Back to Introduction to Mathematical Thinking

4.8

stars

1,978 ratings

•

465 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....

PD

Jun 30, 2020

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.

NR

Mar 05, 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

Filter by:

By Justin L

•Feb 19, 2017

With consistent effort, I have found this course to re-ignite my passion for mathematics. Keith Devlin, the instructor, does an excellent job of helping us to develop our ability to think in mathematical and logical ways. In short, I have found a new joy and excitement for doing mathematics, even stuff I consider hard. I have a new-found passion and new "eyes" for maths that I didn't have before. Excellent course!

By George P

•Mar 19, 2017

It is very good course that teaches simple at first glance concepts that later evolve to something more complex. Mr. Keith Devlin is very charismatic professor who knows his material very well and passes his energy and enthusiasm to students. One minor notice about the real numbers material, in my opinion it is too brief and needs slightly more time to be understood by many students.

By El A F

•Nov 26, 2017

Thank you for the course, it really helped me understand more about thinking skills. Another benefit of the course for me , was understading mathematical symbols used in some foreign countries, since the ones unsed in this course were not the ones i have using during my scholarity(in France and Morroco) [for the negation of a statement for example]. Thank you again :)

By Patricia M

•Jul 27, 2019

I'm in my last week of this course. I like this course very much, and the assessment of how many hours I needed to study gave me a reference point. I enjoyed the lectures online, the tutorials helped me to understand the professor Devlin. I definitely recommend this course, I'm thinking about taking another course relative to Introduction to Mathematical Thinking.

By Voo T V

•Jan 28, 2017

5/5

Although I am really familiar with all the course materials and etc., I could still learn a thing or two from this course. Or in another words, the "Mathematical Thinking".

The quiz itself is not that challenging or hard, but there are a lot to ponder on with the assignments! Try to complete the course with a friend or two, and you will even get out of this.

By Mia D

•Aug 30, 2019

This well-designed course casts light on some essentials of mathematics as well as fills some gaps between high-school-level and university-level mathematics (esp. in how to read a proof and how to catch the "big idea"). Plus, Prof. Keith is both passionate and encouraging.

Highly recommend to learners who are taking first year's mathematics in university.

By Marin L

•Mar 13, 2017

Wonderful and usable course. I graduated mathematics 20 years ago, and I regret I didn't have such clear and informative lessons back then when I needed them most. Even now, watching tutorials and doing exercises gave me great pleasure and some new insights into the problems and techniques I failed to catch.

Thank you for your effort and dedication!

By Sarah E B

•Aug 10, 2017

So far, this course has changed the way I think and view things. Professor Devlin's genuine enthusiasm is contagious and I love interacting with other students online. The TA is very active. There is a great interview with Prof. Devlin here: https://onbeing.org/programs/keith-devlin-the-joy-of-math-learning-and-what-it-means-to-be-human/

By Paolo I

•Jun 08, 2020

I think classes like these should be mandatory on colleges, for some courses at least. I think many people tend to have trouble with maths not because of the content, but because we have trouble reading and understanding its language. I think a class like this course helps to develop maths skills that helps in maths courses in general

By Jordi A

•Nov 29, 2018

This is a fantastic introduction to the world of college-level math. Recommended to HS students, social science majors who are quite analytical, and maybe even some STEM freshmen. While it takes considerable effort to follow the course and assignments, it's quite a learning experience, and I with I had taken it earlier in my life.

By bj d

•May 13, 2017

Excellent course! Started off slowly and methodically laying the foundations for successive lessons. Prof. Devlin explains, demonstrates and allows one to "hear" him think through solutions. My math skills got stronger, but more importantly, my approach to the logic of mathematical thinking can be transferred to other disciplines.

By Abhay G

•Jun 17, 2019

I get a new thinking in Mathematics. Now, i get a new approach to tackle mathematical problems.

I learnt some new different methods to prove the theorems and get a paradox(in which we have proved 1 = 2) that give me a new sight to see a problem.

I realise "Mathematics does not depend upon solution, it depends upon a process".

By Mikhail Z

•Sep 18, 2017

This course is a fun, thorough and thoughtful introduction to the basics of mathematical thinking. I've used it as a supplementary course for series of seminars for philosophy of mathematics. The peer-review assignment is a brilliant way to grasp the difference between solving a problem and thinking about solving a problem.

By Thong D L B

•Mar 26, 2019

I just want to say thanks to Prof. Keith Devlin. I have never been quite comprehend the proof techniques and usually have to prove statements arithmetically directly. Thanks to this course, I finally see how I can approach the problems more systematically, thus being able to find the answers faster and more consistently

By Adam M

•Mar 26, 2020

A great assignment-based introduction to discrete math with an emphasis on communication and thinking. This is a course to improve how you approach problems, and although it provides highly useful skills for university math courses, the disciplined thought process outlined in the course is applicable to the real-world.

