• 3. Analysis of language – implication
蕴含
• 4. Analysis of language – equivalence
等价
• 5. Analysis of language – quantifiers
量词
• 6. Working with quantifiers
• 课程目标：帮助我们形成一种有益 的心智能力——我们祖先三千年前 形成的一种强大的思考方式.
Introduction to mathematical thingking
• 数学思维不等同于做数
• Mathematical thinking is not the same as doing mathematics – at
• 校园数学成功的关键是了解数学内部世界.相比而言， 数学思维的主要特征是考虑数学外部世界--种必要的 技能在当今世界.这门课帮助我们形成思维方式的关 键.
Introduction to mathematical thingking
• The primary audience is firstyear students at college or university who are thinking of majoring in mathematics or a mathematically-dependent subject, or high school seniors who have such a college career in mind.
学运算-至少不像数学那
least not as mathematics is
样是我们教育系统的主
typically presented in our school system. School math typically
流课程.校园数学主要集
focuses on learning procedures 中在学习函数去去解决
量词加工
• 7. Proofs
证明
• 8. Proofs involving quantifiers
量词证明
• 9. Elements of number theory
数论原理
10. Beginning real a要的学生是在 大学校园的大一 学生，他们主修 的是数学或与数 学相关的课题， 或高中毕业班的 学生有考考大学 的决心.
About the student
• They will need mathematical thinking to succeed in their major. Because mathematical thinking is a valuable life skill, however, anyone over the age of 17 could benefit from taking the course.
课程目标 数学思维简介
课程大纲
About the course
• The goal of the course is to help you develop a valuable mental ability – a powerful way of thinking that our ancestors have developed over three thousand years.
to solve highly stereotyped problems. Professional
非常刻板问题.专业数学
mathematicians think a certain 家考虑一些特定的方法
way to solve real problems, problems that can arise from the
• 他们这类人需要数学思维去使他们的主 修成功.因为数学思维是一门有益的生 活技能，并且，任何超过17岁的人都能 从中获益.
Course syllabus
• Instructor’s welcome and introduction
• 1. Introductory material
目录
• 2. Analysis of language – the logical combinators 逻辑联结词
来解决实际问题，这些
everyday world, or from science, 问题来源于日常生活世
or from within mathematics itself.
界或者科学，或者来源 于数学本身.
Introduction to mathematical thingking
• 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.