À propos de ce cours
4.8
1,075 ratings
255 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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Cours en ligne à 100 %

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Calendar

Dates limites flexibles

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Intermediate Level

Niveau intermédiaire

Clock

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

Approx. 23 heures pour terminer
Comment Dots

English

Sous-titres : English

Compétences que vous acquerrez

Mathematical LogicNumber TheoryReal AnalysisLanguage
Globe

Cours en ligne à 100 %

Commencez dès maintenant et apprenez aux horaires qui vous conviennent.
Calendar

Dates limites flexibles

Réinitialisez les dates limites selon votre disponibilité.
Intermediate Level

Niveau intermédiaire

Clock

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

Approx. 23 heures pour terminer
Comment Dots

English

Sous-titres : English

Programme du cours : ce que vous apprendrez dans ce cours

1

Section
Clock
3 heures pour terminer

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 vidéos (Total 84 min), 1 quiz
Video6 vidéos
Lecture 1 - Introductory Material27 min
Lecture 2 - Logical Combinators26 min
Tutorial for Assignment 12 min
Tutorial for Assignment 29 min
Tutorial for Problem Set 19 min
Quiz1 exercice pour s'entraîner
Problem Set 1 min

2

Section
Clock
4 heures pour terminer

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 vidéos (Total 131 min), 1 quiz
Video6 vidéos
Lecture 4 - Equivalence24 min
SUPPLEMENT: Using the course evaluation rubric4 min
Tutorial for Assignment 311 min
Tutorial for Assignment 421 min
Tutorial for Problem Set 237 min
Quiz1 exercice pour s'entraîner
Problem Set 2 min

3

Section
Clock
4 heures pour terminer

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 vidéos (Total 128 min), 1 quiz
Video4 vidéos
SUPPLEMENT - How to Read Mathematical Formulas27 min
Tutorial for Assignment 547 min
Tutorial for Problem Set 323 min
Quiz1 exercice pour s'entraîner
Problem Set 3 min

4

Section
Clock
3 heures pour terminer

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 vidéos (Total 88 min), 1 quiz
Video4 vidéos
Lecture 6B - Working with Quantifiers 228 min
Tutorial for Assignment 616 min
Tutorial for Problem Set 427 min
Quiz1 exercice pour s'entraîner
Problem Set 4 min
4.8
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Meilleurs avis

par 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

par 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!

Enseignant

Dr. Keith Devlin

Co-founder and Executive Director
H-STAR institute

À propos de Stanford University

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....

Foire Aux Questions

  • 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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