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--- math105-s22:start [2022/03/30 17:13]
pzhou
+++ math105-s22:start [2022/05/02 14:25] (current)
pzhou
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 Office: Evans 931, [[https://berkeley.zoom.us/my/pzhoumath | zoom office]] \\
 Office Hour:  TuTh, 11:10 - 12:30, Friday 4-4:50 (zoom, by appointment. send me a message on discord to let me know)
+** Final **: May 12: 3-6pm, Evans 3
   * Online Lecture: [[https://berkeley.zoom.us/j/92843375230 | Zoom ]] \\
@@ Line 101: / Line 103: @@
 |	Spring Recess	|	Mar 22, 24. |		|
 |	Lecture 19	|	Mar 29	Tue	| finishing implicit function theorem and inverse function theorem		|	 | [[https://berkeley.zoom.us/rec/share/U-WpeGdM7Qi9vfzjJzhB6rxVhxXHHl8yJz6ysWgHZQHxJ-GTKReiTgVNoNhC8VmH.Yy0AZMsVGqiMnb5Y | video ]] |
-|	Lecture 20	|	Mar 31	Thu	| finishing Rudin inverse function theorem. 		|
+|	Lecture 20	|	Mar 31	Thu	| finishing Rudin inverse function theorem. begin differential form		| Rudin, Pugh 5.8 | 	[[https://berkeley.zoom.us/rec/share/WFC96pTm9Zwqw0NFyVCLgQCEShEWliFxAYx2WHgo0U9KhDHi40U69cPBsS-sUblK.91-j4cj-TbTVhQxs | video ]], [[./hw/hw10]]  |
-|	Lecture 21	|	Apr 5	Tue	|		|
+|	Lecture 21	|	Apr 5	Tue	|	exterior derivative, wedge product	| Pugh 5.8 | [[https://berkeley.zoom.us/rec/share/0WSMiHX0xg8lEr2dR0aqkJhfAhWtxHStoYWV2NgVQ8ucmJidE87o_lIa9JQkawvl.ZDfUz0va7AIERcvM | video]]	|
-|	Lecture 22	|	Apr 7	Thu	|		|
+|	Lecture 22	|	Apr 7	Thu	| Stokes formula		| Pugh 5.9 | [[https://berkeley.zoom.us/rec/share/7SmRkNa7L6UlI57_wPjAyrg3LIf0SsloINl_lXnE04BzTZVyO87UZzFpLqz5_Sq1.zYIcbuWIM06oV1tz | video]], [[./hw/hw11]] |
-|	Lecture 23	|	Apr 12	Tue	|		|
+|	Lecture 23	|	Apr 12	Tue	| Exact and Closed form, Poincare Lemma		| Pugh 5.9 | [[https://berkeley.zoom.us/rec/share/7TpHOrK42TvcjVXzX-abPgbwj-PxRewMh9nyW2PvGbQe1GsEM834vjddQa_Kg9nX.BeLWu9td8DIK_3wu | video]] |
-|	Lecture 24	|	Apr 14	Thu	|		|
+|	Lecture 24	|	Apr 14	Thu	| Poincare Lemma, more examples and general proof		| Pugh 5.9 | [[https://berkeley.zoom.us/rec/share/uTAcXhr6tzq_4wJ94FJeCpIfr9JZTrnQZnM106lVR_AtIkCSo3OhNyDvox37PzsG.DLzZpLzYuYtrhO7o | video]], [[./hw/hw12]]  |
-|	Lecture 25	|	Apr 19	Tue	|		|
+|	Lecture 25	|	Apr 19	Tue	| Tao 5.1-5.3 		|
-|	Lecture 26	|	Apr 21	Thu	|		|
+|	Lecture 26	|	Apr 21	Thu	| CANCELLED <del>Tao 5.4, 5.5	</del>	| NO HW， read Tao 5.4, 5.5 |
-|	Lecture 27	|	Apr 26	Tue	|		|
+|	Lecture 27	|	Apr 26	Tue	| Tao 5.4, 5.5		| [[https://berkeley.zoom.us/rec/share/kI8zCl4Fp7JU8A2NDzN50VUZ930wZ3jc56bC43JUY9IrZacIx-PTUPIQEQ5llSSi.RCGWRsv_EX06vM-k | video]]	|
-|	Lecture 28	|	Apr 28	Thu	|		|
+|	Lecture 28	|	Apr 28	Thu	| 		| [[https://berkeley.zoom.us/rec/share/bAaTtDc6bTcH4uhPuDlZc1GBrPXAyTlwoEc956HDypYChVv6VUb6nEpt29r6JgnN.w5IJHEBVaX29L4SM | video]]	|
 |	RRR	|	May 3	Tue	|		|
 |	RRR	|	May 5	Thu	|		|
+===== Final and Essay =====
+For the sake of grading, we will still have an in class final. It will be an open book exam. Exam will be on May 12 (Thursday, 3-6pm, Evans 3). It will consist of 5 problems, where you will decide if a statement is true or false; if true give a proof, if false, give a counter-example.
+In addition to the final, if you are interested in writing an essay (post on your homepage), or give a 15-min presentation (in the class day of class), here are some topics and you are free to choose your own.
+  * The Banach-Tarski paradox (see wikipage)
+  * Some counter-examples in analysis (see the book in discord)
+  * What is Fast Fourier transformation? What is wavelet transformation? How to relate to uncertainty principle? (use wiki)
+  * How to put a measure on the space of Brownian motion?

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