Symbolic Models

1
Symbolic Models

• Problem Solving with Computers

2
Symbolic Models

• Use symbols to convey information
• Highly structured
• Symbols
• Words
• Grammar (syntax)
• Languages are symbolic models
• So is mathematics (algebras)

3
Variables Constants

• Variable
• A value that can change
• Constant
• A value that does not change

4
Arithmetic Operations

• Addition 2 3 2 3
• Subtraction 5 2 5 - 2
• Multiplication 10 ? 4 10 4
• Division 12 ? 3 12 / 3
• Exponentiation 32 32

5
Order of Operations

• Arithmetic expressions are evaluated according to
  the following order of operations
• At each level, operations are evaluated left to
  right
• (1) Parenthesis, Functions, Exponentiation
• (2) Multiplication, Division
• (3) Addition, Subtraction

6
Parenthesis

• Parenthesis are used to alter the order with
  which operations are evaluated
• Ex.
• 4 5 2 equals 14
• (4 5) 2 equals 18
• Why?

7
Equations

• An expression that sets two expressions equal to
  one another
• Example
• Final Cost Price Discount
• Note the use of words for each value
• These are called identifiers

8
Identifiers

• Use common words and/or abbreviations
• Should reflect the nature of the represented
  value
• Bad example
• A1 XY Z Q
• What does that mean?

9
Electronic Spreadsheets

• Consists of values, formulae and labels
• Arranged into rows and columns
• Each row is numbered
• Each column is lettered
• The intersection of a row and a column is called
  a cell

10
Electronic Spreadsheets
11
Electronic Spreadsheets

• Creating a worksheet
• Develop a solution
• Write the solution as a set of equations
• Design a layout
• Convert the equations into formulas
• Enter labels, values and formulas into worksheet
• Ta Da!

12
Try This!

• Develop a method for determining the net pay for
  an employee based upon the employees gross pay,
  federal income tax rate and union dues
• Your method should include names (identifiers)
  for all known and unknown values

13
Know?

• Gross pay
• Tax rate
• Union dues

14
Need?

• Tax
• Net Pay
• How to calculate the above

15
Create an algorithm

• Tax is tax rate times gross payTax Tax Rate ?
  Gross Pay
• Net pay is gross pay less all deductionsNet Pay
  Gross Pay - (Tax Union Dues)

16
Design a Layout

• Which are the cells where you plan to place your
  formulas?

17
Convert to Formulas

• Tax Tax Rate ? Gross Pay
• B4 D2 x B3
• Net Pay Gross Pay - (Tax Union Dues)
• B6 B3 - ( B4 B5
  )

18
Problem

• Develop a worksheet to calculate the cost of a
  meal consisting of an appetizer, a beverage, a
  main entrée, and a desert.
• Assume a sales tax rate of 7 and an automatic
  gratuity of 15.

19
Functions

• Examples
• F(x) 2x x2
• F(3) 2(3) 32
• 6 9
• 15

20
Functions

• Maps inputs to outputs
• Ex. F(x) 7x - 3

F(x)
F(2)
7(2)-3
14-3
21
Excel Functions

• Math
• SQRT(x)
• FLOOR(x), CEILING(x)
• MIN(list), MAX(list)
• SUM(list), COUNT(list)
• Trigonometric
• SIN(x), COS(x), TAN(x)
• And lots more!

22
Free Meal Example

• Problem At a restaurant, patrons can use a
  coupon to get 3 entrees for the price of 2. To do
  this, the entrée with the lowest price is free.
• How do we do this?

Hint Youll need to use one of the functions
previous mentioned
23
Free Meal Example

• Know
• There are 3 entrees
• One will be free
• Need
• A way to determine the lower price
• A way to calculate the final bill

24
Free Meal Example

• Do
• Develop set of equations (algorithm)
• Create layout
• Convert equations to formulas
• Put it all together

25
Free Meal Example

• Set of equations (algorithm)
• Use MIN( )
• Lowest MIN(First, Second, Third)
• Cost First Second Third - Lowest

26
Free Meal Example

• Layout

27
Free Meal Example

• Formulas
• Lowest MIN(First, Second, Third)
• D2 MIN(B2, B3, B4 )
• Cost First Second Third Lowest
• D4 B2 B3 B4 - D2

28
Free Meal Example

• Put it all together!

Free Meal Example
29
Try this!

