Algebra, Topology, Differential Calculus, and
Optimization TheoryFor Computer Science and Machine LearningJean Gallier and Jocelyn Quaintance
Department of Computer and Information ScienceUniversity of Pennsylvania
Philadelphia, PA 19104, USA
e-mail: jean@cis.upenn.educ:copyright: Jean GallierAugust 2, 20192ContentsContents 31 Introduction 172 Groups, Rings, and Fields 19
2.1 Groups, Subgroups, Cosets . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2 Cyclic Groups . . . . . . . . . .
1