This course is an introduction to abstract mathematical structures, principally groups, and rings. Students investigate axiomatic and abstract structures by exploring elementary group, ring, and field theory. They examine the properties of Symmetry Groups, Permutation Groups, and subgroups of the Real Numbers, homomorphisms, and isomorphisms and refine proof-writing and proof reading skills.Prerequisites: MAT 2420 Calculus II and MAT 2880 Mathematical Rigor.