This book is a compilation of approximately nine hundred problems, which have appeared on the preliminary exams in Berkeley over the last twenty years. It is an invaluable source of problems and solutions for every mathematics student who plans to enter a Ph.D. program. Students who work through this book will develop problem solving skills in areas such as real analysis, multivariable calculus, differential equations, metric spaces, complex analysis, algebra, and linear algebra. The problems are organized by subject and ordered in an increasing level of difficulty. This new edition contains approximately 120 new problems and 200 new solutions. It is an ideal means for students to strengthen their foundation in basic mathematics and to prepare for graduate studies.
Morris W. Hirsch, Stephen Smale, Robert Devaney, “Differential Equations, Dynamical Systems, and an Introduction to Chaos”
Academic Press; 2 edition | ISBN:0123497035 | 425 pages | PDF | 2,9 Mb
“The exposition is excellent. I particularly liked how the proofs are fairly easy to follow…a readable and informative text.” - Gareth Roberts, Holy Cross
“..from three mathematicians who are…among the world’s most prominent experts in dynamical systems…[and] the world’s best mathematical expositors.”
- Bruce Peckham, University of Minnesota
” (…) a standard on mathematical bookshelves (…). Readers familiar with the first edition will find much that is familiar, but with an increased emphasis on the behaviour of families of solutions”. Annalisa Cranell, MAA Online, Feb 2005
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