ÿþ<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN"> <!-- saved from url=(0050)http://www.math.ntu.edu.tw/~jkchen/S07AA/S07AA.htm --> <!-- saved from url=(0050)http://www.math.ntu.edu.tw/~jkchen/S07AA/S07AA.htm --><HTML><HEAD><TITLE>Advanced Algebra</TITLE> <META http-equiv=Content-Language content=zh-tw> <META content="MSHTML 6.00.2900.3059" name=GENERATOR> <META content=FrontPage.Editor.Document name=ProgId> <META http-equiv=Content-Type content="text/html; charset=big5"></HEAD> <BODY> <H1><FONT face="Courier New">Advanced Algebra II</FONT></H1> <P><FONT face="Times New Roman">&nbsp;&nbsp;&nbsp; NB: most documents are in pdf format. You might need <A href="http://www.adobe.com/">Acrobat Reader</A> (which is free to download) to view it. Some version of Ghostview also works.</FONT></P> <P><font face="Times New Roman" size="5"><a href="S07AA2Final.pdf">Take-home Final Exam</a> :&nbsp; 6/15 ~ <font color="#FF0000">6/27</font> 12 p.m. </font></P> <P><font face="Times New Roman" size="4">(either put your term papers into the mailbox or send them to the office directly.)</font></P> <P><a href="http://www.math.ntu.edu.tw/~jkchen/S07AA/S06AA2syllabus.pdf"> <span style="font-weight: 400"><font face="Times New Roman" size="5">S</font></span></a><SPAN style="FONT-WEIGHT: 400"><FONT face="Times New Roman" size=5><A href="http://www.math.ntu.edu.tw/~jkchen/S07AA/S06AA2syllabus.pdf">yllabus</A></FONT></SPAN></P> <blockquote> <p><B><FONT face="Times New Roman">Homeworks:</FONT></B></p> <TABLE id=table1 style="BORDER-COLLAPSE: collapse" borderColor=#111111 cellSpacing=0 cellPadding=0 width="90%" border=1> <TBODY> <TR> <TD width="20%"><FONT face="Times New Roman">&nbsp;hw1 (<A href="http://www.math.ntu.edu.tw/~jkchen/S07AA/S07AA2HW1.tex">tex</A>, <A href="http://www.math.ntu.edu.tw/~jkchen/S07AA/S07AA2HW1.pdf">pdf</A>)</FONT></TD> <TD width="20%"><FONT face="Times New Roman">&nbsp;hw2 (<A href="http://www.math.ntu.edu.tw/~jkchen/S07AA/S07AA2HW2.tex">tex</A>, <A href="http://www.math.ntu.edu.tw/~jkchen/S07AA/S07AA2HW2.pdf">pdf</A>)</FONT></TD> <TD width="20%"><FONT face="Times New Roman">&nbsp;hw3 (<a href="http://www.math.ntu.edu.tw/~jkchen/S07AA/S07AA2HW3.tex">tex</a>, <A href="http://www.math.ntu.edu.tw/~jkchen/S07AA/S07AA2HW3.pdf">pdf</A>)</FONT></TD> <TD width="20%"><FONT face="Times New Roman">&nbsp;hw4 (<a href="http://www.math.ntu.edu.tw/~jkchen/S07AA/S07AA2HW4.tex">tex</a>, <a href="http://www.math.ntu.edu.tw/~jkchen/S07AA/S07AA2HW4.pdf">pdf</a>)</FONT></TD> <TD width="21%">&nbsp;<FONT face="Times New Roman">hw5 (<a href="http://www.math.ntu.edu.tw/~jkchen/S07AA/S07AA2HW5.tex">tex</a>, <a href="http://www.math.ntu.edu.tw/~jkchen/S07AA/S07AA2HW5.pdf">pdf</a>)</FONT></TD> </TR> <TR> <TD width="20%"><FONT face="Times New Roman">&nbsp;hw6 (<a href="http://www.math.ntu.edu.tw/~jkchen/S07AA/S07AA2HW6.tex">tex</a>, <a