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Feb 05, 2025
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MA 385 - Modern Algebra with Applications3 lecture hours 0 lab hours 3 credits
Course Description
This course is an introduction to abstract algebra with a focus on elementary group theory and some of its applications. Topics include modular arithmetic, groups, subgroups, isomorphism, external direct products, rings, integral domains and fields. Applications include error checking/correction and the RSA encryption algorithm. (prereq: MA 383 or MA 2830 or MA 2310 )
Course Learning Outcomes
Upon successful completion of this course, the student will be able to:
- 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
Prerequisites by Topic
Course Topics
- Division algorithm, Euclidean algorithm, modular arithmetic and error-checking
- Binary operations and groups
- Finite groups and subgroups
- Cyclic groups
- Mappings and isomorphisms
- External direct products
- RSA encryption and modular arithmetic with large numbers
- Fundamental Theorem of Finite Abelian Groups
- Rings
- Impossible constructions
- Reviews
- Exams
Coordinator
Dr. Anthony van Groningen
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