Introduction to Computer Science

Lab 1: Numbers and Arithmetic

Numbers and Arithmetic

Simple Expressions(+ 5 5)      (+ -5 5)     (+ 5 -5)     (- 5 5)     (* 3 4)      (/ 8 12)   

Numbers and Arithmetic

As in arithmetic or algebra, we can nest expressions:

(* (+ 2 2) (/ (* (+ 3 5) (/ 30 10)) 2))

Numbers and Arithmetic

(* (+ 2 2) (/ (* (+ 3 5) (/ 30 10)) 2))

= (* 4 (/ (* 8 3) 2)) = (* 4 (/ 24 2)) = (* 4 12) = 48

Numbers and Arithmetic

advanced mathematical operations on numbers

1. (sqrt A) computes (A) expt. 1/2;2. (expt A B) computes A expt. B;3. (remainder A B) computes the remainder of

the integer division A/B;4. (log A) computes the natural logarithm of A;

and5. (sin A) computes the sine of A radians.

Variables and Programs

In algebra we learn to formulate dependencies between quantities using VARIABLE EXPRESSIONS

A variable is a placeholder that stands for an unknown quantity. For example, a disk of radius r has the approximate area

pi * r * r

Variables and Programs

Expressions that contain variables are rules that describe how to compute a number when we are given values for the variables

A program is such a rule. It is a rule that tells us and the computer how to produce data from some other data

(define (area-of-disk r) (* 3.14 (* r r)))

Variables and Programs

The two lines say that area-of-disk is a rule, that it consumes a single INPUT, called r, and that the result, or OUTPUT, is going to be (* 3.14 (* r r)) once we know what number r represents.

Variables and Programs

(area-of-disk 5)

(area-of-disk 5) = (* 3.14 (* 5 5)) = (* 3.14 25) = 78.5

Variables and Programs

Many programs consume more than one input. Say we wish to define a program that computes the area of a ring, that is, a disk with a hole in the center:

Variables and Programs

(define (area-of-ring outer inner) (- (area-of-disk outer)

(area-of-disk inner)))

Variables and Programs

;; 1. Contract: area-of-ring : number number -> number

;; 2. Purpose: to compute the area of a ring whose radius is;; outer and whose hole has a radius of inner

;; 4. Definition(define (area-of-ring outer inner) (- (area-of-disk outer) (area-of-disk inner))) ;; 3. Tests:(check-expect (area-of-ring 5 3) 50.24)