Next Level Learning: Honors Modern Algebra

Eleven students are enrolled in Dr. Mirabi's Honors Modern Algebra class this semester, one of the highest-level mathematics courses ever taught at Taft.

 

The depth and breadth of the academic talent in the Taft community has allowed our faculty to continuously look for and create new opportunities for learning at the highest levels. Enter Dr. Mostafa Mirabi.

          With undergraduate and master’s degrees in pure mathematics in hand from Tehran Polytechnic University, Dr. Mirabi spent time as a research scholar at the Institute for Research in Fundamental Science before making his way to Wesleyan University, where he earned a Ph.D. in pure mathematics. His primary research centers around mathematical logic, focusing on model theory and its applications in combinatorics and algebra. At Taft, Dr. Mirabi teaches a range of high-level courses, including BC-Calculus, Linear Algebra, and Differential Equations. This semester, he is offering one of the highest-level mathematics classes ever taught at Taft: Honors Modern Algebra.

          “The class was developed to meet the growing demand for advanced mathematical concepts and to challenge students in abstract reasoning,” explains Dr. Mirabi. “Honors Modern Algebra stands out as the ‘most abstract’ and challenging math course.”

          As a discipline, modern algebra—also known as abstract algebra—is rooted in the exploration of group theory. The primary goal for Dr. Mirabi’s students is to explore the Sylow theorem, which states that if we have a group (a mathematical set with a specific operation) with a particular order or size, and if a prime number divides that size, then the group contains a subgroup of that size.

          “The theorem provides insights into the structure of groups and their subgroups, making it a fundamental tool in group theory,” explains Dr. Mirabi.

          And while that may feel like an abstract concept to some, the applications are both concrete and varied.

          “Group theory has numerous applications, including cryptography, coding theory, and symmetry analysis in various scientific fields,” Dr. Mirabi says.

          In cryptography, for example, group theory is important in designing secure encryption algorithms by leveraging the mathematical properties of groups. In the surging field of Artificial Intelligence, group theory can be applied to recognize and classify patterns, contributing to image and signal processing in AI systems. In physics (specifically quantum mechanics), group theory is used to understand the behavior of particles and the structure of atomic orbitals, while in biology, group theory helps scientists analyze the symmetrical properties of biological molecules in the study of protein structures. It also has powerful and practical applications in chemistry, engineering, geometry and topology, economics, music, and more.

          Honors Modern Algebra is designed for students who are passionate about theoretical mathematics and who are looking for a rigorous intellectual challenge. Eleven students are currently enrolled in the course, among them, Martyna Glowacka ’25.

Honors Modern Algebra students with Dr. Mirabi.
In photo, back row from left: Vincent Chen, Martyna Glowacka, Helen Liao, Dr. Mirabi, Anmay Suri, Noah Cinel, Steven Yang; front row, from left: Rina Kurihara, Tiffany Zong, Kyla O’Byrne Missing from photo: Luke Zhang and Maggie Zeng

          “I decided to enroll in Honors Modern Algebra because of the unique perspective on mathematics this class provides,” says Martyna. “The course is proof-based, which, in my view, is the essence of mathematics. This approach not only allows me and other students to understand the theory thoroughly, but also discover new connections between different portions of the material.”

          Discovering connections within the material is an element of learning that speaks to Vincent Chen ’24, as well.

          “Dr. Mirabi provides students with ample time for independent thought, encouraging us to explore connections between the steps of proofs. Moreover, he consistently places new topics within a broader context, using them to clarify fundamental concepts. This approach shattered my preconception that math is a dull, linear process. Beyond being an exceptional lecturer, Dr. Mirabi is a very dedicated teacher. His teaching style has significantly altered my perspective on mathematics.”

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