The deterministic view is adopted throughout the course. Among other models, the course includes decay of pollution, radioactive decay, plant growth, simple ecosystems, economic growth, population dynamics, chemical dynamics, and traffic dynamics. Computer experiments form an integral part of this course. This course consists of lectures and computer labs and meets six hours per week. Polynomial approximation, numerical differentiation and integration, numerical solution of differential equations, and numerical linear algebra are some of the topics covered in this course.
Emphasis is placed on error analysis.
Computer programs are implemented to investigate these topics. This is an extension of the theory of algebraic structures including rings, fields, associative fields, etc. Associated topics such as category, morphism, isomorphism, coset, ideal, etc., are discussed. Some applications in other branches of mathematics and physics, genetics, and information theory are also included. This course develops the theory of calculus.