Learn how to think the way mathematicians do – a powerful cognitive process developed over thousands of years.

## About this Course

## Skills you will gain

- Number Theory
- Real Analysis
- Mathematical Logic
- Language

## Offered by

### 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.

## Syllabus - What you will learn from this course

**3 hours to complete**

## 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.

**3 hours to complete**

**4 hours to complete**

## 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.

**4 hours to complete**

**4 hours to complete**

## 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 hours to complete**

**3 hours to complete**

## 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!)

**3 hours to complete**

## Reviews

### TOP REVIEWS FROM INTRODUCTION TO MATHEMATICAL THINKING

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

It was an amazing course! Lots of interesting content. The content is also explained really well, i found it really easy to understand. The assessments are a little challenging, but reasonably sized.

It has help evaluate what I put into decision in any applicable context. Since I've noted what decision I make and how outcome can be made to vary when I consider all components in a isolated manner.

This course is great because it teaches you the foundations of mathematical thinking, namely how to write rigorous and concise proofs. I really enjoyed the course and would recommend it to a friend.

## Frequently Asked Questions

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