Lecture Notes

User Tools

Site Tools

You are here: Course Notes » Math 105: A second course to real analysis (2022 Spring)
math105-s22:start

Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Both sides previous revision Previous revision
Next revision 		Previous revision
Last revision Both sides next revision
math105-s22:start [2022/03/14 23:53]
pzhou 		math105-s22:start [2022/04/30 00:41]
pzhou [Journal]
Line 96: Line 96:
 | [[.notes:lecture_14 | Lecture 14 ]] | Mar 3 Thu | Lebesgue Mean Value theorem | Pugh 6.9 |  [[./hw/hw7]] |  | [[.notes:lecture_14 | Lecture 14 ]] | Mar 3 Thu | Lebesgue Mean Value theorem | Pugh 6.9 |  [[./hw/hw7]] |
 | [[.notes:lecture_15 | Lecture 15]] | Mar 8 Tue |  Absolute Continuous function. Lebesgue main theorem | Pugh 6.9 |  | [[.notes:lecture_15 | Lecture 15]] | Mar 8 Tue |  Absolute Continuous function. Lebesgue main theorem | Pugh 6.9 |
-| [[.notes:lecture_16 | Lecture 16]] | Mar 10 Thu | linear algebra | Pugh 5.1, 5.2 | [[./hw/hw8]] |  +| [[.notes:lecture_16 | Lecture 16]] | Mar 10 Thu | linear algebra | Pugh 5.1 | [[./hw/hw8]] |  
-| [[.notes:lecture_17 | Lecture 17]] | Mar 15 Tue | definition of derivative. |  +| [[.notes:lecture_17 | Lecture 17]] | Mar 15 Tue | definition of derivative. | Pugh 5.2 |  
-| [[.notes:lecture_18 | Lecture 18]] | Mar 17 Thu | | +| [[.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.txt · Last modified: 2022/05/02 14:25 by pzhou

Page Tools

Except where otherwise noted, content on this wiki is licensed under the following license: CC Attribution-Share Alike 4.0 International
CC Attribution-Share Alike 4.0 International Donate Powered by PHP Valid HTML5 Valid CSS Driven by DokuWiki