This book is unique in that it looks at geometry from 4 different viewpoints - Euclid-style axioms, linear algebra, projective geometry, and groups and their invariants Approach makes the subject accessible to readers of all mathematical tastes, from the visual to the algebraic Abundantly supplemented with figures and exercises
This textbook provides a unified and concise exploration of undergraduate mathematics by approaching the subject through its history. Readers will discover the rich tapestry of ideas behind familiar topics from the undergraduate curriculum, such as calculus, algebra, topology, and more. Featuring historical episodes ranging from the Ancient Greeks to Fermat and Descartes, this volume offers a glimpse into the broader context in which these ideas developed, revealing unexpected connections that make this ideal for a senior capstone course. The presentation of previous versions has been refined by omitting the less mainstream topics and inserting new connecting material, allowing instructors to cover the book in a one-semester course. This condensed edition prioritizes succinctness and cohesiveness, and there is a greater emphasis on visual clarity, featuring full color images and high quality 3D models. As in previous editions, a wide array of mathematical topics are covered, from geometry to computation; however, biographical sketches have been omitted. Mathematics and Its History: A Concise Edition is an essential resource for courses or reading programs on the history of mathematics. Knowledge of basic calculus, algebra, geometry, topology, and set theory is assumed. From reviews of previous editions: “Mathematics and Its History is a joy to read. The writing is clear, concise and inviting. The style is very different from a traditional text. I found myself picking it up to read at the expense of my usual late evening thriller or detective novel.... The author has done a wonderful job of tying together the dominant themes of undergraduate mathematics.” Richard J. Wilders, MAA, on the Third Edition "The book...is presented in a lively style without unnecessary detail. It is very stimulating and will be appreciated not only by students. Much attention is paid to problems and to the development of mathematics before the end of the nineteenth century.... This book brings to the non-specialist interested in mathematics many interesting results. It can be recommended for seminars and will be enjoyed by the broad mathematical community." European Mathematical Society, on the Second Edition
In this new textbook, acclaimed author John Stillwell presents a lucid introduction to Lie theory suitable for junior and senior level undergraduates. In order to achieve this, he focuses on the so-called "classical groups'' that capture the symmetries of real, complex, and quaternion spaces. These symmetry groups may be represented by matrices, which allows them to be studied by elementary methods from calculus and linear algebra. This naive approach to Lie theory is originally due to von Neumann, and it is now possible to streamline it by using standard results of undergraduate mathematics. To compensate for the limitations of the naive approach, end of chapter discussions introduce important results beyond those proved in the book, as part of an informal sketch of Lie theory and its history. John Stillwell is Professor of Mathematics at the University of San Francisco. He is the author of several highly regarded books published by Springer, including The Four Pillars of Geometry (2005), Elements of Number Theory (2003), Mathematics and Its History (Second Edition, 2002), Numbers and Geometry (1998) and Elements of Algebra (1994).
A beautiful and relatively elementary account of a part of mathematics where three main fields - algebra, analysis and geometry - meet. The book provides a broad view of these subjects at the level of calculus, without being a calculus book. Its roots are in arithmetic and geometry, the two opposite poles of mathematics, and the source of historic conceptual conflict. The resolution of this conflict, and its role in the development of mathematics, is one of the main stories in the book. Stillwell has chosen an array of exciting and worthwhile topics and elegantly combines mathematical history with mathematics. He covers the main ideas of Euclid, but with 2000 years of extra insights attached. Presupposing only high school algebra, it can be read by any well prepared student entering university. Moreover, this book will be popular with graduate students and researchers in mathematics due to its attractive and unusual treatment of fundamental topics. A set of well-written exercises at the end of each section allows new ideas to be instantly tested and reinforced.
This book offers a unique opportunity to understand the essence of one of the great thinkers of western civilization. A guided reading of Euclid's Elements leads to a critical discussion and rigorous modern treatment of Euclid's geometry and its more recent descendants, with complete proofs. Topics include the introduction of coordinates, the theory of area, history of the parallel postulate, the various non-Euclidean geometries, and the regular and semi-regular polyhedra.
