Algebra I -- Fall 2018
Emory University
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| | Lecture Room: | E406
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| Lecture Time: | TuTh 1-2:15 |
| Final Exam: | TBA |
| Lecturer: | David Zureick-Brown |
| Office: | W430 MSC |
| Phone: | (608) 616-0153 |
| Email: | dzb@math.emory.edu |
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| Text: | See below |
| Office Hours: | by appointment (in W430) |
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Textbook
We will use Abstract
Algebra, 3rd Edition by David S. Dummit, Richard M. Foote.
About this course
We will cover roughly 1-16 of Dummit and Foote, and some additional topics.
Groups: cosets, Lagrange's theorem, normal subgroups and quotient
groups, three isomorphism theorems, symmetric groups, cycle
decomposition and signatures, dihedral groups, group action on sets
and proof of Sylow theorems, direct products, automorphism groups and
semidirect products, solvable and nilpotent groups p-groups, determination of groups of low orders, groups of order p^2 and p^3, simple groups.
Rings: Definitions and examples, unit groups, integral domains and their quotient fields, ideals, prime and maximal ideals, PID, Euclidean domains, factorisation in integral domains, UFD, PID's are UFD, Polynomial ring of a PID is a PID, examples from algebraic numbers and affine curves of UFD and non-UFD's, Noetherian rings, Hilbert Basis theorem.
Modules: homomorphism of R-modules, direct sums, free modules and the
universal property, Noetherian modules and their characterisation, structure theorem for modules over PID, consequences, structure theorem for finitely generated abelian groups and linear algebra (Jordan canonical form).
Syllabus
Here is an official pdf of the syllabus for this course. (There is no information on this pdf that is not on the webpage.)
Course details
This class will meet 28 times; there will be 2 exams and a final, and weekly homework (due in my mailbox, on Fridays).
Grading policy
The midterms are worth 25 percent.
The final exam will be comprehensive and will count for 25 percent.
Homework is worth 25 percent.
The midterm dates below are tenative (and likely to be adjusted), but the date of the final exam is set in stone;
| Homework | 25% | (Weekly) |
| Midterm I | 25% | (October 4 (Tentative)) |
| Midterm II | 25% | (Nov 8 (Tentative)) |
| Final Exam | 25% | (not scheduled yet) |
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Calculators, notes, and textbooks are not allowed in exams.
Homework
There will be homework assigned every week, usually on Thursday, due the following Friday, in my mailbox. There
will be many simple problems, checking your understanding of the
definitions, that will be collected and graded for completness but not
correctness. I will usually grade 3 of the longer problems in full detail.
The homework assignments are available at this link, and will be updated after each lecture.
Exams
The exam problems will be similar to the homework problems and examples/theorems/proofs from class (some will be identical, and some will be similar but not identical).
Plagarism Policy
For homework: you are free to consult any sources (animate or
inanimate) while doing your homework (working in groups is
encouraged!), but if you use anything (or anyone) other than your
class notes or the texts listed above, you should say so on your
homework -- please state at the end of every problem any sources used.
On the other hand, you are expected to make an honest attempt to do every problem on your own before consulting other sources. Remember that copying another student's work is a violation of the Honor Code and will be treated as such.
A good rule of thumb to avoid plagarism is the following -- when doing
the final write up of a problem, do not have any text books, web
pages, or classmate's write up in front of you. If you get stuck when
writing up an assignment, go back and look again; just make sure that
you organize the mathematics in your head before writing a proof
rather than copying a solution from some source. This is a
generous homework policy. Please do not abuse it.
