August 31, 2009
Lie Groups: A Problem-Oriented Introduction via Matrix Groups
189 pp., hardcover, 2009. Series: MAA Textbooks
This textbook is an introduction to Lie groups for undergraduate students—and it requires background knowledge of only multivariable calculus and linear algebra. It emphasizes algebraic ideas, with just enough analysis to define the tangent space and the differential, and to explain the exponential map. Every chapter has a section called "Putting the pieces together" in which all definitions and results are collected and further readings are suggested.
Lie Groups, which works on the principle that students learn best when they are actively engaged in mathematics, offers 200 problems, ranging from the routine to the challenging.
The book can be used as supplementary reading in a linear algebra course, or as a primary text in a “bridge” course that helps students make the transition to courses that emphasize definitions and proofs, as well as for an upper-level elective.
1. 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 Appendix I. Linear algebra facts Appendix II. Paper assignment used at Mount Holyoke College Appendix III. Opportunities for further study. Solutions to selected problems Bibliography. Index. Notation.
About the Author:
Harriet Pollatsek (Mount Holyoke College, South Hadley, Mass.) has served as chair of the MAA's Committee on the Undergraduate Program in Mathematics and led the writing team for Undergraduate Programs and Courses in the Mathematical Sciences: CUPM Curriculum Guide 2004. She now chairs the MAA's Council on Programs and Students in the Mathematical Sciences.
Order Lie Groups from the MAA Bookstore or call 1.800.331.1622.
MAA Member Price: $51.95