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Book Reviewsjective schemes in terms of Gersten’s coniveau spectralsequence for the higher K-theory of rings. Finally, Chernclasses for rings and schemes are depicted in the contextof higher K-theory.The concluding Chapter 6 turns to the problem ofcomputing the higher K-groups of fields. More precisely,the goal of this chapter is to explain what the presentstate of knowledge of the algebraic K-theory of (number)fields is, thereby largely illuminating the historical developmentsfrom the early 1970s until now. This includestopics such as the K-theory of algebraically closed fields,the K-theory of R, relations to motivic cohomology, K 3ofa field, and various K-theoretic results for special numberfields, local fields, and the ring Z of integers.Each section of the book ends with a large set of relatedexercises, which are mainly of purely theoretical nature.These exercises mostly refer to additional conceptsand theorems from the respective research literature,therefore requiring intensive further reading. However,ample hints to the original papers are given throughoutthe text, thereby referring to the sweeping bibliographywith more than 230 references at the end of the book.Indeed, Charles Weibel’s “K-book” offers a plethoraof material from both classical and more recent algebraicK-theory. It is a perfect source book for seasoned graduatestudents and working researchers, who are willingand eager to follow the author’s expository path, andwho are ready for a lot of additional reading and self-reliantwork. The many instructive examples and clarifyingremarks help the reader grasp the essentials of algebraicK-theory from a panoramic view, and the entire expositionrepresents a highly valuable and useful guide to thesubject in all its diversity and topicality. Although barelybeing a textbook for neophytes in the field, despite thewealth of background material sketched wherever necessary,the book under review is certainly the most topicalpresentation of algebraic K-theory at this time, and anexcellent enhancement of the existing literature in anycase.References[1] Bass, Hyman. Algebraic K-theory. Mathematics Lecture Note Series.New York-Amsterdam: W.A. Benjamin (1968).[2] Swan, R.G. Algebraic K-theory. Lecture Notes in Mathematics 76.Berlin-Heidelberg-New York: Springer-Verlag (1968).[3] Milnor, John W. Introduction to algebraic K-theory. Annals ofMathematics Studies. No.72. Princeton, N. J.: Princeton UniversityPress and University of Tokyo Press (1971).[4] Srinivas, V. Algebraic K-theory. 2nd ed. Progress in Mathematics(Boston, Mass.) 90. Boston, MA: Birkhäuser (1996).[5] Rosenberg, Jonathan. Algebraic K-theory and its applications.Graduate Texts in Mathematics. 147. New York, NY: Springer-Verlag(1994).[6] Inassaridze, Hvedri. Algebraic K-theory. Mathematics and its Applications(Dordrecht). 311. Dordrecht: Kluwer Academic Publishers(1995).[7] Magurn, Bruce A. An algebraic introduction to K-theory. Encyclopediaof Mathematics and Its Applications. 87. Cambridge: CambridgeUniversity Press (2002).Werner Kleinert received his doctoraldegree in commutative algebra in 1971.After his postdoctoral qualification (habilitation)in the field of algebraic geometryin 1979, he was promoted to universitylecturer at Humboldt University inBerlin, an academic position that he heldthere until his retirement in 2010. His main research interestshave always been the geometry of moduli spacesof algebraic curves and abelian varieties, together with relatedtopics such as Riemann surfaces, theta functions andTeichmueller theory.Reviewer: Ghislaine GueudetEncyclopedia of MathematicsEducationStephen Lerman (Editor)Springer New York, 2014xxii, 672 p.ISBN 978-94-007-4977-1An invitation to readThe Encyclopedia of Mathematics Education, written underthe direction of Stephen Lerman, was published in2014 simultaneously as a traditional book and a dynamiconline resource on the Springer Reference website.This article does not claim to be a complete review ofthis Encyclopedia – I have not yet read all the 163 articles!Its aim is more to present the perspective retained by theEditorial Board and give a flavour of the content of theEncyclopedia, as an invitation to the potential reader.A comprehensive resource for a large audienceThe Encyclopedia project was to write a “comprehensivereference text, covering every topic in the field of mathematicseducation research” (Lerman, Preface, vii). Moreover,this text was to be informative, taking into accountthe very latest results of research, but also accessible toanyone who has an interest in mathematics education:not only researchers in mathematics education but alsomathematicians, teachers, students and policymakers. Forthis purpose, the Editorial Board has gathered togethera team of 174 authors from more than 30 countries, specialistsof different aspects of mathematics education.The entries can concern specific mathematic topics (andthe related learning and teaching issues) like “Algebrateaching and learning” (by Carolyn Kieran) and “CalculusTeaching and Learning” (by Ivy Kidron) or moretransverse issues like “Inquiry-based mathematics edu-58 EMS Newsletter December 2014