MATS 2103 Abstract Algebra Exam 2021

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MATS 2103: First Semester Examination, University of Bamenda, Faculty of Science, Department of Maths and Computer Science, Lecturer Nforba G., 12th March 2021: Question 1, defining 12 foundational concepts spanning logic, number theory and group theory (statement, proposition, divisor, g.c.d., relatively prime, congruence, injective function, group, homomorphism, monomorphism, isomorphism, kernel); Question 2, stating the Principle of Mathematical Induction, the Division Algorithm and the subgroup criterion, a truth-table/tautology check, a De Morgan's-law set proof, the infinitude of primes, and a modular-arithmetic proof; Question 3, the Euclidean Algorithm to find and express a g.c.d. as a linear combination, then solving a linear congruence; Question 4, two injective-function/set-image proofs; Question 5, verifying a custom binary operation forms an Abelian group, proving a log map is a group isomorphism, defining subgroups, and proving the centralizer and the kernel of a homomorphism are subgroups.