Fall and Spring.
Score: 7.0963445 Details | Listing | Web page
This is the first part of the four semester calculus sequence (Math-035-036 and 137-150) for mathematics and science majors. Topics include limits, derivatives, techniques of differentiation, applications of the derivative, the Riemann integral, the trigonometric and inverse trigonometric functions, and the logarithmic and exponential functions. Fall and Spring.
Score: 7.0963445 Details | Listing | Web page
Credits: 4
Score: 7.0963445 Details | Listing | Web page
Topics include graphical and numerical methods for describing data, probability and sampling distributions, estimation, hypothesis testing, and simple linear regression with inference. This course has two lectures and one recitation section. Fall and Spring.
Score: 7.0963445 Details | Listing | Web page
Credits: 4
Score: 7.0963445 Details | Listing | Web page
This course provides an introduction to basic concepts in probability theory and applied statistics. Topics to be covered include methods of enumeration, properties of random variables, common discrete and continuous distributions, expectations, the central limit theorem, parameter estimation, confidence intervals, hypothesis testing, and linear regression. Concepts will be illustrated and applied to data using the statistical package Minitab.
Score: 7.0963445 Details | Listing | Web page
Credits: 4
Score: 7.0963445 Details | Listing | Web page
Formerly called Foundations of Mathematics, this course will introduce different methods for constructing simple proofs, including forwards/backwards proofs, contradiction, contraposition, and induction. The students will apply these methods to a variety of areas of mathematics, including simple number theory, relations, calculus concepts, and a study of infinity. This course is required for Math Majors and is a prerequisite for many upper level courses. Fall and Spring.
Score: 7.0963445 Details | Listing | Web page
This course provides an introduction to the theory, techniques, and applications of ordinary differential equations. Topics include first order equations, second order linear equations, series solutions, the method of Laplace transforms, systems of equations, and an introduction to nonlinear equations and stability theory. Fall.
Score: 7.0963445 Details | Listing | Web page
Development of methods for solving numerical problems on digital computers. Problems discussed include solution of systems of linear and nonlinear equations, interpolation, numerical integration, and solution of ordinary differential equations. Work will include solving practical problems using the computer.
Score: 7.0963445 Details | Listing | Web page
Credits: 3
Score: 7.0963445 Details | Listing | Web page
Solutions of nonlinear differential equations exhibit a remarkable range of dynamic behavior -- from equilibira to chaos. This course will build students' intuition and skills for identifying and analyzing such behavior. It is based on possibly the best undergraduate mathematics textbook ever written, "Nonlinear Dynamics and Chaos" by Steven Strogatz. There will be regular reading assignments, in-class discussion and problem-solving sessions. Topics will include flows on the line and circle, limit cycles and bifurcations, fractals and chaos.
Score: 7.0963445 Details | Listing | Web page
Credits: 3
Score: 7.0963445 Details | Listing | Web page
Credits: 3
Score: 7.0963445 Details | Listing | Web page
This is a rigorous introduction to algebraic structures and their homomorphisms with emphasis on proofs. Topics from group theory will include permutation groups and Sylow theory. Topics from ring theory will include integral domains, unique factorization domains, and polynomial rings. Spring. Prerequisite: MATH-150 and MATH-200.
Score: 7.0963445 Details | Listing | Web page
This course is an introduction to the theory of algebraic curves. We will start with lines and conics from elementary geometry. After a review of the algebra of polynomials we will consider curves in the real affine plane and discuss their singularities and tangents. Later we will discuss curves in more general fields and indicate applications to number theory. Time permitting, we shall see how to extend the real affine plane, by adding points at infinity, to the projective plane, a natural setting for curves. Projective curves and their singularities, tangents, and flexes will be discussed.
Score: 7.0963445 Details | Listing | Web page
This course treats the basic concepts of graph theory, including graphs and digraphs, trees, networks, Eulerian and Hamiltonian graphs, and crossing numbers. Applications will be given to VLSI chips, RNA folding, and traffic signal design. Map colorings (including the famous four color theorem) will also be considered.
Score: 7.0963445 Details | Listing | Web page
This course will begin with a brief survey of sets, functions, logic, equivalence relations, and partial orders. The principal topics will include permutations and combinations, recurrence relations, generating functions, and inclusion-exclusion principles, with assorted applications. The course will conclude with a brief introduction to graph theory. Fall.
Score: 7.0963445 Details | Listing | Web page
Topics of significance in operations research, game theory, and economics will be treated. Examples are linear programming, Newton's method, conjugate gradient methods, Kuhn-Tucker theory, dynamic programming, spanning trees, and Nash equilibria.
Score: 7.0963445 Details | Listing | Web page
Credits: 3
Score: 7.0963445 Details | Listing | Web page
Credits: 3
Score: 7.0963445 Details | Listing | Web page
Not only is the geometry of 2-dimensional surfaces in 3-dimensional space of great practical and theoretical importance in many fields of mathematics and physics, but so is the geometry of n-dimensional surfaces in (n+1)-dimensional space. This course uses and reinforces topics from Multivariable Calculus and Linear Algebra to study the geometry of oriented surfaces in 3-dimensional space, as well as n-dimensional surfaces in the (n+1)-dimensional space. Topics include level surfaces, parametrized surfaces, Vector fields on surfaces, the Gauss map, geodesics, surfaces area, the curvature of surfaces, the exponential map, and the Gauss-Bonnet Theorem.
Score: 7.0963445 Details | Listing | Web page