Conditionals (with solutions)

J a v a Quiz (Unit 3, Test 0 Practice)

Computer Science S-111a: Intensive Introduction to Computer Science Using Java Handout #11 Your Name Teaching Fellow J a v a Quiz (Unit 3, Test 0 Practice) Multiple-choice questions are worth 2 points

9 Control Statements. 9.1 Introduction. 9.2 Objectives. 9.3 Statements

9 Control Statements 9.1 Introduction The normal flow of execution in a high level language is sequential, i.e., each statement is executed in the order of its appearance in the program. However, depending

Variables, Constants, and Data Types

Variables, Constants, and Data Types Primitive Data Types Variables, Initialization, and Assignment Constants Characters Strings Reading for this class: L&L, 2.1-2.3, App C 1 Primitive Data There are eight

Chapter 2: Elements of Java

Chapter 2: Elements of Java Basic components of a Java program Primitive data types Arithmetic expressions Type casting. The String type (introduction) Basic I/O statements Importing packages. 1 Introduction

System.out.println("\nEnter Product Number 1-5 (0 to stop and view summary) :

Benjamin Michael Java Homework 3 10/31/2012 1) Sales.java Code // Sales.java // Program calculates sales, based on an input of product // number and quantity sold import java.util.scanner; public class

CS 241 Data Organization Coding Standards

CS 241 Data Organization Coding Standards Brooke Chenoweth University of New Mexico Spring 2016 CS-241 Coding Standards All projects and labs must follow the great and hallowed CS-241 coding standards.

Chapter 5. Selection 5-1

Chapter 5 Selection 5-1 Selection (Decision) The second control logic structure is selection: Selection Choosing between two or more alternative actions. Selection statements alter the sequential flow

Introduction to Java Applications. 2005 Pearson Education, Inc. All rights reserved.

1 2 Introduction to Java Applications 2.2 First Program in Java: Printing a Line of Text 2 Application Executes when you use the java command to launch the Java Virtual Machine (JVM) Sample program Displays

Output: 12 18 30 72 90 87. struct treenode{ int data; struct treenode *left, *right; } struct treenode *tree_ptr;

50 20 70 10 30 69 90 14 35 68 85 98 16 22 60 34 (c) Execute the algorithm shown below using the tree shown above. Show the exact output produced by the algorithm. Assume that the initial call is: prob3(root)

CS 141: Introduction to (Java) Programming: Exam 1 Jenny Orr Willamette University Fall 2013

Oct 4, 2013, p 1 Name: CS 141: Introduction to (Java) Programming: Exam 1 Jenny Orr Willamette University Fall 2013 1. (max 18) 4. (max 16) 2. (max 12) 5. (max 12) 3. (max 24) 6. (max 18) Total: (max 100)

Iteration CHAPTER 6. Topic Summary

CHAPTER 6 Iteration TOPIC OUTLINE 6.1 while Loops 6.2 for Loops 6.3 Nested Loops 6.4 Off-by-1 Errors 6.5 Random Numbers and Simulations 6.6 Loop Invariants (AB only) Topic Summary 6.1 while Loops Many

Moving from CS 61A Scheme to CS 61B Java

Moving from CS 61A Scheme to CS 61B Java Introduction Java is an object-oriented language. This document describes some of the differences between object-oriented programming in Scheme (which we hope you

Name: Class: Date: 9. The compiler ignores all comments they are there strictly for the convenience of anyone reading the program.

Name: Class: Date: Exam #1 - Prep True/False Indicate whether the statement is true or false. 1. Programming is the process of writing a computer program in a language that the computer can respond to

Introduction to Java Lecture Notes. Ryan Dougherty [email protected]

1 Introduction to Java Lecture Notes Ryan Dougherty [email protected] Table of Contents 1 Versions....................................................................... 2 2 Introduction...................................................................

5.2 Q2 The control variable of a counter-controlled loop should be declared as: a.int. b.float. c.double. d.any of the above. ANS: a. int.

Java How to Program, 5/e Test Item File 1 of 5 Chapter 5 Section 5.2 5.2 Q1 Counter-controlled repetition requires a.a control variable and initial value. b.a control variable increment (or decrement).

