This is an old-fashioned text in beginning discrete math, that emphasizes logic, sets, and relations; includes a lot of material on combinatorics (including expositions of recurrences and of generating functions); and somewhat mysteriously has extensive sections on linear algebra and on group theory. Some things that we would expect to see in a modern text, but that are not in this one, include graphs and trees, algorithms, number theory, and probability. There is also no usage of computers here.

The title is misleading, as the structures it primarily deals with are algebraic: lattices, linear spaces, and groups. The group theory part is especially puzzling, as it is about 50 pages and goes into quite a lot of detail. The problem is that it is the detail usually found in group theory courses and focuses on normal subgroups and the things needed for Galois theory. It does not mention the combinatorial aspects of groups such as orbits, Burnside’s lemma, and Pólya’s theory of counting.

This is a proofs book and assumes you already understand how to do proofs. It doesn’t cover any proof techniques. It does define well-ordered sets but doesn’t use them for mathematical induction or anything else. The exercises are nearly all numerical drill.

There’s no bibliographic information provided about this fourth edition. It appears to be an expanded version of the same authors’ *Discrete Mathematics* (New Age International, New Delhi, fourth revised edition, 2009), so the first through third editions did not exist with this title.

The one to beat is this field is Rosen’s *Discrete Mathematics and Its Applications*, which is a gigantic and expensive book but has everything you could possibly want in an introductory discrete math course. Two other good modern introductions that are less overwhelming are Aigner’s *Discrete Mathematics* and Ross & Wright’s *Discrete Mathematics*.

Allen Stenger is a math hobbyist and retired software developer. He is an editor of the Missouri Journal of Mathematical Sciences. His mathematical interests are number theory and classical analysis.