{"id":85685,"date":"2024-01-25T14:26:03","date_gmt":"2024-01-25T22:26:03","guid":{"rendered":"https:\/\/sou.edu\/academics\/?p=85685"},"modified":"2024-02-09T14:20:32","modified_gmt":"2024-02-09T22:20:32","slug":"math-students-gain-invaluable-experience-in-summer-research-program","status":"publish","type":"post","link":"https:\/\/sou.edu\/academics\/math-students-gain-invaluable-experience-in-summer-research-program\/","title":{"rendered":"Math Students Gain Invaluable Experience Exploring Symmetry in Summer Research Program"},"content":{"rendered":"\n<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-5n8q1it-c318a92add966868bc3cc8ef5271b058\">\n.avia-section.av-5n8q1it-c318a92add966868bc3cc8ef5271b058{\nbackground-color:#f3f3f3;\nbackground-image:unset;\n}\n<\/style>\n<div id='av_section_1' aria-label='ºÚ¹Ï³ÔÁÏÍø English Stories - Blog Roll Template - Intro Section' class='avia-section av-5n8q1it-c318a92add966868bc3cc8ef5271b058 main_color 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300w, https:\/\/sou.edu\/academics\/wp-content\/uploads\/sites\/14\/2024\/01\/Math-Students-Gain-Invaluable-Experience-Exploring-Symmetry-in-Summer-Research-Program-OG-1030x441.jpg 1030w, https:\/\/sou.edu\/academics\/wp-content\/uploads\/sites\/14\/2024\/01\/Math-Students-Gain-Invaluable-Experience-Exploring-Symmetry-in-Summer-Research-Program-OG-768x329.jpg 768w, https:\/\/sou.edu\/academics\/wp-content\/uploads\/sites\/14\/2024\/01\/Math-Students-Gain-Invaluable-Experience-Exploring-Symmetry-in-Summer-Research-Program-OG-705x302.jpg 705w\" sizes=\"(max-width: 1200px) 100vw, 1200px\" class=\"wp-image-86401 avia-img-lazy-loading-not-86401 avia_image  sp-no-webp\" alt=\"Math Students Gain Invaluable Experience Exploring Symmetry in Summer Research Program OG\" decoding=\"async\" fetchpriority=\"high\" itemprop=\"thumbnailUrl\"  > <\/picture><\/div><\/div><\/div><br \/>\n\n<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-lrtiomuf-3f2a0e1524f6553d2acfa8320d0630d3\">\n#top .av-special-heading.av-lrtiomuf-3f2a0e1524f6553d2acfa8320d0630d3{\npadding-bottom:0;\nfont-size:24px;\n}\nbody .av-special-heading.av-lrtiomuf-3f2a0e1524f6553d2acfa8320d0630d3 .av-special-heading-tag .heading-char{\nfont-size:25px;\n}\n#top #wrap_all .av-special-heading.av-lrtiomuf-3f2a0e1524f6553d2acfa8320d0630d3 .av-special-heading-tag{\nfont-size:24px;\n}\n.av-special-heading.av-lrtiomuf-3f2a0e1524f6553d2acfa8320d0630d3 .av-subheading{\nfont-size:18px;\n}\n\n@media only screen and (min-width: 480px) and (max-width: 767px){ \n#top #wrap_all .av-special-heading.av-lrtiomuf-3f2a0e1524f6553d2acfa8320d0630d3 .av-special-heading-tag{\nfont-size:0.8em;\n}\n}\n\n@media only screen and (max-width: 479px){ \n#top #wrap_all .av-special-heading.av-lrtiomuf-3f2a0e1524f6553d2acfa8320d0630d3 .av-special-heading-tag{\nfont-size:0.8em;\n}\n}\n<\/style>\n<div  class='av-special-heading av-lrtiomuf-3f2a0e1524f6553d2acfa8320d0630d3 av-special-heading-h1 custom-color-heading blockquote modern-quote  avia-builder-el-7  el_after_av_image  el_before_av_textblock  top-30 av-inherit-size av-linked-heading'><h1 class='av-special-heading-tag '  itemprop=\"headline\"  >Math Students Gain Invaluable Experience Exploring Symmetry in Summer Research Program<\/h1><div class=\"special-heading-border\"><div class=\"special-heading-inner-border\"><\/div><\/div><\/div><br \/>\n\n<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-lrtit0fa-9cd87fdb08c286709b03c78923f014b1\">\n#top .av_textblock_section.av-lrtit0fa-9cd87fdb08c286709b03c78923f014b1 .avia_textblock{\nfont-size:15px;\n}\n<\/style>\n<section  class='av_textblock_section av-lrtit0fa-9cd87fdb08c286709b03c78923f014b1 '   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><div class='avia_textblock'  itemprop=\"text\" ><p>Most people are aware of the many ways in which symmetry can appear in the world around<br \/>\nus, be