Berkeley Problems in Mathematics (Problem Books in Mathematics)

By

**Paulo Ney De Souza, Jorge-Nuno Silva, Paulo Ney De Souza**

**Product Description:**

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.

By D. O. Shklarsky, N. N. Chentzov, I. M. Yaglom

**Book Description:**

Over 300 challenging problems in algebra, arithmetic, elementary number theory and trigonometry, selected from the archives of the Mathematical Olympiads held at Moscow University. Most presuppose only high school mathematics but some are of uncommon difficulty and will challenge any mathematician. Complete solutions to all problems. 27 black-and-white illustrations. 1962 edition.

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Challenging Problems in Geometry

By

**Alfred S. Posamentier, Charles T. Salkind**

**Book Description:**

Stimulating collection of unusual problems dealing with congruence and parallelism, the Pythagorean theorem, circles, area relationships Ptolemy and the cyclic quadrilateral, collinearity and concurrency and many other topics. Arranged in order of difficulty. Detailed solutions.

**Description**

From the Introduction:

“This volume grew from a discussion by the editors on the difficulty of finding good thesis problems for graduate students in topology. Although at any given time we each had our own favorite problems, we acknowledged the need to offer students a wider selection from which to choose a topic peculiar to their interests. One of us remarked, `Wouldn't it be nice to have a book of current unsolved problems always available to pull down from the shelf?' The other replied `Why don't we simply produce such a book?' Two years later and not so simply, here is the resulting volume. The intent is to provide not only a source book for thesis-level problems but also a challenge to the best researchers in the field.”