|aLie groups : |ba problem-oriented introduction via matrix groups / |cHarriet Pollatsek.
|a[Washington, D.C.] : |bMathematical Association of America, |cc2009.
|axii, 177 p. : |bill. ; |c27 cm.
|aIncludes bibliographical references (p. 169-170) and indexes.
|a1. Symmetries of vector spaces -- 2. Complex numbers, quaternions and geometry -- 3. Linearization -- 4. One-parameter subgroups and the exponential map -- 5. Lie algebras -- 6. Matrix groups over other fields.
This textbook is a complete introduction to Lie groups for undergraduate students. The only prerequisites are multi-variable calculus and linear algebra. The emphasis is placed on the algebraic ideas, with just enough analysis to define the tangent space and the differential and to make sense of the exponential map. This textbook works on the principle that students learn best when they are actively engaged. To this end nearly 200 problems are included in the text, ranging from the routine to the challenging level. Every chapter has a section called 'Putting the pieces together' in which all definitions and results are collected for reference and further reading is suggested.