Solutions of equations in integers is the central problem of number theory and is the focus of this book. The amount of material is suitable for a one-semester course. The author has tried to avoid the ad hoc proofs in favor of unifying ideas that work in many situations. There are exercises at the end of almost every section, so that each new idea or proof receives immediate reinforcement.
Suitable for college courses, this introductory text covers the language of mathematics, geometric sets of points, separation and angles, triangles, parallel lines, similarity, polygons and area, circles, and space and coordinate geometry. 1974 edition.
* Be Sure to Read The Details at The Bottom of This Page "The Four Pillars of Singing" is the world's most comprehensive and preferred home study program for vocal training in the world today. It has been sold in over 120 countries around the world and enjoys nearly a 100%, 5-Star reviews at Amazon.com and from customers around the world at www.TheFourPillarsofSinging.com. Voice expert and author Robert Lunte shows you exactly how to practice each vocal workout by demonstrating all the original TVS vocal exercises and providing detailed training routines that clearly show anyone that wants to get serious about voice training, exactly what to do. Included in the complete program, ( Book + Video/Audio Media + Online Course ), are all the elements of the original TVS vocal training method developed by Maestro Lunte and vocal training experts from around the world who collaborated on this system. Each vocal exercise can be viewed from four angles in HD video or listened to at your leisure in audio. Read, see and hear in the clearest possible way how to train your voice or sing along to solo piano tracks of all 40+ original vocal workouts. To accompany vocalists on piano full, notated sheet music is also provided. The system also offers over 40 lectures of the most cutting-edge, vocal techniques and training ideas available in the business. This is product has become popular for singers that are prepared to train, practice and do the work Lastly, The Four Pillars of Singing offers comprehensive training routines that give direction and guidance on how to train the TVS method and workouts. "The Four Pillars of Singing" ONLINE allows students of the TVS Method to take their training to a whole new level with the world's most comprehensive, learning management system for vocal training as an online course. Students can access the training content and book from any device, any where in the world. Students also have the option to download the source files. Now with "The Four Pillars of Singing" ONLINE you can learn from Robert Lunte with a comprehensive, online course work system to accompany your book. There truly is no other home study vocal training program that is more comprehensive, accessible, or highly rated by the industry then "The Four Pillars of Singing." We hope you will enjoy this vocal training experience. * Please Note: The complete version of The Four Pillars of Singing, includes an online course in addition to the book. The complete offering with the course includes: 135+ lesson course w/quizzes. (Become a TVS Certified Vocalist). 500+ videos & audio training content. 62 workouts in slow, medium & fast speed. Special sets for men & women. Demonstrations & step by step training routines that show you how to practice. 3 day FREE trial * Please Note: Used offerings of this product do will NOT provide you with access to the complete training program and course work online. To recieve the complete training program and online course work for "The Four Pillars of Singing," you must purchase a new offering. * Please Note: The login information you will need for the complete training program and course work will be provided to you by The Vocalist Studio. A special amazon.com purchase discount code will be provided to you to give you access to the complete training program. * Please Note: The Four Pillars of Singing and a hard copy of the book can also be purchased at http: //www.TheFourPillarsofSinging.com.
Projective geometry is one of the most fundamental and at the same time most beautiful branches of geometry. It can be considered the common foundation of many other geometric disciplines like Euclidean geometry, hyperbolic and elliptic geometry or even relativistic space-time geometry. This book offers a comprehensive introduction to this fascinating field and its applications. In particular, it explains how metric concepts may be best understood in projective terms. One of the major themes that appears throughout this book is the beauty of the interplay between geometry, algebra and combinatorics. This book can especially be used as a guide that explains how geometric objects and operations may be most elegantly expressed in algebraic terms, making it a valuable resource for mathematicians, as well as for computer scientists and physicists. The book is based on the author’s experience in implementing geometric software and includes hundreds of high-quality illustrations.
This text focuses on developing an intimate acquaintance with the geometric meaning of curvature and thereby introduces and demonstrates all the main technical tools needed for a more advanced course on Riemannian manifolds. It covers proving the four most fundamental theorems relating curvature and topology: the Gauss-Bonnet Theorem, the Cartan-Hadamard Theorem, Bonnet’s Theorem, and a special case of the Cartan-Ambrose-Hicks Theorem.
