Challenging Problems in Algebra

Challenging Problems in Algebra

Author: Alfred S. Posamentier

Publisher: Courier Corporation

Published: 2012-05-04

Total Pages: 288

ISBN-13: 0486131548

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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.


Linear Algebra

Linear Algebra

Author: Fuzhen Zhang

Publisher: JHU Press

Published: 1996-08-22

Total Pages: 192

ISBN-13: 9780801854590

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"Linear algebra is an increasingly important part of any curriculum in mathematics in our days... A well-organized problem book, like this, will surely be welcomed by students as well as by instructors." -- Zentralblatt fuer Mathematik


Problems in Abstract Algebra

Problems in Abstract Algebra

Author: A. R. Wadsworth

Publisher: American Mathematical Soc.

Published: 2017-05-10

Total Pages: 277

ISBN-13: 1470435837

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This is a book of problems in abstract algebra for strong undergraduates or beginning graduate students. It can be used as a supplement to a course or for self-study. The book provides more variety and more challenging problems than are found in most algebra textbooks. It is intended for students wanting to enrich their learning of mathematics by tackling problems that take some thought and effort to solve. The book contains problems on groups (including the Sylow Theorems, solvable groups, presentation of groups by generators and relations, and structure and duality for finite abelian groups); rings (including basic ideal theory and factorization in integral domains and Gauss's Theorem); linear algebra (emphasizing linear transformations, including canonical forms); and fields (including Galois theory). Hints to many problems are also included.


How to Solve Word Problems in Algebra, 2nd Edition

How to Solve Word Problems in Algebra, 2nd Edition

Author: Mildred Johnson

Publisher: McGraw Hill Professional

Published: 1993-01-21

Total Pages: 209

ISBN-13: 0071368213

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Solving word problems has never been easier than with Schaum's How to Solve Word Problems in Algebra! This popular study guide shows students easy ways to solve what they struggle with most in algebra: word problems. How to Solve Word Problems in Algebra, Second Edition, is ideal for anyone who wants to master these skills. Completely updated, with contemporary language and examples, features solution methods that are easy to learn and remember, plus a self-test.


Open Middle Math

Open Middle Math

Author: Robert Kaplinsky

Publisher: Taylor & Francis

Published: 2023-10-10

Total Pages: 193

ISBN-13: 1003839886

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This book is an amazing resource for teachers who are struggling to help students develop both procedural fluency and conceptual understanding.. --Dr. Margaret (Peg) Smith, co-author of5 Practices for Orchestrating Productive Mathematical Discussions Robert Kaplinsky, the co-creator of Open Middle math problems, brings hisnew class of tasks designed to stimulate deeper thinking and lively discussion among middle and high school students in Open Middle Math: Problems That Unlock Student Thinking, Grades 6-12. The problems are characterized by a closed beginning,- meaning all students start with the same initial problem, and a closed end,- meaning there is only one correct or optimal answer. The key is that the middle is open- in the sense that there are multiple ways to approach and ultimately solve the problem. These tasks have proven enormously popular with teachers looking to assess and deepen student understanding, build student stamina, and energize their classrooms. Professional Learning Resource for Teachers: Open Middle Math is an indispensable resource for educators interested in teaching student-centered mathematics in middle and high schools consistent with the national and state standards. Sample Problems at Each Grade: The book demonstrates the Open Middle concept with sample problems ranging from dividing fractions at 6th grade to algebra, trigonometry, and calculus. Teaching Tips for Student-Centered Math Classrooms: Kaplinsky shares guidance on choosing problems, designing your own math problems, and teaching for multiple purposes, including formative assessment, identifying misconceptions, procedural fluency, and conceptual understanding. Adaptable and Accessible Math: The tasks can be solved using various strategies at different levels of sophistication, which means all students can access the problems and participate in the conversation. Open Middle Math will help math teachers transform the 6th -12th grade classroom into an environment focused on problem solving, student dialogue, and critical thinking.


