I am looking for grad/undergrad level math and physics resources. In many topics, the most popular textbooks are not meant for either self-studying, or as an introductory text on the topic, which are, nonetheless recommended. It is often very difficult to find the desired resources which are self-contained. That is they provide both the theory, so as to explain the the concepts, rather than delve into confusing formalities, and provide full problem sets with solutions. In other words, I am looking for resources that will allow self-studying as efficiently as taking a good university course. My main requirements are:
- Clear explanations, intuition behind ideas, motivated definitions, rather than formality and rigor
- Problem sets, carefully prepared for the student to master the ideas covered in the chapter rather than randomly scattered exercises, for example when the author couldn't be bothered to provide an explanation
- It doesn't have to be a formal textbook - it could be a set of lectures from a university, or some other format
- It doesn't have to be in English, because from my experience, it is easier to read a good explanation in a foreign language, rather than abstract, confusing arguments in your mother tongue. Besides, it may be translated in years to come.
I will provide a few examples
- Most fundamental maths topics, from calculus to abstract algebra by Robert and Carol Ash. Also, Robert Ash has written article on expository writing, which is very much the style of resources I am looking for.
- Series on general physics by Igor Irodov (I'm afraid only mechanics and electromagnetism have English translations). Here is the full list of the series in Russian.
- Problem solving approach (with solutions, of course) to elementary topology by a team of St. Petersburg authors.
Also, if you know that an author has written more than one book in a style that suits my requirements, please mention it. Because once you find a good style that suits you, you may want to read the whole series of the same origin, rather than looking for a new resource for each topic. Besides, it could be a study-guide for beginners.