it in art, architecture, nature, or geometry. Far fewer of us, however, have been exposed to how symmetries can be used to help solve problems in mathematics. Last summer, two ºÚ¹Ï³ÔÁÏÍø mathematics students, Will Helman and Daniel Sinderson, embarked on an undergraduate research project through ºÚ¹Ï³ÔÁÏÍø\u2019s Summer Research Experience program to do just that. However, instead of studying the symmetries of triangles or squares (or any other shape for that matter), their project focused on studying the symmetries of an important class of equations in math and physics called <em>differential equations<\/em>.<\/p>\n<\/div><\/section><br \/>\n\n<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-lrtita6q-f9f224d7ea91aae3215bdc0a419c29b6\">\n#top .av_textblock_section.av-lrtita6q-f9f224d7ea91aae3215bdc0a419c29b6 .avia_textblock{\nfont-size:15px;\n}\n<\/style>\n<section  class='av_textblock_section av-lrtita6q-f9f224d7ea91aae3215bdc0a419c29b6 '   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><div class='avia_textblock'  itemprop=\"text\" ><p>Differential equations allow us to relate how quantities change with respect to one or more variables. Nearly all important physical phenomena, from the humble falling apple to the supermassive black holes of general relativity, are modeled with differential equations. Naturally then, mathematicians and physicists alike have devoted an immense amount of effort to their analysis. Despite these efforts, very little is actually known about solving differential equations. In fact, for most differential equations, we have no standard techniques for finding solutions, even if we can prove solutions exist.<\/p>\n<\/div><\/section><br \/>\n\n<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-lrtitknm-b339d2066c807f0522e4c1966487a2a0\">\n#top .av_textblock_section.av-lrtitknm-b339d2066c807f0522e4c1966487a2a0 .avia_textblock{\nfont-size:15px;\n}\n<\/style>\n<section  class='av_textblock_section av-lrtitknm-b339d2066c807f0522e4c1966487a2a0 '   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><div class='avia_textblock'  itemprop=\"text\" ><p>In the late 1800s, the Norwegian mathematician Sophus Lie discovered that if a differential equation has enough symmetry (transformations which leave the equation unchanged), then those symmetries can be exploited to rewrite the equation in a simpler form, possibly leading to its solution. From then on, mathematicians have been concerned, not only with finding the solutions to differential equations, but also with trying to analyze what symmetries an equation might possess.<\/p>\n<\/div><\/section><br \/>\n\n<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-lrtitsuj-ddd39b7587d45fc38239db0f5f82bcff\">\n#top .av_textblock_section.av-lrtitsuj-ddd39b7587d45fc38239db0f5f82bcff .avia_textblock{\nfont-size:15px;\n}\n<\/style>\n<section  class='av_textblock_section av-lrtitsuj-ddd39b7587d45fc38239db0f5f82bcff '   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><div class='avia_textblock'  itemprop=\"text\" ><p>The so-called classical symmetries studied by Lie were expanded upon in the 1960s by mathematicians Bluman and Cole. These new nonclassical symmetries were shown to always contain the classical symmetries. However, they could also lead to solutions that the classical symmetries might miss.