Introduction to Mathematical Thinking – Stanford University | Coursera
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Learn how to think the way mathematicians do – a powerful cognitive process developed over thousands of years.
The goal of the course is to help you develop a valuable mental ability – a powerful way of thinking that our ancests 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 wld, from science, 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 wld. This course helps to develop that crucial way of thinking.
The course is offered in two versions. The eight-week-long Basic Course is designed f people who want to develop improvemathematics-based, analytic thinking f professional general life purposes. The ten-week-long Extended Course is aimed primarily at first-year students at college university who are thinking of majing in mathematics a mathematically-dependent subject, high school senis who have such a college career in mind. The final two weeks are me intensive and require me mathematical background than the Basic Course. There is no need to make a fmal election between the two. Simply skip drop out of the final two weeks if you decide you want to complete only the Basic Course.
Course Syllabus
1. Introducty material
2. Analysis of language – the logical combinats
3. Analysis of language – implication
4. Analysis of language – equivalence
5. Analysis of language – quantifiers
6. Wking with quantifiers
7. Proofs
8. Proofs involving quantifiers
9. Elements of number they
10. Beginning real analysis
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