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