The if Statement and Practice Problems

The if Statement and Practice Problems The Simple if Statement Use To specify the conditions under which a statement or group of statements should be executed. Form if (boolean-expression) statement; where

Informatica e Sistemi in Tempo Reale

Informatica e Sistemi in Tempo Reale Introduction to C programming Giuseppe Lipari http://retis.sssup.it/~lipari Scuola Superiore Sant Anna Pisa October 25, 2010 G. Lipari (Scuola Superiore Sant Anna)

Outline. Conditional Statements. Logical Data in C. Logical Expressions. Relational Examples. Relational Operators

Conditional Statements For computer to make decisions, must be able to test CONDITIONS IF it is raining THEN I will not go outside IF Count is not zero THEN the Average is Sum divided by Count Conditions

Embedded Systems. Review of ANSI C Topics. A Review of ANSI C and Considerations for Embedded C Programming. Basic features of C

Embedded Systems A Review of ANSI C and Considerations for Embedded C Programming Dr. Jeff Jackson Lecture 2-1 Review of ANSI C Topics Basic features of C C fundamentals Basic data types Expressions Selection

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) The JDK command to compile a class in the file Test.java is A) java Test.java B) java

While and Do-While Loops. 15-110 Summer 2010 Margaret Reid-Miller

While and Do-While Loops 15-110 Margaret Reid-Miller Loops Within a method, we can alter the flow of control using either conditionals or loops. The loop statements while, do-while, and for allow us execute

CASCADING IF-ELSE. Cascading if-else Semantics. What the computer executes: What is the truth value 1? 3. Execute path 1 What is the truth value 2?

CASCADING IF-ELSE A cascading if- is a composite of if- statements where the false path of the outer statement is a nested if- statement. The nesting can continue to several levels. Cascading if- Syntax

Stacks. Linear data structures

Stacks Linear data structures Collection of components that can be arranged as a straight line Data structure grows or shrinks as we add or remove objects ADTs provide an abstract layer for various operations

3/13/2012. Writing Simple C Programs. ESc101: Decision making using if-else and switch statements. Writing Simple C Programs

Writing Simple C Programs ESc101: Decision making using if- and switch statements Instructor: Krithika Venkataramani Semester 2, 2011-2012 Use standard files having predefined instructions stdio.h: has

Masters programmes in Computer Science and Information Systems. Object-Oriented Design and Programming. Sample module entry test xxth December 2013

Masters programmes in Computer Science and Information Systems Object-Oriented Design and Programming Sample module entry test xxth December 2013 This sample paper has more questions than the real paper

Handout 1. Introduction to Java programming language. Java primitive types and operations. Reading keyboard Input using class Scanner.

Handout 1 CS603 Object-Oriented Programming Fall 15 Page 1 of 11 Handout 1 Introduction to Java programming language. Java primitive types and operations. Reading keyboard Input using class Scanner. Java

Translating to Java. Translation. Input. Many Level Translations. read, get, input, ask, request. Requirements Design Algorithm Java Machine Language

Translation Translating to Java Introduction to Computer Programming The job of a programmer is to translate a problem description into a computer language. You need to be able to convert a problem description

Pseudo code Tutorial and Exercises Teacher s Version

Pseudo code Tutorial and Exercises Teacher s Version Pseudo-code is an informal way to express the design of a computer program or an algorithm in 1.45. The aim is to get the idea quickly and also easy

Pseudo Code Practice Problems:

Pseudo Code Practice Problems: Listed below is a brief explanation of Pseudo code as well as a list of examples and solutions. Pseudo code Pseudo code can be broken down into five components. Variables:

Keywords are identifiers having predefined meanings in C programming language. The list of keywords used in standard C are : unsigned void

1. Explain C tokens Tokens are basic building blocks of a C program. A token is the smallest element of a C program that is meaningful to the compiler. The C compiler recognizes the following kinds of

1. Use the class definition above to circle and identify the parts of code from the list given in parts a j.

public class Foo { private Bar _bar; public Foo() { _bar = new Bar(); public void foobar() { _bar.moveforward(25); 1. Use the class definition above to circle and identify the parts of code from the list

Software Testing. Definition: Testing is a process of executing a program with data, with the sole intention of finding errors in the program.

