Group Theory Under The Microscope
MP4 | Video: h264, 1920x1080 | Audio: AAC, 44.1 KHz
Language: English | Size: 15.25 GB
| Duration: 17h 27m
Groups, Isomorphism, Actions
What you'll learn
Basic definitions of group theory: group, subgroup, group homomorphism, normal subgroups
Direct product of groups, isomorphism theorems
Group actions
Sylow's theorems
Requirements
Although there'll be an extra section for a brief recalling you still need to know confidently: school algebra, naive set theory, basics from linear algebra.
Description
This course covers the fundamentals of group theory from scratch.StructureThis course is intended to watch in a strict order as proposed to avoid some confusions. Each lecture covers important definitions and crucial theorems with detailed proofs for expanding knowledge of group theory further. For a better reasoning examples are provided as well. For reinforcing the completed lecture a pdf file with practical problems are furnished.PrerequisitesThis is in principle suitable for beginners provided that one has a grasp of school algebra, some proof techniques, naive set theory and basic number theory. Latter two would be recalled in brief.Who might want to studyIt is required for any mathematician to retain some facts about group theory, especially for those who pursuits doing research in algebra further. Also the group theory will be helpful if you want to study: algebraic topology, ring theory, fields.This might be also suitable for computer science students as well, so that one can build a rigorous theory based on this language, seek for symmetries or optimize some algorithms.UpdatesGroup Theory under the microscope is a dynamic course, meaning that videos might be updated, content and problem sets might be expanded, minor issues might be fixed.What's expected to add:Sylow's theoremsSimplicity of A_nFree groupsComposition series
Suitable for undergraduate students if you want to do research in the future.