MATH 447-01
Abstract Algebra
Syllabus for Spring 2023
Mon & Fri, 9:00 – 9:50am – 223 Gildemeister Hall
Wed, 8:00 – 9:50am – 223 Gildemeister Hall
Instructor: Dr. Eric Errthum Winona Email Username: eerrthum Office: 205 Gildemeister Hall Office Hours: See homepage. Or by appointment on any day.
Texts: “A Gentle Introduction to Abstract Algebra”
by B.A. Sethuraman -- A pdf version of this text can be found on Brightspace or here:
http://www.csun.edu/~asethura/GIAAFILES/GIAAV1.0/GIAAV1.0.pdf
“Abstract Algebra: Theory and Applications” by Thomas W. Judson –
Located here: http://abstract.ups.edu/aata/aata-toc.html
Prerequisite: MATH327: Foundations of Mathematics. (MATH347: Number Theory is also highly recommended.)
Course Website: http://course1.winona.edu/eerrthum/math447
About This Course: This course is designed to explore and classify abstract, algebraic structures through rigorous proof as well as provide a solid foundation on which to begin a study in the field of Algebra.
Nobody needs proofs in order to get something done, but understanding the theorems and their proofs will make anyone think more deeply about the domain, become better at problem solving, and feel more comfortable with the meaning - and limitations - of the practical procedures. -- Alon Amit (http://qr.ae/TUNYYw)
Expectations: Students who complete this course with a passing grade are expected to be able to demonstrate the following skills: (i) Mastery of prerequisite material (discrete math, basic proof writing, etc.), (ii) Memorize and use new definitions, (iii) Write algebra proofs, (iv) Explain the relevant conceptual ideas from algebra, (v) Communicate mathematical reasoning clearly in both an oral and written format.
Seems to me the goal of undergraduate math is to provide experience in concept formation (finding meaning in abstract definitions), a wide variety of examples of structures, relationships, and approaches to proof, and generally develop mathematical thinking. The actual content is less important than suitability of the topic for elementary development.
Remember that traditional undergraduate math is not a professional degree in that it is not intended to provide information needed for specific jobs. Not even graduate study. The expectation is that beginning graduate students should be able to pick basic stuff up quickly, not that they already know it. Non-academic employers of people with math degrees have the same expectation.
Questions about whether specific content is really needed downstream miss the point. -- Frank Quinn (https://mathoverflow.net/q/25916)
Grading: Oral
Homework (scaled as needed) 150
points------- 21.4%
Written
Homework (scaled as needed) 100
points------- 14.3%
Memory Quizzes
(scaled as needed) 150
points------- 21.4%
Relevancy
Presentations (scaled as needed) 50
points-------- 7.2%
Chapter Exams (2 @
50 points) 100
points------- 14.3%
Comprehensive
Final (oral & written) 150
points------- 21.4%
--------
700
points total
Grades: A = 90% (630 pts), B = 75% (525 pts), C = 60% (420 pts), D = 50% (350 pts). There will be no curving of individual assessments.
Homework: Homework will be completed in two ways:
· Oral Homework: According to the approximate schedule below, on Oral Homework days students will be chosen randomly to present individual solutions to problems from the homework assigned since the last homework day. For each problem presented, students will be graded a 0, 1, or 2 out of 2 corresponding to their level of preparedness (not necessarily correctness). When presenting a solution, you should be prepared to answer questions clarifying your work. It is not acceptable to write out a whole solution, but then when asked about a particular step to say “I don’t know.” To me this indicates you copied the homework from someone else without understanding it. If you miss an Oral Homework day, you will need to present on problems during office hours to make up the lost points.
· Written Homework: The written portion of the homework is due the period after a Homework Day. This work should be typed in LaTeX, stapled, and presented in order. Each problem will be graded 0 – 2 on its level of mathematical correctness and 0 – 2 on how well-written it is. The written homework problems will be a subset of the oral homework problems. (If you don’t know about LaTeX, I recommend using Overleaf.com. They have a tutorial “Learning LaTeX in 30-minutes”, but you will only need sections 1-4, 10, and maybe 12.)
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Don't just read it; fight it! Ask your own questions, look for your own
examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? What happens in the classical special case? What about the degenerate cases? Where does the proof use the hypothesis? ---
Paul R. Halmos |
Memory Quizzes: About once a week there will be a short quiz over the newly defined terms and simple proofs from the book. The best way to memorize these is to actually understand them. Mathematics is not a series of incantations. The second-best way to memorize these is flash cards.
Relevancy Presentations: Students should pick a topic that
illustrates the intersection of this course with their interests in Math, MathEd, or some other field. Some example topics are below.
Remember to give a good talk as you should have learned in CMST191/192 or
MATH/STAT/DSCI395. If you don’t know how, ask the
instructor.
Important Dates: Project Topic Okayed
by February 20, First Draft of
Slides Due March 29, Best Version of Slides Due April 10, Presentation Given April
26.