\u201cThe thing that\u2019s unique about this program is that the graduate students were the leads…. (They) took charge of crafting what the program would look like,\u201d said Harris.<\/p>\n\n\n\n
How did GEMS work? Here\u2019s the story.<\/p>\n\n\n\n
The methods and the math<\/strong><\/h2>\n\n\n\nGraph theory was the perfect mathematical concept around which to build a research program. Also known as \u201cnetwork science,\u201d it has many practical applications \u2013 for example, finding the least amount of cell phone towers needed to service a particular area so there are no gaps in coverage.<\/p>\n\n\n\n
\u201cI think graph theory is nice because you can get into it relatively easily. You don\u2019t have to study a whole semester to understand every concept,\u201d said Pinter. \u201cYou can come up with new ideas and new questions that no one else has actually looked at before.\u201d<\/p>\n\n\n\n![\"A](\"https:\/\/uwm.edu\/letters-science\/wp-content\/uploads\/sites\/255\/2026\/01\/Math-Calatrava-group-300x225.webp\")
Graduate students often accompanied undergraduate students in the new GEMS program on excursions around Milwaukee, including to the Milwaukee Art Museum. Photo courtesy of Lilly Carrillo.<\/figcaption><\/figure>\n\n\n\nSo, graduate students Jillian Cervantes, Kimberly Harry, Matt McClinton, and Melissa Beerbower began to build a curriculum. They created a schedule for the six-week summer program, starting with a week of lectures and skill-building \u2013 for example, teaching students to use the mathematical typing software LaTeX or showing them how to write a mathematical proof. After they had the basics down, the mentors coached their mentees to craft a research project that they would later present at the Society for Industrial and Applied Mathematics Great Lakes Sectional Meeting in September.<\/p>\n\n\n\n
But the program went beyond mathematics. The mentors also arranged several outings for the undergrads, including trips to the Milwaukee County Zoo, the Milwaukee Art Museum, and a Brewers baseball game.<\/p>\n\n\n\n
\u201cWe wanted (the GEMS students) to feel connected to the department as well, so we invited other grad students on outings,\u201d Harry said. \u201c(They\u2019re) realizing all of a sudden they can talk to a grad student and tell them about the research they\u2019re doing and have someone be excited about it with them.\u201d<\/p>\n\n\n\n
And, perhaps most importantly for the students, they were paid for their work and the program included meals. Harris wanted to ensure that there were no barriers for students who wanted to participate in GEMS, so meals were included as working breakfasts and lunches to ensure the participants never had to worry about food costs.<\/p>\n\n\n\n
The mentors<\/strong><\/h2>\n\n\n\nThe graduate students blossomed as the program progressed. They learned the best ways to motivate their mentees, how to foster collaboration, and how to prepare the undergraduates to present research.<\/p>\n\n\n\n
\u201cWhat was really lovely to see how they were growing as mentors,\u201d Harris said. \u201cAt the end of the day, our graduate students are going to become the professors. What better opportunity than to have them start learning how to be professors by helping students start doing research?\u201d<\/p>\n\n\n\n
Though Cervantes had participated in research when she was an undergraduate at 51ÁÔÆæ, this was her first formal mentoring experience. Harry, on the other hand, never had a research experience as an undergraduate, but did have experience writing lectures and designing homework as a graduate student during her PhD program at 51ÁÔÆæ (Harry graduated this August). With both of their perspectives, plus those of their collaborators, they were able to design a program they could be proud of.<\/p>\n\n\n\n
\u201cI think that each one of us can say we left the program more confident in mentoring students,\u201d Harry said.<\/p>\n\n\n\n
\u201cLearning how to mentor is something that I wouldn\u2019t have really been able to learn without getting some practical experience doing it and seeing what challenges come up,\u201d Cervantes added.<\/p>\n\n\n\n
The mentees<\/strong><\/h2>\n\n\n\n![\"A](\"https:\/\/uwm.edu\/letters-science\/wp-content\/uploads\/sites\/255\/2026\/01\/Lilly-at-conference-300x225.webp\")
Mathematical sciences major Lilly Carrillo presented her GEMS program research project at a conference in September and plans to present her research at other symposiums next semester. Photo courtesy of Gabriella Pinter.<\/figcaption><\/figure>\n\n\n\nUndergraduate student Lilly Carrillo just changed her major to mathematical sciences last year. She had never participated in undergraduate research or even written a mathematical proof when she enrolled in the GEMS program.<\/p>\n\n\n\n
\u201cI started at 51ÁÔÆæ at the lowest math level and have clawed my way up \u2013 and I\u2019m still clawing!\u201d she said. \u201cI started this program feeling like an imposter. I lacked confidence. But the mentors really helped me shine, and they assured me that I\u2019m actually smart and creative. It feels good to have the support that they gave me in writing proofs, supporting my ideas, and letting me venture through these research problems.\u201d<\/p>\n\n\n\n
Over the six weeks, Carrillo gained new math skills and learned more about the practical applications of theoretical research. Her project focused on (t,r) broadcast domination of the Petersen Graph \u2013 \u201cIt\u2019s kind of like placing cell phone towers or satellites where lines meet (which we could call objects), and they emit a reception to other objects that are within the graph,\u201d she explained.<\/p>\n\n\n\n
She and her fellow undergraduate researchers created posters and publicly presented their work as a capstone to the GEMS program. This coming year, she plans to present her research at two symposiums. In fact, three of the four GEMS undergraduates decided to participate in the 51ÁÔÆæ SURF program<\/a> after their research experience this summer.<\/p>\n\n\n\n
