このコースについて
4.8
1,122 ratings
261 reviews
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....
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Intermediate Level

中級レベル

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

約23時間で修了
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Number TheoryReal AnalysisMathematical LogicLanguage
Globe

100%オンラインコース

自分のスケジュールですぐに学習を始めてください。
Calendar

柔軟性のある期限

スケジュールに従って期限をリセットします。
Intermediate Level

中級レベル

Clock

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

約23時間で修了
Comment Dots

English

字幕:English

シラバス - 本コースの学習内容

1

セクション
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3時間で修了

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....
Reading
6本の動画(合計84分), 1 quiz
Video6件のビデオ
Lecture 1 - Introductory Material27 分
Lecture 2 - Logical Combinators26 分
Tutorial for Assignment 12 分
Tutorial for Assignment 29 分
Tutorial for Problem Set 19 分
Quiz1の練習問題
Problem Set 1

2

セクション
Clock
4時間で修了

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. ...
Reading
6本の動画(合計131分), 1 quiz
Video6件のビデオ
Lecture 4 - Equivalence24 分
SUPPLEMENT: Using the course evaluation rubric4 分
Tutorial for Assignment 311 分
Tutorial for Assignment 421 分
Tutorial for Problem Set 237 分
Quiz1の練習問題
Problem Set 2

3

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Clock
4時間で修了

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....
Reading
4本の動画(合計128分), 1 quiz
Video4件のビデオ
SUPPLEMENT - How to Read Mathematical Formulas27 分
Tutorial for Assignment 547 分
Tutorial for Problem Set 323 分
Quiz1の練習問題
Problem Set 3

4

セクション
Clock
3時間で修了

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!)...
Reading
4本の動画(合計88分), 1 quiz
Video4件のビデオ
Lecture 6B - Working with Quantifiers 228 分
Tutorial for Assignment 616 分
Tutorial for Problem Set 427 分
Quiz1の練習問題
Problem Set 4
4.8
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人気のレビュー

by 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

by HDJun 1st 2018

Great course about mathematical thinking, mathematical logic and proofs. I have a much better grasp on doing rigorous proofs after taking this course. Thanks for putting it together for us!

講師

Dr. Keith Devlin

Co-founder and Executive Director
H-STAR institute

Stanford Universityについて

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....

よくある質問

  • Once you enroll for a Certificate, you’ll have access to all videos, quizzes, and programming assignments (if applicable). Peer review assignments can only be submitted and reviewed once your session has begun. If you choose to explore the course without purchasing, you may not be able to access certain assignments.

  • When you purchase a Certificate you get access to all course materials, including graded assignments. Upon completing the course, your electronic Certificate will be added to your Accomplishments page - from there, you can print your Certificate or add it to your LinkedIn profile. If you only want to read and view the course content, you can audit the course for free.

  • 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.

さらに質問がある場合は、受講者向けヘルプセンターにアクセスしてください。