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Introduction to Mathematical Thinking (Coursera)

Learn how to think the way mathematicians do – a powerful cognitive process developed over thousands of 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 – a valuable ability in today’s world. This course helps to develop that crucial way of thinking.

Introduction to Mathematical Thinking with Keith Devlin

Who is this class for: This ten-week course is designed with two particular audiences in mind. First, people who want to develop or improve mathematics-based, analytic thinking for professional or general life purposes. Second, high school seniors contemplating a mathematics or math-related major at college or university, or first-year students at college or university who are thinking of majoring in mathematics or a math-dependent subject. To achieves this aim, the first part of the course has very little traditional mathematical content, focusing instead on the thinking processes required for mathematics. The more mathematical examples are delayed until later, when they are more readily assimilated.

Suggested Readings:
Introduction to Mathematical Thinking