Author : James Casey
Publisher : Springer Science & Business Media
Page : 305 pages
File Size : 26,45 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 3322802744
This introductory book is organized around a collection of simple experiments which the reader can perform at home or in a classroom setting. Methods for physically exploring the intrinsic geometry of commonplace curved objects (such as bowls, balls and watermelons) are described. The concepts of Gaussian curvature, parallel transport, and geodesics are treated.
Author : Iva Stavrov
Publisher : American Mathematical Soc.
Page : 243 pages
File Size : 50,2 MB
Release : 2020-11-12
Category : Education
ISBN : 1470456281
This book introduces advanced undergraduates to Riemannian geometry and mathematical general relativity. The overall strategy of the book is to explain the concept of curvature via the Jacobi equation which, through discussion of tidal forces, further helps motivate the Einstein field equations. After addressing concepts in geometry such as metrics, covariant differentiation, tensor calculus and curvature, the book explains the mathematical framework for both special and general relativity. Relativistic concepts discussed include (initial value formulation of) the Einstein equations, stress-energy tensor, Schwarzschild space-time, ADM mass and geodesic incompleteness. The concluding chapters of the book introduce the reader to geometric analysis: original results of the author and her undergraduate student collaborators illustrate how methods of analysis and differential equations are used in addressing questions from geometry and relativity. The book is mostly self-contained and the reader is only expected to have a solid foundation in multivariable and vector calculus and linear algebra. The material in this book was first developed for the 2013 summer program in geometric analysis at the Park City Math Institute, and was recently modified and expanded to reflect the author's experience of teaching mathematical general relativity to advanced undergraduates at Lewis & Clark College.
Author : Shlomo Sternberg
Publisher : Courier Corporation
Page : 418 pages
File Size : 47,74 MB
Release : 2013-04-17
Category : Mathematics
ISBN : 0486292711
Expert treatment introduces semi-Riemannian geometry and its principal physical application, Einstein's theory of general relativity, using the Cartan exterior calculus as a principal tool. Prerequisites include linear algebra and advanced calculus. 2012 edition.
Author : Siri Chongchitnan
Publisher : Springer Nature
Page : 521 pages
File Size : 46,40 MB
Release : 2023-12-01
Category : Computers
ISBN : 303146270X
This book provides a unique tour of university mathematics with the help of Python. Written in the spirit of mathematical exploration and investigation, the book enables students to utilise Python to enrich their understanding of mathematics through: Calculation: performing complex calculations and numerical simulations instantly Visualisation: demonstrating key theorems with graphs, interactive plots and animations Extension: using numerical findings as inspiration for making deeper, more general conjectures. This book is for all learners of mathematics, with the primary audience being mathematics undergraduates who are curious to see how Python can enhance their understanding of core university material. The topics chosen represent a mathematical overview of what students typically study in the first and second years at university, namely analysis, calculus, vector calculus and geometry, differential equations and dynamical systems, linear algebra, abstract algebra and number theory, probability and statistics. As such, it can also serve as a preview of university mathematics for high-school students. The prerequisites for reading the book are a familiarity with standard A-Level mathematics (or equivalent senior high-school curricula) and a willingness to learn programming. For mathematics lecturers and teachers, this book is a useful resource on how Python can be seamlessly incorporated into the mathematics syllabus, assuming only basic knowledge of programming.
Author : Victor Andreevich Toponogov
Publisher : Springer Science & Business Media
Page : 215 pages
File Size : 36,55 MB
Release : 2006-09-10
Category : Mathematics
ISBN : 0817644024
Central topics covered include curves, surfaces, geodesics, intrinsic geometry, and the Alexandrov global angle comparision theorem Many nontrivial and original problems (some with hints and solutions) Standard theoretical material is combined with more difficult theorems and complex problems, while maintaining a clear distinction between the two levels
Author : Harold Abelson
Publisher : MIT Press
Page : 502 pages
File Size : 22,11 MB
Release : 1986-07-09
Category : Computers
ISBN : 9780262510370
Turtle Geometry presents an innovative program of mathematical discovery that demonstrates how the effective use of personal computers can profoundly change the nature of a student's contact with mathematics. Using this book and a few simple computer programs, students can explore the properties of space by following an imaginary turtle across the screen. The concept of turtle geometry grew out of the Logo Group at MIT. Directed by Seymour Papert, author of Mindstorms, this group has done extensive work with preschool children, high school students and university undergraduates.
Author : L.Christine Kinsey
Publisher : Springer Science & Business Media
Page : 524 pages
File Size : 49,53 MB
Release : 2006-05-09
Category : Mathematics
ISBN : 9781930190092
This book will appeal to at least three groups of readers: prospective high school teachers, liberal arts students, and parents whose children are studying high school or college math. It is modern in its selection of topics, and in the learning models used by the authors. The book covers some exciting but non-traditional topics from the subject area of geometry. It is also intended for undergraduates and tries to engage their interest in mathematics. Many innovative pedagogical modes are used throughout.
Author : Malgorzata Marciniak
Publisher : Springer
Page : 452 pages
File Size : 30,55 MB
Release : 2009-10-01
Category : Computers
ISBN : 3642047351
For many years Leonard Bolc has played an important role in the Polish computer science community. He is especially known for his clear vision in the development of artificial intelligence, inspiring research, organizational and editorial achievements in areas such as e.g.: logic, automatic reasoning, natural language processing, and computer applications of natural language or human-like reasoning. This Festschrift volume, published to honor Leonard Bolc on his 75th birthday includes 17 refereed papers by leading researchers, his friends, former students and colleagues to celebrate his scientific career. The essays present research in the areas which Leonard Bolc and his colleagues investigated during his long scientific career. The volume is organized in three parts; the first is devoted to logic - the domain which was one of the most explored by Leonard Bolc himself. The second part contains papers focusing on different aspects of computational linguistics; the third part comprises papers describing different applications in which natural language processing or automatic reasoning plays an important role.
Author : Catherine A. Gorini
Publisher : Cambridge University Press
Page : 244 pages
File Size : 40,85 MB
Release : 2000-10-12
Category : Mathematics
ISBN : 9780883851647
Beginning with art and architecture and culminating with science and mathematics itself, this book discusses geometric ideas and their many applications throughout history. These range from ancient to modern, concrete to abstract, and familiar to cutting edge. Each chapter is written by a leading expert or pioneer in their own field, and the book should be a valuable resource for students and teachers of geometry alike.
Author : L. Christine Kinsey
Publisher : John Wiley & Sons
Page : 960 pages
File Size : 48,76 MB
Release : 2010-04-19
Category : Mathematics
ISBN : 0470499494
This new book for mathematics and mathematics education majors helps students gain an appreciation of geometry and its importance in the history and development of mathematics. The material is presented in three parts. The first is devoted to a rigorous introduction of Euclidean geometry, the second covers various noneuclidean geometries, and the last part delves into symmetry and polyhedra. Historical contexts accompany each topic. Exercises and activities are interwoven with the text to enable the students to explore geometry. Some of the activities take advantage of geometric software so students - in particular, future teachers - gain a better understanding of its capabilities. Others explore the construction of simple models or use manipulatives allowing students to experience the hands-on, creative side of mathematics. While this text contains a rigorous mathematical presentation, key design features and activities allow it to be used successfully in mathematics for teachers courses as well.
