Linear Algebra as Modern Equation: Father Costa, Professors Saccoman and Gross Publish 4th Edition of Algebra Text

Three Seton Hall professors from the Department of Mathematics and Computer Science have collaborated to create the fourth edition of Linear Algebra: Algorithms, Applications and Techniques (Elsevier, 2023). Father Gabriel Costa, Professor John T. Saccoman, Ph.D., and Daniel Gross, Ph.D., are long-time collaborators. Professor Gross and Saccoman are former schoolmates, as both attended Stevens Institute of Technology for their M.S. degrees and were part of the graph theory research group there. Gross, who has taught at Seton Hall for over 40 years, has coauthored sixteen research papers with Saccoman. The two also teach the Introduction to Discrete Math class at Seton Hall, which is compulsory for every math or computer science major or minor.

Over time, they have become an effective team, with a specialty. Another book they authored, Saccoman explains, features a Peterson Graph on the cover. Now, a matrix that is representational of the same data appears on the cover of their recent edition of Linear Algebra. "It’s become our calling card," he said, of his ongoing collaborations with Gross. "It's a great working relationship to have a colleague that you can bounce ideas off," says Saccoman. "There are no egos here. We get the thing done, and if we do not like it, we tell each other, fix it and then it’s good."

Additionally, Professor Saccoman and Father Costa have collaborated on several talks, papers and at least four books about Sabermetrics (“the search for objective truth about baseball"), according to Costa. Many say that one can find math in most areas of intellectual curiosity and life in general, and baseball is no exception. "Sometimes people don't realize they are doing mathematical thinking when they actually are, and this may be due to the way it was taught at the lower grades in primary and secondary schools," says Saccoman.

Originally written in 1995 by Professor Richard Bronson, the essential math text Linear Algebra is now in its fourth edition. A second edition was co-authored by Seton Hall’s Father Gabriel Costa in 2007, and then Professor John T. Saccoman joined the 2014 release.

Linear Algebra: Algorithms, Applications, and Techniques begins with concrete and computational explanations of linear algebra, and then explains the major applications. The latest edition was updated with appendices on Jordan canonical forms and Markov chains, notes Saccoman.

"The 3rd edition had been out for a while, and a lot of the main topics are still there," he says, "but some of the applications like data science are very big now for linear algebra and algebraic graph theory, which is what I practice." He and Gross, who Saccoman notes is a great teacher of proof techniques, added modern utilizations of linear algebra, and included them in chapter zero, which is unique to math texts.

At Seton Hall since he was a boy, Saccoman often visited his father John J. Saccoman, a professor at the university for 45 years. He has fond memories of the campus from his youth, which include visits to the math club his father ran when he was twelve, and Walsh Gymnasium, where both PE classes and plays were held. Saccoman later attended Seton Hall Prep when it was located on the South Orange campus.

"I was stage crew for some of our productions in high school," recalls Saccoman, who served as Editor in Chief of The Setonian "for 2 percent of its history" and loved seeing basketball games as an undergraduate. "I have fun memories of [Walsh] when it was tightly packed with some 3,600 people," he recalls.

He drew upon his father’s legacy at Seton Hall by attending the University and becoming a math professor himself; for more than ten years, he and his father taught at Seton Hall together. Long a subject specialist in graph theory, Saccoman says, "It’s a very interdisciplinary area; you could be in the math department doing graph theory research, or computer science, electrical engineering or operations research."

Professor Saccoman has been busy balancing his teaching and research with his role as co-chair of the 2.5-year current Middle States Accreditation process (with Leigh Onimus of the Business School) for Seton Hall, which has been accredited since 1932 and undergoes a lengthy and rigorous re-accreditation process every 8 years.  

And yet, Saccoman has already begun another book with Professor Gross and is in talks with other colleagues about another on discrete mathematics, which will enhance existing texts in this subject area, albeit with a different approach, utilizing graph theory. He seems most proud of the collaborative work he does with colleagues to support graduate thesis students, something he learned while at Stevens collaborating with his late mentor, Charles Suffel, Ph.D.

"When Charlie Suffel passed away, he had two students [at Stevens] that hadn't finished [their thesis] - part of the death sentence for graduate students: if your thesis advisor passes away, there often isn't someone to take over. And so Professor Gross, myself, Kristi Luttrell, Ph.D., and Monica Heinig, Ph.D., pulled together and we were able to help those two students finish."

Categories: Education