Mathematical Thinking for Advanced Mathematics

О курсе

The objective of this course is to teach the mathematical thinking processes that are used in all college-level math-theory courses (such as discrete math, abstract algebra, and real analysis, for example). The goal is to reduce the time and frustration involved in learning such courses and to provide mathematical skills that are needed for graduate work and research in areas such as engineering, statistics, computer science, physics, the pure sciences, operations research, and economics, for example. This goal is accomplished by describing the following fundamental thinking processes that are used in advanced mathematical reasoning, each of which is illustrated with carefully explained examples: -Working with visual images. -Generalization (creating, from an original mathematical concept, a new and more encompassing concept that not only contains the original concept but something new and different as well) -Unification (combining two or more mathematical concepts into a single concept that includes the original ones). -Creating and working with mathematical definitions. -Creating and working with axiomatic systems (used in all abstract math courses).

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Daniel Solow

Professor