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
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Stanford University
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97,325Kompetenzen, die Sie erwerben
Number TheoryReal AnalysisMathematical LogicLanguage
Lehrplan - Was Sie in diesem Kurs lernen werden
Woche
13 Stunden zum Abschließen
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.
6 Videos (Gesamt 84 min), 1 Quiz
6 Videos
Lecture 1 - Introductory Material27m
Lecture 2 - Logical Combinators26m
Tutorial for Assignment 12m
Tutorial for Assignment 29m
Tutorial for Problem Set 19m
1 praktische Übung
Problem Set 1
Woche
24 Stunden zum Abschließen
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.
6 Videos (Gesamt 131 min), 1 Quiz
6 Videos
Lecture 4 - Equivalence24m
SUPPLEMENT: Using the course evaluation rubric4m
Tutorial for Assignment 311m
Tutorial for Assignment 421m
Tutorial for Problem Set 237m
1 praktische Übung
Problem Set 2
Woche
34 Stunden zum Abschließen
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.
4 Videos (Gesamt 128 min), 1 Quiz
4 Videos
SUPPLEMENT - How to Read Mathematical Formulas27m
Tutorial for Assignment 547m
Tutorial for Problem Set 323m
1 praktische Übung
Problem Set 3
Woche
43 Stunden zum Abschließen
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!)
4 Videos (Gesamt 88 min), 1 Quiz
4 Videos
Lecture 6B - Working with Quantifiers 228m
Tutorial for Assignment 616m
Tutorial for Problem Set 427m
1 praktische Übung
Problem Set 4
50%
nahm einen neuen Beruf nach Abschluss dieser Kurse auf
47%
ziehen Sie für Ihren Beruf greifbaren Nutzen aus diesem Kurs
13%
erhalten Sie eine Gehaltserhöhung oder Beförderung
Top-Bewertungen
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
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 !
Dozent
Dr. Keith Devlin
Co-founder and Executive DirectorH-STAR institute
Über 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.
Häufig gestellte Fragen
Wann erhalte ich Zugang zu den Vorträgen und Aufgaben?
Sobald Sie sich für ein Zertifikat angemeldet haben, haben Sie Zugriff auf alle Videos, Quizspiele und Programmieraufgaben (falls zutreffend). Aufgaben, die von anderen Kursteilnehmern bewertet werden, können erst dann eingereicht und überprüft werden, wenn Ihr Unterricht begonnen hat. Wenn Sie sich den Kurs anschauen möchten, ohne ihn zu kaufen, können Sie womöglich auf bestimmte Aufgaben nicht zugreifen.
Was bekomme ich, wenn ich das Zertifikat erwerbe?
Wenn Sie ein Zertifikat erwerben, erhalten Sie Zugriff auf alle Kursmaterialien, einschließlich bewerteter Aufgaben. Nach Abschluss des Kurses wird Ihr elektronisches Zertifikat zu Ihrer Seite „Errungenschaften“ hinzugefügt – von dort können Sie Ihr Zertifikat ausdrucken oder es zu Ihrem LinkedIn Profil hinzufügen. Wenn Sie nur lesen und den Inhalt des Kurses anzeigen möchten, können Sie kostenlos als Gast an dem Kurs teilnehmen.
Wie erfolgen Rückerstattungen?
Ist finanzielle Unterstützung möglich?
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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