The purpose of this book, or possibly series of books, is indicated precisely by the title Physics for Mathematicians. It is only necessary for me to explain what I mean by a mathematician, and what I mean by physics.
By a mathematician I mean some one who has been trained in modern mathematics and been inculcated with its general outlook. ...
And by physics I mean -- well, physics, what physicists mean by physics, i.e., the actual study of physical objects ... (rather than the study of symplectic structures on cotangent bundles, for example). In addition to presenting the advanced physics, which mathematicians find so easy, I also want to explore the workings of elementary physics ... which I have always found so hard to fathom.
As these remarks probably reveal, basically I have written this work in order to learn the subject myself, in a form that I find comprehensible. And readers familiar with some of my previous books probably realize that this has pretty much been the reason for those works also. ... Perhaps this travelogue of an innocent abroad in a very different field will also turn out to be a book that mathematicians will like.
Michael David Spivak is a mathematician specializing in differential geometry, an expositor of mathematics, and the founder of Publish-or-Perish Press. He is the author of the five-volume Comprehensive Introduction to Differential Geometry. He received a Ph.D. from Princeton University under the supervision of John Milnor in 1964.
His book Calculus takes a very rigorous and theoretical approach to introductory calculus. It is used in calculus courses, particularly those with a pure mathematics emphasis, at many universities.
Spivak's book Calculus on Manifolds (often referred to as little Spivak) is also rather infamous as being one of the most difficult undergraduate mathematics textbooks.