数学思维导论

你将学到什么

Number Theory

Real Analysis

Mathematical Logic

Language

课程概况

这门课的目标是帮你形成一种有价值的思维能力，这是人类祖先在三千多年历史中逐渐发展出来的强大思维方式。

数学思维并不等同于数学本身，至少同现行教育体系中所教的那种数学有所不同。学校教的数学主要关注典型数学题的求解过程学习；而数学家会思考特定方式，来求解日常生活中、科学中、或数学本身中会出现的实际问题。学校数学的成功关键在于按照常规套路解题；而数学思维的关键却在于超常规创造性思考，这在现今世界中是非常有价值的能力。这门课将帮你形成至关重要的思维方式。

这门课所针对的主要对象是正在考虑主修数学或数学相关专业的大学一年级学生，或者即将从高中毕业、心中有相关大学规划的高中生。这类学生需要数学思维才能在自己的专业学习中取得成功。不过，因为数学思维是一种很有价值的生活技能，所以任何超过17岁并选修这门课的人，都将会从中受益。

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.