FMS1205M



FS: Analogy & Intuition in Mathematics

The development of mathematical concepts and theories is often influenced by an intuition acquired from physical experience and by analogy with various areas of scientific and mathematical knowledge. Analogy is an important factor in preparing, if not predicting, new concepts while an experience-based intuition can sometimes be an obstacle. The objective of this seminar module is to present case studies of the creative role of analogy in mathematics and of the ground-breaking importance of "counter-intuition" in modern mathematics. A wealth of examples of both can be found in geometry, number theory, analysis, algebra, logic, set theory and theoretical computer science. Students of this module are expected to source for relevant material in books, journals and the internet under the guidance of the lecturer. The emphasis, however, will be on the spirit of the mathematical enterprise rather than on the technical mastery. To illustrate the use of analogy and intuition in problem solving, some elementary problems and puzzles will be posed in class for attempt and discussion. The main prerequisite for this module is an inquiring mind open to new ideas. Seminar website address (if available): http:// http://ivle.nus.edu.sg/module/student/?CourseID=3472d372-c693-4a82- 81a2-a049ca4a3efc&ClickFrom=Outline

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