Sums of Squares
In this chapter we start our main journey into the realms of algebra and number theory.
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Menny Aka Manfred Einsiedler Thomas Ward
A Journey Through The Realm of Numbers From Quadratic Equations to Quadratic Reciprocity
Springer Undergraduate Mathematics Series SUMS Readings
Advisory Editors Mark A. J. Chaplain, St. Andrews, UK Angus Macintyre, Edinburgh, UK Simon Scott, London, UK Nicole Snashall, Leicester, UK Endre Süli, Oxford, UK Michael R. Tehranchi, Cambridge, UK John F. Toland, Bath, UK
SUMS Readings is a collection of books that provides students with opportunities to deepen understanding and broaden horizons. Aimed mainly at undergraduates, the series is intended for books that do not fit the classical textbook format, from leisurely-yet-rigorous introductions to topics of wide interest, to presentations of specialised topics that are not commonly taught. Its books may be read in parallel with undergraduate studies, as supplementary reading for specific courses, background reading for undergraduate projects, or out of sheer intellectual curiosity. The emphasis of the series is on novelty, accessibility and clarity of exposition, as well as selfstudy with easy-to-follow examples and solved exercises. More information about this series at http://www.springer.com/series/16607
Menny Aka • Manfred Einsiedler • Thomas Ward
A Journey Through The Realm of Numbers From Quadratic Equations to Quadratic Reciprocity
Menny Aka Department of Mathematics ETH Zürich, Switzerland
Manfred Einsiedler Department of Mathematics ETH Zürich, Switzerland
Thomas Ward School of Mathematics University of Leeds Leeds, UK
ISSN 1615-2085 ISSN 2197-4144 (electronic) Springer Undergraduate Mathematics Series ISSN 2730-5813 ISSN 2730-5821 (electronic) SUMS Readings ISBN 978-3-030-55232-9 ISBN 978-3-030-55233-6 (eBook) https://doi.org/10.1007/978-3-030-55233-6 Mathematics Subject Classification (2020): 11A15, 11A51, 11D09, 11D25, 11E25, 11R04, 97E60 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020 This work is subject to copyright. All rights are solely and exclusively licensed 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. The 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. The 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, expressed or implied, with respect to the material contained
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