1. R. Smith - University of St Thomas - Minnesota
Today’s Class
Recap
Homework
Running Matlab
Arithmetic Expressions
Talking about syntax
Variables
Notational alternatives
Fibonacci numbers
9/20/2018
R. Smith - University of St Thomas - Minnesota

2. Computer Fundamentals
CPU – RAM – Hard Drive
CPU does the work
RAM holds the information (“working storage”)
Programs to follow (“execute”)
Data to process (“inputs”)
Results of the processing (“outputs”)
Hard Drive provides large capacity “permanent storage”
Programs – sequences of instructions
Instructions are absurdly simple (“add 2 numbers”)
It takes THOUSANDS to create an interesting program
It takes MILLIONS to create a ‘computer desktop’
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R. Smith - University of St Thomas - Minnesota

3. R. Smith - University of St Thomas - Minnesota
Homework
Matlab text - Kaplan
Read Chapters 1 through 3.
We will cover 1.3 in more detail later
Do Exercises 2.1 through 2.4 (pp 32-33)
Due at the start of class, Monday.
Do Exercises 3.1, -2, -3, -4, -7, -8, -9 (pp 61-63)
Due at the start of class, Wednesday
9/20/2018
R. Smith - University of St Thomas - Minnesota

4. MATLAB and the computer
For now, we focus on the CPU and RAM
(There’s a hard drive, but we’ll ignore it for now)
When we start MATLAB, it is read into RAM
The program resides in RAM
MATLAB operations use data from RAM
Input data resides in RAM
MATLAB stores its results in RAM
We store the outputs and results in RAM
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R. Smith - University of St Thomas - Minnesota

5. R. Smith - University of St Thomas - Minnesota
Starting Up Matlab
Tour of the windows
Invoking a Computation (Ch. 2)
Expressions
Add, subtract, multiply, divide, dot notation
2+3
8/2
10^3
Evaluating an Expression
The value of an expression
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R. Smith - University of St Thomas - Minnesota

6. R. Smith - University of St Thomas - Minnesota
Compound expressions
“Simple” expressions – one operator
“Compound expressions – multiple operators
Substitute any number with an expression that yields a number
At least, that’s what is allowed by the language
Issues
Ambiguities
Order of evaluation
When it’s ambiguous, use parentheses
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R. Smith - University of St Thomas - Minnesota

7. R. Smith - University of St Thomas - Minnesota
Syntax Options
What does syntax mean, anyway
“Infix” notation, like 2+3
“Functional style” notation, like plus(2,3)
Examples: Calculate a hypotenuse
sqrt(5^2 + 6^2)
sqrt(plus(power(5,2),power(6,2)))
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R. Smith - University of St Thomas - Minnesota

8. Language and Meta-Language
When I give language examples, I need to distinguish between literal language elements (words, symbols) and “meta” elements that may take on any of a variety of possibilities
Example of Addition:
number + number
Literal values are bold
Meta elements are underlined words
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R. Smith - University of St Thomas - Minnesota

9. Meta Language for Notations
Infix Notation
number symbol number
number = any properly formed number
symbol = character for arithmetic operator: + - / * ^
Functional Notation
operator ( number , number )
operator = name of arithmetic operator
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R. Smith - University of St Thomas - Minnesota

10. ‘Properly formed’ number
A number may start with a sign (optional)
Signs are ‘+’ or ‘-’
Next comes a ‘decimal number’
Consists of 1 or more digits
Optionally, one decimal point ‘.’ may appear
May be at the start, middle, or end
Next, may come an ‘e’ to specify exponent
‘e’ is followed by
‘+’ or ‘-’ sign (optional)
1 or more digits (at least 1 required)
Examples: 123, 2.4, .5, -1, -.23, 1e-2
The numeric value is then used in expressions
Non-numbers .e2, -e2, 0e, -23e4.5, 1e.5
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R. Smith - University of St Thomas - Minnesota

