I collected a list of free lectures and video series. Most of them i watched completely and enjoyed. The collection has a focus on STEM, and includes math, probability, information theory and electronics. I will probably add lectures to the collection when i stumble on further good ones. In the meantime, i hope you enjoy them, too!
As a side note, i also want to recommend a couple of good books. What do i mean by good? I mean that these books are written in a way that you can learn and understand by reading them – and they are not just a bunch of collected axioms, proofs and formulas at best useful for reference – in my experience the curse of STEM textbooks. All of them are best to read after watching Strangs lecture, to have a solid foundation in basic linear algebra. Start with The Scientist and Engineer’s Guide to Digital Signal Processing by Steven Smith. It is free and in my opinion the best introductory text book on digital signal processing. If you can only read one book on DSP, make it this one.
Good books on machine learning are Hands-On Machine Learning with Scikit-Learn and TensorFlow by Aurélien Géron or Dynamical Systems in Neuroscience by Eugene M. Izhikevich. More application-oriented is the An Introduction to the Event-Related Potential Technique by Steven Luck. A must-read if you are doing EEG or MEG research. Mixing more math into the applications is Electrical Neuroimaging by Michel et.al. It suffers a little bit from being a collected volume, but there is a lot of useful content inside.
Linear Algebra by Gilbert Strang / MIT
In my opinion THE lecture on Linear Algebra. Clear and structured, and offers a solid foundation.
Information Theory and Pattern Recognition by David MacKay, Cambridge
Inspiring and well-done lecture on a wide range of topics, some with application to neuroscience, others more concerned about physical systems.
Electronics by Digilent Inc.
Nice overview. But understanding electronics is in my experience part theory, and at least half making and testing, and a video lecture can hardly replace that.
Building an Bio-Amplifier by Bernd Porr
A perfect example how i would envision perfect teaching of electronics. There is only one drawback – i want to see more!
Statistic 110 by Joe Blitzstein, Harvard
Clear and thorough lectures. I found it often too focused on proofs instead of applications, but enjoyed the use of narrative proofs.