History of mathematics Books

Book SynopsisTest Prep Books'' GED Math Study Guide 2023-2024: 3 Practice Exams and GED Test Prep Book [6th Edition]Taking the GED Math test? Want to get a good score?Written by Test Prep Books, this comprehensive study guide includes: Quick Overview Test-Taking Strategies Introduction Math Reference Sheet Mathematical Reasoning Practice Questions Detailed Answer Explanations Disclaimer: GED is a registered trademark of the American Council on Education (ACE) and administered exclusively by GED Testing Service LLC under license. This material is not endorsed or approved by ACE or GED Testing Service.Studying is hard. We know. We want to help. You can ace your test.Each part of the test has a full review. This study guide covers everything likely to be on the test.Lots of GED Math practice test questions are included. Miss one and want to know why? There are detailed answer explanations to help you avoid missing the same question a second time.Are you a bad test taker?Use your time wisely with the latest test-taking strategies. Don''t settle for just learning what is on the test. Learn how to be successful with that knowledge.Test Prep Books has drilled down the top test-taking tips. This will help you save time and avoid making common mistakes on test day.Get your GED Math study guide. It includes review material, practice test questions, and test-taking strategies.It has everything you need for success.

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Book SynopsisA Mathematician''s Apology is the famous essay by British mathematician G. H. Hardy. It concerns the aesthetics of mathematics with some personal content, and gives the layman an insight into the mind of a working mathematician. Indeed, this book is often considered one of the best insights into the mind of a working mathematician written for the layman.?A Mathematician''s Apology is the famous essay by British mathematician G. H. Hardy. It concerns the aesthetics of mathematics with some personal content, and gives the layman an insight into the mind of a working mathematician. Indeed, this book is often considered one of the best insights into the mind of a working mathematician written for the layman.

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Book SynopsisThis book presents, for the first time, the unpublished manuscripts of Lars Hörmander, written between 1951 and 2007. Hörmander himself organised the manuscripts and also wrote the notes explaining their origins, presenting the material in the form he fully intended it to be published in. As his daughter, Sofia Broström, mentions in the Foreword, towards the end of his life, Hörmander "carefully went through his unpublished manuscripts, checking and revising each of them with his very critical eye, deciding what should be kept for posterity and what should be thrown out". He also compiled the complete bibliography of all his published mathematical works that is included at the end of the present book. Of both historical and mathematical value, the contents of this book will undoubtedly inspire mathematicians of different horizons.Table of ContentsForeword.- Origin of the manuscripts.- 25 Unpublished Manuscripts of L Hörmander.- Short Autobiography.- Looking forward from ICM 1962.- Complete Mathematical Bibliography of Lars Hörmander.- Published Articles.- Published Books.- Lecture Notes.

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Book SynopsisThe book offers a collection of essays on various aspects of Leibniz’s scientific thought, written by historians of science and world-leading experts on Leibniz. The essays deal with a vast array of topics on the exact sciences: Leibniz’s logic, mereology, the notion of infinity and cardinality, the foundations of geometry, the theory of curves and differential geometry, and finally dynamics and general epistemology. Several chapters attempt a reading of Leibniz’s scientific works through modern mathematical tools, and compare Leibniz’s results in these fields with 19th- and 20th-Century conceptions of them. All of them have special care in framing Leibniz’s work in historical context, and sometimes offer wider historical perspectives that go much beyond Leibniz’s researches. A special emphasis is given to effective mathematical practice rather than purely epistemological thought. The book is addressed to all scholars of the exact sciences who have an interest in historical research and Leibniz in particular, and may be useful to historians of mathematics, physics, and epistemology, mathematicians with historical interests, and philosophers of science at large.Trade Review“The volume should be of value to scholars of Leibniz with interests in the ‘exact sciences’ and the formal dimensions of his thinking, as well as to historians and philosophers concerned with understanding how Leibniz’s thinking anticipates later approaches. … the volume is a valuable contribution to our understanding of Leibniz’s projects in the exact sciences.” (Christopher P. Noble, Metascience, August 20, 2020)Table of ContentsChapter 1. Leibniz on the Logic of Conceptual Containment and Coincidence (Marko Malink and Anubav Vasudevan).- Chapter 2. Leibniz’s Mereology (Massimo Mugnai).- Chapter 3. Leibniz in Cantor’s Paradise: A Dialogue on the Actual Infinite (Richard T.W. Arthur).- Chapter 4. Leibniz and the Continuity of Space (Vincenzo De Risi).- Chapter 5. On the Plurality of Spaces in Leibniz (Valérie Debuiche and David Rabouin).- Chapter 6. One String Attached: Geometrical Exactness in Leibniz’s Parisian Manuscripts (Davide Crippa).- Chapter 7. Leibniz and the Calculus of Variations (Jürgen Jost).- Chapter 8. Teleology and Realism in Leibniz’s Philosophy of Science (Nabeel Hamid).