Software Testing Definition: Testing is a process of executing a program with data, with the sole intention of finding errors in the program. Testing can only reveal the presence of errors and not the

Topic 11 Scanner object, conditional execution

Topic 11 Scanner object, conditional execution "There are only two kinds of programming languages: those people always [complain] about and those nobody uses." Bjarne Stroustroup, creator of C++ Copyright

QUIZ-II QUIZ-II. Chapter 5: Control Structures II (Repetition) Objectives. Objectives (cont d.) 20/11/2015. EEE 117 Computer Programming Fall-2015 1

QUIZ-II Write a program that mimics a calculator. The program should take as input two integers and the operation to be performed. It should then output the numbers, the operator, and the result. (For

While Loop. 6. Iteration

While Loop 1 Loop - a control structure that causes a set of statements to be executed repeatedly, (reiterated). While statement - most versatile type of loop in C++ false while boolean expression true

Unit 6. Loop statements

Unit 6 Loop statements Summary Repetition of statements The while statement Input loop Loop schemes The for statement The do statement Nested loops Flow control statements 6.1 Statements in Java Till now

LOOPS CHAPTER CHAPTER GOALS

jfe_ch04_7.fm Page 139 Friday, May 8, 2009 2:45 PM LOOPS CHAPTER 4 CHAPTER GOALS To learn about while, for, and do loops To become familiar with common loop algorithms To understand nested loops To implement

Debugging. Common Semantic Errors ESE112. Java Library. It is highly unlikely that you will write code that will work on the first go

Debugging ESE112 Java Programming: API, Psuedo-Code, Scope It is highly unlikely that you will write code that will work on the first go Bugs or errors Syntax Fixable if you learn to read compiler error

Building Java Programs

Building Java Programs Chapter 4 Lecture 4-1: Scanner; if/else reading: 3.3 3.4, 4.1 Interactive Programs with Scanner reading: 3.3-3.4 1 Interactive programs We have written programs that print console

Some Scanner Class Methods

Keyboard Input Scanner, Documentation, Style Java 5.0 has reasonable facilities for handling keyboard input. These facilities are provided by the Scanner class in the java.util package. A package is a

Chapter 8 Selection 8-1

Chapter 8 Selection 8-1 Selection (Decision) The second control logic structure is selection: Selection Choosing between two or more alternative actions. Selection statements alter the sequential flow

Introduction to Computer Programming, Spring Term 2014 Practice Assignment 3 Discussion 15.3.2014-20.3.2014

German University in Cairo Media Engineering and Technology Prof. Dr. Slim Abdennadher Dr. Ahmed Gamal Introduction to Computer Programming, Spring Term 2014 Practice Assignment 3 Discussion 15.3.2014-20.3.2014

Number Representation

Number Representation CS10001: Programming & Data Structures Pallab Dasgupta Professor, Dept. of Computer Sc. & Engg., Indian Institute of Technology Kharagpur Topics to be Discussed How are numeric data

CompSci 125 Lecture 08. Chapter 5: Conditional Statements Chapter 4: return Statement

CompSci 125 Lecture 08 Chapter 5: Conditional Statements Chapter 4: return Statement Homework Update HW3 Due 9/20 HW4 Due 9/27 Exam-1 10/2 Programming Assignment Update p1: Traffic Applet due Sept 21 (Submit

Boolean Expressions, Conditions, Loops, and Enumerations. Precedence Rules (from highest to lowest priority)

Boolean Expressions, Conditions, Loops, and Enumerations Relational Operators == // true if two values are equivalent!= // true if two values are not equivalent < // true if left value is less than the

Boolean Expressions 1. In C++, the number 0 (zero) is considered to be false, all other numbers are true.

Boolean Expressions Boolean Expressions Sometimes a programmer would like one statement, or group of statements to execute only if certain conditions are true. There may be a different statement, or group

Conditional Statements. 15-110 Summer 2010 Margaret Reid-Miller

Conditional Statements 15-110 Summer 2010 Margaret Reid-Miller Conditional statements Within a method, we can alter the flow of control (the order in which statements are executed) using either conditionals

TETRIX Add-On Extensions. Encoder Programming Guide (ROBOTC )

Introduction: In this extension, motor encoders will be added to the wheels of the Ranger Bot. The Ranger Bot with Encoders will be programmed to move forward until it detects an object, turn 90, and move

PROGRAMMING IN C PROGRAMMING IN C CONTENT AT A GLANCE

PROGRAMMING IN C CONTENT AT A GLANCE 1 MODULE 1 Unit 1 : Basics of Programming Unit 2 : Fundamentals Unit 3 : C Operators MODULE 2 unit 1 : Input Output Statements unit 2 : Control Structures unit 3 :

12-6 Write a recursive definition of a valid Java identifier (see chapter 2).

