CSE 20
DISCRETE MATH
Prof. Shachar Lovett
http://cseweb.ucsd.edu/classes/wi15/cse20-a/
iClicker frequency: CA
Learning goals
• Mathematics lies at the core of all computer science
• It it used to develop fast algorithms that solve complex
problems
• This course is the first step
Learning goals
Logistics
http://cseweb.ucsd.edu/classes/wi15/cse20-a/
About this class: grading
• Final: 40%
• March 16th
• Midterms (best out of two): 30%
• Midterm 1: February 2nd
• Midterm 2: March 2nd
• Homework: 20%
• Online quizzes: 5%
• Class participation (Clicker): 5%
About this class: attendance
• This class is interactive – you read the material at home,
we discuss it in class. You need an iClicker. Register it on
TED.
• Discussion sections: highly recommended. That is the
place to understand the material in a slower pace, see
more examples, ask more questions.
• Office hours: highly recommended. This is your one-on-
one time to ask questions and make sure you understand
everything.
About this class: HW
• Homeworks are in groups of 3-4 students
• Submitted online via TED, by Monday 2pm (before class)
• Collaboration is allowed only within groups, no other
collaboration / discussion is allowed
• Need help? Come to discussion sections and office hours
About this class: online quizzes
• Basic questions about definitions from required reading
• Should take no more than 10 mins
• Due before each W/F class
• Online on TED
About this class: Academic integrity
• You are working on a homework question with your group
members and are stuck on a question. You run into a
friend who solved the problem already and shows you her
solution. You look at it, but put it away before continuing
the group conversation. Is this cheating?
Yes
B. No
A.
About this class: Academic integrity
• You form a group to work on a homework assignment.
There are three group members and three questions. You
split up the work so that each student gets one question.
After you work on your individual questions for a while,
you get together as a group and proofread the solutions,
then hand them in. Is this cheating?
Yes
B. No
A.
About this class: Academic integrity
• You’re working on a homework question and run across a
definition you don’t understand. You Google the term
and, ‘lo and behold, the first hit is a full solution to the
homework question. You avoid reading the solution and
close the browser. You keep working on the solution and
hand in the assignment, without mentioning the Google
search since you didn’t use the result. Is this cheating?
Yes
B. No
A.
About this class: Algorithms!
Multiply 17 x 142.
What did we do?
Is there another way? The RPM Algorithm
Write the factors in two columns.
Repeatedly double the LEFT and halve the right.
(Truncate fractions, i.e. toss remainders)
Cross out the LEFT values where the RIGHT values are even.
Add the remaining LEFT values together.
A needle in a haystack
• You’re working in lab and realize your phone is no longer
in your pocket. You turned off the ringer as you came into
the room so you know you had it with you. How do you
find it?
Cutting a cake
For N=6 how many pieces?
How about for N=600?
Two algorithms
Alg1(real a, pos int n)
x  1.0
for i between 1 and n :
x  x * a
return x
Alg2(real a, pos int n)
x  1.0
i  n
while i>0 :
if i is odd :
x  x * a
i  i/2
if i > 0:
a  a * a
return x
Are they correct? Compute the same thing?
Which one is better?
Two algorithms
Alg1(real a, pos int n)
x  1.0
for i between 1 and n :
x  x * a
return x
Are they correct?
A.
B.
C.
D.
Only Alg1 is correct
Only Alg2 is correct
Both correct
Both incorrect
Alg2(real a, pos int n)
x  1.0
i  n
while i>0 :
if i is odd :
x  x * a
i  i/2
if i > 0:
a  a * a
return x
Two algorithms
Alg1(real a, pos int n)
x  1.0
for i between 1 and n :
x  x * a
return x
Are they the same algorithm?
A. Yes
B. No
Alg2(real a, pos int n)
x  1.0
i  n
while i>0 :
if i is odd :
x  x * a
i  i/2
if i > 0:
a  a * a
return x
Two algorithms
Alg1(real a, pos int n)
x  1.0
for i between 1 and n :
x  x * a
return x
Do they compute the same function?
A. Yes
B. No
Alg2(real a, pos int n)
x  1.0
i  n
while i>0 :
if i is odd :
x  x * a
i  i/2
if i > 0:
a  a * a
return x
Two algorithms
Alg1(real a, pos int n)
x  1.0
for i between 1 and n :
x  x * a
return x
Which one is better?
A.
B.
C.
D.
Alg1
Alg2
Both the same
Depends on the inputs
Alg2(real a, pos int n)
x  1.0
i  n
while i>0 :
if i is odd :
x  x * a
i  i/2
if i > 0:
a  a * a
return x
What’s an algorithm?
A. A step by step process
B. Any way of solving complex problems
C. Computer code
D. Math
An algorithm?
• Definition: a step-by-step process
• Each basic step is simple
• Together they can compute very complicated things
• What properties do we care about?
A. It should have the correct format (“compile”)
B. It should always terminate
C. It should give the correct answer
D. All of the above
For next class
• Get the book:
Jenkyns, Stephenson
and read sections 1.1, 1.2
• HW1 is due Monday Jan 12 5pm
• Ask any questions you have about the course,
expectations, requirements either in person or via TED
• Make note of important dates.