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Book SynopsisThis book focuses on the ancient Near East, early imperial China, South-East Asia, and medieval Europe, shedding light on mathematical knowledge and practices documented by sources relating to the administrative and economic activities of officials, merchants and other actors. It compares these to mathematical texts produced in related school contexts or reflecting the pursuit of mathematics for its own sake to reveal the diversity of mathematical practices in each of these geographical areas of the ancient world. Based on case studies from various periods and political, economic and social contexts, it explores how, in each part of the world discussed, it is possible to identify and describe the different cultures of quantification and computation as well as their points of contact. The thirteen chapters draw on a wide variety of texts from ancient Near East, China, South-East Asia and medieval Europe, which are analyzed by researchers from various fields, including mathematics, history, philology, archaeology and economics. The book will appeal to historians of science, economists and institutional historians of the ancient and medieval world, and also to Assyriologists, Indologists, Sinologists and experts on medieval Europe.Trade Review“Mathematics, Administrative and Economic Activities in Ancient Worlds fills a longstanding need to situate mathematics into its context of administration in which it originated and developed in various societies. … These publications attest to the lively and active community of historians of science working on ancient sources and the potential to learn about the origin and early development of sciences … within societies which–judging by recent developments–has become a point of concern in many parts of the world.” (Annette Imhausen, NTM, Vol. 30 (3), September, 2022)“As an economist, I thoroughly enjoyed and was impressed at the many details and analysis of those examples of these activities in the varied places during these early time periods. … The is book is very comprehensive in its discussion. Math formulas explaining different ways of computing interest and many other types of financial economic analysis are given. Each chapter has an ample number of references.” (Paul Gentle, HEI History of Economic Ideas, Vol. 29 (2), 2021)Table of ContentsChapter ​1. Mathematics, Administrative and Economic Activities in the Ancient Worlds: An introduction (Cécile Michel and Karine Chemla)Part 1: Mathematical Writings, Regulations, Laws and NormsChapter 2. A Comparative Study of Prices and Wages in Royal Inscriptions, Administrative Texts and Mathematical Texts in the Old Babylonian Kingdom of Larsa (Cécile Michel, with contributions by Robert Middeke-Conlin and Christine Proust)Chapter 3. Computation in the Arthaśāstra (Mark McClish)4. Official Salaries and State Taxes as Seen in Qin-Han Manuscripts, with a Focus on Mathematical Texts (Peng Hao)Part 2: Quantifying Work, Quantifying Volume and CapacityChapter 5. Insights into the Administration of Ancient Irrigation Systems in Third Millennium BCE Mesopotamia (Stephanie Rost)Chapter 6. Mathematical Computations in the Management of Public Construction Work in Mesopotamia (End of the Third and Beginning of the Second Millennium BCE) (Martin Sauvage)Chapter 7. The use of volume in the measurement of grain in early imperial China (Karine Chemla and Ma Biao)Part III: Quantifying Lands and SurfacesChapter 8. The Measurement of Fields During the Pre-Sargonic Period (Camille Lecompte)Chapter 9. Early-Dynastic Tables from Southern Mesopotamia, or the Multiple Facets of the Quantification of Surfaces (Christine Proust)Part IV: Prices, Rates, Loans and InterestsChapter 10. Computation Practices of the Assyrian Merchants during the Nineteenth Century BCE (Cécile Michel)Chapter 11. Connecting a Disconnect. Can Evidence for a Scribal Education be Found in a Professional Setting During the Old Babylonian Period? (Robert Middeke-Conlin)Chapter 12. Loans and Interest in Sanskrit Legal and Mathematical Texts (Sreeramula Rajeswara Sarma and Takanori Kusuba)Chapter 13. Computational Practices Around Coins and Coinage: John of Murs’ Quadripartitum Nnumerorum and French Money Changers’ Books (Marc Bompaire and Matthieu Husson)

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Book SynopsisPreface.- How is Mathematics Put Together?.- How Does Mathematics Work?.- Mathematics and Civilization.- Mathematics in Nature and Art.- Epilogue.- Reference List of Illustrations.- Bibliography.- Index.

