Brad Osgood's lectures are phenomenal. He was trained as a mathematician, so his explanations are crystal clear in terms of definitions and where physicists swe

Brad Osgood's lectures are phenomenal. He was trained as a mathematician, so his explanations are crystal clear in terms of definitions and where physicists sweep mathematical formalisms under the rug. After watching his entire lecture for this course, and spending a lot of time reading the course reader, I learned a lot about how to decrypt the kind of mathematical nonsense that physicists tend to say (as well as learning about the real foundations, c.f. tempered distributions and others). That being said, a lot of these lectures can be summarized in a few sentences if you already have a strong foundation in linear algebra. For example, the fact that complex exponentials form an orthonormal basis for periodic functions is the content of the first handful of lectures, and deriving the Fourier transform is only slightly messier to explain in terms of linear algebra (this is not because of the linear algebra but because Fourier transforms are inherently a little messy).