href="http://www.math.ntu.edu.tw/~jkchen/S07AA/S07AA2HW6.pdf">pdf</a>)</FONT></TD> <TD width="20%"><FONT face="Times New Roman">&nbsp;hw7 (<a href="http://www.math.ntu.edu.tw/~jkchen/S07AA/S07AA2HW7.tex">tex</a>, <a href="http://www.math.ntu.edu.tw/~jkchen/S07AA/S07AA2HW7.pdf">pdf</a>)</FONT></TD> <TD width="20%"><FONT face="Times New Roman">&nbsp;hw8 (<a href="http://www.math.ntu.edu.tw/~jkchen/S07AA/S07AA2HW8.tex">tex</a>, <a href="http://www.math.ntu.edu.tw/~jkchen/S07AA/S07AA2HW8.pdf">pdf</a>)</FONT>0</TD> <TD width="20%"><FONT face="Times New Roman">&nbsp;hw9 (<a href="http://www.math.ntu.edu.tw/~jkchen/S07AA/S07AA2HW9.tex">tex</a>, <a href="http://www.math.ntu.edu.tw/~jkchen/S07AA/S07AA2HW9.pdf">pdf</a>)</FONT>0</TD> <TD width="21%"><FONT face="Times New Roman">&nbsp;hw10 (<a href="http://www.math.ntu.edu.tw/~jkchen/S07AA/S07AA2HW10.tex">tex</a>, <a href="http://www.math.ntu.edu.tw/~jkchen/S07AA/S07AA2HW10.pdf">pdf</a>)</FONT>0</TD> </TR> <TR> <TD width="20%"><FONT face="Times New Roman">&nbsp;hw11 (<a href="http://www.math.ntu.edu.tw/~jkchen/S07AA/S07AA2HW11.tex">tex</a>, <a href="http://www.math.ntu.edu.tw/~jkchen/S07AA/S07AA2HW11.pdf">pdf</a>)</FONT>00</TD> <TD width="20%"><FONT face="Times New Roman">&nbsp;hw12 (<a href="http://www.math.ntu.edu.tw/~jkchen/S07AA/S07AA2HW12.tex">tex</a>, <a href="http://www.math.ntu.edu.tw/~jkchen/S07AA/S07AA2HW12.pdf">pdf</a>)</FONT>0</TD> <TD width="20%">0</TD> <TD width="20%">0</TD> <TD width="21%">0</TD> </TR> </TBODY> </TABLE> <H4><B><FONT face="Times New Roman">Homework Solutions:</FONT></B></H4> <p>&nbsp;&nbsp;&nbsp; These exercise solutions are courtesy of&nbsp;one of the students,<font FACE="TTdcbx10" SIZE="3"> Ju-Chen</font>&nbsp;<font FACE="TTdcbx10" SIZE="3">Yang</font>. Used with permission.</p> <p><FONT face="Times New Roman">&nbsp;&nbsp;&nbsp; sol1 (<a href="S07sol1.tex">tex</a>, <a href="S07sol1.pdf">pdf</a>)&nbsp; sol2 (<a href="S07sol2.tex">tex</a>, <a href="S07sol2.pdf">pdf</a>)&nbsp; sol3 (<a href="S07sol3.tex">tex</a>, <a href="S07sol3.pdf">pdf</a>)&nbsp; sol4 (<a href="S07sol4.tex">tex</a>, <a href="S07sol4.pdf">pdf</a>)&nbsp; sol5 (<a href="S07sol5.tex">tex</a>, <a href="S07sol5.pdf">pdf</a>)</FONT></p> <p><FONT face="Times New Roman"><b>Lecture Notes:</b></FONT></p> <p>&nbsp;&nbsp;&nbsp; Click here (<A href="http://www.math.ntu.edu.tw/~jkchen/S07AA/S07AA2.tex">tex</A>, <A href="http://www.math.ntu.edu.tw/~jkchen/S07AA/S07AA2.pdf">pdf</A>)&nbsp; for the file for everything up to date. Or you can click on the individual one for the note presented in class.