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It plays a similar role in discrete operations research problems and in finite probability. Two of the most basic mathematical aspects of computer science concern the speed and logical structure of a computer program. Speed involves enumeration of the number of times each step in a program can be performed. Logical structure involves flow charts, a form of graphs. Analysis of the speed and logical structure of operations research algorithms to optimize efficient manufacturing or garbage collection entails similar combinatorial mathematics.
It plays a similar role in discrete operations research problems and in finite probability. Two of the most basic mathematical aspects of computer science concern the speed and logical structure of a computer program. Speed involves enumeration of the number of times each step in a program can be performed. Logical structure involves flow charts, a form of graphs.
Analysis of the speed and logical structure of operations research algorithms to optimize efficient manufacturing or garbage collection entails similar combinatorial mathematics. Determining the probability that one of a certain subset of equally likely outcomes occurs requires counting the size of the subset. Such combinatorial probability is the basis of many nonparametric statistical tests.
Thus, enumeration and graph theory are used pervasively throughout the mathematical sciences. This book teaches students how to reason and model combinatorially. It seeks to develop proficiency in basic discrete math problem solving in the way that a calculus textbook develops proficiency in basic analysis problem solving.
The three principal aspects of combinatorial reasoning emphasized in this book are the systematic analysis of different possibilities, the exploration of the logical structure of a problem e. Although important uses of combinatorics in computer science, operations research, and finite probability are mentioned, these applications are often used solely for motivation.
Numerical examples involving the same concepts use more interesting settings such as poker probabilities or logical games. Theory is always first motivated by examples, and proofs are given only when their reasoning is needed to solve applied problems.
Elsewhere, results are stated without proof, such as the form of solutions to various recurrence relations, and then applied in problem solving.
Occasionally, a few theorems are stated simply to give students a flavor of what the theory in certain areas is like. For decades, collegiate curriculum recommendations from the Mathematical Association of America have included combinatorial problem solving as an important component of training in the mathematical sciences. Combinatorial problem solving underlies a wide spectrum of important subjects in the computer science curriculum.
Indeed, it is expected that most students in a course using this book will be computer science majors. Bookmark it to easily review again before an exam. The best part?
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