{"id":16,"date":"2025-06-26T18:48:51","date_gmt":"2025-06-26T18:48:51","guid":{"rendered":"https:\/\/courses.lsa.umich.edu\/krasny\/?page_id=16"},"modified":"2025-07-23T23:34:56","modified_gmt":"2025-07-23T23:34:56","slug":"math-156","status":"publish","type":"page","link":"https:\/\/courses.lsa.umich.edu\/krasny\/math-156\/","title":{"rendered":"Math 156"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">Math 156 &#8211; Applied Honors Calculus II &#8211; Fall 2024<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Math 156 is a calculus 2 class designed for STEM majors (though all majors are welcome). The prerequisite is a score of 4 or 5 on the AP Calculus exam (AB or BC) or equivalent. For more details see the course&nbsp;<a href=\"https:\/\/dept.math.lsa.umich.edu\/~krasny\/math156_description.pdf\">description<\/a>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\" \/>\n\n\n\n<p class=\"wp-block-paragraph\">all sections meet MonTuesWedFri in 4096 East Hall (except for sections 3 and 4 on Tuesdays)<br>section 1, 9-10am, Nizhum Rahman<br>section 2, 10-11am, Robert Krasny<br>section 3, 11am-12pm, Allen Wu, Tues in 1866 EH<br>section 4, 12-1pm, Allen Wu, Tues in 3096 EH<br>section 5, 1-2pm, James Wheeler<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\" \/>\n\n\n\n<h4 class=\"wp-block-heading\">Information<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/courses.lsa.umich.edu\/krasny\/wp-content\/uploads\/sites\/202\/2025\/06\/math156_organization.pdf\">organization<\/a>,&nbsp;<a href=\"https:\/\/courses.lsa.umich.edu\/krasny\/wp-content\/uploads\/sites\/202\/2025\/06\/math156_topics.pdf\">topics<\/a>,&nbsp;<a href=\"https:\/\/courses.lsa.umich.edu\/krasny\/wp-content\/uploads\/sites\/202\/2025\/06\/math156_schedule.pdf\">schedule<\/a>,&nbsp;<a href=\"https:\/\/courses.lsa.umich.edu\/krasny\/wp-content\/uploads\/sites\/202\/2025\/06\/math156_notes.pdf\">lecture notes<\/a>&nbsp;: complete to Wed Dec 4<br><a href=\"https:\/\/courses.lsa.umich.edu\/krasny\/wp-content\/uploads\/sites\/202\/2025\/06\/math156_notes_thanksgiving.pdf\">Thanksgiving notes<\/a>,&nbsp;<a href=\"https:\/\/courses.lsa.umich.edu\/krasny\/wp-content\/uploads\/sites\/202\/2025\/06\/math156_5_books.png\">5 books<\/a><br><a href=\"https:\/\/courses.lsa.umich.edu\/krasny\/wp-content\/uploads\/sites\/202\/2025\/06\/math156_notes_2023.pdf\">2023 lecture notes<\/a><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\" \/>\n\n\n\n<h4 class=\"wp-block-heading\">Homework<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/courses.lsa.umich.edu\/krasny\/wp-content\/uploads\/sites\/202\/2025\/06\/math156_hw01.pdf\">hw1<\/a>&nbsp;due: Tues Sept 3&nbsp;<a href=\"https:\/\/www.youtube.com\/watch?reload=9&amp;v=dNVrdYGiULM\">Cesaria Evora<\/a><br><a href=\"https:\/\/courses.lsa.umich.edu\/krasny\/wp-content\/uploads\/sites\/202\/2025\/06\/math156_hw02.pdf\">hw2<\/a>&nbsp;due: Tues Sept 10&nbsp;<a href=\"https:\/\/www.youtube.com\/watch?v=2LDPUfbXRLM\">Louis Armstrong<\/a><br><a href=\"https:\/\/courses.lsa.umich.edu\/krasny\/wp-content\/uploads\/sites\/202\/2025\/06\/math156_hw03.pdf\">hw3<\/a>&nbsp;due: Tues Sept 17&nbsp;<a