Computer Mathematics for Programmers

1 Number Systems

1.0 Introduction

1.1 Base Ten, or the Decimal System

1.2 Base Two, or the Binary System

1.3 Base Eight, or the Octal System

1.4 Base Sixteen, or the Hexadecimal System

1.5 Converting Decimal Numbers into Binary Numbers

1.6 Converting Decimal Numbers into Octal Numbers

1.7 Converting Decimal Numbers into Hexadecimal Numbers

1.8 Converting Binary Numbers into Hexadecimal Numbers

1.9 Converting Hexadecimal Numbers into Binary Numbers

1.10 Summary

Problem Set A

Problem Set B

Practice Exam


2 Arithmetic Operations

2.0 Introduction

2.1 Addition Tables

2.2 Addition in the Binary System

2.3 Addition in the Octal System

2.4 Addition in the Hexadecimal System

2.5 Subtraction in the Binary System

2.6 Subtraction in the Octal System

2.7 Subtraction in the Hexadecimal System

2.8 Summary

Problem Set A

Problem Set B

Practice Exam


3 Computer Arithmetic

3.0 Introduction

3.1 Integer Storage

3.2 Integer Arithmetic

3.3 Exponential Notation

3.4 Floating Point Storage

3.5 Floating Point Arithmetic

3.6 Round-off Errors

3.7 Summary

Problem Set A

Problem Set B

Practice Exam


4 Algorithms and Flowcharts

4.0 Introduction

4.1 Algorithms

4.2 Flowcharts

4.3 Decisions

4.4 Summary

Problem Set A

Problem Set B

Practice Exam


5 Selected Topics in Algebra

5.0 Introduction

5.1 Order of Operations

5.2 Evaluating Algebraic Expressions

5.3 Addition and Subtraction of Like Terms

5.4 Removing Parentheses by Using the Distributive Law

5.5 Solving Equations in One Unknown

5.6 Equations in Two Unknowns

5.7 Simultaneous Equations (Substitution Method)

5.8 Simultaneous Equations (Elimination by Addition)

5.9 Summary

Problem Set A

Problem Set B

Practice Exam


6 Sets

6.0 Introduction

6.1 Set Descriptions

6.2 The Empty Set and the Universal Set

6.3 Operations with Sets

6.4 Subsets

6.5 Venn Diagrams

6.6 Summary

Problem Set A

Problem Set B

Practice Exam


7 Logic

7.0 Introduction

7.1 Statements

7.2 Truth Tables

7.3 Expansion of Truth Tables

7.4 Computer Applications

7.5 Summary

Problem Set A

Problem Set B

Practice Exam


8 Boolean Algebra

8.0 Introduction

8.1 The Basis of Boolean Algebra

8.2 Simplifying Boolean Expressions

8.3 Veitch Diagrams

8.4 A Security System

8.5 A Final Comment on Simplifying Boolean Expressions

8.6 Switching Circuits

8.7 Summary

Problem Set A

Problem Set B

Practice Exam


9 Matrices

9.0 Introduction

9.1 Addition and Subtraction of Matrices

9.2 Multiplication by a Constant

9.3 Multiplication of Matrices

9.4 Row Reduction

9.5 Equations with Three Unknowns

9.6 Summary

Problem Set A

Problem Set B

Practice Exam


10 Graphing and Linear Programming

10.0 Introduction

10.1 Graph Paper

10.2 Tables

10.3 Systems of Equations

10.4 Introduction to Linear Inequalities

10.5 Systems of Inequalities

10.6 An Introduction to Linear Programming

10.7 Summary

Problem Set A

Problem Set B

Practice Exam


11 Statistics

11.0 Introduction

11.1 Collection of Data

11.2 Grouped Data

11.3 Measures of the Center (Averages)

11.4 Measure of Variation (Standard Deviation)

11.5 Probability

11.6 The Normal Probability Curve

11.7 Applied Problems

11.8 Summary

Problem Set A

Problem Set B

Practice Exam

Appendices

A Basic Programs

A.0 Introduction

A.1 BASE/BAS

A.2 CONVERT/BAS

A.3 UNIVAC/BAS

A.4 IBM/BAS

A.5 COMM/BAS

A.6 CAR/BAS

A.7 EQS/BAS

A.8 GAUSE/BAS

A.9 STAT/BAS

A.10 STATBAR/BAS

A.11 RNDNOR/BAS

A.12 SNT/BAS

B Tables

B.1 Addition

B.2 Powers of Two

B.3 Truth Tables

B.4 Normal Probability Table

C Glossary

D Answers to Problem Sets A and Practice Exams

Index