CS107: Computing for Math CS107: Computing for Math and Science - - PowerPoint PPT Presentation

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CS107: Computing for Math CS107: Computing for Math and Science - - PowerPoint PPT Presentation

Aug 15, 2022 181 likes •697 views

CS107: Computing for Math CS107: Computing for Math and Science and Science Instructor: Prof. Louis Steinberg office: Hill 401 email: lou@cs.rutgers.edu Office hours: by appointment TAs: Andre Cohen office: CBIM

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Lecture 02

CS107: Computing for Math CS107: Computing for Math and Science and Science

  • Instructor: Prof. Louis Steinberg

– office: Hill 401 – email: lou@cs.rutgers.edu – Office hours: by appointment

  • TAs:

– Andre Cohen

  • ffice: CBIM

acohen@ cs.rutgers.edu – Xiaoye Han

  • ffice: Hill 405

xiaoye @ cs.rutgers.edu

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Lecture 02

CS107: Computing for Math CS107: Computing for Math and Science and Science

  • Instructor: Prof. Apostolos Gerasoulis

– office: Core 328 – email: grasoul@cs.rutgers.edu – Office hours: by appointment

  • TA:

– Nader Boushehrinejadmoradi Office: Hill 353 naderb@cs.rutgers.edu

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Items posted on web site Items posted on web site

  • Assignment 1 on Sakai ???
  • Practice problems 1 on Remus
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Web Sites Web Sites

  • http://

http://remus remus.rutgers.edu/cs107 .rutgers.edu/cs107

– Policies – Syllabus – Lecture notes – etc....

– You are assumed to know anything

posted.

– Also Sakai site

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Should you take CS107? Should you take CS107?

  • Math or science major, had calc I: YES
  • Exceptions:

– Computer Science major or minor: NO

– Except: unsure about CS: MAYBE

– Option B: The Computer-Oriented Mathematics Major: NO

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Lecture 02

Kinds of Knowledge Kinds of Knowledge

  • Knowing that

– Knowing a fact, e.g. rules of Chess

  • Knowing how

– Knowing how to use facts to achieve a goal, e.g. how to win at chess

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E.G., Algebra E.G., Algebra

  • Knowing that

If X = Y then X + a = Y + a

  • Knowing how

– To solve 3*x - 5 = 10, start by adding 5 to both sides of the equation 3*x - 5 + 5 = 10 + 5 3*x = 15

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Learning Learning “ “Knowing How Knowing How” ”

  • The only way to learn “How” is practice
  • Only way to learn most of the course

material is to do homework

  • Purpose of lecture and textbook is to

prepare you to do this work

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Lecture 02

Review Review

  • What is a computer
  • Anthropomorphisms

– Follow instructions – Process data – Language

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What is a computer? What is a computer?

  • A machine that follows instructions and

processes data

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How can a machine follow How can a machine follow instructions? instructions?

  • Example: Washing machine controller

– Controls hot water, cold water, drain, motor

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Lecture 02

Hot Wash, Warm Rinse Hot Wash, Warm Rinse

C M D H

Peg No Peg

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Lecture 02

Machine Instructions Machine Instructions

  • A pattern of physical objects
  • Pegs, electrons, etc
  • Physically causes the specified behavior
  • Can be thought of as a language
  • Expresses commands
  • Made of pieces combined according to rules
  • Extremely detailed, so need “higher level”

language

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Higher Level Language Higher Level Language

  • Compromise

– Easier for humans to deal with

– Write, check, understand, …

– Still not too hard to make a machine obey

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Data processing Data processing

  • What Kaplan text calls “computation”
  • Any process that transforms some data

into other data, e.g. addition

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Representation Representation

  • For a machine to process data, the data

must be represented by some physical quantity

– Length, voltage, …

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Lecture 02

Matlab Matlab

  • Matlab is:

– A programming language – A library of programs and pieces – An Interactive Development Environment (IDE)

– A program that helps you build and test programs

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Matlab Matlab as a Calculator as a Calculator

  • E.g., convert 75 degrees Fahrenheit to

Celsius

  • E.g. convert $100 to Euros ($1 = .79 Eur.)
  • E.g. wall area of a room 10’ x 12’ x 8’
  • Note: precedence
  • Note: infix vs prefix form
  • Note: lack of units
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Lecture 02

Operations Operations

  • Plus

+ 4 + 5

  • Minus
  • 4 - 5
  • Times

.* 4 .* 5

  • Divide

./ 4 ./ 5

  • Power

.^ 4 .^ 5

  • Square root

sqrt sqrt(4)

  • Sin

sin sin(4)

  • … etc.
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Lecture 02

Variables Variables

  • Typically, calculators have a memory;

matlab has many memory cells

  • Memory cell in matlab is called a

“variable”

  • A variable has

– a name, e.g. age, year, area, … – a value

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Variables Variables

  • The first time you type a variable’s name,

Matlab:

– Reserves a space in the computer’s memory – Associates that space with the name you typed

  • After that, when you type the name,

Matlab uses the associated memory space

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Lecture 02

Using Variables Using Variables

  • To refer to a variable just type its name
  • Most of the time name means “the value

stored there”

(degreesF - 32) .* 5 ./ 9

  • To say “store this value here”, use =

degreesF = 72 degreesC = (degreesF - 32) .* 5 ./ 9

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Why use a variable? Why use a variable?