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Book Synopsis- 1. The Greek Legacy.- 2. Perspective in the Renaissance.- 3. New ways of looking at conics.- 4. Desargues, the dawn of projective geometry.- 5. Pascal's geometrical achievements.- 6. An interlude a century and a half long.- 7. Towards a new geometry.- 8. Poncelet, the projective properties of figures.- 9. The algebraic way to projective geometry.- 10. The synthetic route: the contributions of Steiner and Chasles.- 11. Von Staudt's pure synthetism.- 12. Projective geometry 1870-1930 and beyond.

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Book SynopsisPreface.- Foreword.- Life and Teaching of Pythagoras.- Numbers and Number Mysticism.- Mathematics, Mathematicians, and Proofs.- Prime Numbers.- Pythagorean Theorem.- Pythagorean Triples.- Pythagorean Figurative Numbers.- Pythagorean Irrationality of Numbers.- Name Index.- Subject Index.

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Book SynopsisChapter 1: On Partially Ordered Sets and the 1/3-2/3 Conjecture.- Chapter 2: Group Actions and Riemann Surfaces.- Chapter 3: Challenges in Using Data for Public Policy Decisions.- Chapter 4: A Taste of Discretized Differential Geometry: Communicating Mathematics With Conceptual Metaphor.- Chapter 5: The Scholarship of Teaching and Learning.- Chapter 6: My Journey In Geometry.- Chapter 7: Continued Fractions Connecting Number Theory, Dynamical Systems, And Hyperbolic Geometry.- Chapter 8: Stochastic Models in Biology.- Chapter 9: Finding Your Path.

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Book SynopsisIntroduction.- Historical background.- Riemann's habilitation.- Presentation of the texts.- Reception and impact on history.- Modern research.- Bibliography.

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Book SynopsisThabit ibn Qurra (826–901) was one of history’s most original thinkers and displayed expertise in the most difficult disciplines of this time: geometry, number theory, and astronomy as well as ontology, physics, and metaphysics. Approximately a dozen of this shorter mathematical and philosophical writings are collected in this volume. Critically edited with accompanying commentary, these writings show how Thabit Ibn Qurra developed and reconceived the intellectual inheritance of ancient Greece in all areas of knowledge.

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Book SynopsisEvery age and every culture has relied on the incorporation of mathematics in their works of architecture to imbue the built environment with meaning and order. Mathematics is also central to the production of architecture, to its methods of measurement, fabrication and analysis. This two-volume edited collection presents a detailed portrait of the ways in which two seemingly different disciplines are interconnected. Over almost 100 chapters it illustrates and examines the relationship between architecture and mathematics. Contributors of these chapters come from a wide range of disciplines and backgrounds: architects, mathematicians, historians, theoreticians, scientists and educators. Through this work, architecture may be seen and understood in a new light, by professionals as well as non-professionals.Volume I covers architecture from antiquity through Egyptian, Mayan, Greek, Roman, Medieval, Inkan, Gothic and early Renaissance eras and styles. The themes that are covered range from symbolism and proportion to measurement and structural stability. From Europe to Africa, Asia and South America, the chapters span different countries, cultures and practices.Trade Review“It presents several alternative historical and theoretical contexts of the relationship between architecture and mathematics which has been pushed to the foreground during the past decades with the increasing use of computer-aided design in their profession … . Historians of mathematics, too, will no doubt find useful material here for their research, especially if they are interested in the more practical concerns that have shaped the development of their field … .” (Yelda Nasifoglu, BSHM Bulletin, Vol. 31 (3), October, 2016)“The study of connections between mathematics and the arts has grown considerably in recent decades, influenced by the work of Doris Schattschneider, Jay Kappraff, and Michele Emmer, among others. The use of mathematics is particularly a necessity in architecture, so the present set is welcome. … This is a valuable resource for mathematics, architecture, and the arts in general. Summing Up: Highly recommended. All readers.” (C. A. Gorini, Choice, Vol. 53 (2), October, 2015)“The ambitious goal is to describe both the intimate relation but also the alienation between mathematics and architecture and between mathematicians and architects. … It is an important and highly inspiring collection of papers that will be of interest to researchers from as many disciplines as illustrated by the diversity of the background of the authors. … Highly recommended for readers who do not want to drown or hide in their own abyss of specialization.” (Adhemar Bultheel, euro-math-soc.eu, June, 2015)Table of ContentsPart I: Introduction.- Part II: From 2000 BC to 300AD.- Part III: Theories of Measurement and Structure.- Part IV: From 1100 AD to 1400 AD.- Part V: Theories of Proportion, Symmetry, Periodicity.- Part VI: From 1500 AD to 1600 AD.- Index.- Acknowledgements.

