(14021601-3 ) A Welcome Lecture ! What Motivated This Course? - - PowerPoint PPT Presentation

Problem Solving Skills (14021601-3 )

A Welcome Lecture !

What Motivated This Course?

 Improving students’ analytical and proving

(argue) abilities

 Improving student’s ability to design and develop

algorithms

Goals of This Course

 Make you a better problem solver in general

 Understand how you operate  Recognize limitations and pitfalls  Learn general techniques that you can apply to

solve problems

 Prepare you to

 occupy upper levels of professional hierarchy  Success your degree  find a high-end job even in adverse conditions  work for highly creative companies

Course Organization/Process

 Learn about yourself  Learn problem-solving techniques  Solve a wide variety of problems, so as to learn

how to apply the specific heuristics

 Understand errors typically made by poor

problem solvers. Learn to avoid.

Know Yourself

 Whimbey Analytical Skills Inventory (WASI)  Myers-Briggs Personality Type (Homework

Assignment 1)

http://www.humanmetrics.com/cgi-win/JTypes1.htm http://similarminds.com/jung.html (It is good to do a couple of different MB tests, results vary somewhat. Then, read the descriptions.)

 Soloman & Felder Index of Learning Styles  Thomas-Kilmann Conflict Mode Instrument

I took the test

6

Problem Solving Skills (14021601-3 )

 Instructor



Hassen Sallay, Ph.D.



Office: 1137, Email: hmsallay@uqu.edu.sa, hmsallay@gmail.com

 Text Book



Algorithmic Problem Solving, R. Blackhouse, John Wiley & Sons, 2011, ISBN-13: 978-0470684535



Puzzle-based Learning: Introduction to critical thinking, mathematics, and problem solving. Matthew Michalewicz,ISBN-13: 978-187646263

 Grading



Quizzes 20%, midterm 20%, lab exams: 30%, final exam 30%

 Course web page



http://amansystem.com/?c=people/sallay/PSS

Getting Started with a Problem

 “Eighty percent of success is showing up.”

 Woody Allen

 “Success is 1% inspiration and 99% perspiration.”

– Thomas Edison.

 To successfully solve any problem, the most important

step is to get actively involved.

 The Principle of Intimate Engagement: You must commit to the

problem

 “Roll up your sleeves”  “Get your hands dirty.”

8

The key premise:

Problem solving is not an innate ability (you either have it or you don’t). It’s a skill that can be learned and honed.

What Kinds of Problems?

 Puzzles  Math problems (simple math)  Algorithmic problems (will very require basic

programming skills)

Easy vs. Hard Problems

 Exercises: (e.g. compute 10! without a calculator)  Easy problems: See the answer  Medium problems: See the answer once you

engage

 Hard problems: You need strategies for coming up

with a potential solution, sometimes for even getting

• started. Open-ended problems are
• ften like this. Often, multiple possible solutions,

you need a strategy to choose “the best” one.

11

Effective vs. Ineffective Problem Solvers

 Effective: Believe that problems can be solved through

the use of heuristics and careful persistent analysis

 Ineffective: Believe ``You either know it or you don't.''  Effective: Active in the problem-solving process: draw

figures, make sketches, ask questions of themselves and others.

 Ineffective: Don't seem to understand the level of

personal effort needed to solve the problem.

 Effective: Take great care to understand all the facts and

relationships accurately.

 Ineffective: Make judgments without checking for

accuracy

12

Mental Toughness

 Need the attributes of confidence and

concentration

 Confidence comes with practice  Attack a new problem with an optimistic

attitude

 Unfortunately, it takes time

 You can’t turn it on and off at will  Need to develop a life-long habit

13

Engagers vs. Dismissers

 Engagers typically have a history of success

with problem solving.

 Dismissers have a history of failure.  You might be an engager for one type of

problem, and a dismisser for another.

 You can “intervene with yourself” to change your

attitude of dismissal

14

The Mental Block

 Many students do significant problem solving for

recreation (computer games, recreational puzzles.)

 These same students might dismiss math and

analytical computer science problems due to a historical lack

• f

success (the mental block)

 To be successful in life you will need to find ways to

get over any mental blocks you have

 Learn

to transfer successful problem-solving strategies from one part of your life to other parts.

 Example: Writing is a lot like programming

15

Example Problem

 Connect each box with its same-letter mate without

letting the lines cross or leaving the large box.

(Actual problem used in software company job interview)

A B C C B

A

16

Strategy: solve a simpler problem first.

A B C C B

A

17

C A

Heuristic: Wishful Thinking

A B C C B

A

C B A C B

A

A B C C B

A

C B A C B

A

The 9 coin problem

 9 coins that look alike. One is fake, can be

heavier or lighter (not known). Using a simple balance scale and 3 weighings, single out the fake one.

 Hint: solve a simpler problem first. Which one?

19

The solution for 3 coins:

 the weighings are: 

1 against 2



1 against 3

 Both of these can have three outcomes: fall to

the left (l), fall to the right (r), or balance (b). The following table gives the answer for each of these outcomes:

20

• utcome

fake coin # why:

• l l

1 too heavy l b 2 too light l r (not possible) b l 3 too light b b no fake coin b r 3 too heavy r l (not possible) r b 2 too heavy r r 1 too light

The solution for 9 coins:

 Step 1. Divide 9 coins into 3 piles of 3 coins each. Use

the 3-coin strategy to weigh:



pile 1 against pile 2



pile 1 against pile 3

 From Step 1, you will determine:

a) which pile contains the fake and b) if the fake is heavier or lighter.

 Step 2: Weigh 2 coins from the pile that contains fake.  Total # of weighings: 2+1 = 3.

 For 12 coins problem see

https://wn.com/12coins

Any Question ???