</p> <TABLE id=table2 style="BORDER-COLLAPSE: collapse" borderColor=#111111 height=318 cellSpacing=0 cellPadding=0 width="92%" border=0> <TBODY> <TR> <TD width="2%">0</TD> <TD width="90%"> <A href="http://www.math.ntu.edu.tw/~jkchen/S07AA/S07AA2L1p.pdf">Lecture 1</A>:&nbsp;&nbsp; (2007/3/2)&nbsp;&nbsp;&nbsp; i. basic definitions,&nbsp; ii. factorization,&nbsp; iii. localization</TD> </TR> <TR> <TD width="2%">0</TD> <TD width="90%"> <A href="http://www.math.ntu.edu.tw/~jkchen/S07AA/S07AA2L2p.pdf">Lecture 2</A>:&nbsp;&nbsp; (2007/3/9)&nbsp;&nbsp;&nbsp; i. localization (II), ii. modules </TD> </TR> <TR> <TD width="2%">0</TD> <TD width="90%"> <A href="http://www.math.ntu.edu.tw/~jkchen/S07AA/S07AA2L3p.pdf">Lecture 3</A>:&nbsp;&nbsp; (2007/3/16)&nbsp; tensor product</TD> </TR> <TR> <TD width="2%">0</TD> <TD width="90%"> <a href="http://www.math.ntu.edu.tw/~jkchen/S07AA/S07AA2L4p.pdf">Lecture 4</a>:&nbsp;&nbsp; (2007/3/23)&nbsp; chain conditions</TD> </TR> <TR> <TD width="2%">0</TD> <TD width="90%"> <a href="http://www.math.ntu.edu.tw/~jkchen/S07AA/S07AA2L5p.pdf">Lecture 5</a>:&nbsp;&nbsp; (2007/3/30)&nbsp; i. chain conditions (II),&nbsp; ii. integral dependence (I) </TD> </TR> <TR> <TD width="2%">0</TD> <TD width="90%"> <a href="http://www.math.ntu.edu.tw/~jkchen/S07AA/S07AA2L6p.pdf">Lecture 6</a>:&nbsp;&nbsp; (2007/4/13)&nbsp; i. integral dependence (II),&nbsp; ii. affine varieties</TD> </TR> <TR> <TD width="2%">0</TD> <TD width="90%"> <a href="http://www.math.ntu.edu.tw/~jkchen/S07AA/S07AA2L7p.pdf">Lecture 7</a>:&nbsp;&nbsp; (2007/4/27)&nbsp; i. dimension theory,&nbsp; ii. projective varieties (I)0</TD> </TR> <TR> <TD width="2%">0</TD> <TD width="90%"> <a href="http://www.math.ntu.edu.tw/~jkchen/S07AA/S07AA2L8p.pdf">Lecture 8</a>:&nbsp;&nbsp; (2007/5/4)&nbsp;&nbsp;&nbsp; i. projective varieties (II),&nbsp; ii. morphisms</TD> </TR> <TR> <TD width="2%">0</TD> <TD width="90%"> <a href="http://www.math.ntu.edu.tw/~jkchen/S07AA/S07AA2L9p.pdf">Lecture 9</a>:&nbsp;&nbsp; (2007/5/11)&nbsp; nonsingular varieties and singularities.</TD> </TR> <TR> <TD width="2%">0</TD> <TD width="90%"> <a href="http://www.math.ntu.edu.tw/~jkchen/S07AA/S07AA2L10p.pdf">Lecture10</a>:&nbsp; (2007/5/18)&nbsp; i. divisors,&nbsp; ii. elliptic curves (I)0</TD> </TR> <TR> <TD width="2%">0</TD> <TD width="90%"> <a href="http://www.math.ntu.edu.tw/~jkchen/S07AA/S07AA2L11p.pdf">Lecture11</a>:&nbsp; (2007/5/25)&nbsp; i. elliptic curves (II),&nbsp; ii. modular forms,&nbsp; iii. Dedekind domains (I)00</TD> </TR> <TR> <TD width="2%">0</TD> <TD width="90%"> <a href="http://www.math.ntu.edu.tw/~jkchen/S07AA/S07AA2L12p.pdf">Lecture12</a>:&nbsp; (2007/6/1)&nbsp; &nbsp; Dedekind domains (II)00</TD> </TR> <TR> <TD width="2%">0</TD> <TD width="90%"> <a href="http://www.math.ntu.edu.tw/~jkchen/S07AA/S07AA2L13p.pdf">Lecture13</a>:&nbsp; (2007/6/8)&nbsp;&nbsp;&nbsp; i. Dedekind domains (III),&nbsp; ii. valuation (I)00</TD> </TR> <TR> <TD width="2%">0</TD> <TD width="90%"> <a href="http://www.math.ntu.edu.tw/~jkchen/S07AA/S07AA2L14p.pdf">Lecture14</a>:&nbsp; (2007/6/15)&nbsp; valuation (II)0</TD> </TR> <TR> <TD width="2%">0</TD> <TD width="90%">0</TD> </TR> <TR> <TD width="2%">0</TD> <TD width="90%">0</TD> </TR> </TBODY> </TABLE> </blockquote> </BODY></HTML>