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Book SynopsisEvery age and every culture has relied on the incorporation of mathematics in their works of architecture to imbue the built environment with meaning and order. Mathematics is also central to the production of architecture, to its methods of measurement, fabrication and analysis. This two-volume edited collection presents a detailed portrait of the ways in which two seemingly different disciplines are interconnected. Over almost 100 chapters it illustrates and examines the relationship between architecture and mathematics. Contributors of these chapters come from a wide range of disciplines and backgrounds: architects, mathematicians, historians, theoreticians, scientists and educators. Through this work, architecture may be seen and understood in a new light, by professionals as well as non-professionals.Volume II covers architecture from the Late Renaissance era, through Baroque, Ottoman, Enlightenment, Modern and contemporary styles and approaches. Key figures covered in this volume include Palladio, Michelangelo, Borromini, Sinan, Wren, Wright, Le Corbusier, Breuer, Niemeyer and Kahn. Mathematical themes which are considered include linear algebra, tiling and fractals and the geographic span of the volume’s content includes works in the United States of America and Australia, in addition to those in Europe and Asia.Trade Review“It presents several alternative historical and theoretical contexts of the relationship between architecture and mathematics which has been pushed to the foreground during the past decades with the increasing use of computer-aided design in their profession … . Historians of mathematics, too, will no doubt find useful material here for their research, especially if they are interested in the more practical concerns that have shaped the development of their field … .” (Yelda Nasifoglu, BSHM Bulletin, Vol. 31 (3), October, 2016)Table of ContentsPart VII: Theories of Representation.- Part VIII: From 1600 AD to 1900 AD.- Part IX: 1900–2000.- Part X: Contemporary Approaches to Design and Analysis.- Part XI: Theories and Applications of Computer Sciences.- Index.- Acknowledgements.​

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Book SynopsisThis is a comprehensive book on the life and works of Leon Henkin (1921–2006), an extraordinary scientist and excellent teacher whose writings became influential right from the beginning of his career with his doctoral thesis on “The completeness of formal systems” under the direction of Alonzo Church. Upon the invitation of Alfred Tarski, Henkin joined the Group in Logic and the Methodology of Science in the Department of Mathematics at the University of California Berkeley in 1953. He stayed with the group until his retirement in 1991. This edited volume includes both foundational material and a logic perspective. Algebraic logic, model theory, type theory, completeness theorems, philosophical and foundational studies are among the topics covered, as well as mathematical education. The work discusses Henkin’s intellectual development, his relation to his predecessors and contemporaries and his impact on the recent development of mathematical logic. It offers a valuable reference work for researchers and students in the fields of philosophy, mathematics and computer science.Table of ContentsPart I Biographical Studies.- Leon Henkin.- Lessons from Leon.- Tracing back “Logic in Wonderland” to my work with Leon Henkin.- Henkin and the Suit.- A Fortuitous Year with Leon Henkin.- Leon Henkin and a Life of Service.- Part II Henkin‘s Contribution to XX Century Logic.- Leon Henkin and Cylindric Algebras.- A Bit of History Related to Logic Based on Equality.- Pairing Logical and Pedagogical Foundations for the Theory of Positive Rational Numbers. Henkin‘s unfinished work.- Leon Henkin the Reviewer.- Henkin‘s Theorem in Textbooks.- Henkin on Completeness.- Part III Extensions and Perspectives in Henkin‘s Work.- The Countable Henkin Principle.- Reflections on a Theorem of Henkin.- Henkin‘s Completeness Proof and Glivenko‘s Theorem.- From Classical to Fuzzy Type Theory.- The Henkin Sentence.- April the 19th.- Henkin and Hybrid Logic.- Changing a Semantics: Oportunism or Courage?.- Appendix Curriculum Vitae: Leon Henkin.

