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Two books by Ömer Eğecioğlu invite students to explore the fascinating world of combinatorics by University of California - Santa Barbara.
Photo: Ömer Eğecioğlu
At first pass, it may seem odd for a computer science professor to pen a book about mathematical topics. But a chat with quickly dispels the notion that the fields are that different, at least from his point of view. The two titles, "Lessons in Enumerative Combinatorics" (2021) and "Lectures in Algebraic Combinatorics" (2020) offer an insightful introduction to the branch of mathematics that gives rise to theoretical computer science.
Ömer Eğecioğlu co-authored the works with his own Ph.D. advisor, Adriano Garsia, emeritus professor of mathematics at UC San Diego. He put together most of "Lessons" from his own teaching materials, while "Lectures" traces its origins to over six decades of Garsia's research and unique perspective. "I was more of a collaborator on the 'Lectures' book," Ömer Eğecioğlu said.
A combinatorial structure is a visual representation of some mathematical construct which often reveals aspects not readily apparent in the original formulation. The methods for counting these structures form the discipline known as enumerative combinatorics.
Among its many other applications, combinatorics opens up the basic theory of computability itself. The mathematics of counting, combinations and ordering eventually leads to symbolic representations, algorithmic thinking and finally, the Turing machine model...
Ömer Eğecioğlu hopes that the two books make combinatorics accessible to people just beginning to learn about the subject, whether they're actually pursuing an advanced degree or simply interested in the topic. And he hopes that these books can help students see the connections between topics in computer science and mathematics that they may otherwise have overlooked.
Source: EurekAlert
