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\begin{center} {\Large\bf V63.0349 Undergraduate Honors Algebra II, Spring 15} \end{center}
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Time & Monday, Wednesday 11:00-12:15 \\
Location & TBA \\
Instructor & Prof. Joel Spencer, wwh 829 \\
Phone & x8-3219\\ email & {lowercaselastname}@cims.nyu.edu \\
Office Hours & TBA \\
Text & Topics in Algebra \\
& i.n. herstein\\
{\tt Website:}& http://www.cs.nyu.edu/cs/faculty/spencer/algebra/index.html\\
T.A. & TBA \\
TA Session Time & TBA \\
TA Session Place & TBA \\
Midterm & TBA (in Class) \\
Final Exam & as scheduled by University \\
Final Exam & place TBA \\
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\par This is basically a course in Field Theory with Galois Theory
a highlight. We begin with elements of Rings and of Linear Algebra
over arbitrary fields. We consider field extensions of the rationals by
irrationals such as $\sqrt{2}$. We also study Finite Fields.
Throughout, number theory provides a wealth of
examples and applications.
On the opposite side is a
{\em rough} outline of the course. We expect to
cover these topics but not necessarily on the precise days indicated.
In addition there may be several topics
that will only be covered through lecture. Students
are responsible for all such material.
For the Galois Theory, notes specially prepared by Prof. Spencer
will be made available.
Submission of assignments
(unless clearly marked otherwise) will be {\em mandatory}.
\\ {\tt Special note:} Collaboration on the assignments is {\em encouraged}.
Each student must submit the assignment separately and must note on the
assignment the names of other students with which he/she has collaborated.
The final grade will be based $60\%$ on the Final Exam, $30\%$ on the
Midterm, and $10\%$ on the Homework.
But grades are not determined by an
algorithm, subjective factors such as class participation are a ``fudge
factor'' that can carry great weight.
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\noindent A {\em tentative} schedule. Check website for changes.
\\ H = Herstein, L= Lecture, N=Notes, GN= Special Galois Theory Notes
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CLASS & TOPIC & CHAPTER \\
Jan 26 & Rings & H3.1-3 \\
28 & Rings & H3.4,5,7 \\
Feb 2 & Polynomial Rings & H3.9 \\
4 & Polynomial Rings & H3.10\\
9 & Linear Algebra & H4.1 \\
11 & Linear Algebra & H4.2 \\
16 & NOCLASS!! & (Thanks George!) \\
18 & Extension Fields & H5.1 \\
23 & Extension Fields & H5.1 \\
25 & Roots of Polynomials & H5.3 \\
Mar 2 & Compass-Straightedge & H5.4 \\
4 & Finite Fields & H7.1,L \\
9 & Finite Fields & H7.1,L \\
11 & MIDTERM & (Tentative!) \\
16 & Spring & Break \\
18 & Spring & Break \\
23 & Magic Squares & L \\
25 & Galois & GN \\
30 & Galois & GN \\
Apr 1 & Galois & GN \\
6 & Galois & GN \\
8 & Galois & GN \\
13 & Galois & GN \\
15 & Galois & GN \\
20 & Galois & GN \\
22 & Cyclotomic Polys & L,N \\
27 & Representation by Radicals I & L \\
29 & Representation by Radicals II & L \\
May 4 & Fibonacci Plus & L,N \\
6 & Fibonacci mod p & L \\
11 & Slack & -- \\
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