csci 246 – class 2mdale/courses/csci246/slides/csci 246 - cla… · csci 246 –class 7 proofs...
TRANSCRIPT
CSCI 246 – Class 7PROOFS
Plan for today:
- Quiz
- Normal review of video lesson (Euclidean Algo)
- Quiz question over video
- Review
- Homework
- Python IDE Demo
- Break – Download preferred IDE
- Python
Quiz Questions
Lecture 13:
Remember that Euclidean Algorithm is:
Function gcd(a,b)
If(a<b) return gcd (b,a)
If (b=0) return a
Else return gcd(b, a mod b)
Step through the algorithm gcd of gcd(57, 9):
Notes
Have a good weekend
Lesson 13
Lemma:
Let a>b
By the Quotient – Remainder Theoerm: a=q*b+r
=> r = a mod b
Then GCD (a,b) = GCD(b,r)
Lesson 13
Lemma:
Let a>b
By the Quotient – Remainder Theoerm: a=q*b+r
=> r = a mod b
Then GCD (a,b) = GCD(b,r)
Lesson 13
Proof:
1) let d|a and d|b
Lesson 13
Proof:
1) let d|a and d|b
a=u*d b=v*d
Lesson 13
Proof:
1) let d|a and d|b
a=u*d b=v*d
r = a-q*b = (ud)-q*(v*d) =(u-qv)d
Lesson 13
Proof:
1) let d|a and d|b
a=u*d b=v*d
r = a-q*b = (ud)-q*(v*d) =(u-qv)d
=> d|r
Lesson 13
Euclid or Euclidean's Algorithm
Function gcd(a,b)
If (a<b) return gcd(b,a)
If (b=0) return a
Else return gcd(b, a mod b)
Homework (Group)
Walk through Euclidean's Algorithm for the following:
1. gcd(24, 60)
2. gcd(24, 105)
3. gcd(60, 7)
Homework (Individual)
Walk through Euclidean's Algorithm for the following:
1. gcd(4, 14)
2. gcd(14, 4)
3. gcd(14, 89)
Demo
Python IDEs
Visual Studio Express with Python Plug-in
Pycharm
Break
Python IDEs
Visual Studio Express with Python Plug-in
https://www.visualstudio.com/en-us/downloads/visual-studio-2015-downloads-vs.aspx
https://pytools.codeplex.com/
Pycharm
https://www.jetbrains.com/pycharm/
Awesome resources
First Learning
Learn Python the Hard way: http://learnpythonthehardway.org/book/
Check IO Game: http://www.checkio.org/
References:
Hitchhiker’s Guide to Python: http://docs.python-guide.org/en/latest/
Python.org: https://docs.python.org/3/