Math for Scientists Refreshing the Essentials

Accessible and comprehensive, this guide is an indispensable tool for anyone in the sciences – new and established researchers, students and scientists – looking either to refresh their math skills or to prepare for the broad range of math, statistical an

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EFRESHING THE ESSENTIALS

Math for Scientists

Natasha Maurits • Branislava Ćurčic-Blake

Math for Scientists Refreshing the Essentials

Natasha Maurits Department of Neurology University Medical Center Groningen Groningen, The Netherlands

Branislava Ćurčic-Blake Neuroimaging Center University Medical Center Groningen Groningen, The Netherlands

ISBN 978-3-319-57353-3 ISBN 978-3-319-57354-0 (eBook) DOI 10.1007/978-3-319-57354-0 Library of Congress Control Number: 2017943515 © Springer International Publishing AG 2017 This 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. 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, 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. Printed on acid-free paper This 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

Preface

Almost every student or scientist will at some point run into mathematical formulas or ideas in scientific papers that may be hard to understand or apply, given that formal math education may be some years ago. These math issues can range from reading and understanding mathematical symbols and formulas to using complex numbers, dealing with equations involved in calculating medication equivalents, applying the General Linear Model (GLM) used in, e.g., neuroimaging analysis, finding the minimum of a function, applying independent component analysis, or choosing the best filtering approach. In this book we explain the theory behind many of these mathematical ideas and methods and provide readers with the tools to better understand them. We revisit high-school mathematics and extend and relate them to the mathematics you need to understand and apply the math you may encounter in the course of your research. In addition, this book teaches you to understand the math and formulas in the scientific papers you read. To achieve this goal, each chapter mixes theory with practical pen-an