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中級

完成時間大約為23 小時

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

英語(English)

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Number TheoryReal AnalysisMathematical LogicLanguage

100% 在線

立即開始,按照自己的計劃學習。

可靈活調整截止日期

根據您的日程表重置截止日期。

中級

完成時間大約為23 小時

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

英語(English)

字幕:英語(English)

教學大綱 - 您將從這門課程中學到什麼

1
完成時間為 3 小時

Week 1

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 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
6 個視頻
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
1 個練習
Problem Set 12小時
2
完成時間為 4 小時

Week 2

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 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
6 個視頻
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
1 個練習
Problem Set 22小時
3
完成時間為 4 小時

Week 3

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 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
4 個視頻
SUPPLEMENT - How to Read Mathematical Formulas27分鐘
Tutorial for Assignment 547分鐘
Tutorial for Problem Set 323分鐘
1 個練習
Problem Set 32小時
4
完成時間為 3 小時

Week 4

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 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
4 個視頻
Lecture 6B - Working with Quantifiers 228分鐘
Tutorial for Assignment 616分鐘
Tutorial for Problem Set 427分鐘
1 個練習
Problem Set 42小時
4.8
316 個審閱Chevron Right

50%

完成這些課程後已開始新的職業生涯

47%

通過此課程獲得實實在在的工作福利

13%

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來自数学思维导论的熱門評論

創建者 NRMar 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 MFAug 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 !

講師

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Dr. Keith Devlin

Co-founder and Executive Director
H-STAR institute

關於 斯坦福大学

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....

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  • 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.

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