New and Special Courses: Spring 2001-2002

SM484 Mathematics of Quantum Mechanics (2-0-2). (Prof B. M. Baker) Introduction to mathematical structures of quantum mechanics; matrices, operators, and Hilbert space. Although this course does not satisfy requirements in any major, it does count toward the minimum load of 15 credits required of all midshipmen. Prereq: SM261 or SM311p or consent of instructor.

SM485B The History of Mathematics via The Sciences (3-0-3). (Prof. R. Maruszewski) The relationship between mathematics and the sciences is a two-way street. Mathematics is applied to the sciences and the sciences to mathematics. This course will examine the history of mathematics by studying the advancements achieved by the great mathematical scientists such as Archimedes, Kepler, Galileo, and Newton. Counts as a 300-level major elective for SMA or SMAH majors. Prereq: SM212 or SM222.

SM486 Error-Correcting Codes (3-0-3). (Prof. D. Joyner) We will explore, in detail, coding and decoding algorithms. Finite field theory will be developed and encoding and decoding algorithms for BCH and Golay codes will be explored. Lexicodes will be discussed as well if there is time. MAGMA or GAP or MAPLE will be used to compute examples. Counts as a 400-level major elective for SMA and SMAH majors. Prereq: SM362.

SM486A Chaos (3-0-3). A reading course about the mathematics associated with chaos. Students will read and present the implications of chaos to the sciences. The instructor will present the mathematics. MAPLE will be used to illustrate the concepts. Counts as a 400-level major elective for SMA and SMAH majors. Prerequisite: SM212 or SM222.

SM486B The Theory of Knots and Links (3-0-3). (Prof. M. Kidwell) Employing the text The Knot Book, by Colin C. Adams, W. H. Freeman & Co., 1994, we will study the many possible embeddings of circles (in the flexible sense) into three-dimensional space. The notations that have been introduced to describe knots and the knot enumeration problem will be examined. Then, we will introduce the polynomials that have been used to distinguish one knot or link from another. Student projects will cover other topics, such as applications of knots in chemistry and DNA research. Counts as a 400-level major elective for SMA or SMAH majors. Prereq: SM331 or SM331H.

SM486C The Mathematics of GPS and Mapping (3-0-3). (Prof. C. Bailey) This course will investigate the mathematics used in the global positioning system
(GPS). It will deal with the structure of the signal sent down to earth from each of the 29 orbiting satellites and how a GPS receiver uses these signals to calculate its position. We will also look at various map projections used and the mathematics behind them. This course will be taught using available web materials; there will be no textbook. Counts as a 400-level major elective for SMA and SMAH majors. Prereq: none.

SM486D Introduction to Mathematical General Relativity (3-0-3). (Prof. D. Konkowski) Using the text Introducing Einstein's Relativity by R. d'Inverno, this course will begin with the mathematical underpinnings of general relativity: tensor algebra and tensor calculus. After a short discussion of the physical principles underlying the theory, the field equations of general relativity will be derived. This system of coupled non-linear partial differential equations will then be used to derive some of the classic spacetime solutions which describe stars, black holes, and cosmological models. Counts as a 400-level major elective for SMA and SMAH majors. Prereq: SM212 or SM222.

SM486E Introduction to Computational Science and Engineering (3-0-3). (Prof. P. Turner) This course is multidisciplinary and will be team-taught, using faculty from several departments. There will be four projects drawn from a variety of subject areas in science, engineering and economics. Each will begin with some background science and culminate in the computer-assisted solution of the resulting mathematical or computational problems. The basic idea behind the course is to introduce students to the overall scientific process of solving real problems using teams with varied expertise and experiences to proceed from practical problem to solution. The computational techniques presented will be typical of processes that are widely used in solving scientific and engineering problems so that their applicability will be much wider than the particular problems discussed. Faculty involved in this project come from several departments including Computer Science, Economics, Mathematics, Mechanical Engineering and Physics. Counts as a 400-level major elective for SMA and SMAH majors. Prereq: SM212 or SM222.