href=\"https:\/\/www.youtube.com\/watch?v=inNBpizpZkE\">Nina Simone<\/a><br><a href=\"https:\/\/courses.lsa.umich.edu\/krasny\/wp-content\/uploads\/sites\/202\/2025\/06\/math156_hw04.pdf\">hw4<\/a>&nbsp;due: Tues Sept 24&nbsp;<a href=\"https:\/\/www.youtube.com\/watch?reload=9&amp;v=F7P6YBc9KFA\">Jacqueline du Pre<\/a><br><a href=\"https:\/\/courses.lsa.umich.edu\/krasny\/wp-content\/uploads\/sites\/202\/2025\/06\/math156_hw05.pdf\">hw5<\/a>&nbsp;due: Fri Oct 4&nbsp;<a href=\"https:\/\/www.youtube.com\/watch?v=LuT8gA9KT6I\">Aretha Franklin<\/a><br><a href=\"https:\/\/courses.lsa.umich.edu\/krasny\/wp-content\/uploads\/sites\/202\/2025\/06\/math156_hw06.pdf\">hw6<\/a>&nbsp;due: Fri Oct 11&nbsp;<a href=\"https:\/\/www.youtube.com\/watch?v=ApmNziTwU6g\">Monte Alexander<\/a><br><a href=\"https:\/\/courses.lsa.umich.edu\/krasny\/wp-content\/uploads\/sites\/202\/2025\/06\/math156_hw07.pdf\">hw7<\/a>&nbsp;due: Tues Oct 22&nbsp;<a href=\"https:\/\/www.youtube.com\/watch?v=L07TKGjseyg\">Gordon Lightfoot<\/a><br><a href=\"https:\/\/courses.lsa.umich.edu\/krasny\/wp-content\/uploads\/sites\/202\/2025\/06\/math156_hw08.pdf\">hw8<\/a>&nbsp;due: Tues Oct 29&nbsp;<a href=\"https:\/\/www.youtube.com\/watch?v=EdhoX1Xu6ZI\">Gil Scott Heron<\/a><br><a href=\"https:\/\/courses.lsa.umich.edu\/krasny\/wp-content\/uploads\/sites\/202\/2025\/06\/math156_hw09.pdf\">hw9<\/a>&nbsp;due: Fri Nov 15&nbsp;<a href=\"https:\/\/www.youtube.com\/watch?v=ZL81tPHp82g\">Dion DiMucci<\/a><br><a href=\"https:\/\/courses.lsa.umich.edu\/krasny\/wp-content\/uploads\/sites\/202\/2025\/06\/math156_hw10.pdf\">hw10<\/a>&nbsp;due: Mon Nov 20&nbsp;<a href=\"https:\/\/www.youtube.com\/watch?v=-JwmIBSMzSM\">Leonard Cohen<\/a><br><a href=\"https:\/\/courses.lsa.umich.edu\/krasny\/wp-content\/uploads\/sites\/202\/2025\/06\/math156_hw11.pdf\">hw11<\/a>&nbsp;due: Fri Dec 6&nbsp;<a href=\"https:\/\/www.youtube.com\/watch?v=mwn97weAxa0\">Laura Nyro<\/a><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\" \/>\n\n\n\n<h4 class=\"wp-block-heading\">Exams<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">1st midterm exam, Wed Sept 25, 6-7:30pm,&nbsp;<a href=\"https:\/\/courses.lsa.umich.edu\/krasny\/wp-content\/uploads\/sites\/202\/2025\/06\/math156_1324_East_Hall.pdf\">1324 East Hall<\/a>,&nbsp;<a href=\"https:\/\/courses.lsa.umich.edu\/krasny\/wp-content\/uploads\/sites\/202\/2025\/06\/math156_exam_midterm1_review.pdf\">review sheet<\/a>,&nbsp;<a href=\"https:\/\/courses.lsa.umich.edu\/krasny\/wp-content\/uploads\/sites\/202\/2025\/06\/math156_exam_midterm1_review_sol.pdf\">solutions<\/a><br>2nd midterm exam, Wed Nov 6, 6-7:30pm,&nbsp;<a href=\"https:\/\/courses.lsa.umich.edu\/krasny\/wp-content\/uploads\/sites\/202\/2025\/06\/math156_1324_East_Hall.pdf\">1324 East Hall<\/a>,&nbsp;<a href=\"https:\/\/courses.lsa.umich.edu\/krasny\/wp-content\/uploads\/sites\/202\/2025\/06\/math156_exam_midterm1_review.pdf\">review sheet<\/a>,&nbsp;<a href=\"https:\/\/courses.lsa.umich.edu\/krasny\/wp-content\/uploads\/sites\/202\/2025\/06\/math156_exam_midterm1_review_sol.pdf\">solutions<\/a><br>final exam, Thurs Dec 12, 8-10am,&nbsp;sections 1, 2, 5 in 1200 CHEM, sections 3, 