MA 385 - Modern Algebra with Applications

• Perform modular arithmetic operations including powers and inverses of large numbers
• Identify whether or not a set together with a binary operation is a group
• Relate divisibility facts to properties of cyclic groups
• Identify isomorphic groups
• Perform arithmetic operations with external direct products of cyclic groups
• Prove basic theorems involving groups
• Perform error-checking and error-correction computations including the ISBN system
• Use the RSA algorithm to encrypt and decrypt large numbers
• Solve second-degree equations in various rings
• Prove basic theorems involving rings

• None 

• Division algorithm, Euclidean algorithm, modular arithmetic and error-checking (4 classes)
• Binary operations and groups (3 classes)
• Finite groups and subgroups (3 classes)
• Cyclic groups (3 classes)
• Mappings and isomorphisms (3 classes)
• External direct products (3 classes)
• RSA encryption and modular arithmetic with large numbers (2 classes)
• Fundamental Theorem of Finite Abelian Groups (1 class)
• Rings (3 classes)
• Impossible constructions (1 class)
• Reviews (2 classes)
• Exams (2 classes)