About this Course
4.8
1,123 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....
Globe

100% 온라인 강좌

지금 바로 시작해 나만의 일정에 따라 학습을 진행하세요.
Calendar

유연한 마감

일정에 따라 마감일을 재설정합니다.
Intermediate Level

중급 단계

Clock

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

완료하는 데 약 23시간 필요
Comment Dots

English

자막: English

귀하가 습득할 기술

Number TheoryReal AnalysisMathematical LogicLanguage
Globe

100% 온라인 강좌

지금 바로 시작해 나만의 일정에 따라 학습을 진행하세요.
Calendar

유연한 마감

일정에 따라 마감일을 재설정합니다.
Intermediate Level

중급 단계

Clock

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

완료하는 데 약 23시간 필요
Comment Dots

English

자막: English

강의 계획 - 이 강좌에서 배울 내용

1

섹션
Clock
완료하는 데 3시간 필요

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
6개 동영상(총 84분), 1 quiz
Video6개의 동영상
Lecture 1 - Introductory Material27m
Lecture 2 - Logical Combinators26m
Tutorial for Assignment 12m
Tutorial for Assignment 29m
Tutorial for Problem Set 19m
Quiz1개 연습문제
Problem Set 1m

2

섹션
Clock
완료하는 데 4시간 필요

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
6개 동영상(총 131분), 1 quiz
Video6개의 동영상
Lecture 4 - Equivalence24m
SUPPLEMENT: Using the course evaluation rubric4m
Tutorial for Assignment 311m
Tutorial for Assignment 421m
Tutorial for Problem Set 237m
Quiz1개 연습문제
Problem Set 2m

3

섹션
Clock
완료하는 데 4시간 필요

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
4개 동영상(총 128분), 1 quiz
Video4개의 동영상
SUPPLEMENT - How to Read Mathematical Formulas27m
Tutorial for Assignment 547m
Tutorial for Problem Set 323m
Quiz1개 연습문제
Problem Set 3m

4

섹션
Clock
완료하는 데 3시간 필요

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
4개 동영상(총 88분), 1 quiz
Video4개의 동영상
Lecture 6B - Working with Quantifiers 228m
Tutorial for Assignment 616m
Tutorial for Problem Set 427m
Quiz1개 연습문제
Problem Set 4m
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최상위 리뷰

대학: 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

대학: 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!

강사

Dr. Keith Devlin

Co-founder and Executive Director
H-STAR institute

Stanford University 정보

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....

자주 묻는 질문

  • 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.

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