4 in 1300 CHEM,&nbsp;<a href=\"https:\/\/courses.lsa.umich.edu\/krasny\/wp-content\/uploads\/sites\/202\/2025\/07\/math156_CHEM_floor_map.pdf\">CHEM floor map<\/a>, <a href=\"https:\/\/courses.lsa.umich.edu\/krasny\/wp-content\/uploads\/sites\/202\/2025\/06\/math156_exam_final_review.pdf\">review sheet<\/a>,&nbsp;<a href=\"https:\/\/courses.lsa.umich.edu\/krasny\/wp-content\/uploads\/sites\/202\/2025\/06\/math156_exam_final_review_sol.pdf\">solutions<\/a><br>review classes for final exam<br>Mon Dec 9 at 4-5pm in 269 Weiser (AW)<br>Mon Dec 9 at 5-6pm in 1084 East Hall (RK)<br>Tues Dec 10 at 10am-12pm in 4096 East Hall (NR)<br>Wed Dec 11 at 5-6pm in B745 East Hall (JW)<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\" \/>\n\n\n\n<h4 class=\"wp-block-heading\">Study Groups<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">The&nbsp;<a href=\"https:\/\/lsa.umich.edu\/slc\">Science Learning Center<\/a>&nbsp;offers&nbsp;<a href=\"https:\/\/lsa.umich.edu\/slc\/study-groups.html\">study groups<\/a>&nbsp;for Math 156 students. The groups meet weekly to review course material.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\" \/>\n\n\n\n<p class=\"wp-block-paragraph\">&#8220;You need the willingness to fail all the time. You have to generate many ideas and then you have to work very hard only to discover that they don&#8217;t work. And you keep doing that over and over until you find one that does work.&#8221; &#8211;&nbsp;<a href=\"http:\/\/en.wikipedia.org\/wiki\/John_Backus\">John Backus<\/a>, lead developer of Fortran<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\" \/>\n\n\n\n<h4 class=\"wp-block-heading\">Links<\/h4>\n\n\n\n<figure class=\"wp-block-embed aligncenter is-type-video is-provider-mivideo wp-block-embed-mivideo\"><div class=\"wp-block-embed__wrapper\">\n<iframe title=\"math156_parabola_1\" id=\"kaltura_player\" src='https:\/\/cdnapisec.kaltura.com\/p\/1038472\/embedPlaykitJs\/uiconf_id\/54883762?iframeembed=true&amp;entry_id=1_jsfeo31f&amp;config%5Bprovider%5D=%7B%22widgetId%22%3A%221_z6ujnyjg%22%7D&amp;config%5Bplayback%5D=%7B%22startTime%22%3A0%7D' style=\"width: 1280px;height: 720px;border: 0;\" allowfullscreen webkitallowfullscreen allow=\"autoplay *; fullscreen *; encrypted-media *\" sandbox=\"allow-downloads allow-forms allow-same-origin allow-scripts allow-top-navigation allow-pointer-lock allow-popups allow-modals allow-orientation-lock allow-popups-to-escape-sandbox allow-presentation allow-top-navigation-by-user-activation\" mozAllowFullScreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<figure class=\"wp-block-embed aligncenter is-type-video is-provider-mivideo wp-block-embed-mivideo\"><div class=\"wp-block-embed__wrapper\">\n<iframe title=\"math156_parabola_2\" id=\"kaltura_player\" src='https:\/\/cdnapisec.kaltura.com\/p\/1038472\/embedPlaykitJs\/uiconf_id\/54883762?iframeembed=true&amp;entry_id=1_ugssfxwc&amp;config%5Bprovider%5D=%7B%22widgetId%22%3A%221_kq6tvbzy%22%7D&amp;config%5Bplayback%5D=%7B%22startTime%22%3A0%7D' style=\"width: 1280px;height: 720px;border: 0;\" allowfullscreen webkitallowfullscreen allow=\"autoplay *; fullscreen *; encrypted-media *\" sandbox=\"allow-downloads allow-forms allow-same-origin allow-scripts allow-top-navigation allow-pointer-lock allow-popups allow-modals allow-orientation-lock allow-popups-to-escape-sandbox allow-presentation allow-top-navigation-by-user-activation\" mozAllowFullScreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/courses.lsa.umich.edu\/krasny\/wp-content\/uploads\/sites\/202\/2025\/06\/math156_parabola.pdf\">parabolas<\/a>&nbsp;at the Michigan League<br><a href=\"https:\/\/www.youtube.com\/watch?v=rI1f762o6Jc\">trig substitution<\/a>&nbsp;by Hanliang Guo<\/li>\n\n\n\n<li><a href=\"https:\/\/www.desmos.com\/calculator\/oe0hphgofl\">Desmos demonstration of Euler&#8217;s method<\/a>&nbsp;by James Wheeler<\/li>\n\n\n\n<li><a href=\"http:\/\/www.khanacademy.org\/\">videos from Khan Academy<\/a>&nbsp;by Salman Khan<\/li>\n\n\n\n<li><a href=\"https:\/\/ocw.mit.edu\/resources\/res-18-006-calculus-revisited-single-variable-calculus-fall-2010\/\">videos from MIT Open Courseware<\/a>&nbsp;by Herbert Gross<\/li>\n\n\n\n<li><a href=\"https:\/\/admissions.umich.edu\/apply\/first-year-applicants\/ap-ib-credit\/ap-guidelines#LSA\">University of Michigan policy on granting AP credit<\/a><\/li>\n\n\n\n<li><a href=\"http:\/\/apcentral.collegeboard.com\/apc\/Controller.jpf\">Advanced Placement homepage<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/courses.lsa.umich.edu\/krasny\/wp-content\/uploads\/sites\/202\/2025\/06\/math156_pt_cover02_2005.pdf\">torus&nbsp;<\/a>cover illustration from Physics Today, Feb 2005<\/li>\n\n\n\n<li><a href=\"http:\/\/lsa.umich.edu\/math\/undergraduates.html\">information on majoring or minoring in math<\/a><\/li>\n\n\n\n<li><a href=\"http:\/\/lsa.umich.edu\/math\/undergraduates\/extracurricular-activities\/math-talks\/math-club.html\">Undergraduate Math Club<\/a><\/li>\n\n\n\n<li><a href=\"http:\/\/www.jstor.org\/stable\/10.4169\/collmathj.41.5.0392\">Proof Without Words: Double Sum for Sine and Cosine<\/a>&nbsp;by Hasan Unal, The College Mathematics Journal, Vol. 41 (2010) p. 392<\/li>\n\n\n\n<li><a href=\"http:\/\/www.jstor.org\/stable\/10.4169\/college.math.j.45.3.190\">Proof Without Words: Sine Sum Identity<\/a>&nbsp;by Long Wang, The College Mathematics Journal, Vol. 45 (2014) p. 190<\/li>\n\n\n\n<li><em>Research on Student Notetaking<\/em>&nbsp;by D. DeZure, M. Kaplan &amp; M. A. Deerman&nbsp;<a href=\"https:\/\/courses.lsa.umich.edu\/krasny\/wp-content\/uploads\/sites\/202\/2025\/06\/math156_crlt.pdf\">[pdf]<\/a><br><em>Occasional Paper No. 16<\/em>, Center for Research on Learning and Teaching, University of Michigan&nbsp;<a href=\"http:\/\/crlt.umich.edu\/\">[CRLT]<\/a><br>&#8220;&#8230; Research on student notetaking shows that taking notes in class and reviewing those notes (either in class or afterward) have a positive impact on student learning. &#8230;&#8221;<\/li>\n\n\n\n<li><a href=\"https:\/\/sites.lsa.umich.edu\/krasny\/links\/fellowships\/\">student fellowships, summer programs, etc.