11. What about Expressions??
Infix Notation
expression symbol expression
expression = any properly formed expression
symbol = character for arithmetic operator: + - / * ^
Functional Notation
operator (expression , expression )
operator = name of arithmetic operator
9/20/2018
R. Smith - University of St Thomas - Minnesota

12. Elements of Functional Notation
Function Name
Follows “variable name” rules (described later)
Identifies a function defined elsewhere
Parentheses enclose “argument list”
Also called the “parameter list”
Number of arguments?
Some functions demand a precise number
power(2,5)
Some functions are flexible – take an arbitrary number
Common in C, but not in Matlab
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R. Smith - University of St Thomas - Minnesota

13. R. Smith - University of St Thomas - Minnesota
Text vs. Numbers
Matlab lets you do calculations on TEXT
Text is indicated by single quote marks
Numbers in text are DIFFERENT
They do not represent a numeric value
They represent the numeric value of inidivual CHARACTERS
We see this when doing arithmetic on text
Examples
‘0’ + 2
‘1’ + 1
‘A’ + 4
‘C’ + 2
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R. Smith - University of St Thomas - Minnesota

14. R. Smith - University of St Thomas - Minnesota
Variables
Lets us save intermediate or final results
Assignment statement
name = expression
Examples: add some numbers, square root, multiply
Variables let us easily identify locations in RAM
We can use variables anywhere we can use numbers or expressions
Variables, numbers, and expressions all reduce to numbers
They are syntactically interchangeable
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R. Smith - University of St Thomas - Minnesota

15. R. Smith - University of St Thomas - Minnesota
What’s really going on?
The appearance
We evaluate an expression
We save the result in a variable
The implementation
We do a series of arithmetic calculations
We save the final result in RAM
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R. Smith - University of St Thomas - Minnesota

16. Good vs Bad Assignments
Legitimate variable name
Variable name left of =
Expression right of =
Single arithmetic expression
Expression calculates what you expect (disambiguated)
Bad
Bogus variable name
Badly formed
Using the wrong variable
Poorly named
Expression left of =
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R. Smith - University of St Thomas - Minnesota

17. “States” and saving results
In high school algebra, a mathematical expression does not normally have a “state”
You “evaluate” an expression
It may have a value or result
It may be ‘true’ or ‘false’
Computations have state
You “perform” a computation – it goes through a set of steps, and each step has intermediate results
The intermediate and final results reflect the “state”
“State” indicates that we are remembering a result, saving it in memory (RAM), for example
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R. Smith - University of St Thomas - Minnesota

18. R. Smith - University of St Thomas - Minnesota
Naming Variables
Syntax of a name
Any combination of upper- or lower-case letters
Digits, as long as it’s not the first character
May contain _ as in rick_smith
No ‘special’ characters (operators, syntax markers)
Certain keywords can’t be used
If, else, elseif, while, end, for, break, switch, case, otherwise, try, catch, return, global, function, persistent
Suggestions
Mnemonic – suggests the variable’s content and use
Not too long – make them understandable but type-able
Not misleading – don’t name Sqrt3 = sqrt(2)
Avoid ‘i, j’ – used with imaginary numbers
Use typical, mundane names where appropriate
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R. Smith - University of St Thomas - Minnesota

19. R. Smith - University of St Thomas - Minnesota
Fibonacci numbers:
Leonardo of Pisa’s book on algebra
Alias “Filius Bonacci” shortened to Fibonacci
Defined an ‘interesting sequence’ of numbers
Converges on the Golden Section
Ratio appearing in nature and in Greek architecture
Algorithm:
Next number in the sequence = sum of previous two numbers
3 Variables
New (“next”), Previous, Final
new = previous + final
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R. Smith - University of St Thomas - Minnesota