<\/p>\n<\/div><\/section><br \/>\n\n<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-lrtiwjmh-9e21d27caff9a34bac7e7cbe976289ae\">\n#top .av_textblock_section.av-lrtiwjmh-9e21d27caff9a34bac7e7cbe976289ae .avia_textblock{\nfont-size:15px;\n}\n<\/style>\n<section  class='av_textblock_section av-lrtiwjmh-9e21d27caff9a34bac7e7cbe976289ae '   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><div class='avia_textblock'  itemprop=\"text\" ><p>The project, led by Dr. Brandon Ashley of the ºÚ¹Ï³ÔÁÏÍø Mathematics Department, analyzed the classical and nonclassical symmetries of two physically relevant differential equations: the Born-Infeld (BI) equation of relativistic string theory:<\/p>\n<\/div><\/section><br \/>\n\n<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-lrtqcxwg-44b423fb1cd8623753696231649f8be4\">\n.avia-image-container.av-lrtqcxwg-44b423fb1cd8623753696231649f8be4 img.avia_image{\nbox-shadow:none;\n}\n.avia-image-container.av-lrtqcxwg-44b423fb1cd8623753696231649f8be4 .av-image-caption-overlay-center{\ncolor:#ffffff;\n}\n<\/style>\n<div  class='avia-image-container av-lrtqcxwg-44b423fb1cd8623753696231649f8be4 av-styling-no-styling avia-align-  avia-builder-el-13  el_after_av_textblock  el_before_av_textblock '   itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" ><div class=\"avia-image-container-inner\"><div class=\"avia-image-overlay-wrap\"><picture><source srcset=\"https:\/\/sou.edu\/academics\/wp-content\/uploads\/sites\/14\/2024\/01\/equation1_styled.webp 1200w,https:\/\/sou.edu\/academics\/wp-content\/uploads\/sites\/14\/2024\/01\/equation1_styled-300x50.webp 300w,https:\/\/sou.edu\/academics\/wp-content\/uploads\/sites\/14\/2024\/01\/equation1_styled-1030x172.webp 1030w,https:\/\/sou.edu\/academics\/wp-content\/uploads\/sites\/14\/2024\/01\/equation1_styled-768x128.webp 768w,https:\/\/sou.edu\/academics\/wp-content\/uploads\/sites\/14\/2024\/01\/equation1_styled-705x118.webp 705w\" sizes=\"(max-width: 1200px) 100vw, 1200px\" type=\"image\/webp\"><img src=\"https:\/\/sou.edu\/academics\/wp-content\/uploads\/sites\/14\/2024\/01\/equation1_styled.png\" height=\"200\" width=\"1200\" srcset=\"https:\/\/sou.edu\/academics\/wp-content\/uploads\/sites\/14\/2024\/01\/equation1_styled.png 1200w, https:\/\/sou.edu\/academics\/wp-content\/uploads\/sites\/14\/2024\/01\/equation1_styled-300x50.png 300w, https:\/\/sou.edu\/academics\/wp-content\/uploads\/sites\/14\/2024\/01\/equation1_styled-1030x172.png 1030w, https:\/\/sou.edu\/academics\/wp-content\/uploads\/sites\/14\/2024\/01\/equation1_styled-768x128.png 768w, https:\/\/sou.edu\/academics\/wp-content\/uploads\/sites\/14\/2024\/01\/equation1_styled-705x118.png 705w\" sizes=\"(max-width: 1200px) 100vw, 1200px\" class=\"wp-image-85710 avia-img-lazy-loading-not-85710 avia_image  sp-no-webp\" alt=\"Equation in basic form: (1 + ux2)uxx -2uxuyuxy + (1-uy2)uyy = 0\" decoding=\"async\" fetchpriority=\"high\" itemprop=\"thumbnailUrl\"  > <\/picture><\/div><\/div><\/div><br \/>\n\n<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-lrtqulsc-0004156262d857708e16b28944b645a8\">\n#top .av_textblock_section.av-lrtqulsc-0004156262d857708e16b28944b645a8 .avia_textblock{\nfont-size:15px;\n}\n<\/style>\n<section  class='av_textblock_section av-lrtqulsc-0004156262d857708e16b28944b645a8 '   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><div class='avia_textblock'  itemprop=\"text\" ><p>and the Reduced Gibbons-Tsarev (RGT) equation of dispersionless systems:<\/p>\n<\/div><\/section><br \/>\n\n<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-lrtquyzo-67be666d7c7931fd20a53b70058e93c6\">\n.avia-image-container.av-lrtquyzo-67be666d7c7931fd20a53b70058e93c6 img.avia_image{\nbox-shadow:none;\n}\n.avia-image-container.av-lrtquyzo-67be666d7c7931fd20a53b70058e93c6 .av-image-caption-overlay-center{\ncolor:#ffffff;\n}\n<\/style>\n<div  class='avia-image-container av-lrtquyzo-67be666d7c7931fd20a53b70058e93c6 av-styling-no-styling avia-align-  avia-builder-el-15  el_after_av_textblock  el_before_av_textblock '   itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" ><div class=\"avia-image-container-inner\"><div class=\"avia-image-overlay-wrap\"><picture><source srcset=\"https:\/\/sou.edu\/academics\/wp-content\/uploads\/sites\/14\/2024\/01\/equation2_styled.webp 1200w,https:\/\/sou.edu\/academics\/wp-content\/uploads\/sites\/14\/2024\/01\/equation2_styled-300x50.webp 