Math 501 Course Webpage
Algebraic Structures I
Fall 2017, Duke University
General information |
Course description |
Lecture notes |
Homework schedule |
Lectures: Wednesday and Friday, 15:05 – 16:20, Physics Building 227
Text: Abstract Algebra,
by David S. Dummit and Richard M. Foote (third edition)
Topics in Algebra
Contact information for the Instructor
Name: Professor Ezra Miller
Address: Mathematics Department,
Duke University, Box 90320,
Durham, NC 27708-0320
Office: Physics 209
Phone: (919) 660-2846
Course webpage: you're already
looking at it... but it's
Tuesday 14:00 – 15:00 &
Wednesday 12:00 – 13:15, in Physics 209
Groups encapsulate the notion of symmetry. They constitute the
simplest way to compose a single type of invertible operation,
such as addition of numbers, multiplication of matrices with
nonzero determinant, rotations of spheres, rigid motions of
polygons and polyhedra, or permutations of sets of objects.
The study of groups in this course includes decompositions,
enumerations, quotients, and actions.
- quotient groups
- group actions
- permutation representations
- Sylow theorems
- structure theorem over PID
Rings combine two operations: addition and multiplication. In
familiar situations, particularly the integers and univariate
polynomials, interactions between the two operations lead to
fundamental theorems concerning factorization into primes.
What results is a main goal of the course: a single structure
theorem that classifies all finite abelian groups and also
produces Jordan canonical forms of linear transformations.
Math 501 is a demanding course. Students are expected to have
a firm grasp of linear algebra before beginning the course. In
addition, it is expected that every student begins the course
comfortable and proficient at writing rigorous mathematical
Check here two weeks before each homework is due, or 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; other times, I might simply have neglected to copy the
assignment into the appropriate directory, or to set the permissions
properly. (I do try to check these things, of course, but sometimes
web pages act differently for users inside and outside the Math
- Reading assignments are included at the top of each homework
- Due dates for the five homework assignments this semester are
listed in the table below.
- All assignments, including the midterms, will be
take-home. All are due at the start of class time on the
- All solutions you turn in, including midterms, homework, and
term projects, must be typewritten using the provided LaTeX
template. Communicating your ideas is an integral part of
mathematics. In addition to the usual PDF files, LaTeX source
files for each of the homework assignments as well as each of
the midterms will be provided. You should use these as LaTeX
templates for your solutions, by filling in your responses in
those files. I am happy to answer any questions you might have
about LaTeX, although you should ask your classmates first.
- Turn in your homework solutions to me by email. Send at
least your .tex file (the grader or I may comment on your TeX
usage); if you include your .pdf file as well then it can serve
as verification that your system produces the same output as
ours do. Do not email your midterm solutions to the
grader; email them only to me.
- Collaboration on homework is encouraged, 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 or
electronic sources—except for the
"Text" listed above"—is
allowed for either of the two midterms or the final exam.
- 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 dual rank theorem" is
not precise; in contrast, "[Climenhaga, Theorem 5.10]" is.
Theorems are often known by many names, so I'm likely not to
recognize many theorems by names you might attach.
| Homework #1
|| Wed. 13 September
||§1.1–1.6, §2.1, §2.3
| Homework #2
|| Wed. 27 September
||§2.2, §2.4, §3.1–3.3, §5.1
| Midterm 1
|| Wed. 4 October
||§1.7, §4.1, §3.5
| Homework #3
|| Fri. 20 October
||§4.2–4.6, §5.3–5.5, §6.3
| Homework #4
|| Fri. 3 November
| Midterm 2
|| Fri. 10 November
| Homework #5
|| Fri. 1 December
||§10.1–10.3, §10.5, §12.1
| Final exam
|| Wed. 13 December, noon
Final course grades:
Participation in class discussion and office hours can contribute
substantially to your homework score.
- 50% Homework
- 30% Midterms
- 20% Final exam
University academic links
I will do my best to keep this web page for Math 403 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
templates for this webpage many years ago.
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 Duke University.
Fri Nov 17 04:54:50 EST 2017
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