• Problem
• At a diving competition you plan to attend, a
  divers score is the sum of the scores for all
  the judges, less the low and high scores, and
  multiplied by a difficulty factor.
• Create a worksheet to compute divers score based
  on the scores for seven judges and a difficulty
  factor

30
Boolean Operations

• Relational
• Logical

31
Relational Operations

• Traditional
• Less than
• A lt B
• Greater than
• A gt B
• Equal to
• A B

• Excel
• A lt B
• A gt B
• A B

32
Relational Operations

• Traditional
• Not less than
• A ? B
• Not greater than
• A ? B
• Not equal to
• A ? B

• Excel
• A gt B
• A lt B
• A ltgt B

33
Logical Operations

• Traditional
• A ? B
• A ? B
• ? A

• Excel
• AND(A, B)
• OR(A, B)
• NOT(A)

34
Decision Statement

• Q What is a decision?
• Something that represents a branching point in a
  solution
• Outcomes are often dependent on initial conditions

35
Try this!

• Problem
• You have a numerical grade for a student
• 65 or better is passing
• Youd like to see a P for passing or a N for
  not passing in the worksheet
• How do you do this?

36
Know?

• Starting numerical grade
• 65 or better is passing

37
Need?

• Final letter grade (P or N)
• Method for performing conversion

38
Do?

• If the grade is greater than or equal to 65, then
  the students passes, else the student does not
  pass.

39
Can I write this less wordy?

• Yes!
• Use Pseudocode
• Wait!
• What the CENSORED is Pseudocode?

40
Pseudocode

• Looks like a programming language
• Has all the structure of a programming language
• Has a verrrrrry loose syntax

41
Pseudocode

• Example get x result lt- x2 5x 7 print
  result
• Thats it!
• Sloppy, aint it?

42
Do? (Less wordy)

• If Grade ? 65 Then P Else N

43
If statement

• The condition is a Boolean expression
• When the condition is True, the then-action is
  executed
• When the condition is False, the else-action is
  executed

44
If function

• IF(condition, then, else)
• condition is a Boolean expression(same as for If
  statement)
• Function evaluates to then expression when
  condition is true
• Function evaluates to else expression when
  condition is false

45
Layout
46
Try this!

• Problem
• Youd like to go see a movie.
• The movie costs 8.00, a soda costs 2.50 and a
  large popcorn costs 4.50.
• Based on the amount of money in your pocket,
  determine whether you could...
• (a) Just see the movie,
• (b) See the movie and buy a soda, or
• (c) See the movie, and buy soda and popcorn.

47
Know?

• Movie costs 8.00
• Soda costs 2.50
• Popcorn costs 4.50
• How much money I have in my pocket

48
Need?

• Cost of movie and soda
• Cost of movie, soda and popcorn
• Way to select one of the three options(that is,
  make a decision!)

49
Do?

• Option (a) costs 8.00
• Option (b) costs 10.50
• Option (c) costs 15.00
• Is there a hidden option?
• Yes! Stay home!
• So, what next?

50
How about a diagram?
Money lt 8

• Say, isnt this a flowchart?

Money lt 10.50
Stay home
Money lt 15.00
Movie
Movie soda
Movie, soda popcorn
51
How about a diagram?
Money lt 8

• Boxes represent actions

Money lt 10.50
Stay home
Money lt 15.00
Movie
Movie soda
Movie, soda popcorn
52
How about a diagram?
Money lt 8

• Diamonds represent decision points

Money lt 10.50
Stay home
Money lt 15.00
Movie
Movie soda
Movie, soda popcorn
53
How about a diagram?
Money lt 8

• Arrows show flow

Money lt 10.50
Stay home
Money lt 15.00
Movie
Movie soda
Movie, soda popcorn
54
How about a diagram?
Money lt 8

• The arrow at the top tells us there were previous
  steps
• The arrow at the bottom tells us there are
  subsequent steps

Money lt 10.50
Stay home
Money lt 15.00
Movie
Movie soda
Movie, soda popcorn
55
And as Pseudocode
If (Money lt 8) ThenStay homeElse If (Money lt
10.50) Then Movie Else If (Money lt
15.00) Then Movie soda Else
Movie, soda popcorn
56
How would I write this?

• Using Microsoft Excel...
• Wait (again) !
• Dont you need to design a layout first?

57
Try This!

• Problem Your bowling team (five members) wishes
  to create a worksheet to keep track of its
  performance. The worksheet will show, for each
  team member as well as the entire team, scores,
  number of games, average, low score and high
  score.
• Question How would you determine who on the team
  has the highest score?