300w,https:\/\/sou.edu\/academics\/wp-content\/uploads\/sites\/14\/2024\/01\/equation2_styled-1030x172.webp 1030w,https:\/\/sou.edu\/academics\/wp-content\/uploads\/sites\/14\/2024\/01\/equation2_styled-768x128.webp 768w,https:\/\/sou.edu\/academics\/wp-content\/uploads\/sites\/14\/2024\/01\/equation2_styled-705x118.webp 705w\" sizes=\"(max-width: 1200px) 100vw, 1200px\" type=\"image\/webp\"><img src=\"https:\/\/sou.edu\/academics\/wp-content\/uploads\/sites\/14\/2024\/01\/equation2_styled.png\" height=\"200\" width=\"1200\" srcset=\"https:\/\/sou.edu\/academics\/wp-content\/uploads\/sites\/14\/2024\/01\/equation2_styled.png 1200w, https:\/\/sou.edu\/academics\/wp-content\/uploads\/sites\/14\/2024\/01\/equation2_styled-300x50.png 300w, https:\/\/sou.edu\/academics\/wp-content\/uploads\/sites\/14\/2024\/01\/equation2_styled-1030x172.png 1030w, https:\/\/sou.edu\/academics\/wp-content\/uploads\/sites\/14\/2024\/01\/equation2_styled-768x128.png 768w, https:\/\/sou.edu\/academics\/wp-content\/uploads\/sites\/14\/2024\/01\/equation2_styled-705x118.png 705w\" sizes=\"(max-width: 1200px) 100vw, 1200px\" class=\"wp-image-85711 avia-img-lazy-loading-not-85711 avia_image  sp-no-webp\" alt=\"Equation in basic form: utuxt-uxutt+uxx = 0\" decoding=\"async\" fetchpriority=\"high\" itemprop=\"thumbnailUrl\"  > <\/picture><\/div><\/div><\/div><br \/>\n\n<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-lrtqxmiu-41e414c3f96dfa0476dcaf82834c5e86\">\n#top .av_textblock_section.av-lrtqxmiu-41e414c3f96dfa0476dcaf82834c5e86 .avia_textblock{\nfont-size:15px;\n}\n<\/style>\n<section  class='av_textblock_section av-lrtqxmiu-41e414c3f96dfa0476dcaf82834c5e86 '   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><div class='avia_textblock'  itemprop=\"text\" ><p>In earlier work, Dr. Ashley was able to show that both of these equations have special properties which allow them to be transformed to especially simple, linear equations, but it was unclear whether or not these transformations could be detected using either classical or nonclassical symmetry methods. Will and Daniel were tasked first with learning the general theory behind the classical and nonclassical symmetry methods and then with calculating the classical and nonclassical symmetries of the BI and RGT equations to see what connections could be made.<\/p>\n<\/div><\/section><br \/>\n\n<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-lrtq36a0-1a9cf44ebca4aef896dcd77ff33d8070\">\n.avia-image-container.av-lrtq36a0-1a9cf44ebca4aef896dcd77ff33d8070 img.avia_image{\nbox-shadow:none;\n}\n.avia-image-container.av-lrtq36a0-1a9cf44ebca4aef896dcd77ff33d8070 .av-image-caption-overlay-center{\ncolor:#ffffff;\n}\n<\/style>\n<div  class='avia-image-container av-lrtq36a0-1a9cf44ebca4aef896dcd77ff33d8070 av-styling- avia-align-center  avia-builder-el-17  el_after_av_textblock  el_before_av_textblock '   itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" ><div class=\"avia-image-container-inner\"><div class=\"avia-image-overlay-wrap\"><picture><source srcset=\"https:\/\/sou.edu\/academics\/wp-content\/uploads\/sites\/14\/2024\/01\/Math_Representation-of-Solutions-Born-Equation.webp \"  type=\"image\/webp\"><img src=\"https:\/\/sou.edu\/academics\/wp-content\/uploads\/sites\/14\/2024\/01\/Math_Representation-of-Solutions-Born-Equation.gif\" height=\"512\" width=\"512\" class=\"wp-image-85698 avia-img-lazy-loading-not-85698 avia_image  sp-no-webp\" alt=\"Spherical Representation of Solutions to the Born-Infeld Equation\" decoding=\"async\" fetchpriority=\"high\" itemprop=\"thumbnailUrl\"  > <\/picture><\/div><\/div><\/div><br \/>\n\n<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-lrtr6yol-6b0ffac2d106c05ef7d68fbb5ba47768\">\n#top .av_textblock_section.av-lrtr6yol-6b0ffac2d106c05ef7d68fbb5ba47768 .avia_textblock{\nfont-size:12px;\ntext-align:center;\n}\n<\/style>\n<section  class='av_textblock_section