{"id":55044,"date":"2025-12-03T11:00:51","date_gmt":"2025-12-03T16:00:51","guid":{"rendered":"https:\/\/engineering.jhu.edu\/ams\/?post_type=news&p=55044"},"modified":"2026-01-07T11:40:49","modified_gmt":"2026-01-07T16:40:49","slug":"finding-order-in-complexity","status":"publish","type":"news","link":"https:\/\/engineering.jhu.edu\/ams\/news\/finding-order-in-complexity\/","title":{"rendered":"Finding order in complexity\u00a0"},"content":{"rendered":"

When Adam Tobin-Williams \u201926 enrolled at Johns Hopkins University as a Chemical and Biomolecular Engineering major, he didn\u2019t expect to fall in love with mathematics. But a single course\u2014Linear Differential Equations with Mario Micheli, senior lecturer of applied mathematics and statistics\u2014sparked an entirely new academic path.<\/span>\u00a0<\/span><\/p>\n

\u201cThat class really drew me in,\u201d he says. \u201cI realized I was more fascinated by the math behind engineering than by the engineering itself.\u201d<\/span>\u00a0<\/span><\/p>\n

Now pursuing a dual <\/span>bachelor\u2019s\/master\u2019s degree<\/span><\/a> in both applied mathematics and statistics and chemical and biomolecular engineering, Tobin-Williams is blending two disciplines that share a common goal: using theory and computation to solve complex, practical problems.<\/span>\u00a0<\/span><\/p>\n

Tobin-Williams says that the rigor of applied math at Hopkins became a defining challenge\u2014and a source of motivation.<\/span>\u00a0<\/span><\/p>\n

\u201cAMS courses are consistently the hardest I\u2019ve taken,\u201d he says. \u201cThe concepts come quickly, the workload is demanding, and exams really test your understanding. But that\u2019s what makes it exciting. You\u2019re constantly learning how to think more critically and how to collaborate more effectively.\u201d<\/span>\u00a0<\/span><\/p>\n

The academic rigor of his coursework provides benefits that extend beyond the classroom.\u00a0<\/span>\u00a0<\/span><\/p>\n

\u201cIn some courses, the class average might be 50%, so you have to get comfortable not knowing everything right away. That process of struggling, failing, and then understanding\u2014that\u2019s what gives you the skills needed for real technical challenges, whether in research.\u201d<\/span>\u00a0<\/span><\/p>\n

Tobin-Williams\u2019 passion for applied math goes beyond equations. After his freshman year, he joined a research team at the <\/span>Johns Hopkins Applied Physics Laboratory<\/span><\/a>, where he helped integrate large language models into a system designed to assist military medics in high-pressure environments.<\/span>\u00a0<\/span><\/p>\n

\u201cWe were building a tool designed to provide quick, accurate guidance for medics and warfighters treating specific battlefield <\/span>injuries,\u201d he explains. \u201cI analyzed how well the system performed using data science tools like confusion matrices in Python. It showed me how <\/span>powerful well-designed algorithms can be in high-pressure situations.\u201d<\/span>\u00a0<\/span><\/p>\n

That experience deepened his interest in the interconnectedness of mathematics, programming, and optimization\u2014an interest he is continuing to pursue in his master\u2019s thesis.\u00a0<\/span>\u00a0<\/span><\/p>\n

Working under <\/span>Mahyar Fazlyab<\/span><\/a>, assistant professor in the Department of Electrical and Computer Engineering, and <\/span>Mateo D\u00edaz<\/span><\/a>, assistant professor in the Department of Applied Mathematics and Statistics, he\u2019s developing and implementing a new algorithm in semidefinite programming to help estimate Lipschitz constants\u2014a key part of understanding how stable deep neural networks are.<\/span>\u00a0<\/span><\/p>\n

\u201cOur goal is to create a faster, more efficient way to determine how stable a neural network is,\u201d he says. \u201cIt\u2019s still early, but I love that I get to help test and implement theories that could improve the performance and reliability of AI systems.\u201d<\/span>\u00a0<\/span><\/p>\n

Across his courses and research, Tobin-Williams continually finds ways to merge applied math with engineering.\u00a0<\/span>\u00a0<\/span><\/p>\n

\u201cGraph theory, Monte Carlo methods, and optimization\u2014these all show up in my chemical engineering work,\u201d he says. \u201cFor example, I\u2019ve used graph theory to study crystal structures, figuring out which crystals connect and how particles move across surfaces. It\u2019s amazing how these abstract concepts become tangible when you see them applied.\u201d<\/span>\u00a0<\/span><\/p>\n

He\u2019s also shared his enthusiasm as the head teaching assistant for the course, Linear Differential Equations for five semesters. His leadership earned him the Professor Joel Dean Excellence in Teaching Award, presented by the applied mathematics and statistics department.\u00a0<\/span>\u00a0<\/span><\/p>\n

\u201cHelping other students find their footing in math has been one of the most rewarding experiences I\u2019ve had at Hopkins,\u201d said Tobin-Williams.<\/span>\u00a0<\/span><\/p>\n

His time at Johns Hopkins has inspired him to continue his studies and he now is planning to pursue a PhD in chemical engineering, with a focus on optimization.<\/span>\u00a0<\/span><\/p>\n

His advice to students? \u201cTalk to your professors. Explore everything. Applied math can seem abstract, but once you start making connections to hands-on problems, you realize it\u2019s everywhere.\u201d<\/span>\u00a0<\/span><\/p>\n","protected":false},"template":"","class_list":["post-55044","news","type-news","status-publish","hentry","news_categories-applied-mathematics","news_categories-student-experience"],"acf":[],"yoast_head":"\nFinding order in complexity\u00a0 | Department of Applied Mathematics and Statistics<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/engineering.jhu.edu\/ams\/news\/finding-order-in-complexity\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Finding order in complexity\u00a0 | Department of Applied Mathematics and Statistics\" \/>\n<meta property=\"og:description\" content=\"When Adam Tobin-Williams \u201926 enrolled at Johns Hopkins University as a Chemical and Biomolecular Engineering major, he didn\u2019t expect to fall in love with mathematics. 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