Lie Groups Textbook by Mathematical Association of America | Algebra & Geometry Study Guide | Perfect for Math Students & Researchers

A novel approach, not expository, but a "learn by doing" text. Chapter 3 on the Tangent Space is explained nicely, leading into the general tangent space on an N-Manifold. In a distant context, "advanced" expositions of general relativity, Wald especially, now becomes clear as to what a "tangent" at a point is, as well as the "tangent space" at that point. All motivated by a simple visual analogy on S2. For someone with enough background in abstract algebraic structures and manifolds, one might wish, occasionally, to have the results stated for the general Lie Group rather than a matrix group, but the end notes on each chapter mostly put this in place.Highly recommended for budding undergraduates anxious for more challenges after the first Linear Algebra semester, and for Physics wanting to get right into the SO3 and SU2 groups. Plenty of very useful analogies and motivations from standard R2 and R3 analysis. The quite extensive use of The Hamiltonian Algebra in developing the topology of S3 and the isomorphism of S3 and SO3, in Chapter 2, feels very modern and right on.