A Vector Space Approach to Geometry (Dover Books on Mathematics)

Book Details

• Author: Melvin Hausner

• Publisher: Dover

• Language: English

• Edition: Reprint

• ISBN: 9780486829128

• Pages: 416

• Cover: Paperback

• Dimensions:

  • 8.5 x 5.5 x 1.0 inches

About The Book

Geometry and Linear Algebra by Melvin Hausner offers a unique exploration of the relationship between two core fields of mathematics: geometry and linear algebra. Hausner challenges the traditional view of geometry as an independent subject by emphasizing its deep connection with linear algebra, providing readers with a fresh perspective on both disciplines.

Key features of the book include:

• Geometric Motivations: The text showcases how geometry can be better understood through the use of linear algebra, revealing the underlying geometric motivations in vector space theory and matrix theory.

• Interdisciplinary Insights: Hausner’s exploration goes beyond mathematics, discussing the role of geometry in fields like physics, analysis, and group theory, as well as its applications in understanding probability, determinant theory, and function spaces.

• Key Mathematical Concepts: The book offers accessible explanations of complex topics like barycentric coordinates, determinants, and the particle problem, making them approachable for students and math enthusiasts.

• Systematic Approach: The treatment is both systematic and clear, providing step-by-step explanations, allowing readers to grasp geometric concepts and their importance in various branches of mathematics.

• Axiomatic Development: In-depth discussions of axiomatic developments, such as the introduction of determinants in the context of area and volume, make the book a valuable resource for students in both mathematics and science.

This book is ideal for students, educators, and mathematically inclined readers looking to gain a deeper understanding of the interplay between geometry and linear algebra. Its clear explanations and practical approach will inspire readers to appreciate the beauty and utility of these interconnected fields.