James T. Smith

The Italian mathematician Mario Pieri (1860–1913) played a major role in the development of algebraic geometry and foundations of mathematics around the turn of the twentieth century. This volume is the second in a series intended to make Pieri’s research in diverse fields—mathematical logic and philosophy of mathematics, foundations of projective, inversive, and elementary geometry, algebraic and differential geometry, and vector analysis—accessible to today’s scholars and to assess its importance (yet little recognized) in historical and modern contexts. The Legacy of Mario Pieri in Foundations and Philosophy of Mathematics examines Pieri’s underlying philosophy of mathematics and his research goals, highlighting one of his most influential achievements, his axiomatizations of projective and elementary geometry. Its chapters include three of Pieri’s pioneering works, translated by the authors and appearing in English for the first time, as well as an analysis of the role of this research in its larger context. Together, these translations and the accompanying interpretation accurately capture Pieri’s expository style, philosophical perspective, and his foundational research, which has influenced generations. With an excellent index, exhaustive references, and engaging discussions that reveal Pieri’s work in its historical context, this volume will appeal to scholars and advanced students interested in the history and philosophy of mathematics and logic, as well as readers with a general knowledge of geometry at the intermediate level. A list of errata can be found on the author Smith’s personal webpage.

by Ivor Grattan-Guinness One of the distortions in most kinds of history is an imbalance between the study devoted to major figures and to lesser ones, concerning both achievements and influence: the Great Ones may be studied to death while the others are overly ignored and thereby remain underrated. In my own work in the history of mathematics I have noted at least a score of outstanding candidates for neglect, of whom Mario Pieri (1860–1913) is one. A most able contributor to geometry, arithmetic and mathematical analysis, and mat- matical logic during his rather short life, his work and its legacy are not well known. The main reason is that Pieri worked “in the shadow of giants,” to quote one of the authors 1 of this volume. Born into a scholarly family in Lucca, Pieri was educated briefly at the University of Bologna and principally at the prestigious Scuola Normale Superiore, in Pisa; under the influence of Luigi Bianchi (1856–1928) he wrote there his doctoral dissertations on al-braic and differential geometry. During his twenties came appointments in Turin, first at the military academy and then also at the university, where he fell under the sway of Corrado Segre (1863–1924) in algebraic geometry, and Giuseppe Peano (1858–1932) in the foundations of arithmetic, mathematical analysis, and mathematical logic. From 1900 to 1908 he held a chair at the University of Catania before moving to Parma, where he died from cancer. A list of errata can be found on the author Smith’s personal webpage.

based upon a most user-friendly and flexible NUMBER-LETTER CODE COMPATIBLE WITH THAT OF MEMORY MASTER DOMINIC O'BRIEN and optioning all letters in the alphabet to personal preference * many techniques based upon a basic favorite Person-Action-Object formula, easily expandable from (or revertible to) Dominic's work* complete list of all possible one-and two-letter combos from A to Z and AA to ZZ with generous suggestions for the people, animals and creatures you find most interesting and how to effortlessly interchange these with numbers* how to build "memory palaces" using any favorite environments (real or fantastic) and objects * suggested ways to make the use of the traditional memory journey system even more interesting and efficient including an ordered series of your favourite smells and tastes* many suggestions for engaging interest with and recalling material initially found dull * many suggested "fluid intelligence" exercises that can be done at any time and without the need for a computer or a book* optimum study tips such as when to study and revise, and Mind Mapping * thorough dietary (essentially food combining and Omega-3 intake), exercise and optimum study environment recommendations * the most sensible "make the most of your life" recommendations including the "compound interest" investment strategy * ample further reading recommendations * You may also preview and purchase my eBook co-authored with Phil Chambers, HOW TO REMEMBER EQUATIONS AND FORMULAE here: http: //www.rememberequations.co.uk/ and in a Kindle edition from most Amazon sites, at Apple's iTunes bookstore, live on Google Play and at Apple's iTunes bookstore. Our GCSE adaptation is also available at all the preceding outlets except Google Play

A practical, accessible introduction to advanced geometryExceptionally well-written and filled with historical andbibliographic notes, Methods of Geometry presents a practical andproof-oriented approach. The author develops a wide range ofsubject areas at an intermediate level and explains how theoriesthat underlie many fields of advanced mathematics ultimately leadto applications in science and engineering. Foundations, basicEuclidean geometry, and transformations are discussed in detail andapplied to study advanced plane geometry, polyhedra, isometries,similarities, and symmetry. An excellent introduction to advancedconcepts as well as a reference to techniques for use inindependent study and research, Methods of Geometry alsofeatures: * Ample exercises designed to promote effective problem-solvingstrategies * Insight into novel uses of Euclidean geometry * More than 300 figures accompanying definitions and proofs * A comprehensive and annotated bibliography * Appendices reviewing vector and matrix algebra, least upperbound principle, and equivalence relations An Instructor's Manual presenting detailed solutions to all theproblems in the book is available upon request from the Wileyeditorial department.