So, graduate students Jillian Cervantes, Kimberly Harry, Matt McClinton, and Melissa Beerbower began to build a curriculum. They created a schedule for the six-week summer program, starting with a week of lectures and skill-building \u2013 for example, teaching students to use the mathematical typing software LaTeX or showing them how to write a mathematical proof. After they had the basics down, the mentors coached their mentees to craft a research project that they would later present at the Society for Industrial and Applied Mathematics Great Lakes Sectional Meeting in September.<\/p>\n\n\n\n
But the program went beyond mathematics. The mentors also arranged several outings for the undergrads, including trips to the Milwaukee County Zoo, the Milwaukee Art Museum, and a Brewers baseball game.<\/p>\n\n\n\n
\u201cWe wanted (the GEMS students) to feel connected to the department as well, so we invited other grad students on outings,\u201d Harry said. \u201c(They\u2019re) realizing all of a sudden they can talk to a grad student and tell them about the research they\u2019re doing and have someone be excited about it with them.\u201d<\/p>\n\n\n\n
And, perhaps most importantly for the students, they were paid for their work and the program included meals. Harris wanted to ensure that there were no barriers for students who wanted to participate in GEMS, so meals were included as working breakfasts and lunches to ensure the participants never had to worry about food costs.<\/p>\n\n\n\n
The mentors<\/strong><\/h2>\n\n\n\nThe graduate students blossomed as the program progressed. They learned the best ways to motivate their mentees, how to foster collaboration, and how to prepare the undergraduates to present research.<\/p>\n\n\n\n
\u201cWhat was really lovely to see how they were growing as mentors,\u201d Harris said. \u201cAt the end of the day, our graduate students are going to become the professors. What better opportunity than to have them start learning how to be professors by helping students start doing research?\u201d<\/p>\n\n\n\n
Though Cervantes had participated in research when she was an undergraduate at 51ÁÔÆæ, this was her first formal mentoring experience. Harry, on the other hand, never had a research experience as an undergraduate, but did have experience writing lectures and designing homework as a graduate student during her PhD program at 51ÁÔÆæ (Harry graduated this August). With both of their perspectives, plus those of their collaborators, they were able to design a program they could be proud of.<\/p>\n\n\n\n
\u201cI think that each one of us can say we left the program more confident in mentoring students,\u201d Harry said.<\/p>\n\n\n\n
\u201cLearning how to mentor is something that I wouldn\u2019t have really been able to learn without getting some practical experience doing it and seeing what challenges come up,\u201d Cervantes added.<\/p>\n\n\n\n
The mentees<\/strong><\/h2>\n\n\n\nMathematical sciences major Lilly Carrillo presented her GEMS program research project at a conference in September and plans to present her research at other symposiums next semester. Photo courtesy of Gabriella Pinter.<\/figcaption><\/figure>\n\n\n\nUndergraduate student Lilly Carrillo just changed her major to mathematical sciences last year. She had never participated in undergraduate research or even written a mathematical proof when she enrolled in the GEMS program.<\/p>\n\n\n\n
\u201cI started at 51ÁÔÆæ at the lowest math level and have clawed my way up \u2013 and I\u2019m still clawing!\u201d she said. \u201cI started this program feeling like an imposter. I lacked confidence. But the mentors really helped me shine, and they assured me that I\u2019m actually smart and creative. It feels good to have the support that they gave me in writing proofs, supporting my ideas, and letting me venture through these research problems.\u201d<\/p>\n\n\n\n
Over the six weeks, Carrillo gained new math skills and learned more about the practical applications of theoretical research. Her project focused on (t,r) broadcast domination of the Petersen Graph \u2013 \u201cIt\u2019s kind of like placing cell phone towers or satellites where lines meet (which we could call objects), and they emit a reception to other objects that are within the graph,\u201d she explained.<\/p>\n\n\n\n
She and her fellow undergraduate researchers created posters and publicly presented their work as a capstone to the GEMS program. This coming year, she plans to present her research at two symposiums. In fact, three of the four GEMS undergraduates decided to participate in the 51ÁÔÆæ SURF program<\/a> after their research experience this summer.<\/p>\n\n\n\n
Undergraduate student Lilly Carrillo just changed her major to mathematical sciences last year. She had never participated in undergraduate research or even written a mathematical proof when she enrolled in the GEMS program.<\/p>\n\n\n\n
\u201cI started at 51ÁÔÆæ at the lowest math level and have clawed my way up \u2013 and I\u2019m still clawing!\u201d she said. \u201cI started this program feeling like an imposter. I lacked confidence. But the mentors really helped me shine, and they assured me that I\u2019m actually smart and creative. It feels good to have the support that they gave me in writing proofs, supporting my ideas, and letting me venture through these research problems.\u201d<\/p>\n\n\n\n
Over the six weeks, Carrillo gained new math skills and learned more about the practical applications of theoretical research. Her project focused on (t,r) broadcast domination of the Petersen Graph \u2013 \u201cIt\u2019s kind of like placing cell phone towers or satellites where lines meet (which we could call objects), and they emit a reception to other objects that are within the graph,\u201d she explained.<\/p>\n\n\n\n
She and her fellow undergraduate researchers created posters and publicly presented their work as a capstone to the GEMS program. This coming year, she plans to present her research at two symposiums. In fact, three of the four GEMS undergraduates decided to participate in the 51ÁÔÆæ SURF program<\/a> after their research experience this summer.<\/p>\n\n\n\n