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Introduction to Mathematical Thinking (https://www.coursera.org/learn/mathematical-thinking). Aims to teach you what it is like to think like a mathematician. Covers the elements of topics that you probably encounter in the first semester of an undergraduate maths degree: logic, induction, proof construction, real analysis, etc.

Machine Learning (https://www.coursera.org/learn/machine-learning). I'm still working through this course but am finding it extremely interesting. I find that having to implement things in matlab/octave gives you a deeper understanding than using a framework like tensorflow or keras.

Both of the above courses have good instructors, which I think is the main factor that makes a good mooc.



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