{"id":400,"date":"2018-12-27T15:15:02","date_gmt":"2018-12-27T23:15:02","guid":{"rendered":"https:\/\/blogs.ubc.ca\/organizingchaos\/?p=400"},"modified":"2018-12-27T16:22:34","modified_gmt":"2018-12-28T00:22:34","slug":"course-review-math-322","status":"publish","type":"post","link":"https:\/\/blogs.ubc.ca\/organizingchaos\/2018\/12\/27\/course-review-math-322\/","title":{"rendered":"Course Review: MATH 322"},"content":{"rendered":"

Introduction to Group Theory<\/b><\/h4>\n
\n
\n
\n
\n
“We say groups have a rich structure because it keeps us mathematicians in business”<\/div>\n
<\/div>\n
<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n

Text:\u00a0<\/strong>Basic Algebra I: Second Edition<\/p>\n

Prof:<\/strong>\u00a0 Dr Vinayak Vatsal<\/p>\n

Nike is a humorous professor who cares about his students. The homework he set was also useful in getting a mastery of the material in the course. Unfortunately, the textbook was made up of large, listless walls of text that prove half a dozen theses arbitrarily\u00a0before deciding to declare that a theorem worthy of a name has been proven. Thus it cannot be readily used as a reference book and is difficult to read.\u00a0The classes were significantly better, but from time to time also suffered from a lack of direction and interest. Group theory, on the other hand, is a fascinating field and the proofs often use a lot of creativity.<\/p>\n

\n

Difficulty<\/strong><\/p>\n

 <\/p>\n

I found the material in this course difficult, but since it was an introductory class, I felt I had enough time to master the relevant concepts. Unfortunately, the relatively few iClickers were weighted 10% of the grade and the exams were not difficult but punished small mistakes a lot. Also, the final exam used a peculiar notation and seemed almost entirely about symmetric groups and had no questions about abstract group theory. As a result, the average was quite low in this course.<\/p>\n

Key Concepts<\/strong><\/p>\n

Groups<\/p>\n

Subgroups<\/p>\n

Action on groups<\/p>\n

Orbit-Stabilizer<\/p>\n

Class equation<\/p>\n

Finite Abelian groups<\/p>\n

Isomorphism Theorems<\/p>\n

Homomorphism<\/p>\n

Free group and generators<\/p>\n

Hard Concepts<\/strong><\/p>\n

Action on groups: Useful to get some practice with a couple of these actions before one can start seeing the action that occurs in problems<\/p>\n

Proving isomorphisms\/finding a bijection: Often one can use the obvious or ‘canonical’ map, other times you need to do some clever<\/p>\n

Counting elements of a certain order in abelian groups: Can make careless mistakes, double check your answer!<\/p>\n

Conclusion<\/strong><\/p>\n

An interesting topic, the homework problems were fun, wished the textbook and exams were structured differently.<\/p>\n","protected":false},"excerpt":{"rendered":"

Introduction to Group Theory “We say groups have a rich structure because it keeps us mathematicians in business” Text:\u00a0Basic Algebra I: Second Edition Prof:\u00a0 Dr Vinayak Vatsal Nike is a humorous professor who cares about his students. The homework he set was also useful in getting a mastery of the material in the course. Unfortunately, […]<\/p>\n","protected":false},"author":28516,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[281864],"tags":[3957456,1171106,3957455,3957453,3957454,3957452,37,3957451],"class_list":["post-400","post","type-post","status-publish","format-standard","hentry","category-course-reviews","tag-group-theory","tag-honours-math","tag-introduction-to-group-theory","tag-math-322","tag-math322","tag-nike-vatsal","tag-ubc","tag-vinayak-vatsal"],"_links":{"self":[{"href":"https:\/\/blogs.ubc.ca\/organizingchaos\/wp-json\/wp\/v2\/posts\/400","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.ubc.ca\/organizingchaos\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.ubc.ca\/organizingchaos\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.ubc.ca\/organizingchaos\/wp-json\/wp\/v2\/users\/28516"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.ubc.ca\/organizingchaos\/wp-json\/wp\/v2\/comments?post=400"}],"version-history":[{"count":2,"href":"https:\/\/blogs.ubc.ca\/organizingchaos\/wp-json\/wp\/v2\/posts\/400\/revisions"}],"predecessor-version":[{"id":407,"href":"https:\/\/blogs.ubc.ca\/organizingchaos\/wp-json\/wp\/v2\/posts\/400\/revisions\/407"}],"wp:attachment":[{"href":"https:\/\/blogs.ubc.ca\/organizingchaos\/wp-json\/wp\/v2\/media?parent=400"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ubc.ca\/organizingchaos\/wp-json\/wp\/v2\/categories?post=400"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ubc.ca\/organizingchaos\/wp-json\/wp\/v2\/tags?post=400"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}