CHAPTER 12 Recursion Recursion is a powerful programming technique that is often difficult for students to understand. The challenge is explaining recursion in a way that is already natural to the student.

JavaScript: Control Statements I

1 7 JavaScript: Control Statements I 7.1 Introduction 2 The techniques you will learn here are applicable to most high-level languages, including JavaScript 1 7.2 Algorithms 3 Any computable problem can

Preet raj Core Java and Databases CS4PR. Time Allotted: 3 Hours. Final Exam: Total Possible Points 75

Preet raj Core Java and Databases CS4PR Time Allotted: 3 Hours Final Exam: Total Possible Points 75 Q1. What is difference between overloading and overriding? 10 points a) In overloading, there is a relationship

Introduction to Java. CS 3: Computer Programming in Java

Introduction to Java CS 3: Computer Programming in Java Objectives Begin with primitive data types Create a main class with helper methods Learn how to call built-in class methods and instance methods

>

GCE. Computing. Mark Scheme for January 2011. Advanced Subsidiary GCE Unit F452: Programming Techniques and Logical Methods

GCE Computing Advanced Subsidiary GCE Unit F452: Programming Techniques and Logical Methods Mark Scheme for January 2011 Oxford Cambridge and RSA Examinations OCR (Oxford Cambridge and RSA) is a leading

Building Java Programs

Building Java Programs Chapter 3 Lecture 3-3: Interactive Programs w/ Scanner reading: 3.3-3.4 self-check: #16-19 exercises: #11 videos: Ch. 3 #4 Interactive programs We have written programs that print

Phys4051: C Lecture 2 & 3. Comment Statements. C Data Types. Functions (Review) Comment Statements Variables & Operators Branching Instructions

Phys4051: C Lecture 2 & 3 Functions (Review) Comment Statements Variables & Operators Branching Instructions Comment Statements! Method 1: /* */! Method 2: // /* Single Line */ //Single Line /* This comment

Chapter 3 Operators and Control Flow

Chapter 3 Operators and Control Flow I n this chapter, you will learn about operators, control flow statements, and the C# preprocessor. Operators provide syntax for performing different calculations or

Abstraction and Abstract Data Types

Abstraction and Abstract Data Types Abstraction: o Whatever is visible to the user? Examples: Variable names & real numbers. o How real numbers are implemented? o How arrays are implemented? The abstraction

Example of a Java program

Example of a Java program class SomeNumbers static int square (int x) return x*x; public static void main (String[] args) int n=20; if (args.length > 0) // change default n = Integer.parseInt(args[0]);

In this Chapter you ll learn:

Now go, write it before them in a table, and note it in a book. Isaiah 30:8 To go beyond is as wrong as to fall short. Confucius Begin at the beginning, and go on till you come to the end: then stop. Lewis

Ad Hoc Advanced Table of Contents

Ad Hoc Advanced Table of Contents Functions... 1 Adding a Function to the Adhoc Query:... 1 Constant... 2 Coalesce... 4 Concatenate... 6 Add/Subtract... 7 Logical Expressions... 8 Creating a Logical Expression:...

Visual Logic Instructions and Assignments

Visual Logic Instructions and Assignments Visual Logic can be installed from the CD that accompanies our textbook. It is a nifty tool for creating program flowcharts, but that is only half of the story.

Selection Statements

Chapter 5 Selection Statements 1 Statements So far, we ve used return statements and expression ess statements. e ts. Most of C s remaining statements fall into three categories: Selection statements:

Part I. Multiple Choice Questions (2 points each):

Part I. Multiple Choice Questions (2 points each): 1. Which of the following is NOT a key component of object oriented programming? (a) Inheritance (b) Encapsulation (c) Polymorphism (d) Parallelism ******

Adding and Subtracting Positive and Negative Numbers

Adding and Subtracting Positive and Negative Numbers Absolute Value For any real number, the distance from zero on the number line is the absolute value of the number. The absolute value of any real number

