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Books  >>  Math

Judith L. Gersting

Mathematical Structures for Computer Science

Judith L. Gersting Mathematical Structures For Computer Science 0007 Edition;
 
 


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Main description:

Judith Gersting's Mathematical Structures for Computer Science has long been acclaimed for its clear presentation of essential concepts and its exceptional range of applications relevant to computer science majors. Now with this new edition, it is the first discrete mathematics textbook revised to meet the proposed new ACM/IEEE standards for the course.

Table of contents:

1.  Formal Logic         

1.1  Statements, Symbolic Representation, and Tautologies   
Connectives and Truth Values      
Tautologies         
Logical Connectives in the Real World     
An Algorithm        
Special Interest Page – Can "And" Ever Be "Or"?
Section 1.1 Review 
Exercises 1.1         

1.2  Propositional Logic        
Valid Arguments        
Derivation Rules for Propositional Logic     
Deduction Method and Other Rules     
Verbal Arguments        
Section 1.2 Review 
Exercises 1.2         

1.3  Quantifiers, Predicates, and Validity      
Quantifiers and Predicates       
Translation         
Validity         
Section 1.3 Review 
Exercises 1.3         

1.4  Predicate Logic        
Derivation Rules for Predicate Logic     
Universal Instantiation      
Existential Instantiation      
Universal Generalization      
Existential Generalization      
More Work with Rules       
Verbal Arguments        
Conclusion         
Section 1.4 Review 
Exercises 1.4         

1.5  Logic Programming        
Prolog         
Horn Clauses and Resolution      
Recursion         
Expert Systems        
Section 1.5 Review 
Exercises 1.5         

1.6  Proof of Correctness        
Assertions         
Assignment Rule        
Conditional Rule        
Section 1.6 Review 
Exercises 1.6         

Chapter 1 Review         
On the Computer         

2.  Proofs, Induction, and Number Theory      

2.1  Proof Techniques        
Theorems and Informal Proofs      
To Prove or Not to Prove       
Exhaustive Proof        
Direct Proof        
Contraposition        
Contradiction        
Serendipity         
Common Definitions       
Section 2.1 Review 
Exercises 2.1         

2.2  Induction           
First Principle of Induction   
Proofs by Mathematical Induction 
Second Principle of Induction 
Section 2.2 Review 
Exercises 2.2 

2.3  More on Proof of Correctness 
Loop Rule 
Euclidean Algorithm 
Special Interest Page – Making Safer Software 
Section 2.3 Review 
Exercises 2.3

2.4  Number Theory 
The Fundamental Theorem of Arithmetic  
More on Prime Numbers 
Euler Phi Function
Section 2.4 Review 
Exercises 2.4 

Chapter 2 Review 
On the Computer

3.  Recursion, Recurrence Relations, and Analysis of Algorithms

3.1  Recursive Definitions 
Recursively Defined Sequences 
Recursively Defined Sets 
Recursively Defined Operations 
Recursively Defined Algorithms
Section 3.1 Review
Exercises 3.1 

3.2  Recurrence Relations  
Linear First-Order Recurrence Relations 
Expand, Guess, and Verify 
A Solution Formula 
Linear Second-Order Recurrence Relations 
Divide-and-Conquer Recurrence Relations 
Section 3.2 Review
Exercises 3.2 

3.3  Analysis of Algorithms 
The General Idea 
Analysis Using Recurrence Relations  
Upper Bound (Euclidean Algorithm) 
Special Interest Page - Of Trees … and Pancakes
Section 3.3 Review
Exercises 3.3 

Chapter 3 Review 
On the Computer 

4.  Sets, Combinatorics, and Probability   

4.1  Sets  
Notation 
Relationships between Sets 
Sets of Sets 
Binary and Unary Operations 
Operations on Sets 
Set Identities 
Countable and Uncountable Sets 
Section 4.1 Review
Exercises 4.1 

4.2  Counting 
Multiplication Principle 
Addition Principle 
Using the Principles Together 
Decision Trees 
Section 4.2 Review
Exercises 4.2 
  
4.3  Principle of Inclusion and Exclusion; Pigeonhole Principle 
Principle of Inclusion and Exclusion 
Pigeonhole Principle 
Section 4.3 Review 
Exercises 4.3 

4.4  Permutations and Combinations 
Permutations 
Combinations 
Eliminating Duplicates 
Permutations and Combinations with Repetitions
Generating Permutations and Combinations
Special Interest Page – Archimedes and the Stomachion 
Section 4.4 Review
Exercises 4.4 

4.5 Binomial Theorem 
Pascal's Triangle 
Binomial Theorem and Its Proof 
Applying the Binomial Theorem 
Section 4.5 Review
Exercises 4.5

4.6   Probability 
Introduction to Finite Probability 
Probability Distributions 
Conditional Probability
Bayes' Theorem 
Expected Value 
Binomial Distribution 
Average Case Analysis of Algorithms
Section 4.5 Review
Exercises 4.6 

Chapter 4 Review 
On the Computer  

5.  Relations, Functions, and Matrices 

5.1  Relations
 
Binary Relations 
Properties of

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