Math 5285H Course Webpage

Fundamental Structures of Algebra I

Fall 2008, University of Minnesota, Twin Cities Campus

General information

Lecture: MWF 10:10 – 11:00am, Vincent Hall 311

Contact information for the Instructor

Name: Prof. Ezra Miller (you can call me "Ezra")
Address: School of Mathematics, University of Minnesota, 206 Church St. SE, Minneapolis, MN 55455, U.S.A.
Office: Vincent Hall 451
Phone: (612) 624-4025
Email: ezramath.umn.edu
Webpage: http://math.umn.edu/~ezra
Course webpage: you're already looking at it... but it's http://math.umn.edu/~ezra/5285/5285.html
Office hours: Monday 1:25 &ndash 2:15 and Friday 11:15 &ndash 12:05

Course description

Course content:

Review of matrix theory and linear algebra
Vector spaces and linear transformations over abstract fields
Group theory, including normal subgroups, quotient groups, homomorphisms, class equation, and Sylow's theorems
Specific examples, including permutation groups, symmetry groups of geometric figures, and matrix groups

Prerequisites: The official guidelines say one of

MATH 2243 – Linear Algebra and Differential Equations
MATH 2373 – IT Linear Algebra and Differential Equations
MATH 2573H – Honors Calculus III

plus one of

MATH 2283 – Sequences, Series, and Foundations
MATH 3283W – Sequences, Series, and Foundations: Writing Intensive
MATH 2574H – Honors Calculus IV.

If you have not taken these classes, or their equivalent, it may still be possible for you to take MATH 5285H, but please see me so that we can talk about it. The main point is to have had previous exposure to matrices, linear algebra, determinants, and so on, plus experience with reading and writing mathematical proofs.

Homework

Tentative due dates for the five homework assignments this semester are listed in the table below. The midterms and the final exam will be take-home. The main differences between the three exams and the five ordinary homeworks will be:

I encourage collaboration on homework, as long as each person understands the solutions, writes them up using their own words, and indicates—on the homework page—who their collaborators were. In contrast, no collaboration or consultation of human sources is allowed for any of the three exams, although they will be open-book, open-library, and open-web.
You will have one week to complete each exam, but two weeks for each homework assignment.
You must type your solutions to the midterms and the final.
Please also print your typed solutions double-sided.
You must cite sources in your solutions. If you rely on so-and-so's theorem, then you must state the theorem and tell me where you found it. Be specific: "the primality lemma" is not precise; in contrast, "Lemma 2.8 in Chapter 3 of the textbook" is. Theorems are often known by many names, so I'm likely not to recognize many theorems by names you might attach.

Unless otherwise specified, all problems are from Artin's textbook, Algebra. Check here two weeks before each homework is due, and one week before each exam is due, for the specifics of the assignments. If an assignment hasn't been posted, and you think it should have been, please do email me. Sometimes I encounter problems (such as, for example, the department's servers going down) while posting assignments.

Assignment Due Date Problems

Homework #1
solutions in PDF
solutions in LaTeX

Wed. 17 September

1.1: 6, 7, 10, 11(b,c), 12, 16
1.2: 2, 6, 12, 13, 17
1.3: 1, 5, 8, 12
1.4: 1, 2, 5
1.5: 1, 3
1.Misc: 3, 5, 7
Homework #2
solutions in PDF
solutions in LaTeX

Wed.   1 October

2.1: 5
2.2: 2, 5, 16, 19, 21
2.3: 1, 11, 14
2.4: 6, 12, 13, 22
2.5: 6
2.6: 5, 11
2.7: 7, 8
2.8: 4, 9
2.9: 8
2.10: 6
*Bonus* 2.Misc: 12
Midterm 1 Wed.   8 October questions (in LaTeX format) answers
Homework #3
solutions in PDF
solutions in LaTeX

Wed. 22 October

3.1: 2
3.2: 7, 10(b), 11, 15
3.3: 1, 4, 7, 10, 16
3.4: 2, 7, 11
3.6: 2
3.Misc: 1
4.1: 4, 8
Homework #4
solutions in PDF
solutions in LaTeX

Wed.   5 November

4.1: 7
4.2: 4, 9
4.3: 6, 9(a), 10
4.4: 1, 4, 8 (every "n-1" should be "n"), *Bonus*: 13
4.5: 8
4.6: 1, 5(a,b,d); do 5(d) only over the real numbers
4.7: 2(a-c), 7
4.8: 1(a), 5
4.Misc: 1, 18(a)
Midterm 2 Wed. 12 November questions (in LaTeX format) answers
Homework #5
solutions in PDF
solutions in LaTeX

