Mathematics

This course uses mathematics to discuss the global environment. Basic fluid dynamics and simple physics for the atmosphere and oceans are used to discuss some of the mechanisms involved in the dispersion of pollutants along coasts and the four-yearly (on average) El Nino oscillation in the equatorial Pacific, with its attendant Australia drought and blight of the Peruvian anchovy industry. Typical analysis involves the solution of linear partial differential equations for the velocity and density of the flows.

This is a graduate level course that is part of the Laurea Magistrale program in Mathematics. Enrollment is by consent of the instructor. The course is intended for students who have a strong background in math, especially calculus. The course focuses on the fundamental aspects of scientific calculus. Emphasis is placed on numerical solutions to problems of scientific calculus. A section of the course is devoted to teaching scientific calculus as described by the Italian Educational Mathematics Curriculum in Secondary Schools. This section emphasizes how to face and solve mathematical problems within a uniform, integrated computer algebra environment. Students are also required to prepare lesson plans and exercises. A special section of the course is devoted to the presentation of numerical methods for solving, via computer, certain mathematical problems, and the comparison with corresponding computer algebra methods, wherever appropriate. The course covers the use of computer tools in Math courses in the Secondary School system in Italy. Required readings are assigned from the following sources, available in the Departmental library: NUMERICAL COMPUTING WITH IEEE FLOATING POINT ARITHMETIC by M. Overton, ACCURACY AND STABILITY OF NUMERICAL ALGORITHMS by N. Higham, NUMERICAL ANALYSIS: MATHEMATICS OF SCIENTIFIC COMPUTING by D. Kincaid, E. W. Cheney, NUMERICAL LINEAR ALGEBRA, by D. Bau, N. Trefethen, AFTERNOTES ON NUMERICAL ANALYSIS by G. W. Stewart. Assessment is based on a laboratory test and a short written report and discussion of course materials.

This course provides a study of the theory of functions of one variable and focuses on the properties of monotonicity, continuity, derivability, and concavity/convexity of functions.

This course offers a study of sets, functions, mappings, and relations; groups, subgroups, cyclic groups, and cosets; homomorphism and isomorphism; group actions on sets; methods of proof; complex numbers; divisibility theory for integers and modular arithmetic; divisibility theory for polynomials; rings, ideals, and quotient rings; and fields and construction of fields from polynomial rings.

This course provides an introduction to probability theory aimed at third-year mathematics majors. Topics include: probability space; random variables: distribution, distribution functions, discrete random variables, moments of discrete random variables; random vectors; sequences of random variables; law of large numbers and the central limit theorem. Recommended prerequisites: introductory differential calculus, introductory integral calculus, multivariable differential calculus, multivariable integral calculus.

This engineering mathematics course covers matrices and gaussian elimination, vector spaces, orthogonality, determinants, eigenvalues and eigenvectors, and positive definite matrices.

 

 

By selecting the important properties of distance many different mathematical contexts are studied simultaneously in the framework of metric and normed spaces. Examines carefully the ways in which the derivative generalizes to higher dimensional situations. These concepts lead to precise studies of continuity, fixed points and the solution of differential equations. A recommended course for all students planning to advance in mathematics.