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Oct 18, 2024
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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 235 or equivalent, junior standing)
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
• No prerequisites by topic appended
Course Topics
• 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)
Coordinator
Edward Griggs
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