[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-114834-en":3,"doc-seo-114834-105":29,"detail-sidebar-cat-0-en-105":89},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},114834,687197207919,"Theodora","https://ap-avatar.wpscdn.com/avatar/a000253d6f5f7c60be?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779446848396160552",4,"Exam","Problem-Solving Through Problems - With 104 Illustrations","Problem-Solving Through Problems systematically presents key techniques typically encountered in undergraduate mathematics, using carefully chosen examples and a large set of practice problems. Each section focuses on a single central idea, illustrating its power and versatility through worked solutions and reinforcing it via targeted exercises. More than 700 problems are included, with over one-third solved in detail, emphasizing natural appeal, beauty, and unique challenge. The book serves as both an anthology and an instructional guide, appropriate for students and teachers preparing for contests and expanding problem-literature knowledge.","Problem Books in Mathematics Series Editor: P.R. Halmos Unsolved Problems In Intuitive Mathematics, Volume I: Unsolved Problems in Number Theory hy Richard K. Guy 1981. xvjii, 161 pages. 17 illus. Theorems and Problems in Functional Analysis by A.A. Kirillov and A.D. Gvishiani (trans. Harold H. McFaderi) 1982. ix, 347 pages. 6 illus. Problems In Analysis by Bernard Gelbaum 1982. vii, 228 pages. 9 illus. A Problem Seminar by Donald J. Newman 1982. viii, 113 pages. ProblemSolving Through Problems by Loren C. Larson 1983. xi, 344 pages. 104 illus.  \nLoren C. Larson Problem-Solving Through Problems With 104 Illustrations Springer-Verlag New York Berlin Heidelberg Tokyo i  \nLoren C. Larson Department of Mathematics St. Olaf College Northfield, MN 55057 U.S.A. Editor Paul R. Halmos Department of Mathematics Indiana University Bloomington, IN 47405 U.S.A. AMS Classification (1981): O0A07 Library of Congress Cataloging in Publication Data Larson, Loren C, 1937-ftobiem-soiving through problems. {Problem books in mathematics) 1. Mathematics—ftoblems, exercises, etc. 2. ftoblem solving.  \nI. Title. II. Series. QA43.L37 1983 510 82-19493 © 1983 by SpringerVeriag New York Inc. All rights reserved. No part of this book may be translated or reproduced in any form without written permission from Springer-Verlag, 175 Fifth Avenue, New York, New York lOOlft U.S.A. Typeset by Computype, St. Paul, Minnesota. Printed and bound by R. R. Donnelley & Sons, Harrisonburg, Virginia. Printed in the United States of America. 98765432 1 ISBN 0-387-90803-X Springcr-Vcrlag New York Berlin Heidelberg Tokyo ISBN 3-540-90803-X Springcr-Vcrlag Berlin Heidelberg New York Tokyo  \nTo Elizabeth  \nPreface The purpose of this book is to isolate and draw attention to the most important problem-solving techniques typically encountered in undergraduate mathematics and to illustrate their use by interesting examples and problems not easily found in other sources. Each section features a single idea, the power and versatilily of which is demonstrated in the examples and reinforced in the problems. The book serves as an  \nintroduction and guide to the problems literature (e.g., as found in the problems sections of undergraduate mathematics journals) and as an easily accessed reference of essential knowledge for students and teachers of mathematics. The book is both an anthology of problems and a manual of instruction. It contains over 700 problems, over one-third of which are worked in detail. Each problem is chosen for its natural appeal and beauty, but primarily for its unique challenge. Each is included to provide the context for illustrating a given problem-solving method. The aim throughout is to show how a basic set of simple techniques can be applied in diverse ways to solve an enormous variety of problems. Whenever possible, problems within sections are chosen to cut across expected course boundaries and to thereby strengthen the evidence that a single intuition is capable of broad application. Each section concludes with \"Additional Examples\" that point to other contexts where the technique is appropriate. The book is written at the upper undergraduate level. It assumes a rudimentary knowledge of combinatorics, number theory, algebra, analysis, and geometry. Much of the content is accessible to students with only a year of calculus, and a sizable proportion does not even require this. However, most of the problems are at a level slightly beyond the usual contents of textbooks. Thus, the material is especially appropriate for students preparing for mathematical competitions.  \nviii Preface The methods and problems featured in this book are drawn from my experience of solving problems at this level. Each new issue of The American Maihemaiical Momhly (and other undergraduate journals) contains material tJiat would be just right for inclusion. Because these ideas continue to find new expression, the reader should regard this collection asa starter set and should be enc","cbCaisVTGj7OrTC1","https://ap.wps.com/l/cbCaisVTGj7OrTC1","pdf",510904,1,184,"English","en",105,"# Preface\n## Purpose and scope\n## Problem structure and teaching approach\n## Skill requirements and level\n# Contents\n## Chapter 1: Heuristics\n## Chapter 2: Two Important Principles: Induction and Pigeonhole\n## Chapter 3: Arithmetic","[{\"question\":\"What is the main goal of the book Problem-Solving Through Problems?\",\"answer\":\"It isolates the most important problem-solving techniques in undergraduate mathematics and demonstrates how to use them through examples and challenging problems.\"},{\"question\":\"How is each section organized in the book?\",\"answer\":\"Each section features a single idea, shown in examples and reinforced by problems, typically with an ending section of “Additional Examples.”\"},{\"question\":\"What level is the book intended for, and what math background does it assume?\",\"answer\":\"It is written at the upper undergraduate level, assuming basic knowledge of combinatorics, number theory, algebra, analysis, and geometry; 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