Wed. 26 November

5.2: 15
5.3: 1, 4(b,c)
5.5: 10(a,b), 12
5.6: 5
5.7: 2, 3
5.8: 3
5.9: 3
5.Misc: 2(b,c)
6.1: 6, 12
6.2: 4, 7, 10
6.3: 13
Final exam Wed. 10 December questions (in LaTeX format)

Assignment	Due Date	Problems
Homework #1 solutions in PDF solutions in LaTeX	Wed. 17 September	1.1: 6, 7, 10, 11(b,c), 12, 16 1.2: 2, 6, 12, 13, 17 1.3: 1, 5, 8, 12 1.4: 1, 2, 5 1.5: 1, 3 1.Misc: 3, 5, 7
Homework #2 solutions in PDF solutions in LaTeX	Wed. 1 October	2.1: 5 2.2: 2, 5, 16, 19, 21 2.3: 1, 11, 14 2.4: 6, 12, 13, 22 2.5: 6 2.6: 5, 11 2.7: 7, 8 2.8: 4, 9 2.9: 8 2.10: 6 Bonus 2.Misc: 12
Midterm 1	Wed. 8 October	questions (in LaTeX format) answers
Homework #3 solutions in PDF solutions in LaTeX	Wed. 22 October	3.1: 2 3.2: 7, 10(b), 11, 15 3.3: 1, 4, 7, 10, 16 3.4: 2, 7, 11 3.6: 2 3.Misc: 1 4.1: 4, 8
Homework #4 solutions in PDF solutions in LaTeX	Wed. 5 November	4.1: 7 4.2: 4, 9 4.3: 6, 9(a), 10 4.4: 1, 4, 8 (every "n-1" should be "n"), Bonus: 13 4.5: 8 4.6: 1, 5(a,b,d); do 5(d) only over the real numbers 4.7: 2(a-c), 7 4.8: 1(a), 5 4.Misc: 1, 18(a)
Midterm 2	Wed. 12 November	questions (in LaTeX format) answers
Homework #5 solutions in PDF solutions in LaTeX	Wed. 26 November	5.2: 15 5.3: 1, 4(b,c) 5.5: 10(a,b), 12 5.6: 5 5.7: 2, 3 5.8: 3 5.9: 3 5.Misc: 2(b,c) 6.1: 6, 12 6.2: 4, 7, 10 6.3: 13
Final exam	Wed. 10 December	questions (in LaTeX format)

Grading policies

Homework policies

See above for policies regarding collaboration and other outside sources on homework and exams.
Late homework and exams will not be accepted. Early homework or exams are fine: early homework can be left in my mailbox in the School of Math mailroom near Vincent Hall 105; early exams must be handed to me in person.
Homework solutions should be thoroughly explained: the grader is told not to give credit for an unsupported answer. Complaints about the grading should be brought to me.

Final course grades will be determined as follows:

Homework = 50% of grade
Each of two midterms = 15% of grade
Final exam = 20% of grade

Other useful texts

All of the following are on reserve in the Math Library.

Level Title Author(s), Publisher, date

Lower A concrete introduction to higher algebra Childs, Springer–Verlag 1995

Lower Contemporary abstract algebra Gallian, Houghton–Mifflin 1998

Same Topics in algebra Herstein, Wiley & Sons 1999

Higher Abstract algebra Dummit and Foote, Wiley & Sons 2004

Level	Title	Author(s), Publisher, date
Lower	A concrete introduction to higher algebra	Childs, Springer–Verlag 1995
Lower	Contemporary abstract algebra	Gallian, Houghton–Mifflin 1998
Same	Topics in algebra	Herstein, Wiley & Sons 1999
Higher	Abstract algebra	Dummit and Foote, Wiley & Sons 2004

Links

Math links

Joel Roberts's interactive polyhedra, for demonstrations of symmetry
Eric Weisstein's World of Mathematics
PlanetMath Encyclopedia

University academic links

Official University schedule for all courses given in the School of Mathematics in Fall 2008.
Course catalog of all courses offered by the School of Mathematics, including brief course descriptions.
Official University calendar for academic year 2008–2009.
cancel/add and refund deadlines for Fall 2008.
Fundamental University policies concerning scholastic conduct and related matters.

Departmental links

The fine print

I will do my best to keep this web page for Math 5285H current, but this web page is not intended to be a substitute for attendance. Students are held responsible for all announcements and all course content delivered in class.

Many thanks are due to Jeremy Martin and Vic Reiner, who provided the template and other information for this webpage.

The views and opinions expressed in this page are strictly those of the page author. The contents of this page have not been reviewed or approved by the University of Minnesota.

ezramath.umn.edu
Tue Dec 2 22:35:37 CST 2008

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