Introduction to Mathematical Thinking: Online course by Stanford Univ

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Introduction to Mathematical Thinking

Learn how to think the way mathematicians do is a powerful cognitive process developed over thousands of years.

About the course
The goal of the course is to help you develop a valuable mental ability, and a powerful way of thinking that our ancestors have developed over three thousand years.

Mathematical thinking is not the same as doing mathematics, at least not as mathematics is typically presented in our school system. School math typically focuses on learning procedures to solve highly stereotyped problems. Professional mathematicians think a certain way to solve real problems,
problems that can arise from the everyday world, or from science, or from within mathematics itself. The key to success in school math is to learn to think inside-the-box. In contrast, a key feature of mathematical thinking is thinking outside-the-box is a valuable ability in today's world. This course helps to develop that crucial way of thinking.

Course Syllabus
1. Introductory material
2. Analysis of language - the logical combinators
3. Analysis of language - implication
4. Analysis of language - equivalence
5. Analysis of language - quantifiers
6. Working with quantifiers
7. Proofs
8. Proofs involving quantifiers
9. Elements of number theory
10. Beginning real analysis

High school mathematics. Specific requirements are familiarity with elementary symbolic algebra, the concept of a number system (in particular, the characteristics of, and distinctions between, the natural numbers, the integers, the rational numbers, and the real numbers), and some elementary set theory (including inequalities and intervals of the real line).

Course Sessions
September 29, 2014 - December 6, 2014

For further information, click here.


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