Logic And Discrete Mathematics

This is a text that covers the standard topics in a sophomore-level course in discrete mathematics: logic, sets, proof techniques, basic number theory, functions, relations, and elementary combinatorics, with an emphasis on motivation.

Integer programming (discrete optimization) is best used for solving problems involving discrete, whole elements. Using integer variables, one can model logical requirements, fixed costs, sequencing and scheduling requirements, and many other problem aspects. Whether it’s taught in OR graduate programs or in math or computer science programs; in courses called "Integer Programming," "Combinatorial Optimization," "Combinatorial Optimization and Integer Programming" or simply "Advanced Operations Management," it’s a part of every OR curriculum, and one of its greatest teachers has developed a text that shows how to use logic in integer programming to develop models with much greater precision.

Discrete math is a popular book topic | start Googling around and you'll nd a zillion dierent textbooks about it. Take a closer look, and you'll discover that most of these are pretty thick, dense volumes packed with lots of equations and proofs. They're prin- cipled approaches, written by mathematicians and (seemingly) to mathematicians. I speak with complete frankness when I say I'm comforted to know that the human race is well covered in this area. We need smart people who can derive complex expressions and prove theorems from scratch, and I'm glad we have them.