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Book SynopsisDer Bericht über das vielleicht größte mathematische Genie des 20. Jahrhunderts liest sich wie ein spannender Roman.Table of ContentsProlog - In der Kühle des Tempels (1887 - 1903) - Lust auf Forschung (1903 - 1908) - Auf der Suche nach Mäzenen (1908 - 1913) - Hardy (GH Hardy bis 1903) - 'Darf ich mich vorstellen ...' (1913 - 1914) - Ramanujans Blütezeit (1914 - 1916) - Die englische Kälte (1916 - 1918) - Nicht ganz gesund (ab 1918) - Epilog

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Book SynopsisCe volume rassemble les notes historiques parues dans les différents livres des éléments de mathématique de l'auteur. Elles concernent donc l'ensemble des matières abordées dans ce traité : théorie des ensembles, algèbre, topologie, fonctions d'une variable réelle, espaces vectoriels topologiques, intégration, algèbre commutative, groupes et algèbres de Lie.Table of ContentsFondements des mathématiques; logique; théorie des ensembles.- Numération; analyse combinatoire.- L’evolution de l’algèbre.- Algèbre linéaire et algèbre multilinéaire.- Polynomes et corps commutatifs.- Divisibilité ; corps ordonnés.- Algèbre commutative; théorie des nombres algébriques.- Algèbre non commutativ.- Formes quadratiques; géometrie élémentaire.- Espaces topologiques.- Espaces uniformes.- Nombres réels.- Exponentielles et logarithmes.- Espaces à n dimensions.- Nombres complexes; mesure des angles.- Espaces métriques.- Calcul ininitésimal.- Développements asymptotiques.- La fonction gamma.- Espaces fonctionnels.- Espaces vectoriels topologiques.- Intégration dans les espaces localement compacts.- Mesure de Haar; convolution.- Intégration dans les espaces non localement compacts.- Groupes de Lie et algèbres de Lie.- Groupes engendrés par des réflections. Systèmes de racines.