av-lrtr6yol-6b0ffac2d106c05ef7d68fbb5ba47768 '   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><div class='avia_textblock'  itemprop=\"text\" ><p>*Spherical Representation of Solutions to the Born-Infield Equation<\/p>\n<\/div><\/section><br \/>\n\n<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-lrtqyx91-0d2c032198ae2ef6d8e407a0fb6ee0ad\">\n#top .av_textblock_section.av-lrtqyx91-0d2c032198ae2ef6d8e407a0fb6ee0ad .avia_textblock{\nfont-size:15px;\n}\n<\/style>\n<section  class='av_textblock_section av-lrtqyx91-0d2c032198ae2ef6d8e407a0fb6ee0ad '   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><div class='avia_textblock'  itemprop=\"text\" ><p>Despite the impressively difficult calculations involved (even when aided by the mathematical software Maple), Will and Daniel were able to show that the set of classical symmetries and the set of nonclassical symmetries for the BI and RGT equations were precisely the same, respectively. Will and Daniel\u2019s results naturally lead one to wonder if the special properties of the BI and RGT equations could have been used to predict the so-called classical equals nonclassical phenomenon and in particular if every equation whose classical symmetries match the nonclassical symmetries will have these special properties.<\/p>\n<p>These questions and others are currently being addressed by Dr. Ashley\u2019s on-going research with talented ºÚ¹Ï³ÔÁÏÍø students like Will and Daniel. When asked about their summer research experience, Will and Daniel had the following to say:<\/p>\n<\/div><\/section><br \/>\n<div  class='avia-testimonial-wrapper av-lsf6vgf5-15be7b08f296b468ca9b1a65138bb745 avia-grid-testimonials avia-grid-1-testimonials avia_animate_when_almost_visible' >\n<section class=\"avia-testimonial-row\"><div class='avia-testimonial av-lsf6s4cc-223428b6046ec98dbc80cbe71438f4bf avia-testimonial-row-1 avia-first-testimonial flex_column no_margin av_one_full'><div class='avia-testimonial_inner'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><div class='avia-testimonial-image'  itemprop=\"image\" ><picture><source srcset=\"https:\/\/sou.edu\/academics\/wp-content\/uploads\/sites\/14\/2024\/01\/William-Helman-Thumb-180x180.webp 180w,https:\/\/sou.edu\/academics\/wp-content\/uploads\/sites\/14\/2024\/01\/William-Helman-Thumb-80x80.webp 80w,https:\/\/sou.edu\/academics\/wp-content\/uploads\/sites\/14\/2024\/01\/William-Helman-Thumb-36x36.webp 36w,https:\/\/sou.edu\/academics\/wp-content\/uploads\/sites\/14\/2024\/01\/William-Helman-Thumb.webp 183w\" sizes=\"auto, (max-width: 180px) 100vw, 180px\" type=\"image\/webp\"><img src=\"https:\/\/sou.edu\/academics\/wp-content\/uploads\/sites\/14\/2024\/01\/William-Helman-Thumb-180x180.jpg\" height=\"180\" width=\"180\" srcset=\"https:\/\/sou.edu\/academics\/wp-content\/uploads\/sites\/14\/2024\/01\/William-Helman-Thumb-180x180.jpg 180w, https:\/\/sou.edu\/academics\/wp-content\/uploads\/sites\/14\/2024\/01\/William-Helman-Thumb-80x80.jpg 80w, https:\/\/sou.edu\/academics\/wp-content\/uploads\/sites\/14\/2024\/01\/William-Helman-Thumb-36x36.jpg 36w, https:\/\/sou.edu\/academics\/wp-content\/uploads\/sites\/14\/2024\/01\/William-Helman-Thumb.jpg 183w\" sizes=\"auto, (max-width: 180px) 100vw, 180px\" class=\"attachment-square size-square sp-no-webp\" alt=\"\" loading=\"lazy\" decoding=\"async\"  > <\/picture><\/div><div class='avia-testimonial-content '><div class='avia-testimonial-markup-entry-content'  itemprop=\"text\" ><p><em>\u201cSummer research with Dr. Ashley was a rewarding experience. Of course, math research is nothing like math class. While investigating your problem, it\u2019s easy to become lost in associated questions you will invariably meet along the way. In (especially lower division) math classes, if a question occurs to you, it\u2019s likely that it has come to many other students before you at the prompt of