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Introduction to Mathematical Thinking

Keith Devlin's Stanford course on how mathematicians think: logic, quantifiers and proofs.

Taught byCoursera
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About this course

Offered by Stanford Online on Coursera, this course helps learners move from school-style calculation to the reasoning used in university mathematics. It covers the language of logic, quantifiers and proof, then applies them to number theory and real analysis.

Best for: Students preparing for proof-based university maths.

What you will be able to do

  • Translate statements into precise logical form
  • Work with implication, equivalence and quantifiers
  • Write and assess simple proofs
  • Evaluate other people's mathematical arguments

Syllabus and your progress

Tick modules off as you finish them on Coursera.

0 of 7 modules done

Plan your pace

At 4 hours a week you would finish in about 10 weeks, using the course time estimate above.

Progress is saved in this browser only. No account needed.

Cost and certificate

Paid certificate

On Coursera's enrol screen many courses offer a free 'Full Course, No Certificate' option; the certificate is paid (financial aid can be requested). Check the options before you start.

Before you start: High school mathematics

Coursera sets the terms and can change them. Check the course page before you commit serious time, and tell us if something changed.

Quick answers

Is Introduction to Mathematical Thinking really free?
Yes, the course material is free on Coursera. On Coursera's enrol screen many courses offer a free 'Full Course, No Certificate' option; the certificate is paid (financial aid can be requested). Check the options before you start.
How long does Introduction to Mathematical Thinking take?
Plan for about 37 hrs in total (Provider module estimates total about 37 hours (page also says 4 weeks at 10 hrs/week).). It is instructor-paced, so you can go faster or slower.
Do I need experience before Introduction to Mathematical Thinking?
It helps to have: High school mathematics.

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Introduction to Mathematical Thinking

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