Lecture 2 Notes: Flow of Control

6.096 Introduction to C++ January, 2011 Massachusetts Institute of Technology John Marrero Lecture 2 Notes: Flow of Control 1 Motivation Normally, a program executes statements from first to last. The

Building Java Programs

Building Java Programs Chapter 3 Lecture 3-3: Interactive Programs w/ Scanner reading: 3.3-3.4 self-check: #16-19 exercises: #11 videos: Ch. 3 #4 Interactive programs We have written programs that print

Python Lists and Loops

WEEK THREE Python Lists and Loops You ve made it to Week 3, well done! Most programs need to keep track of a list (or collection) of things (e.g. names) at one time or another, and this week we ll show

1.00/1.001 - Session 2 Fall 2004. Basic Java Data Types, Control Structures. Java Data Types. 8 primitive or built-in data types

1.00/1.001 - Session 2 Fall 2004 Basic Java Data Types, Control Structures Java Data Types 8 primitive or built-in data types 4 integer types (byte, short, int, long) 2 floating point types (float, double)

Sample CSE8A midterm Multiple Choice (circle one)

Sample midterm Multiple Choice (circle one) (2 pts) Evaluate the following Boolean expressions and indicate whether short-circuiting happened during evaluation: Assume variables with the following names

Conditions & Boolean Expressions

Conditions & Boolean Expressions 1 In C++, in order to ask a question, a program makes an assertion which is evaluated to either true (nonzero) or false (zero) by the computer at run time. Example: In

Boolean Expressions & the if Statement

Midterm Results Boolean Expressions & the if Statement September 24, 2007 Average: 91.6 Median: 94 Standard Deviation: 18.80 Maximum: 129 (out of 130) ComS 207: Programming I (in Java) Iowa State University,

Simple C++ Programs. Engineering Problem Solving with C++, Etter/Ingber. Dev-C++ Dev-C++ Windows Friendly Exit. The C++ Programming Language

Simple C++ Programs Engineering Problem Solving with C++, Etter/Ingber Chapter 2 Simple C++ Programs Program Structure Constants and Variables C++ Operators Standard Input and Output Basic Functions from

Lab Manual. Databases. Microsoft Access. Peeking into Computer Science Access Lab manual

Lab Manual Databases Microsoft Access 1 Table of Contents Lab 1: Introduction to Microsoft Access... 3 Getting started... 3 Tables... 3 Primary Keys... 6 Field Properties... 7 Validation Rules... 11 Input

UIL Computer Science for Dummies by Jake Warren and works from Mr. Fleming

UIL Computer Science for Dummies by Jake Warren and works from Mr. Fleming 1 2 Foreword First of all, this book isn t really for dummies. I wrote it for myself and other kids who are on the team. Everything

Introduction to SQL for Data Scientists

Introduction to SQL for Data Scientists Ben O. Smith College of Business Administration University of Nebraska at Omaha Learning Objectives By the end of this document you will learn: 1. How to perform

Introduction to Python

WEEK ONE Introduction to Python Python is such a simple language to learn that we can throw away the manual and start with an example. Traditionally, the first program to write in any programming language

Chapter 1: Computer Systems

Presentation slides for Java Software Solutions Foundations of Program Design Second Edition by John Lewis and William Loftus Part I (chapters 1 5) Prepared for Java Programming 90.301 by Marjan Trutschl

COSC 1020 3.0 Introduction to Computer Science I Section A, Summer 2005. Question Out of Mark A Total 16. B-1 7 B-2 4 B-3 4 B-4 4 B Total 19

Term Test #2 COSC 1020 3.0 Introduction to Computer Science I Section A, Summer 2005 Family Name: Given Name(s): Student Number: Question Out of Mark A Total 16 B-1 7 B-2 4 B-3 4 B-4 4 B Total 19 C-1 4

13 Classes & Objects with Constructors/Destructors

13 Classes & Objects with Constructors/Destructors 13.1 Introduction In object oriented programming, the emphasis is on data rather than function. Class is a way that binds the data & function together.