such well-explored material. When you dive into higher-level topics, chances are that no one has ever wondered what you are wondering. It can be daunting. During Dr. Ashley\u2019s crash course, very natural questions occurred to Daniel and me, and increasingly they were met with \u201cno one knows,\u201d \u201cthat\u2019s still an open question,\u201d or a shrug and chuckle. It was extremely exciting. When it came time to tackle the research problem, the feeling that we were on untrodden grounds remained. Ultimately, one of those questions proved to be the biggest takeaway from the project, and it has big implications.<\/em><\/p>\n<p><em>We got a taste of theoretical math research, and used specialized computational techniques for our problem. We learned a little differential geometry and Lie theory to do it. The experience was a blast, and solidified my excitement about my future career in research.\u201d<\/em><\/p>\n<\/div><\/div><div class=\"avia-testimonial-meta\"><div class=\"avia-testimonial-arrow-wrap\"><div class=\"avia-arrow\"><\/div><\/div><div class='avia-testimonial-meta-mini'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><strong  class='avia-testimonial-name'  itemprop=\"name\" >William Helman<\/strong><span  class='avia-testimonial-subtitle '  itemprop=\"jobTitle\" >ºÚ¹Ï³ÔÁÏÍø Junior Math Major<\/span><\/div><\/div><\/div><\/div><\/section>\n<section class=\"avia-testimonial-row\"><div class='avia-testimonial av-lsf6s4cc-70141edd20309358fb274d38e2e89763 avia-testimonial-row-2 avia-first-testimonial flex_column no_margin av_one_full'><div class='avia-testimonial_inner'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><div class='avia-testimonial-image'  itemprop=\"image\" ><picture><source srcset=\"https:\/\/sou.edu\/academics\/wp-content\/uploads\/sites\/14\/2024\/01\/Daniel-Sinderson-180x180.webp 180w,https:\/\/sou.edu\/academics\/wp-content\/uploads\/sites\/14\/2024\/01\/Daniel-Sinderson-300x300.webp 300w,https:\/\/sou.edu\/academics\/wp-content\/uploads\/sites\/14\/2024\/01\/Daniel-Sinderson-80x80.webp 80w,https:\/\/sou.edu\/academics\/wp-content\/uploads\/sites\/14\/2024\/01\/Daniel-Sinderson-36x36.webp 36w,https:\/\/sou.edu\/academics\/wp-content\/uploads\/sites\/14\/2024\/01\/Daniel-Sinderson.webp 400w\" sizes=\"auto, (max-width: 180px) 100vw, 180px\" type=\"image\/webp\"><img src=\"https:\/\/sou.edu\/academics\/wp-content\/uploads\/sites\/14\/2024\/01\/Daniel-Sinderson-180x180.jpg\" height=\"180\" width=\"180\" srcset=\"https:\/\/sou.edu\/academics\/wp-content\/uploads\/sites\/14\/2024\/01\/Daniel-Sinderson-180x180.jpg 180w, https:\/\/sou.edu\/academics\/wp-content\/uploads\/sites\/14\/2024\/01\/Daniel-Sinderson-300x300.jpg 300w, https:\/\/sou.edu\/academics\/wp-content\/uploads\/sites\/14\/2024\/01\/Daniel-Sinderson-80x80.jpg 80w, https:\/\/sou.edu\/academics\/wp-content\/uploads\/sites\/14\/2024\/01\/Daniel-Sinderson-36x36.jpg 36w, https:\/\/sou.edu\/academics\/wp-content\/uploads\/sites\/14\/2024\/01\/Daniel-Sinderson.jpg 400w\" sizes=\"auto, (max-width: 180px) 100vw, 180px\" class=\"attachment-square size-square sp-no-webp\" alt=\"Daniel Sinderson Math Major\" loading=\"lazy\" decoding=\"async\"  > <\/picture><\/div><div class='avia-testimonial-content '><div class='avia-testimonial-markup-entry-content'  itemprop=\"text\" ><p>\u201cIt was a huge privilege to be able to work on the project this summer with Will and Dr. Ashley. At the start, I expected it would largely be a pen and paper project involving some proofs. Instead, it was a massive computational project involving a computer algebra system and the scariest looking equations I\u2019ve yet seen.