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\begin{center} {\Large\bf V63.0348 Honors Algebra I, Fall 15} \end{center}
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Time & Tuesday, Thursday 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/algebra15f/index.html\\
T.A. & TBA \\
TA Session Time & TBA \\
TA Session Place & TBA \\
Midterm & TBA \\
Final Exam & TBA \\
Final Exam & place TBA \\
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\par Over the year we will basically cover three kinds of structures, Groups (chapter 2),
Rings (chapter 3), and Fields (chapter 5). Spring 2016 ends with Galois Theory, with
special notes. Our emphasis is more on groups in this (Fall) course, the other topics
will be covered in more detail in the second term. (Students are NOT required to take
the second term V63.0349 and, indeed, many do not.)
Throughout, number theory provides a wealth of examples and applications.
On the next page 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.
Submission of assignments
(unless clearly marked otherwise) is {\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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CLASS & TOPIC & CHAPTER \\
Sept 3 & Symmetries of Regular $n$-gon & \\
8 & GROUPS, a start & 2.1,2.2 \\
10 & Subgroups, Cosets & 2.3,2.4 \\
15 & Some Counting & 2.5 \\
17 & Normal Subgroups & 2.6 \\
22 & Homomorphisms & 2.7 \\
24 & Homomorphisms & 2.7 \\
29 & Automorphisms & 2.8 \\
Oct 1 & Cayley's Theorem & -- \\
6 & Permuation Groups & 2.10 \\
8 & More Counting & 2.11 \\
13 & Monday Schedule & No Class \\
15 & More Counting & 2.11 \\
20 & MIDTERM & Tentative!! \\
22 & Direct Products & 2.13 \\
27 & Finite Abelian Groups & 2.14 \\
29 & RINGS, a start & 3.1 \\
Nov 3 & More Rings & 3.2 \\
5 & Homomorphisms, Ideals & 3.3,4 \\
10 & More Ideals & 3.5 \\
12 & Integers to Rationals & 3.6 \\
14 & Euclidean Rings & 3.7 \\
17 & The Gaussian Integers & 3.8 \\
19 & The Gaussian Integers & 3.8 \\
24 & Polynomial Rings & 3.9 \\
26 & Turkey \& Yams & No Class \\
Dec 1 & Polynomials over Rationals & 3.10 \\
3 & Finite Fields & 7.4 \\
8 & Magic Squares & -- \\
10 & Slack & -- \\
15 & Slack & --
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