Today. Binary addition Representing negative numbers. Andrew H. Fagg: Embedded Real- Time Systems: Binary Arithmetic

Today Binary addition Representing negative numbers 2 Binary Addition Consider the following binary numbers: 0 0 1 0 0 1 1 0 0 0 1 0 1 0 1 1 How do we add these numbers? 3 Binary Addition 0 0 1 0 0 1 1

Searching Guide Version 8.0 December 11, 2013

Searching Guide Version 8.0 December 11, 2013 For the most recent version of this document, visit our documentation website. Table of Contents 1 Searching overview 5 2 Filters 6 2.1 Using filters 6 2.1.1

VB.NET Programming Fundamentals

Chapter 3 Objectives Programming Fundamentals In this chapter, you will: Learn about the programming language Write a module definition Use variables and data types Compute with Write decision-making statements

ASCII Encoding. The char Type. Manipulating Characters. Manipulating Characters

The char Type ASCII Encoding The C char type stores small integers. It is usually 8 bits. char variables guaranteed to be able to hold integers 0.. +127. char variables mostly used to store characters

Program Logic to Java GEEN163

Program Logic to Java GEEN163 In theory, theory and practice are the same. In practice, they're not. Yogi Berra Founders' Day The Founders' Day Convocation is Thursday, March 21 from 10:00 12:00 in the

Java Interview Questions and Answers

1. What is the most important feature of Java? Java is a platform independent language. 2. What do you mean by platform independence? Platform independence means that we can write and compile the java

COMPUTER SCIENCE. Paper 1 (THEORY)

COMPUTER SCIENCE Paper 1 (THEORY) (Three hours) Maximum Marks: 70 (Candidates are allowed additional 15 minutes for only reading the paper. They must NOT start writing during this time) -----------------------------------------------------------------------------------------------------------------------

General Software Development Standards and Guidelines Version 3.5

NATIONAL WEATHER SERVICE OFFICE of HYDROLOGIC DEVELOPMENT Science Infusion Software Engineering Process Group (SISEPG) General Software Development Standards and Guidelines 7/30/2007 Revision History Date

Building Java Programs

Building Java Programs Chapter 5 Lecture 5-2: Random Numbers reading: 5.1-5.2 self-check: #8-17 exercises: #3-6, 10, 12 videos: Ch. 5 #1-2 1 The Random class A Random object generates pseudo-random* numbers.

Section IV.1: Recursive Algorithms and Recursion Trees

Section IV.1: Recursive Algorithms and Recursion Trees Definition IV.1.1: A recursive algorithm is an algorithm that solves a problem by (1) reducing it to an instance of the same problem with smaller

C++ program structure Variable Declarations

C++ program structure A C++ program consists of Declarations of global types, variables, and functions. The scope of globally defined types, variables, and functions is limited to the file in which they

File class in Java. Scanner reminder. Files 10/19/2012. File Input and Output (Savitch, Chapter 10)

File class in Java File Input and Output (Savitch, Chapter 10) TOPICS File Input Exception Handling File Output Programmers refer to input/output as "I/O". The File class represents files as objects. The

Introduction to Java

Introduction to Java The HelloWorld program Primitive data types Assignment and arithmetic operations User input Conditional statements Looping Arrays CSA0011 Matthew Xuereb 2008 1 Java Overview A high

Numeral Systems. The number twenty-five can be represented in many ways: Decimal system (base 10): 25 Roman numerals:

Numeral Systems Which number is larger? 25 8 We need to distinguish between numbers and the symbols that represent them, called numerals. The number 25 is larger than 8, but the numeral 8 above is larger

Statements and Control Flow

Contents 1. Introduction 2. Types and Variables 3. Statements and Control Flow 4. Reading Input 5. Classes and Objects 6. Arrays 7. Methods 8. Scope and Lifetime 9. Utility classes 10. Introduction to

Software development and programming. Software

CHAPTER 15 15 Software Software development and programming Syllabus outcomes 5.2.1 Describes and applies problem-solving processes when creating solutions. 5.2.2 Designs, produces and evaluates appropriate

So far we have considered only numeric processing, i.e. processing of numeric data represented

Chapter 4 Processing Character Data So far we have considered only numeric processing, i.e. processing of numeric data represented as integer and oating point types. Humans also use computers to manipulate

MATHEMATICAL INDUCTION. Mathematical Induction. This is a powerful method to prove properties of positive integers.

MATHEMATICAL INDUCTION MIGUEL A LERMA (Last updated: February 8, 003) Mathematical Induction This is a powerful method to prove properties of positive integers Principle of Mathematical Induction Let P