[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-115660-en":3,"doc-seo-115660-105":31,"detail-sidebar-cat-0-en-105":92},{"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":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":28,"seo_description":14,"update_tm":29,"read_time":30},115660,2336474466412,"Ezra","https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d",4,"Exam","Putnam and Beyond - Second Edition - 2017","Putnam and Beyond is a college-level problem book and study guide for the William Lowell Putnam Mathematical Competition, bridging high school problem solving and mathematical research. Written from a unitary, problem-based perspective, it emphasizes understanding why through proofs and reasoning, reflecting the goal of building graduate-level background. The second edition expands the original with 180 new problems and examples, adds eight new sections, revises prior solutions, and corrects errors and typos.","Răzvan Gelca and Titu Andreescu  \nPutnam and Beyond 2nd ed. 2017  \nRăzvan Gelca  \nDepartment Mathematics and Statistics, Texas Tech University, Lubbock, TX, USA  \nTitu Andreescu  \nMathematics, University of Texas at Dallas, Richardson, TX, USA  \nISBN 978-3-319-58986-2 e-ISBN 978-3-319-58988-6  \n[https://doi.org/10.1007/978-3-319-58988-6](https://doi.org/10.1007/978-3-319-58988-6)  \n[Library of Congress Control Number: 2017943241](Library of Congress Control Number: 2017943241)[ ](Library of Congress Control Number: 2017943241)© Springer International Publishing AG 2017  \nThis work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed.  \nThe use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.  \nThe publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.  \nPrinted on acid-free paper  \nThis Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland  \nPreface to the Second Edition  \nThe first edition of the book has generated great interest and a large amount of input from the readers, who have expressed their views and have suggested corrections and improvements. We are deeply grateful to all, as their contributions have significantly impacted the book.  \nAt the same time, the authors have remained involved in mathematics competitions, being exposed to the constant flow of problems and to the evolution of ideas. The first author has continued training the United States International Mathematical Olympiad team. The second author has started and perfected the Awesome Math Summer program, and as editor-in-chief of Mathematical Reflections , has established it as one of the important journals promoting problem solving at high school and college levels. Both authors have continued writing problems for mathematics contests at highschool and collegiate levels. Some new perspectives in problem solving that appeared since the publication of the first edition have thus found their way into the book.  \nAlso, by using Putnam and Beyond in teaching and coaching, the authors have realized that some material had to be improved and expanded to make it more accessible and complete.  \nThe new edition adds 180 new problems and examples, eight new sections, some new solutions to previously existing problems, and corrects all the errors and typos that have been found in the first edition. It gives more substance to some topics that had a rather shallow treatment before. The experience of ten years of use gave rise to a more polished product.  \nRăzvan Gelca Titu Andreescu April 2017  \nPreface to the First Edition  \nA problem book at the college level. A study guide for the Putnam competition. Abridge between high school problem solving and mathematical research. A friendly introduction to fundamental concepts and results. All these desires gave life to the pages that follow.  \nThe William Lowell Put","cbCainPM7zYT2SOw","https://ap.wps.com/l/cbCainPM7zYT2SOw","pdf",38270714,8,1,1282,"English","en",105,"# Preface to the Second Edition\n## Goals of the new edition\n# Preface to the First Edition\n## Purpose and positioning\n## Philosophy of proofs and reasoning\n## Intended audience and coverage","[{\"question\":\"What is the primary purpose of Putnam and Beyond?\",\"answer\":\"It serves as a college-level problem book and study guide for training for the William Lowell Putnam Mathematical Competition, while bridging high school and research-oriented problem solving.\"},{\"question\":\"What changes are introduced in the second edition?\",\"answer\":\"The second edition adds 180 new problems and examples, includes eight new sections, provides new solutions to some existing problems, and corrects errors and typos.\"},{\"question\":\"What guiding philosophy does the book emphasize in mathematics learning?\",\"answer\":\"It stresses understanding why through proofs and reasoning, presenting correct reasoning as central to mathematical thinking.\"}]","Putnam and Beyond - 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