Finite and Discrete Math Problem Solver

by Research & Education Association, James R. Ogden

h Problem Solver is an insightful and essential study and solution guide chock-full of clear, concise problem-solving gems. All your questions can be found in one convenient source from one of the most trusted names in reference solution guides. More useful, more practical, and more informative, these study aids are the best review books and textbook companions available. Nothing remotely as comprehensive or as helpful exists in their subject anywhere. Perfect for undergraduate and graduate studies.

Here in this highly useful reference is the finest overview of finite and discrete math currently available, with hundreds of finite and discrete math problems that cover everything from graph theory and statistics to probability and Boolean algebra. Each problem is clearly solved with step-by-step detailed solutions.

DETAILS
- The PROBLEM SOLVERS are unique - the ultimate in study guides.
- They are ideal for helping students cope with the toughest subjects.
- They greatly simplify study and learning tasks.
- They enable students to come to grips with difficult problems by showing them the way, step-by-step, toward solving problems. As a result, they save hours of frustration and time spent on groping for answers and understanding.
- They cover material ranging from the elementary to the advanced in each subject.
- They work exceptionally well with any text in its field.
- PROBLEM SOLVERS are available in 41 subjects.
- Each PROBLEM SOLVER is prepared by supremely knowledgeable experts.
- Most are over 1000 pages.
- PROBLEM SOLVERS are not meant to be read cover to cover. They offer whatever may be needed at a given time. An excellent index helps to locate specific problems rapidly.

TABLE OF CONTENTS
Introduction
Chapter 1: Logic
Statements, Negations, Conjunctions, and Disjunctions
Truth Table and Proposition Calculus
Conditional and Biconditional Statements
Mathematical Induction
Chapter 2: Set Theory
Sets and Subsets
Set Operations
Venn Diagram
Cartesian Product
Applications
Chapter 3: Relations
Relations and Graphs
Inverse Relations and Composition of Relations
Properties of Relations
Equivalence Relations
Chapter 4: Functions
Functions and Graphs
Surjective, Injective, and Bijective Functions
Chapter 5: Vectors and Matrices
Vectors
Matrix Arithmetic
The Inverse and Rank of a Matrix
Determinants
Matrices and Systems of Equations, Cramer's Rule
Special Kinds of Matrices
Chapter 6: Graph Theory
Graphs and Directed Graphs
Matrices and Graphs
Isomorphic and Homeomorphic Graphs
Planar Graphs and Colorations
Trees
Shortest Path(s)
Maximum Flow
Chapter 7: Counting and Binomial Theorem
Factorial Notation
Counting Principles
Permutations
Combinations
The Binomial Theorem
Chapter 8: Probability
Probability
Conditional Probability and Bayes' Theorem
Chapter 9: Statistics
Descriptive Statistics
Probability Distributions
The Binomial and Joint Distributions
Functions of Random Variables
Expected Value
Moment Generating Function
Special Discrete Distributions
Normal Distributions
Special Continuous Distributions
Sampling Theory
Confidence Intervals
Point Estimation
Hypothesis Testing
Regression and Correlation Analysis
Non-Parametric Methods
Chi-Square and Contingency Tables
Miscellaneous Applications
Chapter 10: Boolean Algebra
Boolean Algebra and Boolean Functions
Minimization
Switching Circuits
Chapter 11: Linear Programming and the Theory of Games
Systems of Linear Inequalities
Geometric Solutions and Dual of Linear Programming Problems
The Simplex Method
Linear Programming - Advanced Methods
Integer Programming
The Theory of Games
Index

WHAT THIS BOOK IS FOR

Students have generally found finite and discrete math difficult subjects to understand and learn. Despite the publication of hundreds of textbooks in this field, each one intended to provide an improvement over previous textbooks, students of finite and discrete math continue to remain perplexed as a result of numerous subject areas that must be remembered and correlated when solving problems. Various interpretations of finite and discrete math terms also contribute to the difficulties of mastering the subject.

In a study of finite and discrete math, REA found the following basic reasons underlying the inherent difficulties of finite and discrete

No systematic rules of analysis were ever developed to follow in a step-by-step manner to solve typically encountered problems. This results from numerous different conditions and principles involved in a problem that leads to many possible different solution methods. To prescribe a set of rules for each of the possible variations would involve an enormous number of additional steps, making this task more burdensome than solving the problem directly due to the expectation of much trial and error.

Current textbooks normally explain a given principle in a few pages written by a finite and discrete math professional who has insight into the subject matter not shared by others. These explanations are often...

1040 pages, Paperback

First published January 25, 1985