The three primary topics of this course are groups, rings, and fields. Groups will be studied, including homomorphisms, normal subgroups, and the symmetric and alternating groups. The theorems of Lagrange, Cauchy, and Sylow will be developed and proven. Rings, including subrings, ideals, quotient rings, homomorphisms, and integral domains will be covered. Lastly, finite and infinite fields will be discussed. Prerequisite: MATH295.