This course will examine concepts in algebra including: Patterns, arithmetic sequences, geometric sequences, arithmetic and algebra of the integers, least common multiple and greatest common divisor, The Fundamental Theorem of Arithmetic, The Division Algorithm and Euclidean Algorithm, modular arithmetic and systems of numbers, properties of groups and fields, the field of complex numbers, polynomial arithmetic and algebra, The Fundamental Theorem of Algebra, linear equations, matrix algebra determinants, and vectors. Students will engage with these concepts through proofs, problem solving and through activities used in middle school mathematics. Throughout the course students will be given opportunities to relate the mathematical concepts studied to the mathematical concepts they will be teaching.