<\/p>\n<p>We started learning background material for the project in late June. The crash course Dr. Ashley took us through was difficult but well-taught, and it covered both the computer algebra system we used (navigation, programming, and the documentation of some specialized modules we used) and the actual mathematics behind the project including methods for solving problems that, beforehand, would\u2019ve been literally impossible for me to solve. These were the hard skills learned in the project.<\/p>\n<p>The soft skills are what really stand out to me though. It turns out math research is hard. And much different than math classes. I\u2019m 35. I\u2019ve been thrown (or jumped) into at least half-a-dozen projects I\u2019m barely prepared for, but this was the first time I\u2019ve truly doubted if I was up to the task and had to push through. Easily 95% of my working time was spent stuck and churning through failed attempts at a solution. To go through that experience well-supported and then come out the other side with solutions in hand (and a fascinating direction for future research thanks to Will!) was a very rewarding experience. It\u2019s one that I honestly didn\u2019t expect to be available to me at a small regional university like ºÚ¹Ï³ÔÁÏÍø. I\u2019d do it again and would recommend the experience to other students in the department in a heartbeat.\u201d<\/p>\n<\/div><\/div><div class=\"avia-testimonial-meta\"><div class=\"avia-testimonial-arrow-wrap\"><div class=\"avia-arrow\"><\/div><\/div><div class='avia-testimonial-meta-mini'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><strong  class='avia-testimonial-name'  itemprop=\"name\" >Daniel Sinderson<\/strong><span  class='avia-testimonial-subtitle '  itemprop=\"jobTitle\" >ºÚ¹Ï³ÔÁÏÍø Senior Math Major<\/span><\/div><\/div><\/div><\/div><\/section>\n<\/div><br \/>\n\n<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-lrtrdaai-c7aa9e503a36688daf716aa79a2fe736\">\n#top .av_textblock_section.av-lrtrdaai-c7aa9e503a36688daf716aa79a2fe736 .avia_textblock{\nfont-size:15px;\n}\n<\/style>\n<section  class='av_textblock_section av-lrtrdaai-c7aa9e503a36688daf716aa79a2fe736 '   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><div class='avia_textblock'  itemprop=\"text\" ><p>The generous support of donors was essential to the success of the Summer Research Experience. In particular, the Allan and Katherine M. Alsing Fund for STEM Research provided 23% of the funding while numerous donors to the STEM Division Fund for Excellence provided 52% of the funding. The balance came from ºÚ¹Ï³ÔÁÏÍø program funds and allowed for the funding and support of this research by Dr. Ashley, Daniel, and William.<\/p>\n<\/div><\/section><br \/>\n\n<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-2gzzwxh-6694072afa3af995b8db785d03ee4592\">\n#top .hr.av-2gzzwxh-6694072afa3af995b8db785d03ee4592{\nmargin-top:20px;\nmargin-bottom:20px;\n}\n.hr.av-2gzzwxh-6694072afa3af995b8db785d03ee4592 .hr-inner{\nwidth:50;\n}\n<\/style>\n<div  class='hr av-2gzzwxh-6694072afa3af995b8db785d03ee4592 hr-custom  avia-builder-el-22  el_after_av_textblock  el_before_av_button_big  avia-builder-el-last  hr-center hr-icon-no'><span class='hr-inner inner-border-av-border-thin'><span class=\"hr-inner-style\"><\/span><\/span><\/div><br \/>\n<div  class='avia-button-wrap avia-button-center  avia-builder-el-23  el_after_av_hr  el_before_av_hr '>\n<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" 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href="https:\/\/www.facebook.com\/sharer.php?u=https:\/\/sou.edu\/academics\/math-students-gain-invaluable-experience-in-summer-research-program\/&#038;t=Math%20Students%20Gain%20Invaluable%20Experience%20Exploring%20Symmetry%20in%20Summer%20Research%20Program" aria-hidden='false' data-av_icon='\ue8f3' data-av_iconfont='entypo-fontello' title='' data-avia-related-tooltip='Share on Facebook'><span class='avia_hidden_link_text'>Share on Facebook<\/span><\/a><\/li><li class='av-share-link av-social-link-twitter' ><a target=\"_blank\" aria-label=\"Share on