  • One use: to store an intermediate result

for reuse

discriminant = b.^2-4.*a.*c b + sqrt(discriminant)/(2.*a) b - sqrt(discriminant)/(2.*a)

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Why use a variable? Why use a variable?

  • Another use: in a repetitive computation

– E.g. compute square root of 5. Use a variable named, say, root >> root = 2 root = 2 >> root = (root + 5 ./ root) ./ 2 root = 2.2500 >> root = (root + 5 ./ root) ./ 2 root = 2.2361 >> root .* root ans = 5.0000

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Lecture 02

Matlab Matlab Programs Programs

  • A Matlab program is made up of

statements

– One per line

  • One kind of statement is:

Assignment statement

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Assignment statement Assignment statement

  • Purpose: store a piece of data in a variable
  • Form:

variableName = expression

  • Meaning:

– Evaluate expression – Store the result in the variable with name variableName – Print the result

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Assignment statement Assignment statement

  • May end with ; to prevent printing the

value of the expression

degreesF = 72;

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Grammatical Structure Grammatical Structure

  • An assignment statement has parts

cost = nonTaxable + taxable .* 1.065

Variable name Expression

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Grammatical Structure Grammatical Structure

  • Parts can have parts

nonTaxable + taxable .* 1.065

Expression expression expression

  • perator
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Grammatical Structure Grammatical Structure

  • Parts can have parts that have parts

nonTaxable + taxable .* 1.065

Expression expression expression

  • perator

expression

  • perator

expression

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Lecture 02

Grammatical Structure Grammatical Structure

totalCal = mms .* calPerMm position = startPos + time .* speed pay = hours .* rate + overtime * otrate

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Grammatical Structure Grammatical Structure

totalCal = mms .* calPerMm position = startPos + time .* speed pay = hours .* rate + overtime * otrate

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Grammatical Structure Grammatical Structure

totalCal = mms .* calPerMm position = startPos + time .* speed pay = hours .* rate + overtime * otrate

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Grammatical Structure Grammatical Structure

totalCal = mms .* calPerMm position = startPos + time .* speed pay = hours .* rate + overtime * otrate

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Programs Programs

  • So far, we have used Matlab as a

calculator

– Type a line, Matlab does it

  • How do we type instructions once, use

many times?

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Lecture 02

Functions Functions

  • Suppose you want to calculate length of

hypotenuse?

  • In command window, type

sqrt(5.^2 + 4.^2)

base = 5 height = 4 hypotenuse = ?

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Lecture 02

Functions Functions

  • Suppose you want to calculate length of

hypotenuse many times?

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Lecture 02

Functions Functions

  • Suppose you want to calculate length of

hypotenuse many times?

sqrt( 4 .^2 + 5.^2) sqrt( 7 .^2 + 11.^2) sqrt( 20 .^2 + 21.^2) …

  • This is a pain - can’t we just do

hyp(4, 5) hyp(7, 11) hyp(20, 21)

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Lecture 02

Functions Functions

  • To be able to just type hyp(3,4) we need to

define the function hyp to Matlab.

– In a file hyp.m (NOT the command window) function hypot = hype ( base, height ) hypot = sqrt(base .^2 + height .^2);

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Functions Functions

function hypot = hyp ( base, height ) Marks start

  • f a function

definition Name of the function Names used to refer to the arguments Name of the variable that will hold the result

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Lecture 02

Functions as Machines Functions as Machines

sqrt

4 2

hypotenuse

4 5 3

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Functions as Machines Functions as Machines

hypotenuse

4 5 3 Arguments Result

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Functions as Machines Functions as Machines

Names of Arguments Name of Result

function hypot = hyp(base, height)

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Lecture 02

In file hyp.m: function hypot = hyp(base, height) hypot = sqrt(base.^2 + height.^2) In command window: hyp(3, 4)

Functions as Machines Functions as Machines

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Lecture 02

More Examples More Examples

  • Quadratic function: a x2 +b x + c

– See quadratic.m

  • Area of a circle

– See circleArea.m

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Lecture 02

Running Running Matlab Matlab

  • You can run Matlab

– On computers in Rutgers labs

– If you go to the lab

– On your own computer

– If you buy Matlab

– Remotely

– You sit at your computer – Matlab runs on Remus (the CS undergrad server) – X Windows provides the connection

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Running Remotely Running Remotely

  • X Windows is a program that

– Runs on your computer – Communicates over the internet with programs running on Remus

  • X Windows

– Sends what you type to Remus – Displays windows on your screen for programs running on Remus

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Lecture 02

Remote Remote Matlab Matlab

  • Your computer

CPU CPU RAM RAM Disk Disk CPU CPU RAM RAM Disk Disk

remus remus

X11 X11 Matlab Matlab

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Lecture 02

X Windows is available for free X Windows is available for free

– For windows (not sure about Vista), download Cygwin (see our web site) – For Mac, it is on your installation disk (see

  • ur web site)

– For Linux, it is already running

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Lecture 02

Announcements Announcements

  • Announcements were made at the start of

class