Problems and Solutions in Mathematics PDF Download

Author: Ji-Xiu Chen
Publisher: World Scientific
ISBN: 9814304964
Category : Mathematics
Languages : en
Pages : 804

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Book Description
This book contains a selection of more than 500 mathematical problems and their solutions from the PhD qualifying examination papers of more than ten famous American universities. The mathematical problems cover six aspects of graduate school mathematics: Algebra, Topology, Differential Geometry, Real Analysis, Complex Analysis and Partial Differential Equations. While the depth of knowledge involved is not beyond the contents of the textbooks for graduate students, discovering the solution of the problems requires a deep understanding of the mathematical principles plus skilled techniques. For students, this book is a valuable complement to textbooks. Whereas for lecturers teaching graduate school mathematics, it is a helpful reference.

Author: Tatsien Li
Publisher: World Scientific Publishing Company
ISBN: 9813100877
Category : Mathematics
Languages : en
Pages : 804

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Book Description
This book contains a selection of more than 500 mathematical problems and their solutions from the PhD qualifying examination papers of more than ten famous American universities. The mathematical problems cover six aspects of graduate school mathematics: Algebra, Topology, Differential Geometry, Real Analysis, Complex Analysis and Partial Differential Equations. While the depth of knowledge involved is not beyond the contents of the textbooks for graduate students, discovering the solution of the problems requires a deep understanding of the mathematical principles plus skilled techniques. For students, this book is a valuable complement to textbooks. Whereas for lecturers teaching graduate school mathematics, it is a helpful reference.

Author: Stephen Siklos
Publisher:
ISBN: 9781783747764
Category : Mathematics
Languages : en
Pages : 188

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Book Description
This new and expanded edition is intended to help candidates prepare for entrance examinations in mathematics and scientific subjects, including STEP (Sixth Term Examination Paper). STEP is an examination used by Cambridge Colleges for conditional offers in mathematics. They are also used by some other UK universities and many mathematics departments recommend that their applicants practice on the past papers even if they do not take the examination. Advanced Problems in Mathematics bridges the gap between school and university mathematics, and prepares students for an undergraduate mathematics course. The questions analysed in this book are all based on past STEP questions and each question is followed by a comment and a full solution. The comments direct the reader's attention to key points and put the question in its true mathematical context. The solutions point students to the methodology required to address advanced mathematical problems critically and independently. This book is a must read for any student wishing to apply to scientific subjects at university level and for anyone interested in advanced mathematics.

Author: Arthur Engel
Publisher: Springer Science & Business Media
ISBN: 0387226419
Category : Mathematics
Languages : en
Pages : 404

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Book Description
A unique collection of competition problems from over twenty major national and international mathematical competitions for high school students. Written for trainers and participants of contests of all levels up to the highest level, this will appeal to high school teachers conducting a mathematics club who need a range of simple to complex problems and to those instructors wishing to pose a "problem of the week", thus bringing a creative atmosphere into the classrooms. Equally, this is a must-have for individuals interested in solving difficult and challenging problems. Each chapter starts with typical examples illustrating the central concepts and is followed by a number of carefully selected problems and their solutions. Most of the solutions are complete, but some merely point to the road leading to the final solution. In addition to being a valuable resource of mathematical problems and solution strategies, this is the most complete training book on the market.

Author: Alfred S. Posamentier
Publisher: Courier Corporation
ISBN: 0486131548
Category : Mathematics
Languages : en
Pages : 296

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Book Description
Over 300 unusual problems, ranging from easy to difficult, involving equations and inequalities, Diophantine equations, number theory, quadratic equations, logarithms, more. Detailed solutions, as well as brief answers, for all problems are provided.

Author: Alexander Soifer
Publisher: Springer Science & Business Media
ISBN: 0387746463
Category : Education
Languages : en
Pages : 120

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Book Description
Various elementary techniques for solving problems in algebra, geometry, and combinatorics are explored in this second edition of Mathematics as Problem Solving. Each new chapter builds on the previous one, allowing the reader to uncover new methods for using logic to solve problems. Topics are presented in self-contained chapters, with classical solutions as well as Soifer's own discoveries. With roughly 200 different problems, the reader is challenged to approach problems from different angles. Mathematics as Problem Solving is aimed at students from high school through undergraduate levels and beyond, educators, and the general reader interested in the methods of mathematical problem solving.

Author: Alan Sultan
Publisher: World Scientific
ISBN: 981473005X
Category : Mathematics
Languages : en
Pages : 196

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Book Description
This book is a rare resource consisting of problems and solutions similar to those seen in mathematics contests from around the world. It is an excellent training resource for high school students who plan to participate in mathematics contests, and a wonderful collection of problems that can be used by teachers who wish to offer their advanced students some challenging nontraditional problems to work on to build their problem solving skills. It is also an excellent source of problems for the mathematical hobbyist who enjoys solving problems on various levels.Problems are organized by topic and level of difficulty and are cross-referenced by type, making finding many problems of a similar genre easy. An appendix with the mathematical formulas needed to solve the problems has been included for the reader's convenience. We expect that this book will expand the mathematical knowledge and help sharpen the skills of students in high schools, universities and beyond.

Author: Kenneth A. Ross
Publisher: CUP Archive
ISBN:
Category : Mathematics
Languages : en
Pages : 192

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Book Description

Author: Daniel J. Velleman
Publisher: Cambridge University Press
ISBN: 0521861241
Category : Mathematics
Languages : en
Pages : 401

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Book Description
Many students have trouble the first time they take a mathematics course in which proofs play a significant role. This new edition of Velleman's successful text will prepare students to make the transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. The author shows how complex proofs are built up from these smaller steps, using detailed 'scratch work' sections to expose the machinery of proofs about the natural numbers, relations, functions, and infinite sets. To give students the opportunity to construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. This book will be useful to anyone interested in logic and proofs: computer scientists, philosophers, linguists, and of course mathematicians.

Author: Alfred S. Posamentier
Publisher: Corwin Press
ISBN: 1452295573
Category : Education
Languages : en
Pages : 281

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Book Description
"The authors have provided a unique, strategy-focused resource supported by a wealth of engaging examples that mathematics teachers can readily use to help students develop a more purposeful, systematic, and successful approach to problem solving." —Howard W. Smith, Superintendent Public Schools of the Tarrytowns, Sleepy Hollow, NY "Helps both new and veteran teachers better understand the nature of problem solving as a critical mathematics process. The authors present in very simple terms the strategies that are the backbone of mathematics instruction. This indispensable material is useful at all levels, from basic stages to advanced student work to the development of top problem solvers." —Daniel Jaye, Principal Bergen County Academies, Hackensack, NJ Help students become skilled and confident problem solvers! Demonstrating there is always more than one approach to solving a problem, well-known authors and educators Alfred S. Posamentier and Stephen Krulik present ten basic strategies that are effective for finding solutions to a wide range of mathematics problems. These tried-and-true methods—including working backwards, finding a pattern, adopting a different point of view, solving a simpler analogous problem, and making a visual representation—make problem solving easier, neater, and more understandable for students as well as teachers. Providing numerous sample problems that illustrate how mathematics teachers and specialists can incorporate these techniques into their mathematics curriculum, this updated edition also includes: A variety of new problems that show how to use the strategies References to current NCTM standards Solutions to the problems in each chapter Extensive discussions of the empowering strategies used to solve sample problems The second edition of Problem-Solving Strategies for Efficient and Elegant Solutions, Grades 6–12 helps teachers develop students′ creative problem-solving skills for success in and out of school.