提供方

斯坦福大学

課程信息

97,599 次近期查看

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.

立即開始，按照自己的計劃學習。

根據您的日程表重置截止日期。

建議：Expect to require at least 10 hours of study per week to complete this course satisfactorily....

字幕：英語（English）

Number TheoryReal AnalysisMathematical LogicLanguage

立即開始，按照自己的計劃學習。

根據您的日程表重置截止日期。

建議：Expect to require at least 10 hours of study per week to complete this course satisfactorily....

字幕：英語（English）

週

1START 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 format.) This initial orientation lecture is important, since this course is probably not like any math course you have taken before – even if in places it might look like one! AFTER THAT, Lecture 1 prepares the groundwork for the course; then in Lecture 2 we dive into the first topic. This may all look like easy stuff, but tens of thousands of former students found they had trouble later by skipping through Week 1 too quickly! Be warned. If possible, form or join a study group and discuss everything with them. BY THE WAY, the time estimates for watching the video lectures are machine generated, based on the video length. Expect to spend a lot longer going through the lectures sufficiently well to understand the material. The time estimates for completing the weekly Problem Sets (Quiz format) are a bit more reliable, but even they are just a guideline. You may find yourself taking a lot longer....

6 個視頻 （總計 84 分鐘）, 1 個測驗

Lecture 1 - Introductory Material27分鐘

Lecture 2 - Logical Combinators26分鐘

Tutorial for Assignment 12分鐘

Tutorial for Assignment 29分鐘

Tutorial for Problem Set 19分鐘

Problem Set 1

週

2In 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 problems in the associated Assignment sheet; THEN watch the tutorial video for the Assignment sheet. 2. REPEAT sequence for the second lecture. 3. THEN do the Problem Set, after which you can view the Problem Set tutorial. REMEMBER, the time estimates for watching the video lectures are machine generated, based on the video length. Expect to spend a lot longer going through the lectures sufficiently well to understand the material. The time estimates for completing the weekly Problem Sets (Quiz format) are a bit more reliable, but even they are just a guideline. You may find yourself taking a lot longer. ...

6 個視頻 （總計 131 分鐘）, 1 個測驗

Lecture 4 - Equivalence24分鐘

SUPPLEMENT: Using the course evaluation rubric4分鐘

Tutorial for Assignment 311分鐘

Tutorial for Assignment 421分鐘

Tutorial for Problem Set 237分鐘

Problem Set 2

週

3This 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 everyday life? Because the topics become more challenging, starting this week we have just one basic lecture cycle (Lecture -> Assignment -> Tutorial -> Problem Set -> Tutorial) each week. If you have not yet found one or more people to work with, please try to do so. It is so easy to misunderstand this material....

4 個視頻 （總計 128 分鐘）, 1 個測驗

SUPPLEMENT - How to Read Mathematical Formulas27分鐘

Tutorial for Assignment 547分鐘

Tutorial for Problem Set 323分鐘

Problem Set 3

週

4This 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 hundred years after its invention. (You do not need to know calculus for this course.) It is all about being precise and unambiguous. (But only where it counts. We are trying to extend our fruitfully-flexible human language and reasoning, not replace them with a rule-based straightjacket!)...

4 個視頻 （總計 88 分鐘）, 1 個測驗

Lecture 6B - Working with Quantifiers 228分鐘

Tutorial for Assignment 616分鐘

Tutorial for Problem Set 427分鐘

Problem Set 4

4.8

315 個審閱完成這些課程後已開始新的職業生涯

通過此課程獲得實實在在的工作福利

加薪或升職

創建者 NR•Mar 5th 2018

An awesome course. Very easy to follow at the start, becomes more challenging at the end. I have a PhD in economics yet I struggled with the real analysis at the end. And that's just intro level! :-D

創建者 MF•Aug 26th 2017

Great course, it's really shows the way how to think in mathematical rigor. It gave me an intuition about what Mathematics is itself.\n\nThank you Profesor Keith Devlin, you are a great teacher !

The Leland Stanford Junior University, commonly referred to as Stanford University or Stanford, is an American private research university located in Stanford, California on an 8,180-acre (3,310 ha) campus near Palo Alto, California, United States....

我什么时候能够访问课程视频和作业？

注册以便获得证书后，您将有权访问所有视频、测验和编程作业（如果适用）。只有在您的班次开课之后，才可以提交和审阅同学互评作业。如果您选择在不购买的情况下浏览课程，可能无法访问某些作业。

我购买证书后会得到什么？

您购买证书后，将有权访问所有课程材料，包括评分作业。完成课程后，您的电子课程证书将添加到您的成就页中，您可以通过该页打印您的课程证书或将其添加到您的领英档案中。如果您只想阅读和查看课程内容，可以免费旁听课程。

退款政策是如何规定的？

有助学金吗？

What is the passing grade for this course?

Since the focus is to acquire a new way of thinking (as opposed to getting right answers), the passing grade for the weekly Problem Sets is 35%, and for the Test Flight Problem Sets 30%. Basically, this means that if you stick with the course and complete all the work diligently, you should get a passing grade.

還有其他問題嗎？請訪問 學生幫助中心。