All the Mathematics You Missed

Preface; On the structure of mathematics; Brief summaries of topics; 1. Linear algebra; 2. e and d real analysis; 3. Calculus for vector-valued functions; 4. Point set topology; 5. Classical stokes' theorems; 6. Differential forms and Stokes' theorem; 7. Curvature for curves and surfaces; 8. Geometry; 9. Complex analysis; 10. Countability and the axiom of choice; 11. Algebra; 12. Lebesgue integration; 13. Fourier analysis; 14. Differential equations; 15. Combinatorics and probability; 16. Algorithms; A. Equivalence relations.

Williams College, Massachusetts

"This book will fill an interesting niche in a library collection...it should be used by browsing students interested in making sure that they are prepared for success in their graduate programs." Choice "All the Mathematics You Missed...is a help for students going on to graduate school..Since many students beginning graduate school do not have the mathematical knowledge needed, All the Mathematics You Missed aims to fill in the gaps." Berkshire Eagle, Pittsfield, MA "From the preface: 'The goal of this book is to give people at least a rough idea of many topics that beginning graduate students at the best graduate schools are assumed to know." Mathematical Reviews "The writing is lucid mathematical exposition, at a level quite appropriate to beginning graduate students." The American Statistician "Before classes began, I jump started my graduate career with the help of this book. Even though I didn't believe that I could have missed much math, it became clear that my belief was wrong during the first week of class. While proving a theorem, my professor asked if anyone remembered a previous result from calculus. While I did not remember it from my days as an undergraduate, I had read about the theorem and had even seen a sketch of the proof in Garrity's book...This will be one of the books that I keep with me as I continue as a graduate student. It has certainly helped me understand concepts that I have missed." Elizabeth D. Russell, Math Horizons "Point set topology, complex analysis, differential forms, the curvature of surfaces, the axiom of choice, Lebesgue integration, Fourier analysis, algorithms, and differential equations... I found these sections to be the high points of the book. They were a sound introduction to material that some but not all graduate students will need." Charles Ashbacher, School Science and Mathematics