This textbook offers an introductory yet rigorous approach to linear algebra by grounding abstract concepts in geometric intuition. The text progresses from finite-dimensional vector spaces and directed line segments to more complex topics like linear transformations, matrices, and inner product spaces. By focusing on the "viewpoint of geometry," Moore helps students visualize algebraic operati…
This classic textbook provides a rigorous and systematic treatment of Euclidean geometry intended for readers who have a background in basic mathematics but seek a deeper, proof-oriented understanding. Unlike introductory texts that rely on visual intuition, Moise constructs geometry from a modern axiomatic foundation—specifically focusing on betweenness, congruence, and continuity. The "adva…
This volume is part of a two-volume English translation of the Russian work Geometric Transformations, focusing specifically on collinearity-preserving transformations within the projective plane. It introduces the construction of the projective plane and details essential concepts such as projective mappings, fundamental theorems, cross ratios, and harmonic sets. The text also covers inversion…
Part of the Undergraduate Texts in Mathematics series, this book offers a rigorous introduction to geometry through the study of isometries and transformations. Rather than focusing on classical synthetic proofs, Martin uses group theory to explore the symmetries of the plane, including reflections, rotations, translations, and glide-reflections. It covers sophisticated topics such as the class…
This book provides a systematic study of translation planes, a class of projective planes that admit a large group of elations. It explores their connections to algebraic structures such as quasifields and spreads, and presents key classification results. The work is aimed at researchers and graduate students in combinatorics and finite geometry.
Monte Carlo Methods by Hammersley and Handscomb is a classic foundational text in simulation and computational probability. It develops the theory and practice of Monte Carlo techniques for solving mathematical and statistical problems using random sampling. The book covers random number generation, variance reduction techniques, and applications to integration and stochastic systems. It remain…