- Induction and Recursion

- Sections 1.1-1.2 of the text.
- Maple Getting Started
Guide

(also look for "Getting Started" in the Table of Contents in Maple Help) - Using Help - Go to the "Help" menu and select "Table of Contents"
and look for the "Using Help" folder. Also see "Using Help" under the
"Help Menu" within "Help System Menu Bars" in the "Menus" folder.

- Worksheet Management - Go to the "Help" menu and select "Table of
Contents" and look for Overview in the "Worksheet Management" folder.

- Overview of the course.
- Objectives
- Topics
- Grading policy and expectations
- Introduction to Maple
- Maple worksheet interface
- Maple help facility
- Basic capabilities of Maple
- Variables, Values, and Names
- Arithmetic
- Symbolic vs. Numeric Computation
- Watch Out
- End with a semi-colon
- Names vs. Values and Evaluation
- Equal vs. Assignment
- Dynamic Scope
- Case Sensitivity
- Answers you don't understand
- Maple's assumptions might be different than yours
- Maple is not perfect

- Theorem: p|ab => p|a or p|b, p a prime number
- Proof that sqrt(2) is irrational.
- Investigation of Pythagorean triples.
- Unique Factorization (the fundamental theorem of arithmetic) - the existence of the factorization of an integer into primes follows from the correctness proof of a simple algorithm to compute the prime factorization of an integer, and the uniqueness of the factorization follows from the previous theorem - see ufd.mw for worksheet containing the algorithm.
- Example where unique factorization does not hold: Z[sqrt(10)].

- ufd.mw - Maple worksheet illustrating unique factorization and the Euclidean algorithm.
- Getting Started Guide.

Maple 11 User Manual.

- www.maplesoft.com (Maplesoft Web site)
- www.mapleapps.com (Maple Application Center Web site)
- www.maple4students.com
(Maple Student Center Web site)

- Install Maple (go to IRT's software site and download - follow installation directions).
- Load and run the examples from the worksheet from this lecture.
- Create a simple Maple worksheet and perform several computations
- Use
**evalf**to approximate sqrt(3) to 100 decimal places. - Use the
**plot**command to plot x^2-3 over the interval [0,2] - Use the
**solve**command to solve the equation x^2-3=0. - Use the
**fsolve**command to solve the equation x^2-3=0. - Use Maple to determine the number of primes less than 100.
- How many primes are there less than 1000?

- Use
- Create a title and some text explaining your computations.
- Add a section to your worksheet with the title "Bisection"
- Write a Maple procedure to approximate sqrt(3). Your procedure should take as input a number e and should return an approximation s to sqrt(3) such that |s - sqrt(3)| &le e. Use bisection to obtain your approximation. I.E. start with the interval [0,1] and repeatedly compute the midpoint choosing either the left or right subinterval, whichever contains sqrt(3). Continue this until the width of the interval containing sqrt(3) is less than or equal to e. Finally return the midpoint of the final interval.
- Generalize the previous procedure to approximate an arbitrary square root.