DISCRETE MATH W3203 MIDTERM #1
Wed March 4th 2015
open book and notes, no calculators
no electronic equipment of any kind
your name and UNI
PROBLEM POSSIBLE SCORE
1
12
2
16
3
16
4
16
5
20
6
20
TOTAL
100
SUGGESTION: Do the EASIEST problems (or parts of pro
DISCRETE MATH W3203 MIDTERM #1
open book, no calculators
no electronic equipment of any kind
PROBLEM SCORE
1
?
2
?
3
?
4
?
5
?
6
?
TOTAL 100
SUGGESTION: Do the EASIEST problems (or parts of problems) rst.
NB. Partial credit is awarded for meritorious work
Discrete Mathematics
COMS 3203
Fall 2015
http:/www1.ccls.columbia.edu/~ansaf/3203/
Midterm Exam 2
Monday November 23, 2015
There are six questions to solve for a total of 100 points. Please Show your work in all questions.
This exam is open notes and clas
DISCRETE MATH W3203 MIDTERM #2
Wed April 15th 2015
open book and notes, no calculators
no electronic equipment of any kind
your name and UNI
PROBLEM POSSIBLE SCORE
1
13
2
20
3
20
4
14
5
18
6
15
TOTAL
100
SUGGESTION: Do the EASIEST problems (or parts of pr
DISCRETE MATH W3203 MIDTERM #1
Sample Solutions
Quiz 1, Fall 2006
Wed 11 Oct 06
Professor J. L. Gross
CS W3203 Discrete Math
1 (10 pts). Use a truth table to decide whether this argument is valid.
p q
p r
premise 1
premise 2
r q conclusion
SOLUTION: Vali
9/22/2014
Columbia CourseWorks : COMSW3203_001_2014_3 : Test & Quiz
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COMSW3203_001_2014_3: INTRO-COMBINATORICS/GRAPH THR (Fall 2014)
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Discrete Mathematics
COMS 3203 Fall 2015
http:/www1.ccls.columbia.edu/~ansaf/3203/
Homework n 3: Relations & Counting
Released Thursday October 29th , 2015
Due Saturday November 7th , 2015 @11pm
Question 1
Let R and S be relations on the set A = cfw_1, 2,
Discrete Mathematics
COMS 3203 Fall 2015
http:/www1.ccls.columbia.edu/~ansaf/3203/
Homework n 4: Induction & Recursion
Released Monday November 9th , 2015. Due Thursday November 19th , 2015 @11pm
Question 1
1.
1
12
+
1
23
Assume n is a positive integer. U
Discrete Mathematics
COMS 3203 Fall 2015
http:/www1.ccls.columbia.edu/~ansaf/3203/
Homework n 4: Induction & Recursion
Released Monday November 9th , 2015. Due Monday November 16th , 2015 @11pm
Question 1
1.
1
12
+
1
23
Assume n is a positive integer. Use
Appendix D Fundamentals
Numbers
- Natural consist of zero and positive whole numbers
- Integers positive and negative whole numbers and zero
- Rational all fractions of from a/b where a and b are integers and b does not equal 0
o Two rational numbers a/b
SOLUTIONS
open book and notes, no calculators
no electronic equipment of any kind
your name and UNI
PROBLEM POSSIBLE SCORE
1
28
2
24
3
20
4
25
5
24
6
25
7
22
8
32
TOTAL
200
SUGGESTION: Do the EASIEST problems (or parts of problems) rst.
NB. Partial credit
DISCRETE MATH W3203 FINAL
open book, no calculators
no electronic equipment of any kind
PROBLEM SCORE
1
?
2
?
3
?
4
?
5
?
6
?
7
?
8
?
TOTAL 200
SUGGESTION: Do the EASIEST problems (or parts of problems) rst.