By Anhad S B

•Oct 28, 2019

Great course for someone trying to get back in touch with college level mathematics after working professionally and/or more usually, someone trying to get started on graduate level mathematics. Dr. Devlin is quite a thorough professor and I wish I had more professors like him during my undergraduate years as well.

By Anatoly S

•Aug 28, 2020

I did not learn much new facts, but the course helped to structure and put in order what I already was familiar with and what I could remember from school and university. This was an interesting, productive, and thought-provoking experience. I believe it will motivate me to further work on my mathematics skills.

By Minh D

•Dec 11, 2018

The course name itself is a importance not only for individual but for the world. The development of Mathematic can significanly boost if we not only know calculate, how to calculate the formation, but know how to think (Mathematical Thinking). Huge potential course that can change our community! Thank teacher!

By Giovanni P

•Oct 21, 2020

El profesor que dicta este curso es sin lugar a dudas un profesional sumamente capacitado y referente en lo que yo considero educación de calidad. Ha causado gran satisfacción de mi parte al realizar este curso y me ha brindado herramientas que me serán sumamente útiles una vez que ingrese a la universidad.

By Elmer N

•Aug 28, 2019

Excellent instruction and pacing. As a veteran Professional Engineer, I found the course challenging and informative. I enjoyed especially the real-world examples. I would recommend this course to anyone with a desire to discover the fundamental principles of number and set theory.

Elmer A. Norvell, PhD, PE

By Vishal

•May 15, 2020

it is a very fantastic course which improves our ability of thinking. It is a easy course at the beginning but little bit challenging in last weeks of this course also assignments some how hard but overall course is very fantastics and also well design. Thank you sir Dr.Keith Devlin for your guidance .

By Sagar P

•Sep 28, 2017

The 9-week mathematical journey taught me a lot and made fall in love with mathematics back again. I wish , I had worked harder and earned a better grade but commitments to my family and job did not let me do so. I await for another opportunity to get tutored by Dr. Keith Devlin and Stanford Univ. again

By Serhiy O

•Aug 12, 2020

My true thanks to Standford University staff that made this course happen. I believe, this course is a firm stepping stone toward many sorts of precise sciences. With this course, one may: 1) improve consistency in reasoning; 2) learn accurate word usage; 3) get to know a bunch of smart people.

By Luiz F C S

•Jul 29, 2020

This course is extremely good. I just got out of High school and the vision of mathematics this course gave me is totally different. My way of reasoning certainly changed and now I can recognize the importance of the use of language when comunicating, does not matter in what way it's been doing.

By Chloe L

•Jun 08, 2020

I never appreciated math or thought myself capable of doing math well. Now I am excited about real numbers and integers and solving puzzles! This course was a great life experience, and I am indebted to Prof. Devlin for the excellent design and meaningful principles that he put into the course.

- Finding Purpose & Meaning in Life
- Understanding Medical Research
- Japanese for Beginners
- Introduction to Cloud Computing
- Foundations of Mindfulness
- Fundamentals of Finance
- Machine Learning
- Machine Learning Using Sas Viya
- The Science of Well Being
- Covid-19 Contact Tracing
- AI for Everyone
- Financial Markets
- Introduction to Psychology
- Getting Started with AWS
- International Marketing
- C++
- Predictive Analytics & Data Mining
- UCSD Learning How to Learn
- Michigan Programming for Everybody
- JHU R Programming
- Google CBRS CPI Training

- Natural Language Processing (NLP)
- AI for Medicine
- Good with Words: Writing & Editing
- Infections Disease Modeling
- The Pronounciation of American English
- Software Testing Automation
- Deep Learning
- Python for Everybody
- Data Science
- Business Foundations
- Excel Skills for Business
- Data Science with Python
- Finance for Everyone
- Communication Skills for Engineers
- Sales Training
- Career Brand Management
- Wharton Business Analytics
- Penn Positive Psychology
- Washington Machine Learning
- CalArts Graphic Design

- Professional Certificates
- MasterTrack Certificates
- Google IT Support
- IBM Data Science
- Google Cloud Data Engineering
- IBM Applied AI
- Google Cloud Architecture
- IBM Cybersecurity Analyst
- Google IT Automation with Python
- IBM z/OS Mainframe Practitioner
- UCI Applied Project Management
- Instructional Design Certificate
- Construction Engineering and Management Certificate
- Big Data Certificate
- Machine Learning for Analytics Certificate
- Innovation Management & Entrepreneurship Certificate
- Sustainabaility and Development Certificate
- Social Work Certificate
- AI and Machine Learning Certificate
- Spatial Data Analysis and Visualization Certificate

- Computer Science Degrees
- Business Degrees
- Public Health Degrees
- Data Science Degrees
- Bachelor's Degrees
- Bachelor of Computer Science
- MS Electrical Engineering
- Bachelor Completion Degree
- MS Management
- MS Computer Science
- MPH
- Accounting Master's Degree
- MCIT
- MBA Online
- Master of Applied Data Science
- Global MBA
- Master's of Innovation & Entrepreneurship
- MCS Data Science
- Master's in Computer Science
- Master's in Public Health