Equations and Inequalities

Equations and Inequalities

Author: Jiri Herman

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 353

ISBN-13: 1461212707

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A look at solving problems in three areas of classical elementary mathematics: equations and systems of equations of various kinds, algebraic inequalities, and elementary number theory, in particular divisibility and diophantine equations. In each topic, brief theoretical discussions are followed by carefully worked out examples of increasing difficulty, and by exercises which range from routine to rather more challenging problems. While it emphasizes some methods that are not usually covered in beginning university courses, the book nevertheless teaches techniques and skills which are useful beyond the specific topics covered here. With approximately 330 examples and 760 exercises.


Problems in Algebraic Number Theory

Problems in Algebraic Number Theory

Author: M. Ram Murty

Publisher: Springer Science & Business Media

Published: 2006-03-30

Total Pages: 352

ISBN-13: 0387269983

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The problems are systematically arranged to reveal the evolution of concepts and ideas of the subject Includes various levels of problems - some are easy and straightforward, while others are more challenging All problems are elegantly solved


Problems In Linear Algebra And Matrix Theory

Problems In Linear Algebra And Matrix Theory

Author: Fuzhen Zhang

Publisher: World Scientific

Published: 2021-10-25

Total Pages: 477

ISBN-13: 981123910X

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This is the revised and expanded edition of the problem book Linear Algebra: Challenging Problems for Students, now entitled Problems in Linear Algebra and Matrix Theory. This new edition contains about fifty-five examples and many new problems, based on the author's lecture notes of Advanced Linear Algebra classes at Nova Southeastern University (NSU-Florida) and short lectures Matrix Gems at Shanghai University and Beijing Normal University.The book is intended for upper division undergraduate and beginning graduate students, and it can be used as text or supplement for a second course in linear algebra. Each chapter starts with Definitions, Facts, and Examples, followed by problems. Hints and solutions to all problems are also provided.


105 Algebra Problems from the AwesomeMath Summer Program

105 Algebra Problems from the AwesomeMath Summer Program

Author: Titu Andreescu

Publisher:

Published: 2013

Total Pages: 0

ISBN-13: 9780979926952

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The main purpose of this book is to provide an introduction to central topics in elementary algebra from a problem-solving point of view. While working with students who were preparing for various mathematics competitions or exams, the author observed that fundamental algebraic techniques were not part of their mathematical repertoire. Since algebraic skills are not only critical to algebra itself but also to numerous other mathematical fields, a lack of such knowledge can drastically hinder a student's performance. Taking the above observations into account, the author has put together this introductory book using both simple and challenging examples which shed light upon essential algebraic strategies and techniques, as well as their application in diverse meaningful problems. This work is the first volume in a series of such books. The featured topics from elementary and classical algebra include factorizations, algebraic identities, inequalities, algebraic equations and systems of equations. More advanced concepts such as complex numbers, exponents and logarithms, as well as other topics, are generally avoided.Nevertheless, some problems are constructed using properties of complex numbers which challenge and expose the reader to a broader spectrum of mathematics. Each chapter focuses on specific methods or strategies and provides an ample collection of accompanying problems that graduate in difficulty and complexity. In order to assist the reader with verifying mastery of the theoretical component, 105 problems are included in the last sections of the book, of which 52 are introductory and 53 are advanced. All problems come together with solutions, many employing several approaches and providing the motivation behind the solutions offered.


50 Challenging Algebra Problems (Fully Solved)

50 Challenging Algebra Problems (Fully Solved)

Author: Chris McMullen

Publisher:

Published: 2018-04-11

Total Pages: 112

ISBN-13: 9781941691236

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These 50 challenging algebra problems involve applying a variety of algebra skills. The exercises come with a good range of difficulty from milder challenges to very hard problems. On the page following each problem you can find the full solution with explanations. quadratic equations system of equations cross multiplying factoring and distributing the f.o.i.l. method roots and powers fractions and negative numbers slopes and y-intercepts of straight lines word problems applications