NB. Partial credit is awarded for meritorious w
Discrete Mathematics
COMS 3203 Fall 2015
http:/www1.ccls.columbia.edu/~ansaf/3203/
Homework n 3: Relations & Counting
Released Wednesday October 28th , 2015 @11pm
Due Saturday November 7th , 2015 @11pm
Question 1
Let R and S be relations on the set A = cf
Discrete Mathematics
COMS 3203 Fall 2015
http:/www1.ccls.columbia.edu/~ansaf/3203/
Homework n 2: Collections
Released Friday October 9th , 2015. Due Saturday October 17th , 2015 @11pm
Question 1 For each of the following sets, nd a way to rewrite it using
COMS 3203.001
Discrete Mathematics Fall 2014
Instructor: Dawn Strickland, [email protected]
Office: 530 Mudd, (212) 854-8930
Office Hour: Monday 12-1pm or by appointment
Lecture: Tuesday/Thursday 5:40-6:55pm
TAs
Name
Email
Dave Chisholm
[email protected]
10/26/2014
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9/30/2014
Columbia CourseWorks : COMSW3203_001_2014_3 : Test & Quiz
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COMSW3203_001_2014_3: INTRO-COMBINATORICS/GRAPH THR (Fall 2014)
Home
Fi
Name_
COMS 3203
Exam 1
Spring 2013
No calculators, notes, textbooks, or cheating of any kind.
Write your UNI on every page or you will be deducted 5 points!
1. (5 points each) Write the negation of each of the following statements.
a. No one wants to be d
COMS 3203
Exam 1
cheating
Spring 2014
failing
1. (1 point) Write your full name and UNI: _
2. (7 points) Use the truth table below to show that a conditional statement and its contrapositive are equivalent.
T
T
F
F
T
F
T
F
F
F
T
T
F
T
F
T
T
F
T
T
T
F
T
T
Name_
COMS 3203
Exam 1
February 15, 2012
No notes, books, calculators, or cheating allowed.
1. (3 pts each) Negate the following statements.
a. Some clowns are not creepy.
b. If you attend class, then you will learn and grow.
c. p q
2. (5 pts) Use a truth
Chapter 1
A proposition or statement is a declarative
sentence that is either true or false.
Examples of propositions:
The Moon is made of green cheese.
1+0=1
0+0=2
Examples that are not propositions:
Sit down!
What time is it?
That kitten is cute.
The ne
Data Structures in Java
Daniel Bauer
Homework 2
Theory
1.
23N, 42N, 2, N, 3, N, log N, 2/N, 128, N log N, 2, N!
2/N < 128 < log N < N < 23N < N log N < N2 < 42N3 < 2n+1 = 2n < 3n< N!
2. a. int sum = 0;
for (int i = 0; i < n; i+)
for (int k = i; k < n; k+)
Discrete Mathematics
COMS 3203 Fall 2015
http:/www1.ccls.columbia.edu/~ansaf/3203/
Homework n 1: Logic & Proofs
Released September 25th , 2015. Due October 5th , 2015 @5pm
Logic
Question 1
Prove by use of truth tables the following:
(x y) = (x) (y) and (
Discrete Mathematics
COMS 3203 Fall 2015
http:/www1.ccls.columbia.edu/~ansaf/3203/
Homework n 2: Collections
Released Friday October 9th , 2015. Due Saturday October 17th , 2015 @11pm
Question 1 For each of the following sets, nd a way to rewrite it using
Discrete Mathematics
COMS 3203 Fall 2015
http:/www1.ccls.columbia.edu/~ansaf/3203/
Homework n 1: Logic & Proofs
Released September 25th , 2015. Due October 5th , 2015 @5pm
Logic
Question 1
Prove by use of truth tables the following:
(x y) = (x) (y) and (
DISCRETE MATH W3203 MIDTERM #2
open book, no calculators
no electronic equipment of any kind
PROBLEM SCORE
1
?
2
?
3
?
4
?
5
?
6
?
TOTAL 100
SUGGESTION: Do the EASIEST problems (or parts of problems) rst.
NB. Partial credit is awarded for meritorious work
Discrete Math W3203, Spring 2015
Homework 5 Solutions
7.1, 36) Reasoning as in Example 2, we see that there are 5 ways to get a total of 8 when
two dice are rolled: (6,2), (5,3), (4,4), (3,5), and (2,6). There are 62 = 36 equally likely
possible out
Discrete Mathematics
COMS 3203 Fall 2015
http:/www1.ccls.columbia.edu/~ansaf/3203/
Recitation n 3: Relations, Counting, Induction, Recurrence Relaions
Question 1 From Scheinermans book, page 146, exercise 22.4 and 22.5.
Assume n is a positive integer. Use
Discrete Mathematics
COMS 3203 Fall 2015
http:/www1.ccls.columbia.edu/~ansaf/3203/
Homework n 2: Collections
Released Friday October 9th , 2015. Due Saturday October 17th , 2015 @11pm
Question 1 For each of the following sets, find a way to rewrite it usi