## Mathematics for Algorithm and Systems AnalysisDiscrete mathematics is fundamental to computer science, and interesting, challenging problems in discrete mathematics arise in programming languages, computer architecture, networking, distributed systems, database systems, artificial intelligence, theoretical computer science, and elsewhere. This up-to-date text prepares undergraduates with four units of study: counting and listing, functions, decision trees and recursion, and basic concepts of graph theory. Each unit is divided into four sections, and each section contains a selection of problems that vary in difficulty. Solutions to these problems are given at the end of the text. Multiple-choice questions for review appear at the end of each unit. The text offers students the mathematical language and sophistication to recognize and articulate the ideas behind these questions and to answer questions similar in concept and difficulty. Those who master the necessary ideas and mathematical language to understand these review questions gain the ability to formulate, in the neutral language of mathematics, the problems that arise in various applications of computer science--a skill that enables them to discuss problems in discrete mathematics with other computer scientists and with mathematicians. |

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answer bijection binary tree block called cards choices choose codomain coimage coin compute conditional probability conﬁguration consonants contains corresponds count cycle form decision tree deﬁned deﬁnition degree sequence depth ﬁrst digraph domain domino elements equation equivalence relation Eulerian event exactly Exercises for Section ﬁgure ﬁnd ﬁnite ﬁrst ﬁve formula function f given gives graph G Gray code Here’s Image(X independent induction injection integers labels leaf leaves letters lex order linear loops move multisets n-set notation number of edges obtain one-line form pair partition path permutation polynomial positive possible previous example probability function probability space problem proof prove random variable RANK real numbers recursive algorithm red ball root Rule of Product Rule of Sum sample space satisﬁes simple graph solution spanning tree speciﬁed Step student subgraph subsets Suppose surjection Theorem toss Towers of Hanoi values Var(X vertex sequence vertices vowels washer words