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math105-s22:start [2022/03/18 05:02]
pzhou 		math105-s22:start [2026/02/21 14:41] (current)
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 Office: Evans 931, [[https://berkeley.zoom.us/my/pzhoumath | zoom office]] \\ 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) 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 ]] \\   * Online Lecture: [[https://berkeley.zoom.us/j/92843375230 | Zoom ]] \\
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 | [[.notes:lecture_18 | Lecture 18]] | Mar 17 Thu | higher derivative; implicit function theorem | Pugh 5.4 | [[./hw/hw9]] |  | [[.notes:lecture_18 | Lecture 18]] | Mar 17 Thu | higher derivative; implicit function theorem | Pugh 5.4 | [[./hw/hw9]] |
 | Spring Recess | Mar 22, 24. | |  | Spring Recess | Mar 22, 24. | |
-| Lecture 19 | Mar 29 Tue | |  +| 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 | |  +| 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 3 Tue | |
 | RRR | May 5 Thu | |  | 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? 
 +
  
   
math105-s22/start.1647579722.txt.gz · Last modified: 2026/02/21 14:43 (external edit)

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