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Summer 2003 Course Descriptions
MATH 103: Mathematical Explorations
This course is for students who wish to experience how mathematical ideas naturally evolve. The homework consists of the students actively investigating mathematical ideas. The course emphasizes ideas and imagination as opposed to techniques and calculations. Topics vary depending on the instructor and are announced (www.math.cornell.edu) several weeks before the semester begins. Some assessment is done through writing assignments. MATH 109: Precalculus Mathematics
MATH 109 cannot be used toward graduation. This course is designed to prepare students for MATH 111. Algebra, trigonometry, logarithms, and exponentials are reviewed. MATH 111: Calculus I
Course topics include: functions and graphs, limits and continuity, differentiation and integration of algebraic, trigonometric, inverse trig, logarithmic, and exponential functions; applications of differentiation, including graphing, max-min problems, tangent line approximation, implicit differentiation, and applications to the sciences; the mean value theorem; and antiderivatives, definite and indefinite integrals, the fundamental theorem of calculus, substitution in integration, the area under a curve. Graphing calculators are used, and their pitfalls are discussed, as applicable to the above topics. MATH 111 can serve as a one-semester introduction to calculus or as part of a two-semester sequence in which it is followed by MATH 112 or 122. MATH 171: Statistical Theory and Application In The Real World
This introductory statistics course discusses techniques for analyzing data occurring in the real world and the mathematical and philosophical justification for these techniques. Topics include: population and sample distributions, central limit theorem, statistical theories of point estimation, confidence intervals, testing hypotheses, the linear model, and the least squares estimator. The course concludes with a discussion of tests and estimates for regression and analysis of variance (if time permits). The computer is used to demonstrate some aspects of the theory, such as sampling distributions and the Central Limit Theorem. In the lab portion of the course, students learn and use computer-based methods for implementing the statistical methodology presented in the lectures. (No previous familiarity with computers is presumed.) MATH 191: Calculus For Engineers
MATH 191 covers essentially the same topics as 190, but is designed for students with some previous successful experience with calculus. Course topics include: plane analytic geometry, differential and integral calculus, and applications. MATH 192: Calculus For Engineers
Course topics include: polar coordinates, infinite series, and power series. Also covered are: vectors and calculus of functions of several variables through double and triple integrals. MATH 293: Engineering Mathematics
The conclusion of vector calculus, including line integrals, vector fields, Green's theorem, Stokes' theorem, and the divergence theorem; followed by an introduction to ordinary and partial differential equations, including Fourier series and boundary value problems. May include computer use in solving problems. MATH 294: Engineering Mathematics
Linear algebra and its applications. Topics include matrices, determinants, vector spaces, eigenvalues and eigenvectors, orthogonality and inner product spaces; applications include brief introductions to difference equations, Markov chains, and systems of linear ordinary differential equations. May include computer use in solving problems. MATH 311: Introduction to Analysis
Provides a transition from calculus to real analysis. Topics include: rigorous treatment of fundamental concepts in calculus: including limits and convergence of sequences and series, compact sets; continuity, uniform continuity and differentiability of functions. Emphasis will be placed upon understanding and constructing mathematical proofs. MATH 332: Algebra and Number Theory
Course covers various topics from number theory and modern algebra, usually including most of the following: Primes and factorization, Diophantine equations, congruences, quadratic reciprocity, continued fractions, rings and fields, finite groups, and an introduction to the arithmetic of the Gaussian integers and quadratic fields. Motivation and examples for the concepts of abstract algebra are derived primarily from number theory and geometry. Last modified: April 23, 2003 |
