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.
START with the Welcome lecture. It explains what this course is about. (It comes with a short Background Reading assignment, to read before you start the course, and a Reading Supplement on Set Theory for use later in the course, both in downloadable PDF forma...
In Week 2 we continue our discussion of formalized parts of language for use in mathematics. By now you should have familiarized yourself with the basic structure of the course: 1. Watch the first lecture and answer the in-lecture quizzes; tackle each of the p...
This week we continue our analysis of language for use in mathematics. Remember, while the parts of language we are focusing have particular importance in mathematics, our main interest is in the analytic process itself: How do we formalize concepts from every...
This week we complete our analysis of language, putting into place the linguistic apparatus that enabled, mathematicians in the 19th Century to develop a formal mathematical treatment of infinity, thereby finally putting Calculus onto a firm footing, three hun...
This week we take our first look at mathematical proofs, the bedrock of modern mathematics.
This week we complete our brief look at mathematical proofs
The topic this week is the branch of mathematics known as Number Theory. Number Theory, which goes back to the Ancient Greek mathematicians, is a hugely important subject within mathematics, having ramifications throughout mathematics, in physics, and in some ...
In this final week of instruction, we look at the beginnings of the important subject known as Real Analysis, where we closely examine the real number system and develop a rigorous foundation for calculus. This is where we really benefit from our earlier analy...
WEEK 9 & 10
Test Flight provides an opportunity to experience an important aspect of "being a mathematician": evaluating real mathematical arguments produced by others. There are three stages. It is important to do them in order, and to not miss any steps
Dr. Keith Devlin
Co-founder and Executive Director