University of Calgary

MATH 315 - Algebra I - Winter 2025

A broad overview of the elementary theory of groups, rings and fields. Group theory: cyclic, symmetric, alternating, dihedral and classical matrix groups, cosets and Lagrange's theorem, group homomorphisms, normal subgroups, quotient groups and the isomorphism theorem. Rings and fields: the integers modulo n, polynomial rings, ring homomorphisms, ideals, quotient rings the isomorphism theorem, unique factorization domains, principal ideal domains, Euclidean domains and the construction of finite fields.
This course may not be repeated for credit.


  • H(3-1T)


  • (formerly Pure Mathematics 315)


  • Mathematics 271 or 273.


  • Credit for Mathematics 315 and Pure Mathematics 317 will not be allowed.


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