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Book SynopsisBoth classical geometry and modern differential geometry have been active subjects of research throughout the 20th century and lie at the heart of many recent advances in mathematics and physics. The underlying motivating concept for the present book is that it offers readers the elements of a modern geometric culture by means of a whole series of visually appealing unsolved (or recently solved) problems that require the creation of concepts and tools of varying abstraction. Starting with such natural, classical objects as lines, planes, circles, spheres, polygons, polyhedra, curves, surfaces, convex sets, etc., crucial ideas and above all abstract concepts needed for attaining the results are elucidated. These are conceptual notions, each built "above" the preceding and permitting an increase in abstraction, represented metaphorically by Jacob's ladder with its rungs: the 'ladder' in the Old Testament, that angels ascended and descended... In all this, the aim of the book is to demonstrate to readers the unceasingly renewed spirit of geometry and that even so-called "elementary" geometry is very much alive and at the very heart of the work of numerous contemporary mathematicians. It is also shown that there are innumerable paths yet to be explored and concepts to be created. The book is visually rich and inviting, so that readers may open it at random places and find much pleasure throughout according their own intuitions and inclinations. Marcel Berger is the author of numerous successful books on geometry, this book once again is addressed to all students and teachers of mathematics with an affinity for geometry.Trade Review“It is a must own book for anyone serious about developing a conceptual understanding of the interconnected web of modern geometry and the ever-growing intertwining of geometry with practically all other branches of mathematics. … It is remarkable for a book to provide such a detailed glimpse of contemporary geometry via well developed discussions of so many questions of current interest. It provides the most extensive exposition of geometric thinking I’ve ever seen in a book at this level.” (William H. Barker, MAA Reviews, August, 2017)“Geometry Revealed is to give the reader a feel for the conceptual frameworks of modern geometry, attempting to reach as far as possible with a minimum of assumed knowledge and formal scaffolding. … Geometry Revealed being useful for research mathematicians as a still reasonably up-to-date survey. … Geometry Revealed offered an ascent into the wonders of a new world.” (Danny Yee, Danny Yee’s Book Reviews, dannyreviews.com, July, 2015)“By considering a hierarchy of ‘natural’ geometrical objects … it sets out to investigate significant geometrical problems which are either unsolved or were solved only recently. … it is undoubtedly a major tour de force, and if you really want to gain an idea of where geometry is going in the 21st century, you will find plenty of exquisite material here.” (Gerry Leversha, The Mathematical Gazette, Vol. 96 (356), July, 2012)“The book contains twelve chapters, each of them is a collection of such problems about geometric objects with more and more complexity … . The chapters are independent from each other, any of them can serve as a course. Researchers in geometry can use it as a source for further research. … the book is accessible to a wide audience of people who are interested in geometry.” (János Kincses, Acta Scientiarum Mathematicarum (Szeged), Vol. 78 (1-2), 2012)“‘Geometry Revealed’ is a massive text of 831 pages which is organized in twelve chapters and which additionally provides indices for names, subjects and symbols … throughout the author quite carefully lays out the historical perspective. … a typical chapter starts with an observation or a problem in elementary geometry. Large parts of the text are very accessible, and a reader who likes (mathematical) physics will often get something extra.” (Michael Joswig, Zentralblatt MATH, Vol. 1232, 2012)“The author provides the reader with an enormous amount of detailed information and thus yields deep insight into the various topics. … All in all an overwhelming book which is a must … for everyone having sufficient mathematical knowledge.” (G. Kowol, Monatshefte für Mathematik, Vol. 164 (2), October, 2011)“The book is a very readable account of several branches of geometry, classical and modern, elementary and advanced. … Every chapter is extremely interesting and alive. … The book is rich in ideas, written in an informal style, with no formulae and no unnecessary technical details. … Every part of this book is interesting and should be accessible to a wide audience of mathematicians. … Every mathematician will experience great pleasure in reading this book.” (Athanase Papadopoulos, Mathematical Reviews, Issue 2011 m)Table of ContentsPoints and lines in the plane.- Circles and spheres.- The sphere by itself: can we distribute points on it evenly?.- Conics and quadrics.- Plane curves.- Smooth surfaces.- Convexity and convex sets.- Polygons, polyhedra, polytopes.- Lattices, packings and tilings in the plane.- Lattices and packings in higher dimensions.- Geometry and dynamics I: billiards.- Geometry and dynamics II: geodesic flow on a surface.

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Book SynopsisDie Mathematik im mittelalterlichen Islam hatte großen Einfluss auf die allgemeine Entwicklung des Faches. Der Autor beschreibt diese Periode der Geschichte der Mathematik und bezieht sich dabei auf die arabischsprachigen Quellen. Zu den behandelten Themen gehören Dezimalrechnen, Geometrie, ebene und sphärische Trigonometrie, Algebra sowie die Approximation von Wurzeln von Gleichungen. Das Buch wendet sich an Mathematikhistoriker und -studenten, aber auch an alle Interessierten mit Mathematikkenntnissen der weiterführenden Schule.Trade ReviewAus den Rezensionen:“... hat neuere Entwicklungen der Forschung aufgenommen und bekannte Fehler der englischsprachigen Version beseitigt. Der Verlag hat – der Zeit und den modernen Druckmedien angemessen – nun farbige Abbildungen zugelassen und das tut dem Erscheinungsbild des Buches natürlich sehr gut. ... Die Einbeziehung von Beschreibungen dieser historisch-kulturellen Entwicklungen macht einen der Reize dieses Buches aus. Ein weiterer großer Pluspunkt ist die Konzentration auf die Quellen. ... ist hervorragend lesbar ... die Übersetzerin Petra Schmidl in Zussamenarbeit mit Heinz Klaus Strick hervorragend gearbeitet haben ...“ (in: Mathematische Semesterberichte, September/2011)Aus den Rezensionen zur englischen Ausgabe "Episodes in the Mathematics of Medieval Islam":"This is a most scholarly book. The presentation is in the style of a textbook; each of the six chapters being followed by a set of exercises and a bibliography. … There is a good table of contents and a comprehensive index. … This is an excellent book full of information and thought-provoking ideas. It is worthy of careful study which will lead to a greater understanding of what the Islamic world has contributed to mathematics." (D.Stander, The Mathematical Gazette, Vol. 89 (515), 2005)"Written in 1986 and inspired by Asger Aaboe’s classic Episodes in the Early History of Mathematics, this book contains a wealth of classroom-ready examples of much of the mathematics one finds in high school and early college … . Springer has taken the right step by issuing a paperback edition to get the book into the hands of a more general readership. … The re-issue of this gem is significant and welcomed. It will enrich your classes and deepen your perspective on mathematics and culture." (Glen van Brummelen, The MAA Mathematical Sciences Digital Library, January, 2004)

