**Prerequisite:** Completion of Geometry or Integrated Math 2.

Can you solve a geometry problem more easily if there is a square root of -1? Are “proofs” just for Geometry or can it apply to Algebra as well? This course is designed to explore advanced topics in algebra, from the point of view of operations and properties of operations. Students will gain a deeper understanding of algebra, and of problem-solving and how to think about mathematics. Students will prove facts of algebra from axioms, and will write both proofs and more informal reasoning. Topics include the familiar properties of operations (such as the distributive property) and unfamiliar properties of other operations (such as anticommutativity); number systems, √-1, and complex numbers; modular arithmetic ("clock arithmetic"); and an introduction to the concepts of group and ring. The atmosphere of the class is cooperative; the emphasis is on understanding why something is true and explaining it, not merely on obtaining answers. This course will introduce some topics covered in college-level Abstract Algebra and will provide additional preparation to students entering Algebra II or Integrated Math 3 and to students interested in engineering.