What Is Combinatorics Anyway?



Broadly speaking, combinatorics is the branch of mathematics dealing



with different ways of selecting objects from a set or arranging objects. It



tries to answer two major kinds of questions, namely, counting questions: how many ways can a selection or arrangement be chosen with a particular set of properties; and structural



questions: does there exist a selection or arrangement of objects with a



particular set of properties?



The authors have presented a text for students at all levels of preparation.



For some, this will be the first course where the students see several real proofs.



Others will have a good background in linear algebra, will have completed the calculus



stream, and will have started abstract algebra.



The text starts by briefly discussing several examples of typical combinatorial problems



to give the reader a better idea of what the subject covers. The next



chapters explore enumerative ideas and also probability. It then moves on to



enumerative functions and the relations between them, and generating functions and recurrences.,



Important families of functions, or numbers and then theorems are presented.



Brief introductions to computer algebra and group theory come next. Structures of particular



interest in combinatorics: posets, graphs, codes, Latin squares, and experimental designs follow. The



authors conclude with further discussion of the interaction between linear algebra



and combinatorics.



Features










Two new chapters on probability and posets.







Numerous new illustrations, exercises, and problems.







More examples on current technology use







A thorough focus on accuracy







Three appendices: sets, induction and proof techniques, vectors and matrices, and biographies with historical notes,







Flexible use of MapleTM and MathematicaTM