X\" href="https:\/\/twitter.com\/share?text=Math%20Students%20Gain%20Invaluable%20Experience%20Exploring%20Symmetry%20in%20Summer%20Research%20Program&#038;url=https:\/\/sou.edu\/academics\/?p=85685" aria-hidden='false' data-av_icon='\ue932' data-av_iconfont='entypo-fontello' title='' data-avia-related-tooltip='Share on X'><span class='avia_hidden_link_text'>Share on X<\/span><\/a><\/li><li class='av-share-link av-social-link-linkedin' 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class='avia_hidden_link_text'>Share by Mail<\/span><\/a><\/li><\/ul><\/div><\/div><\/p><\/div>\n<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-mfoc7p-ca4eaec7cae679eae64beaa046f126db\">\n.flex_column.av-mfoc7p-ca4eaec7cae679eae64beaa046f126db{\nborder-radius:0px 0px 0px 0px;\npadding:0px 0px 0px 0px;\n}\n<\/style>\n<div  class='flex_column av-mfoc7p-ca4eaec7cae679eae64beaa046f126db av_one_fifth  avia-builder-el-26  el_after_av_three_fifth  avia-builder-el-last  flex_column_div av-zero-column-padding  '     ><\/div>\n","protected":false},"excerpt":{"rendered":"<p class=\"pop-0\">ºÚ¹Ï³ÔÁÏÍø Students Will and Daniel join an ongoing research project surrounding classical and nonclassical symmetries of differential equations.<\/p>\n<div class=\"avia-button-wrap avia-button-left\"><a class=\"avia-button avia-color-dark avia-size-large avia-position-left \" href=\"\/academics\/math-students-gain-invaluable-experience-in-summer-research-program\/\" 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ºÚ¹Ï³ÔÁÏÍø - is a Liberal Arts University in Ashland, Oregon. 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The beautiful ºÚ¹Ï³ÔÁÏÍø campus, nestled in the hills of Ashland, OR welcomes the surrounding community to come and enjoy many hosted events, including: sporting events at the ºÚ¹Ï³ÔÁÏÍø Raider Stadium and Lithia Motors Pavilion, theater performances hosted by the ºÚ¹Ï³ÔÁÏÍø Theatre program , musical performances at the ºÚ¹Ï³ÔÁÏÍø Musical Recital Hall, and art exhibitions at the Schneider Museum of Art and other campus art galleries. ºÚ¹Ï³ÔÁÏÍø has many specialized programs which help lower tuition costs, grant in-state tuition, provide accelerated graduation, give opportunities to adult learners, and allow students to graduate with internships leading to job placement.","email":"provostsoffice@sou.edu","telephone":"541-552-6114","legalName":"ºÚ¹Ï³ÔÁÏÍø","foundingDate":"1872-09-01"},{"@type":"Person","@id":"https:\/\/sou.edu\/academics\/#\/schema\/person\/c05ce37e05849dda3cf78b331e7a731f","name":"wulfl","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/sou.edu\/academics\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/9f231c43b0e117a5a358aa67b4b91374c04a7fa01ec38499070f45c48fb0945a?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/9f231c43b0e117a5a358aa67b4b91374c04a7fa01ec38499070f45c48fb0945a?s=96&d=mm&r=g","caption":"wulfl"}}]}},"acf":[],"_links":{"self":[{"href":"https:\/\/sou.edu\/academics\/wp-json\/wp\/v2\/posts\/85685","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sou.edu\/academics\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sou.edu\/academics\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/sou.edu\/academics\/wp-json\/wp\/v2\/users\/69"}],"replies":[{"embeddable":true,"href":"https:\/\/sou.edu\/academics\/wp-json\/wp\/v2\/comments?post=85685"}],"version-history":[{"count":0,"href":"https:\/\/sou.edu\/academics\/wp-json\/wp\/v2\/posts\/85685\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/sou.edu\/academics\/wp-json\/wp\/v2\/media\/86400"}],"wp:attachment":[{"href":"https:\/\/sou.edu\/academics\/wp-json\/wp\/v2\/media?parent=85685"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sou.edu\/academics\/wp-json\/wp\/v2\/categories?post=85685"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sou.edu\/academics\/wp-json\/wp\/v2\/tags?post=85685"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}