Roman P. Some Modern Mathematics for Physicists and Other Outsiders. Volume 1. Algebra, topology, and measure theory

Pergamon Press, 1975. - 426 pages.In these days of rapid proliferation of textbooks, any preface to a new book must begin with an apology, if not with a well-documented justification, concerning the raison d'etre of this new volume. This is particularly true if the author ventures into a field which is not one of his primary competence. In the present case, my apology is quite simple. After many years of research in elementary particle theory and related topics, I realized that my "standard" mathematical background is inadequate to keep up with modern developments in theoretical physics. This realization was followed by a long period of hard study when I tried to dig out from the mountains of existing literature those concepts and tools without which I could no longer continue to be productive. I also realized that my graduate students should be spared this horrendous task and I introduced a new, one-year course on what, somewhat euphemistically, may be called "modern" mathematics. The outcome of these efforts is the present treatise.