We learn by doing. We learn mathematics by doing problems. This book is the first volume of a series of books of problems in mathematical analysis. It is mainly intended for students studying the basic principles of analysis. However, given its organization, level, and selection of problems, it would also be an ideal choice for tutorial or problem-solving seminars, particularly those geared toward the Putnam exam. The volume is also suitable for self-study. 
Each section of the book begins with relatively simple exercises, yet may also contain quite challenging problems. Very often several consecutive exercises are concerned with different aspects of one mathematical problem or theorem. This presentation of material is designed to help student comprehension and to encourage them to ask their own questions and to start research. The collection of problems in the book is also intended to help teachers who wish to incorporate the problems into lectures. Solutions for all the problems are provided. 
The book covers three topics: real numbers, sequences, and series, and is divided into two parts: exercises and/or problems, and solutions. Specific topics covered in this volume include the following: basic properties of real numbers, continued fractions, monotonic sequences, limits of sequences, Stolz's theorem, summation of series, tests for convergence, double series, arrangement of series, Cauchy product, and infinite products.

Problems in Mathematical Analysis I (Student Mathematical Library)

Science & Math

W. J. Kaczor

M. T. Nowak

Mathematics

American Mathematical Society

We learn by doing. We learn mathematics by doing problems. And we learn more mathematics by doing more problems. This is the sequel to Problems in Mathematical Analysis I (Volume 4 in the Student Mathematical Library series). If you want to hone your understanding of continuous and differentiable functions, this book contains hundreds of problems to help you do so. The emphasis here is on real functions of a single variable. Topics include: continuous functions, the intermediate value property, uniform continuity, mean value theorems, Taylors formula, convex functions, sequences and series of functions. 
The book is mainly geared toward students studying the basic principles of analysis. However, given its selection of problems, organization, and level, it would be an ideal choice for tutorial or problem-solving seminars, particularly those geared toward the Putnam exam. It is also suitable for self-study. The presentation of the material is designed to help student comprehension, to encourage them to ask their own questions, and to start research. The collection of problems will also help teachers who wish to incorporate problems into their lectures. The problems are grouped into sections according to the methods of solution. Solutions for the problems are provided. 
This is the sequel to Problems in Mathematical Analysis I (Volume 4 in the Student Mathematical Library series). Also available from the AMS is Problems in Analysis III.

Problems in Mathematical Analysis II: Continuity and Differentiation (Student Mathematical Library, Vol. 12)

See the best price to sell, buy, or rent books by W. J. Kaczor. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by W. J. Kaczor

See the best price to sell, buy, or rent books by W. J. Kaczor. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Problems in Mathematical Analysis I (Student Mathematical Library)

Problems in Mathematical Analysis II: Continuity and Differentiation (Student Mathematical Library, Vol. 12)