An Overview of Selected Discrete Mathematics Texts

While I am currently doing research in analysis and partial differential equations as a Ph.D. student at the University of Tennessee-Knoxville, my love of mathematics was focused in discrete mathematics, particularly combinatorics, during the earlier years of my undergraduate study. This was in part due to a research topics course I took during my freshmen year of college at Carnegie Mellon with visiting professor Steven Miller, and in part due to my experience competing in competitions such as ARML and the Putnam. Nonetheless, my math textbook collection grew to include various discrete math textbooks, particularly those on combinatorics. To this day, combinatorics is my favorite sub-field of discrete mathematics, and I do have a few papers published at the intersection of number theory and combinatorics.

In this article, I’m going to review a selection of these books that are currently on my bookshelf. I’ll talk about the content covered, the intended audience, and anything in particular I’ve found the book useful for. Since the books have different intended audiences and writing styles, I don’t like to plainly say that one book is better than another. That being said I will list the books in alphabetical order by author last name.

“A Walk Through Combinatorics: An Introduction to Enumeration and Graph Theory” by M. Bóna

First up we have “A Walk Through Combinatorics: An Introduction to Enumeration and Graph Theory” by…