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Symbolic Models

Symbolic Models. Problem Solving with Computers. Symbolic Models. Use symbols to convey information Highly structured Symbols Words Grammar (syntax) Languages are symbolic models So is mathematics (algebras). Variables & Constants. Variable A value that can change Constant

brittany-harrell
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Symbolic Models

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  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 3^2

  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. Columns Cell Rows 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 employee’s 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 istax 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. 2 11 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: You’ll 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 diver’s 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 diver’s score based on the scores for seven judges and a difficulty factor

  30. Boolean Operations • Relational • Logical

  31. Traditional Less than A < B Greater than A > B Equal to A = B Excel A < B A > B A = B Relational Operations

  32. Traditional Not less than A  B Not greater than A  B Not equal to A  B Excel A >= B A <= B A <> B Relational Operations

  33. Traditional A  B A  B  A Excel AND(A, B) OR(A, B) NOT(A) Logical Operations

  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 • You’d 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 <- x2 + 5x + 7 print result • That’s it! • Sloppy, ain’t 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. Numerical Grade Formula Layout

  46. Try this! • Problem: • You’d 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 < $8 • Say, isn’t this a flowchart? Money < $10.50 Stay home Money < $15.00 Movie Movie & soda Movie, soda & popcorn

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