Section I. Groups. 1. Background Material. 2. Basic Group Theory. 3. Simple Groups. 4. Group Action. Group Presentation and Representations. 5. Solvable and Nilpotent Groups. Section II. Rings and Fields. Chapter 7. Ring Theory. 8. Integral Domain Theory. 9. Field Theory. 10. Galois Theory.
Biography
Mark DeBonis received his PhD in Mathematics from University of California, Irvine, USA. He began his career as a theoretical mathematician in the field of group theory and model theory, but in later years switched to applied mathematics, in particular to machine learning. He spent some time working for the US Department of Energy at Los Alamos National Lab as well as the US Department of Defense at the Defense Intelligence Agency both as an applied mathematician of machine learning. He held a position as Associate Professor of Mathematics at Manhattan College in New York City, but later left to pursue research working for the US Department of Energy at Sandia National Laboratory as a Principal Data Analyst. His research interests include machine learning, statistics and computational algebra.
"I have reviewed several books on first-year abstract algebra recently, but this is undoubtedly the best. It covers everything from equivalence relations and basic number theory through groups, rings, fields, and Galois theory,taking in topics such as group action and the Sylow theorems on the way. The layout is traditional,with definitions,theorems, and proofs, but there are admirably many examples (I particularly admired the clarity they bring), and numerous by-the-way comments that are very well judged to clarify points that are often confusing."
-Dr. Owen Toller, The Mathematical Gazette
