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http://www.sitemaps.org/schemas/sitemap/0.9/sitemap.xsd"><url><loc>https://mikepawliuk.ca/2012/02/12/the-delta-system-lemma/</loc><lastmod>2025-08-20T14:57:48+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://mikepawliuk.ca/teaching/</loc><lastmod>2024-06-24T18:46:32+00:00</lastmod><changefreq>weekly</changefreq><priority>0.6</priority></url><url><loc>https://mikepawliuk.ca/tutoring/</loc><lastmod>2024-06-24T18:22:56+00:00</lastmod><changefreq>weekly</changefreq><priority>0.6</priority></url><url><loc>https://mikepawliuk.ca/2023/01/04/university-calculus-materials/</loc><lastmod>2023-01-04T18:53:30+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://mikepawliuk.ca/2022/12/12/job-materials/</loc><lastmod>2022-12-13T16:27:08+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://mikepawliuk.ca/mentoring-and-supervised-research-projects/</loc><image:image><image:loc>https://mikepawliuk.ca/wp-content/uploads/2018/09/davoud_dept_hike_sept_2018.jpg</image:loc><image:title>davoud_dept_hike_sept_2018</image:title></image:image><image:image><image:loc>https://mikepawliuk.ca/wp-content/uploads/2018/09/lyra_ubc_ink.jpg</image:loc><image:title>lyra_UBC_ink</image:title></image:image><lastmod>2022-11-13T22:38:59+00:00</lastmod><changefreq>weekly</changefreq><priority>0.6</priority></url><url><loc>https://mikepawliuk.ca/contact-me/</loc><lastmod>2022-09-21T19:37:01+00:00</lastmod><changefreq>weekly</changefreq><priority>0.6</priority></url><url><loc>https://mikepawliuk.ca/2022/09/14/machine-learning-observations-1-turning-a-picture-into-a-vector-doesnt-lose-information/</loc><image:image><image:loc>https://mikepawliuk.ca/wp-content/uploads/2022/09/pexels-photo-6064130.jpeg</image:loc><image:title>brown wooden letters</image:title><image:caption>Photo by Brett Jordan on &lt;a href="https://www.pexels.com/photo/brown-wooden-letters-6064130/" rel="nofollow"&gt;Pexels.com&lt;/a&gt;</image:caption></image:image><lastmod>2022-09-14T19:57:41+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://mikepawliuk.ca/2022/06/22/how-many-sizes-of-infinity-are-there/</loc><image:image><image:loc>https://mikepawliuk.ca/wp-content/uploads/2022/06/pexels-photo-1448673.jpeg</image:loc><image:title>person holding fresh chestnut</image:title><image:caption>Photo by Elviss Railijs Bitu0101ns on &lt;a href="https://www.pexels.com/photo/person-holding-fresh-chestnut-1448673/" rel="nofollow"&gt;Pexels.com&lt;/a&gt;</image:caption></image:image><image:image><image:loc>https://mikepawliuk.ca/wp-content/uploads/2022/06/pexels-photo-3872428.jpeg</image:loc><image:title>photo of assorted spices</image:title><image:caption>Photo by Polina Tankilevitch on &lt;a href="https://www.pexels.com/photo/photo-of-assorted-spices-3872428/" rel="nofollow"&gt;Pexels.com&lt;/a&gt;</image:caption></image:image><image:image><image:loc>https://mikepawliuk.ca/wp-content/uploads/2022/06/walnut-honeycomb-wood-still-life-48188.jpeg</image:loc><image:title>wood honeycomb still life walnut</image:title><image:caption>Photo by Pixabay on &lt;a href="https://www.pexels.com/photo/wood-honeycomb-still-life-walnut-48188/" rel="nofollow"&gt;Pexels.com&lt;/a&gt;</image:caption></image:image><image:image><image:loc>https://mikepawliuk.ca/wp-content/uploads/2022/06/walnuts-nuts-healthy-shell-45211.jpeg</image:loc><image:title>brown nuts on table</image:title><image:caption>Photo by Pixabay on &lt;a href="https://www.pexels.com/photo/brown-nuts-on-table-45211/" rel="nofollow"&gt;Pexels.com&lt;/a&gt;</image:caption></image:image><image:image><image:loc>https://mikepawliuk.ca/wp-content/uploads/2022/06/pexels-photo-1295572.jpeg</image:loc><image:title>variety of brown nuts on brown wooden panel high angle photo</image:title><image:caption>Photo by Marta Branco on &lt;a