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Book SynopsisIn this textbook the authors present first-year geometry roughly in the order in which it was discovered. The first five chapters show how the ancient Greeks established geometry, together with its numerous practical applications, while more recent findings on Euclidian geometry are discussed as well. The following three chapters explain the revolution in geometry due to the progress made in the field of algebra by Descartes, Euler and Gauss. Spatial geometry, vector algebra and matrices are treated in chapters 9 and 10. The last chapter offers an introduction to projective geometry, which emerged in the 19thcentury.Complemented by numerous examples, exercises, figures and pictures, the book offers both motivation and insightful explanations, and provides stimulating and enjoyable reading for students and teachers alike.Trade ReviewFrom the book reviews:Choice - Outstanding Academic Title in 2012“This is an excellent, challenging textbook as well as a valuable resource for historical information, problems, and student projects. The historical content is broad based, comprehensive, and reliable. Each chapter has extensive exercises, many taken directly from or based on historical sources … . Hints and solutions for all problems are given in an appendix. Thorough bibliography. Summing Up: Highly recommended. Lower-division undergraduates and above.” (C. A. Gorini, Choice, Vol. 50 (3), November, 2012)“The book under review is a treasure chest of interesting theorems and problems in geometry together with their illuminating histories. … This is the kind of book that one would enjoy browsing through and reading while sitting relaxedly in an armchair without any paper or pencil and starting at almost any page or paragraph. It should be on the shelf of every lover of geometry.” (Mowaffaq Hajja, zbMATH, Vol. 1288, 2014)“This book belongs on the bookshelf of every geometer. … The authors have penned their book with students of geometry as well as science in mind. In fact, the book would serve well as a second year mathematics course in a classical liberal arts setting. … the book treats many interesting and beautiful problems, introducing powerful concepts along the way, and yet is written at a level suitable for an introductory course of geometry or even advanced mathematics.” (Alan S. McRae, Mathematical Reviews, February, 2013)“There is a lot of interesting material in this book, supplemented by a lot of very nice artwork and many interesting exercises … . I would think that any other college instructor … with an interest in geometry would also want a copy on his or her shelf.” (Mark Hunacek, The Mathematical Association of America, June, 2012)Table of ContentsPreface.- Part I: Classical Geometry.- Thales and Pythagoras.- The Elements of Euclid.- Conic Sections.- Further Results on Euclidean Geometry.- Trigonometry.- Part II: Analytic Geometry.- Descartes' Geometry.- Cartesian Coordinates.- To be Constructible, or not to be.- Spatial Geometry and Vector Algebra.- Matrices and Linear Mappings.- Projective Geometry.- Solutions to Exercises.- References.- Figure Source and Copyright.- Index.

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Book SynopsisTable of ContentsInhaltsübersicht: Abhandlungen zur Zahlentheorie und Algebra.- Abhandlungen zur Funktionentheorie.- Abhandlungen zur Mengenlehre.- Abhandlungen zur Geschichte der Mathematik und zur Philosophie des Unendlichen.- Anhang: Aus dem Briefwechsel zwischen Cantor und Dedekind.- Das Leben Georg Cantors.- Bibliographie weiterer Arbeiten von Georg Cantor.

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