About this course: 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.

Who is this class for: This ten-week course is designed with two particular audiences in mind. First, people who want to develop or improve mathematics-based, analytic thinking for professional or general life purposes. Second, high school seniors contemplating a mathematics or math-related major at college or university, or first-year students at college or university who are thinking of majoring in mathematics or a math-dependent subject. To achieves this aim, the first part of the course has very little traditional mathematical content, focusing instead on the thinking processes required for mathematics. The more mathematical examples are delayed until later, when they are more readily assimilated.

Created by: Stanford University

Taught by: Dr. Keith Devlin, Co-founder and Executive Director
H-STAR institute

Level	Intermediate
Commitment	Expect to require at least 10 hours of study per week to complete this course satisfactorily.
Language	English
How To Pass	Pass all graded assignments to complete the course.
User Ratings	4.8 stars Average User Rating 4.8See what learners said

Syllabus

WEEK 1

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 forma...

6 videos

Graded: Problem Set 1

WEEK 2

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 p...

6 videos

Graded: Problem Set 2

WEEK 3

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 every...

4 videos

Graded: Problem Set 3

WEEK 4

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 hun...

4 videos

Graded: Problem Set 4

WEEK 5

Week 5

This week we take our first look at mathematical proofs, the bedrock of modern mathematics.

4 videos

Graded: Problem Set 5

WEEK 6

Week 6

This week we complete our brief look at mathematical proofs

4 videos

Graded: Problem Set 6

WEEK 7

Week 7

The topic this week is the branch of mathematics known as Number Theory. Number Theory, which goes back to the Ancient Greek mathematicians, is a hugely important subject within mathematics, having ramifications throughout mathematics, in physics, and in some ...

4 videos

Graded: Problem Set 7

WEEK 8

Week 8

In this final week of instruction, we look at the beginnings of the important subject known as Real Analysis, where we closely examine the real number system and develop a rigorous foundation for calculus. This is where we really benefit from our earlier analy...

5 videos

Graded: Problem Set 8

WEEK 9

Weeks 9 & 10: Test Flight

Test Flight provides an opportunity to experience an important aspect of "being a mathematician": evaluating real mathematical arguments produced by others. There are three stages. It is important to do them in order, and to not miss any steps. STAGE 1: You co...

4 videos

Graded: Test Flight Peer Assessments

Graded: Evaluation Exercise 1

Graded: Evaluation Exercise 2

Graded: Evaluation Exercise 3

FAQs

How It Works

Coursework

Each course is like an interactive textbook, featuring pre-recorded videos, quizzes and projects.

Help from Your Peers

Connect with thousands of other learners and debate ideas, discuss course material, and get help mastering concepts.

Certificates

Earn official recognition for your work, and share your success with friends, colleagues, and employers.

Creators

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.

Ratings and Reviews

Rated 4.8 out of 5 of 388 ratings

I really enjoy the clarity of the explanations. Good material too. Amazing job.

Fantastic course. I feel better equipped to deal with discrete math now!

One of the best courses i have taken on this site

I am not familiar with the material and consider this course as a baby step into a completely new language, a journey in a world of thinking that shows our education system fails to inform and develop logic and rational thinking at the basic levels. At 67, I should have the basic knowledge to complete this course with ease. It reflects on the substance, or lack thereof, of the education system and the quality of teachers. Given the time, the effort and the patience of good teachers, every reasonable thinking person ought to be able to manage these basic skills. Thank you, Professor, for sharing your knowledge, it has been a great discovery for which I am immensely grateful.

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Introduction to Mathematical Thinking

Introduction to Mathematical Thinking

Introduction to Mathematical Thinking