href="https://www.pexels.com/photo/variety-of-brown-nuts-on-brown-wooden-panel-high-angle-photo-1295572/" rel="nofollow"&gt;Pexels.com&lt;/a&gt;</image:caption></image:image><image:image><image:loc>https://mikepawliuk.ca/wp-content/uploads/2022/06/pexels-photo-3640631.jpeg</image:loc><image:title>brown walnuts</image:title><image:caption>Photo by YUSUF ARSLAN on &lt;a href="https://www.pexels.com/photo/brown-walnuts-3640631/" rel="nofollow"&gt;Pexels.com&lt;/a&gt;</image:caption></image:image><lastmod>2022-06-22T19:59:34+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://mikepawliuk.ca/2021/09/30/thursday-september-30-national-day-for-truth-and-reconciliation/</loc><lastmod>2022-06-21T15:03:39+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://mikepawliuk.ca/introduction-to-proofs/</loc><lastmod>2022-05-03T23:44:44+00:00</lastmod><changefreq>weekly</changefreq><priority>0.6</priority></url><url><loc>https://mikepawliuk.ca/2014/10/08/delta-epsilon-magic/</loc><lastmod>2022-03-07T02:55:36+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://mikepawliuk.ca/2012/09/06/the-battery-problem-math-for-my-mom/</loc><lastmod>2022-01-31T21:00:04+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://mikepawliuk.ca/teaching/mat-327-summer-2014/</loc><lastmod>2021-08-25T13:33:26+00:00</lastmod><changefreq>weekly</changefreq><priority>0.6</priority></url><url><loc>https://mikepawliuk.ca/2021/07/28/review-of-ungrading-blum-2020-for-use-in-utm-math-courses/</loc><image:image><image:loc>https://mikepawliuk.ca/wp-content/uploads/2021/07/pexels-photo-262367.jpeg</image:loc><image:title>abstract architecture black and white boardwalk</image:title><image:caption>Photo by Pixabay on &lt;a href="https://www.pexels.com/photo/abstract-architecture-black-and-white-boardwalk-262367/" rel="nofollow"&gt;Pexels.com&lt;/a&gt;</image:caption></image:image><image:image><image:loc>https://mikepawliuk.ca/wp-content/uploads/2021/07/pexels-photo-412842.jpeg</image:loc><image:title>building clouds facade glass panels</image:title><image:caption>Photo by Snapwire on &lt;a href="https://www.pexels.com/photo/building-clouds-facade-glass-panels-412842/" rel="nofollow"&gt;Pexels.com&lt;/a&gt;</image:caption></image:image><image:image><image:loc>https://mikepawliuk.ca/wp-content/uploads/2021/07/pexels-photo-911758.jpeg</image:loc><image:title>long exposure photography white dome building interior</image:title><image:caption>Photo by gdtography on &lt;a href="https://www.pexels.com/photo/long-exposure-photography-white-dome-building-interior-911758/" rel="nofollow"&gt;Pexels.com&lt;/a&gt;</image:caption></image:image><image:image><image:loc>https://mikepawliuk.ca/wp-content/uploads/2021/07/pexels-photo-417273.jpeg</image:loc><image:title>architectural design architecture blue build</image:title><image:caption>Photo by Pixabay on &lt;a href="https://www.pexels.com/photo/architectural-design-architecture-blue-build-417273/" rel="nofollow"&gt;Pexels.com&lt;/a&gt;</image:caption></image:image><image:image><image:loc>https://mikepawliuk.ca/wp-content/uploads/2021/07/pexels-photo-1109541.jpeg</image:loc><image:title>person holding black pen</image:title><image:caption>Photo by Lex Photography on &lt;a href="https://www.pexels.com/photo/person-holding-black-pen-1109541/" rel="nofollow"&gt;Pexels.com&lt;/a&gt;</image:caption></image:image><image:image><image:loc>https://mikepawliuk.ca/wp-content/uploads/2021/07/pexels-photo-830891.jpeg</image:loc><image:title>low angle photo of four high rise curtain wall buildings under white clouds and blue sky</image:title><image:caption>Photo by Philipp Birmes on &lt;a href="https://www.pexels.com/photo/low-angle-photo-of-four-high-rise-curtain-wall-buildings-under-white-clouds-and-blue-sky-830891/" rel="nofollow"&gt;Pexels.com&lt;/a&gt;</image:caption></image:image><image:image><image:loc>https://mikepawliuk.ca/wp-content/uploads/2021/07/pexels-photo-1105766.jpeg</image:loc><image:title>aerial view and grayscale photography of high rise buildings</image:title><image:caption>Photo by Tatiana Fet on &lt;a