课程目标 数学思维简介 课程大纲,数学思维,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. 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,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.,数学思维不等同于做数学运算-至少不像数学那样是我们教育系统的主流课程.校园数学主要集中在学习函数去去解决非常刻板问题.专业数学家考虑一些特定的方法来解决实际问题，这些问题来源于日常生活世界或者科学，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 todays world. This course helps to develop that crucial way of thinking. 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 first-year 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.,主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. 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,Instructors welcome and introduction 1. Introductory material 目录 2. Analysis of language the logical combinators 逻辑联结词 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 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 analysis 实分析初步,