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.
Introduction to Mathematical Thinking
от партнера
Stanford University
Об этом курсе
4.8
Оценки: 1,212
Приобретаемые навыки
Number TheoryReal AnalysisMathematical LogicLanguage
Программа курса: что вы изучите
Неделя
1Week 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 видео ((всего 84 мин.)), 1 тест
6 видео
Lecture 1 - Introductory Material27мин
Lecture 2 - Logical Combinators26мин
Tutorial for Assignment 12мин
Tutorial for Assignment 29мин
Tutorial for Problem Set 19мин
1 практическое упражнение
Problem Set 1s
Неделя
2Week 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 видео ((всего 131 мин.)), 1 тест
6 видео
Lecture 4 - Equivalence24мин
SUPPLEMENT: Using the course evaluation rubric4мин
Tutorial for Assignment 311мин
Tutorial for Assignment 421мин
Tutorial for Problem Set 237мин
1 практическое упражнение
Problem Set 2s
Неделя
3Week 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 видео ((всего 128 мин.)), 1 тест
4 видео
SUPPLEMENT - How to Read Mathematical Formulas27мин
Tutorial for Assignment 547мин
Tutorial for Problem Set 323мин
1 практическое упражнение
Problem Set 3s
Неделя
4Week 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 видео ((всего 88 мин.)), 1 тест
4 видео
Lecture 6B - Working with Quantifiers 228мин
Tutorial for Assignment 616мин
Tutorial for Problem Set 427мин
1 практическое упражнение
Problem Set 4s
38%
начал новую карьеру, пройдя эти курсы
27%
получил значимые преимущества в карьере благодаря этому курсу
12%
стал больше зарабатывать или получил повышение
Лучшие рецензии
автор: 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
автор: MF•Aug 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 !
Преподаватель
Dr. Keith Devlin
Co-founder and Executive DirectorH-STAR institute
О 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.
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Зарегистрировавшись на сертификацию, вы получите доступ ко всем видео, тестам и заданиям по программированию (если они предусмотрены). Задания по взаимной оценке сокурсниками можно сдавать и проверять только после начала сессии. Если вы проходите курс без оплаты, некоторые задания могут быть недоступны.
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Оплатив сертификацию, вы получите доступ ко всем материалам курса, включая оцениваемые задания. После успешного прохождения курса на странице ваших достижений появится электронный сертификат. Оттуда его можно распечатать или прикрепить к профилю LinkedIn. Просто ознакомиться с содержанием курса можно бесплатно.
Какие правила возврата средств?
Можно ли получить финансовую помощь?
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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