href="https://www.pexels.com/photo/aerial-view-and-grayscale-photography-of-high-rise-buildings-1105766/" rel="nofollow"&gt;Pexels.com&lt;/a&gt;</image:caption></image:image><lastmod>2021-08-21T20:27:15+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://mikepawliuk.ca/2021/03/23/aligned-teaching-and-punishing-student-success/</loc><image:image><image:loc>https://mikepawliuk.ca/wp-content/uploads/2021/03/pexels-photo-1149019.jpeg</image:loc><image:title>multicolored abstract artwork</image:title><image:caption>Photo by Sharon McCutcheon on &lt;a href="https://www.pexels.com/photo/multicolored-abstract-artwork-1149019/" rel="nofollow"&gt;Pexels.com&lt;/a&gt;</image:caption></image:image><image:image><image:loc>https://mikepawliuk.ca/wp-content/uploads/2021/03/pexels-photo-416832.jpeg</image:loc><image:title>bullseye center illustration round</image:title><image:caption>Photo by Pixabay on &lt;a href="https://www.pexels.com/photo/bullseye-center-illustration-round-416832/" rel="nofollow"&gt;Pexels.com&lt;/a&gt;</image:caption></image:image><image:image><image:loc>https://mikepawliuk.ca/wp-content/uploads/2021/03/pexels-photo-1148496.jpeg</image:loc><image:title>assorted color bricks</image:title><image:caption>Photo by Sharon McCutcheon on &lt;a href="https://www.pexels.com/photo/assorted-color-bricks-1148496/" rel="nofollow"&gt;Pexels.com&lt;/a&gt;</image:caption></image:image><lastmod>2021-03-24T00:51:30+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://mikepawliuk.ca/2019/07/23/how-to-organize-an-equitable-pre-cumc-conference-for-students/</loc><image:image><image:loc>https://mikepawliuk.ca/wp-content/uploads/2019/07/exercise-86200_640.jpg</image:loc><image:title>exercise-86200_640</image:title></image:image><image:image><image:loc>https://mikepawliuk.ca/wp-content/uploads/2019/07/mountain-3850166_640.jpg</image:loc><image:title>mountain-3850166_640</image:title></image:image><image:image><image:loc>https://mikepawliuk.ca/wp-content/uploads/2019/07/zumba-4333580_640.jpg</image:loc><image:title>zumba-4333580_640</image:title></image:image><image:image><image:loc>https://mikepawliuk.ca/wp-content/uploads/2019/07/running-2375066_640.jpg</image:loc><image:title>running-2375066_640</image:title></image:image><image:image><image:loc>https://mikepawliuk.ca/wp-content/uploads/2019/07/sport-2264825_640.jpg</image:loc><image:title>sport-2264825_640</image:title></image:image><image:image><image:loc>https://mikepawliuk.ca/wp-content/uploads/2019/07/push-ups-888024_640.jpg</image:loc><image:title>push-ups-888024_640</image:title></image:image><image:image><image:loc>https://mikepawliuk.ca/wp-content/uploads/2019/07/menti_cumc.png</image:loc><image:title>Menti_CUMC</image:title></image:image><image:image><image:loc>https://mikepawliuk.ca/wp-content/uploads/2019/07/fb_pre_cumc.png</image:loc><image:title>FB_pre_cumc</image:title></image:image><lastmod>2019-08-26T10:55:19+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://mikepawliuk.ca/2012/01/26/a-practical-guide-to-using-countable-elementary-submodels/</loc><lastmod>2019-06-28T18:29:25+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://mikepawliuk.ca/curriculum-vitae/</loc><lastmod>2019-04-26T13:28:23+00:00</lastmod><changefreq>weekly</changefreq><priority>0.6</priority></url><url><loc>https://mikepawliuk.ca/ramsey-doccourse-2016/</loc><lastmod>2019-04-08T20:37:20+00:00</lastmod><changefreq>weekly</changefreq><priority>0.6</priority></url><url><loc>https://mikepawliuk.ca/2017/05/23/euclidean-ramsey-theory-2-ramsey-doccourse-prague-2016/</loc><lastmod>2019-04-08T20:35:34+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://mikepawliuk.ca/2018/12/02/unifying-themes-in-ramsey-theory-birs-2018/</loc><image:image><image:loc>https://mikepawliuk.ca/wp-content/uploads/2018/12/groupphoto.jpg</image:loc><image:title>groupphoto</image:title></image:image><image:image><image:loc>https://mikepawliuk.ca/wp-content/uploads/2018/12/birs_1.jpg</image:loc><image:title>BIRS_1</image:title><image:caption>The cafeteria early in the morning. You can see Venus to the left of one of the trees.