proposé par

Stanford University

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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Approx. 23 heures pour terminer

Sous-titres : English

Mathematical LogicNumber TheoryReal AnalysisLanguage

Commencez dès maintenant et apprenez aux horaires qui vous conviennent.

Réinitialisez les dates limites selon votre disponibilité.

Approx. 23 heures pour terminer

Sous-titres : English

Section

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 vidéos (Total 84 min), 1 quiz

Lecture 0 - Welcome8 min

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

Problem Set 1 min

Section

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 vidéos (Total 131 min), 1 quiz

Lecture 3 - Implication31 min

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

Problem Set 2 min

Section

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 vidéos (Total 128 min), 1 quiz

Lecture 5 - Quantifiers29 min

SUPPLEMENT - How to Read Mathematical Formulas27 min

Tutorial for Assignment 547 min

Tutorial for Problem Set 323 min

Problem Set 3 min

Section

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 vidéos (Total 88 min), 1 quiz

Lecture 6B - Working with Quantifiers 228 min

Tutorial for Assignment 616 min

Tutorial for Problem Set 427 min

Problem Set 4 min

4.8

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par 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

par HD•Jun 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!

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....

When will I have access to the lectures and assignments?

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.

What will I get if I purchase the Certificate?

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.

What is the refund policy?

Is financial aid available?

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.

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