<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/courses.lsa.umich.edu\/krasny\/wp-content\/uploads\/sites\/202\/2025\/06\/math156_Euler_2.jpg\">Portrait of Leonhard Euler<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/courses.lsa.umich.edu\/krasny\/wp-content\/uploads\/sites\/202\/2025\/07\/gautschi-08.pdf\">Leonhard Euler: His Life, the Man, and His Works<\/a>&nbsp;by Walter Gautschi,&nbsp;<em>SIAM Review<\/em>, vol. 50, no. 1 (March 2008), pp. 3-33<\/li>\n\n\n\n<li><a href=\"https:\/\/courses.lsa.umich.edu\/krasny\/wp-content\/uploads\/sites\/202\/2025\/06\/math156_Euler-Kline.pdf\">Euler and Infinite Series<\/a>&nbsp;by Morris Kline,&nbsp;<em>Mathematics Magazine<\/em>, vol. 56 (1983) pp. 307-314<\/li>\n\n\n\n<li><a href=\"http:\/\/en.wikipedia.org\/wiki\/Basel_problem\">Euler&#8217;s solution of the Basel problem<\/a>,&nbsp;<a href=\"https:\/\/www.youtube.com\/watch?reload=9&amp;v=d-o3eB9sfls\">an alternative solution using light from 3Blue1Brown<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.youtube.com\/watch?v=DoAbA6rXrwA&amp;frags=pl%2Cwn\">a video about e by the Mathologer<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/courses.lsa.umich.edu\/krasny\/wp-content\/uploads\/sites\/202\/2025\/06\/math156_article_planck.pdf\">Max Planck: the reluctant revolutionary<\/a>&nbsp;by Helge Kragh,&nbsp;<em>Physics World<\/em>, December 2000, pp. 31-35<\/li>\n\n\n\n<li><a href=\"https:\/\/courses.lsa.umich.edu\/krasny\/wp-content\/uploads\/sites\/202\/2025\/06\/dyson.pdf\">Why is Maxwell&#8217;s Theory so hard to understand?<\/a>&nbsp;by Freeman Dyson<\/li>\n\n\n\n<li><a href=\"https:\/\/www.youtube.com\/watch?v=cUzklzVXJwo\">How Imaginary Numbers Were Invented<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Math 156 &#8211; Applied Honors Calculus II &#8211; Fall 2024 Math 156 is a calculus 2 class designed for STEM majors (though all majors are welcome). The prerequisite is a score of 4 or 5 on the AP Calculus exam (AB or BC) or equivalent. For more details see the course&nbsp;description. all sections meet MonTuesWedFri&hellip; <a class=\"more-link\" href=\"https:\/\/courses.lsa.umich.edu\/krasny\/math-156\/\">Continue reading <span class=\"screen-reader-text\">Math 156<\/span><\/a><\/p>\n","protected":false},"author":4973,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"tw-no-title.php","meta":{"footnotes":""},"class_list":["post-16","page","type-page","status-publish","hentry","entry"],"_links":{"self":[{"href":"https:\/\/courses.lsa.umich.edu\/krasny\/wp-json\/wp\/v2\/pages\/16","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lsa.umich.edu\/krasny\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/courses.lsa.umich.edu\/krasny\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lsa.umich.edu\/krasny\/wp-json\/wp\/v2\/users\/4973"}],"replies":[{"embeddable":true,"href":"https:\/\/courses.lsa.umich.edu\/krasny\/wp-json\/wp\/v2\/comments?post=16"}],"version-history":[{"count":4,"href":"https:\/\/courses.lsa.umich.edu\/krasny\/wp-json\/wp\/v2\/pages\/16\/revisions"}],"predecessor-version":[{"id":223,"href":"https:\/\/courses.lsa.umich.edu\/krasny\/wp-json\/wp\/v2\/pages\/16\/revisions\/223"}],"wp:attachment":[{"href":"https:\/\/courses.lsa.umich.edu\/krasny\/wp-json\/wp\/v2\/media?parent=16"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}