</image:caption></image:image><image:image><image:loc>https://mikepawliuk.ca/wp-content/uploads/2018/12/birs_4.jpg</image:loc><image:title>BIRS_4</image:title></image:image><image:image><image:loc>https://mikepawliuk.ca/wp-content/uploads/2018/11/54pfgvc.jpg</image:loc><image:title>54pfgvc</image:title></image:image><lastmod>2019-03-15T16:07:03+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://mikepawliuk.ca/2012/11/22/math-for-my-mom-birthday-edition/</loc><lastmod>2019-03-14T12:52:37+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://mikepawliuk.ca/about-me/</loc><image:image><image:loc>https://mikepawliuk.ca/wp-content/uploads/2011/10/wedding.jpg</image:loc><image:title>wedding</image:title><image:caption>Me and Janet.</image:caption></image:image><image:image><image:loc>https://mikepawliuk.ca/wp-content/uploads/2011/10/caju.jpg</image:loc><image:title>caju</image:title><image:caption>Caju, my pet hedgehog. She likes catfood and sleeping.</image:caption></image:image><image:image><image:loc>https://mikepawliuk.ca/wp-content/uploads/2011/10/janet.jpg</image:loc><image:title>janet</image:title><image:caption>Me and my wife Janet outside Abbey Road Studio in London.</image:caption></image:image><image:image><image:loc>https://mikepawliuk.ca/wp-content/uploads/2011/10/me.jpg</image:loc><image:title>me</image:title><image:caption>This is me!</image:caption></image:image><image:image><image:loc>https://mikepawliuk.ca/wp-content/uploads/2011/10/tphoto_00002.jpg</image:loc><image:title>TPhoto_00002</image:title><image:caption>Me in my office at school.</image:caption></image:image><image:image><image:loc>https://mikepawliuk.ca/wp-content/uploads/2011/10/improv-1.jpg</image:loc><image:title>improv 1</image:title></image:image><image:image><image:loc>https://mikepawliuk.ca/wp-content/uploads/2011/10/improv-2.jpg</image:loc><image:title>improv 2</image:title></image:image><image:image><image:loc>https://mikepawliuk.ca/wp-content/uploads/2011/10/dominion-1.jpg</image:loc><image:title>dominion 1</image:title></image:image><lastmod>2019-01-14T21:56:35+00:00</lastmod><changefreq>weekly</changefreq><priority>0.6</priority></url><url><loc>https://mikepawliuk.ca/2012/03/06/facts-about-the-urysohn-space-some-useful-some-cool/</loc><lastmod>2019-01-14T16:20:51+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://mikepawliuk.ca/2018/12/16/learning-latex-in-jupyter-notebooks/</loc><image:image><image:loc>https://mikepawliuk.ca/wp-content/uploads/2018/12/latex_8a906c4c6162313a7c99233a4201d667.png</image:loc><image:title>latex_8a906c4c6162313a7c99233a4201d667</image:title></image:image><image:image><image:loc>https://mikepawliuk.ca/wp-content/uploads/2018/12/latex_a09588720c5d1e3a1948e857b5e99c51.png</image:loc><image:title>latex_a09588720c5d1e3a1948e857b5e99c51</image:title></image:image><lastmod>2018-12-17T05:52:40+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://mikepawliuk.ca/2016/10/27/partite-constructions-2-ramsey-doccourse-prague-2016/</loc><lastmod>2018-11-26T18:30:27+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://mikepawliuk.ca/2016/10/23/ramsey-and-ultrafilters-2-ramsey-doccourse-prague-2016/</loc><lastmod>2018-11-22T17:25:36+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://mikepawliuk.ca/2016/10/20/ramsey-and-ultrafilter-1-ramsey-doccourse-prague-2016/</loc><lastmod>2018-11-22T17:17:18+00:00</lastmod><changefreq>monthly</changefreq></url><url><loc>https://mikepawliuk.ca/2018/09/23/how-does-the-size-of-a-cookie-depend-on-the-size-of-the-ball-of-dough/</loc><image:image><image:loc>https://mikepawliuk.ca/wp-content/uploads/2018/09/cookie_line2.png</image:loc><image:title>cookie_line2</image:title><image:caption>Line of best fit is $latex y=2.01x-0.1$, with standard deviation 0.1 and a very small 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