Algebra II - Spring 2012 - V63.0344

Syllabus

Click here postscript LaTeX pdf for an outline and lots of information.

Instructor

Prof. Joel Spencer
wwh 729; x83219; {lowercaselastname}@cims.nyu.edu
Office Hours: Tu 2-4

Final Exam

ALL INFORMATION CONCERNING THE FINAL WILL BE POSTED HERE!

The final exam postscript LaTeX pdf

and the solutions postscript LaTeX pdf

No Notes, No Books, No "Call a Friend"!

The exam will have (tentatively) fourteen problems totally 200 points. You are to do all problems, which vary in point value. The exam covers the entire term and there will definitely be at least one problem from the very first weeks. That said, there will be lots of questions on the Galois Theory part. You should understand the Galois Correspondence Theorem. You should be able to find [K:F] in various situations and know whether or not it is a normal extension. You should know about finite fields and how to calculate in them. There will also be a Bonus Question which will not be graded, but may affect A/A- final grade decisions.

Class Hours

Monday, Wednesday 11-12:15; Place Silver 706

Recitation

Instructor: Lukas Koehler, lmk368@nyu.edu, wwh 510

Place of Recitation: wwh 202; Time: F 9:30

Office Hours: W 4-5 in wwh 605

Texts

Topics in Algebra by Herstein

General Stuff

This website deals with Algebra II, Spring 2012. Students are expected to have taken Algebra I, though not necessarily from Prof. Spencer and not necessarily Fall 2011. The basic subject matter is Fields, including Galois Theory.

Questions?

Send me an email: {lowercaselastname}@cims.nyu.edu

Galois Theory Notes

Part A postscript LaTeX pdf

Part B postscript LaTeX pdf

Part C postscript LaTeX pdf

Part D postscript LaTeX pdf

Part E postscript LaTeX pdf

Part F postscript LaTeX pdf

Part G postscript LaTeX pdf

Part H postscript LaTeX pdf

Part I postscript LaTeX pdf

Part J postscript LaTeX pdf

Scribe

Scribe postings will be here. Click here scribelist for the list of scribes. To volunteer: send your name, email and date requested to Prof. Spencer at spencer@cims.nyu.edu

January 23 (Thanks Shana!) page1 page2 page3 page4 page5

January 25 (Thanks Imran!) .pdf

January 30 (Thanks Frank!) .pdf

February 1 (Thanks Elizabeth!) .pdf .pdf .pdf

February 6 (Thanks Dana!) .docx

February 8 (Thanks Michelle!) page1 page2 page3

February 13 (Thanks Yitao!) .pdf

February 15 (Thanks Hannah!) .pdf

February 22 (Thanks Jason!) page1 page2

February 27 (Thanks Brett!) pdf

March 5 (Thanks Jing!) pdf

March 7 (Thanks Rafi!) pdf

March 19 (Thanks John!) pdf doc

April 25 (Thanks Jake!) pdf

April 30 (Thanks Xiao!) pdf pdf (and Dana!) jpg1 jpg2 jpg3

May 1 (Thanks Dana!) jpg1 jpg2 jpg3

May 7 (Thanks Jason!) jpg

Assignments

Generally there will be assignments every week. They will be put online on Monday and due at recitation on Friday. The first week is an exception, you are to submit just one problem (as noted on assignment) by Wednesday but please do all problems.

Assignment 1 due January 25, in class postscript LaTeX pdf

Assignment 2 due February 3, in recitation postscript LaTeX pdf

Assignment 3 due February 10, in recitation postscript LaTeX pdf

Assignment 4, Just for Fun postscript LaTeX pdf

Assignment 5, due February 24, in recitation postscript LaTeX pdf

Assignment 6, due March 9, in recitation postscript LaTeX pdf

Assignment 7, due March 23, in recitation postscript LaTeX pdf

Assignment 8, due March 30, in recitation postscript LaTeX pdf

Assignment 9, due April 6, in recitation postscript LaTeX pdf

Assignment 10, due April 13, in recitation postscript LaTeX pdf

Assignment 11, due April 20, in recitation postscript LaTeX pdf

Assignment 12, due April 27, in recitation postscript LaTeX pdf

Assignment 13, due May 4, in recitation postscript LaTeX pdf

Solutions

Assignment 1 due January 25, in class postscript LaTeX pdf and two nice picture another nice picture for the final problem (with Z[omega])

Assignment 2 postscript LaTeX pdf and a nice picture for the problem with Z[sqrt -5])

Assignment 3 postscript LaTeX pdf

Assignment 5 postscript LaTeX pdf

Assignment 6 postscript LaTeX pdf

Assignment 7 postscript LaTeX pdf

Assignment 8 postscript LaTeX pdf

Assignment 9 postscript LaTeX pdf

Assignment 10 postscript LaTeX pdf

Assignment 11 postscript LaTeX pdf

Assignment 12 postscript LaTeX pdf

Assignment 13 postscript LaTeX pdf

Midterm

February 29, In Class. No books or notes. No calculators.

Here is the midterm, one version. postscript LaTeX pdf

and its solutions postscript LaTeX pdf

Here is an old midterm. postscript LaTeX pdf

and its solutions postscript LaTeX pdf

Extra Stuff

Magic Squares

postscript LaTeX pdf

Cyclotomic Polynomials

postscript LaTeX pdf

Chinese Remainder Theorem

postscript LaTeX pdf

Linear Recurrances

postscript LaTeX pdf