{"product_id":"9780387745213","title":"Problem Books in Mathematics","description":"\u003ch1\u003eProblem Books in Mathematics\u003c\/h1\u003e \u003ch2\u003ede Souza, Paulo Ney; Silva, Jorge Nuno\u003c\/h2\u003e \u003cp\u003e\u003c\/p\u003e\u003cp\u003eIn 1977, the Mathematics Department at the University of California, Berkeley, instituted a written examination as one of the first major requirements for the Ph.D. degree in Mathematics. Its purpose was to determine whether first-year students in the Ph.D. program had successfully mastered basic mathematics, ensuring they could continue in the program with a strong likelihood of success. Since its inception, the exam has become a significant hurdle in the pursuit of the degree.\u003c\/p\u003e\n\u003cp\u003eThis book, now in its fourth edition, has been updated with the most recent exams up to 2025. Its purpose is to make the material widely available and to aid students in preparing for the examination during their undergraduate years. The book compiles over 1,800 problems that have appeared on Berkeley's preliminary exams, along with solutions to most of them. 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 arranged in increasing order of difficulty. Tags indicating the exact exam year allow students to rehearse complete examinations. The appendix includes instructions for accessing electronic versions of the exams as well as a syllabus.\u003c\/p\u003e\n\u003cp\u003eAll of this makes the book an invaluable resource for every mathematics student who plans to enter a Ph.D. program.\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2026-11-09\u003c\/p\u003e \u003cp\u003eFormat: Hardcover\u003c\/p\u003e \u003cp\u003eISBN-13: 9780387745213\u003c\/p\u003e \u003cp\u003eDOI: \u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: \u003c\/p\u003e ","brand":"Springer New York","offers":[{"title":"Default Title","offer_id":44698034995340,"sku":"9780387745213","price":179.99,"currency_code":"USD","in_stock":true}],"url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9780387745213","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}