Abstract Algebra I

This mathematics course, which is mandatory for students in the pure mathematics track, aims at understanding the algebra concepts that are groups and rings. Groups and rings capture structures that are common to diverse mathematical objects. Once these structures are recognized, their properties are abstractly studied, which can then be applied to different mathematical contexts. This theory is essential for future algebra courses and anyone who will need to work with coding theory, cryptography, geometry or topology. Course Content Group and subgroup, automorphism, direct and semi-direct product, group isomorphism theorems, classification of finite abelian groups, group actions Ring and subring, characteristic, zero divisor, integral domain, ring homomorphism, ideal (two-sided, prime, maximal, principal), quotient ring, ring isomorphism theorem