20. Notation Alternatives
These show up in various computing systems
Infix – Matlab, C, Fortran, Java, etc.
A + (B – C)
Functional-style – Matlab, C, Fortran, Java, etc. ***
plus (A, minus (B, C))
Prefix notation – Lisp and Scheme
(plus a (minus b c))
Postfix notation – Forth, RPN calculators
B C – A +
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R. Smith - University of St Thomas - Minnesota

21. *** Functional Notation in C, …
Most languages use it for “most” functions
Library functions, more advanced math functions, etc.
Log, exp, sine, cosine, etc.
Input/output
Most languages provide infix operators ONLY
You must use x+y, doesn’t provide plus(x,y)
Matlab has built-in functional forms for all arithmetic operations
There are weird cases that require the functional forms
9/20/2018
R. Smith - University of St Thomas - Minnesota

22. Working Notation Problems
“Walking the parentheses”
First, match the parentheses
Do the inside ones first
Postfix
x 2 power sin x 2 power cos +
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R. Smith - University of St Thomas - Minnesota

23. Exercise: Notation Conversion
Mostly infix:
sqrt(a^2, b^2)
Functional:
div(plus(a,plus(b,plus(c,plus(d,e))),5)
Prefix:
(sqrt (minus (power b 2) (times 4 (times a c)))))
Postfix:
a x 2 power times b x times plus c plus
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R. Smith - University of St Thomas - Minnesota

24. R. Smith - University of St Thomas - Minnesota
Parsing
A computing term for analyzing input text
Tokens – discrete chunks of the input text
Operators: + - .* and so on
Assignment statement =
Parentheses
… and more we’ll see later
Identifiers – tokens that name things
Function names and variable names
White space – spaces, tabs, other ‘blanks’
Generally skipped / ignored in parsing
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R. Smith - University of St Thomas - Minnesota

25. R. Smith - University of St Thomas - Minnesota
More on Parsing
Newline ‘token’ marks end of a line
Each line must contain a syntactically complete statement
Continuation with …
Atomic tokens
Tokens that have a meaning all by themselves
Parentheses, operators, =
No atomic tokens allowed in a variable name
Character Strings
Text delimited by single quotes (‘)
Example: ‘This is an example character string’
Parsing rules are different ‘inside’ the string
Semicolon ‘;’ separates statements
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R. Smith - University of St Thomas - Minnesota

26. R. Smith - University of St Thomas - Minnesota
Parsing Examples
A = sqrt( b^2, c^2)
Average = ( two four + 5) / five
Thing = (24/foo)/bar
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R. Smith - University of St Thomas - Minnesota

27. R. Smith - University of St Thomas - Minnesota
Chapter 2 Homework
Read Chapters 1 through 3.
We will cover 1.3 in more detail later
Do Exercises 2.1 through 2.4 – P. 32
Due at the start of class, Monday.
9/20/2018
R. Smith - University of St Thomas - Minnesota

28. R. Smith - University of St Thomas - Minnesota
Storing Numbers in RAM
Numbers stored in bits – binary numbers
8 bits = byte
(4 bits = nibble, 2 bits = ?)
Number of bits -> power of 2 -> number range
Old calculator
Number of digits -> power of 10 -> number range
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R. Smith - University of St Thomas - Minnesota

29. R. Smith - University of St Thomas - Minnesota
Number “Formats”
What about signs, decimal points, exponents?
Signed integers = 1 bit sign, rest magnitude
Floating point numbers
Part set aside for mantissa (‘value’ part)
Part set aside for exponent (‘power’ part)
In Matlab we treat most things as floating point
0 ./ 0 = infinity
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R. Smith - University of St Thomas - Minnesota

30. R. Smith - University of St Thomas - Minnesota
Chapter 3 Homework
Read Chapters 1 through 3.
We will cover 1.3 in more detail later
Do Exercises 3.1, -2, -3, -4, -7, -8, -9
Due at the start of class, Wednesday
9/20/2018
R. Smith - University of St Thomas - Minnesota

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9/20/2018
R. Smith - University of St Thomas - Minnesota