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

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Lecture 01

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 acohen @ cs.rutgers.edu – Xiaoye xiaoye @ cs.rutgers.edu

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Lecture 01

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 naderb@cs.rutgers.edu

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

Course will use the computer for

communication and instruction as much as possible

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Class Web Pages Class Web Pages

http://

http://remus remus. .rutgers rutgers. .edu edu/CS107 /CS107

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

– You are assumed to know anything

posted.

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Class Web Pages Class Web Pages

Sakai:

Sakai: cs cs 107, Fall 2010 107, Fall 2010

– Announcements – Posting grades – Chat room – Etc.

– You are assumed to know anything

posted.

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Lecture 01

What is CS107? What is CS107?

A course about using computers
Aimed at majors in Math and Science
After this class you should know
Methods for using the computer that will be useful

for mathematicians & scientists

Some key ideas in computer science
CS 107 does not prepare you to take further

courses in the CS Dept.

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Lecture 01

Prerequisite Prerequisite

Calc I

– 640:135 or 151 or 153 or 191 – Grade of C or better

No previous programming experience is

assumed

We will assume you do know how to use a

mouse, web browser, etc.

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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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Grade based on Grade based on

Homework
Midterm exam
In-lecture quizzes
Final exam

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Textbooks Textbooks

Introduction to Scientific Computation and Programming

Daniel T Kaplan Brooks/Cole

The Maple Book

Frank Garman Chapman & Hall/CRC

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What is a computer? What is a computer?

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What is a computer? What is a computer?

A machine that follows instructions
Note the anthropomorphism here

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Anthropomorphism: Anthropomorphism:

Use of a term normally applied to people when speaking of something that is not a person

An analogy
Useful but dangerous

– What is the same – What is different

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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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Hot Wash, Warm Rinse Hot Wash, Warm Rinse

C M D H

Peg No Peg

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Washing Machine Instructions Washing Machine Instructions

A pattern of physical objects (pegs)

– Physically causes the specified behavior

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Computer Computer Instructions Instructions

A pattern of electrical voltages

– Physically causes the specified behavior

5 volts

Random Access Memory

0 volts

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Lecture 01

People can read, write, think about the

pattern without really having the pegs

Patterns can be thought of as a language

for expressing washing machine instructions

Washing Machine Language Washing Machine Language

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Anthropomorphism Alert Anthropomorphism Alert

How is washing machine language like a

human (“natural”) language?

How is it different?

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People can read, write, think about the

pattern without really having the voltages

Patterns can be thought of as a language

for expressing computer instructions

Computer Computer Machine Language Machine Language

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Washing Machine Languages Washing Machine Languages

Each washing machine operation does a

very small amount of work

People would find it tedious and error

prone to instruct their washers in this language

So, we have a higher level language

– Warm wash, cold rinse

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Computer Computer Languages Languages

Each computer operation does a

very small amount of work

People would find it tedious and error

prone to instruct their computers in this language

So, we have a higher level language

– Matlab – Java, Basic, Fortran, C, Lisp, ...

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Washing Machine Languages Washing Machine Languages

There is a fixed set of primitive operations

– Hot, Cold, Drain, Motor

And a way of combining operations

– Rows obeyed in sequence

We have to build behavior we want out of

the primitives available

– Hot + Cold => Warm

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Computer Computer Languages Languages

There is a fixed set of primitive operations
And a way of combining operations
We have to build behavior we want out of

the primitives available

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Is a Washing Machine a Is a Washing Machine a Computer? Computer?

A computer is a machine that

follows instructions and processes data

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Data Data

Numbers, words, pictures, …
Data processing

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

ther data, e.g. addition

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Representation Representation

In a computer, data embodied as charge
r voltage

– E.g.: 0 volts means 0, 5 volts means 1 – A “bit”: a 2-way choice, e.g. 0 volts vs 5 volts

Data is represented by groups of bits

– E.g.: 3 bits gives 8 patterns: 000 001 010 011 100 101 110 111

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Translation Translation

Problem: pegs & switches understand
nly machine language
How can we get instructions in higher

level language obeyed?

Translation:

– “warm wash, cold rinse” dial selects a set of pegs

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Translation Translation

Problem: transistors understand only

machine language

How can we get instructions in higher

level language obeyed?

Translation:

– Instructions are also data – A program does the translation

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Grammar Grammar

To make it easier to translate, a program

must have a structure that obeys a grammar

– simple but rigid rules

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A Program A Program

is more like a mechanism you build than a sentence you say.

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

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To Construct a Program To Construct a Program

Is 5% “Know that” and 95% “Know how”

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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 01

Extra Help Extra Help

For some people writing a program is very

hard.

– Even some people who do very well in other courses

Extra help will be available

– See Prof. Steinberg or a TA – Do so as soon as possible if you find the homework extremely hard

Everyone should be able to pass this class, with

hard work.

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Lecture 01

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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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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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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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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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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What does this do? What does this do?

x = 4 + 5 y = x + 3 z = 6 .* 2 x = 1 x = x + 3

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What does this do? What does this do?

total = 0; total = total + 5; total = total + 8; total = total + 7

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Getting help Getting help

The help command gets help, e.g. -

> help + gets help on the + operator

Also, under the Help menu, select

Product Help, type sum in “search for” box

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