CMSC 250
Practice Midterm 2
These are practice problems for the upcoming midterm exam. Warning:
This does not necessarily reect the length, diculty, or coverage of the actual
exam.
1. Use weak induction to that for n 0
n
i2i = (n 1)2n+1 + 2
i=1
(a) Prove

CMSC 250-Discrete Structures, Spring 2011
1
Description
We will study fundamental mathematical concepts that are relevant to computer science. In
particular we will cover propositional and predicate logic, proof techniques, mathematical
induction, element

package cmsc420.pmquadtree;
/*
* A PM Quadtree of order 3 has the following rules:
* <p>
* 1. At most, one vertex can lie in a region represented by a quadtree leaf
* node.
* <p>
* 2. Each region's quadtree leaf node is maximal.
*
* @author Ben Z

CMSC250, Spring 2012, Solutions to Homework 7
1. (30 points)
Use Mathematical Induction to show that for n 1
n
i=1
(a) Show the base case.
For n = 1
n
i=1
1
n
i
1
1
1
1
=
= = 1
1
i
i
i=1
n = 1 = 1
The rst value is greater than or equal the second value

CMSC250
PRINT Name:
0101 (8am, Hui)
0301 (12pm, Reza)
Homework 5
Due Date: October 10, 2012
, UID:
Circle Your Section
0102 (11am, Yoav) 0201 (9am, Hui)
0302 (1pm, Reza)
0303 (9am, Issac)
0202 (10am, Yoav)
1. (10 points) Show that the sum of any ve consec

Sample Questions
Dont use calculators.
1. Let W mean the wind is blowing, P mean Lara passes her exam and H mean Dad is happy.
Express the following statements symbolically, using the notation of propositional logic.
(a) The wind is not blowing.
(b) Lara

Answers to Sample Questions
No calculator was used.
1. Suppose that the predicate P (x) means x is positive. Let the domain of interpretation D
be the set R of all real numbers. Express each of the following sentences in the notation of
predicate logic.
(

Answers to Sample Questions
No calculator was used.
1. Let W mean the wind is blowing, P mean Lara passes her exam and H mean Dad is happy.
Express the following statements symbolically, using the notation of propositional logic.
(a) The wind is not blowi

CMSC 250
Practice Midterm 2
These are practice problems for the upcoming midterm exam. Warning:
This does not necessarily reect the length, diculty, or coverage of the actual
exam.
1. Use weak induction to that for n 0
n
i2i = (n 1)2n+1 + 2
i=1
(a) Prove

CMSC250 Homework 10
Not due
At the end of the semester Reinhardt traditionally invites everyone who has taken cmsc250 over to
her house for a party (even if she did not teach it that semester). It turns out the every semester
exactly n guests show up: n/2

CMSC250 Homework 10
Not due
At the end of the semester Reinhardt traditionally invites everyone who has taken cmsc250 over to
her house for a party (even if she did not teach it that semester). It turns out the every semester
exactly n guests show up: n/2

1
Discrete Mathematics with Applications
Chapter 1 Speaking Mathematically
1.1 Variables
Universal statement- Says that a certain property is true for all elements in a set.
Conditional Statement- Says that if one thing is true, then some other thing also

DISCUSSION #1
25 JANUARY 2017
INTRODUCTIONS
Katherine Scola
My office hours: MW 9:30-11:30 in the TA Room
Contact: [email protected] or through ELMS messenger
WHY IS THIS COURSE IMPORTANT?
Mathematical foundations for computer science
Concepts from

DISCUSSION #3
1 FEBRUARY 2017
TOPICS FOR TODAY
Circuits!
A modification to the full adder
Multiplying two 2-bit numbers
Two other circuit examples
FULL ADDER
FULL ADDER
How would the circuit change if we replace the OR gate with
an XOR gate?
FULL ADD

DISCUSSION #2
30 JANUARY 2017
TOPICS FOR TODAY
Attendance!
A quick reminder about homework
Algebra review
Fractions, exponents, polynomials, inequalities, and proofs
HOMEWORK SUBMISSION
Homeworks are due 5 minutes before lecture on Tuesday (at
10:55am

CMSC 250
Fall 2016
Homework #6
Posted: 10-18-2016
Due: 10-25-2016
Students first and last name:
Grade (grader only):
Students UID:
Students Section:
University Honor Pledge:
I pledge on my honor that I have not given or received
any unauthorized assistanc

CMSC 250
Fall 2016
Homework #4
Posted: 09-20-2016
Due: 09-27-2016
Students first and last name:
Grade (grader only):
Students UID:
Students Section:
University Honor Pledge:
I pledge on my honor that I have not given or received
any unauthorized assistanc

CMSC 250
Fall 2016
Homework #7
Posted: 10-25-2016
Due: 11-01-2016
Students first and last name:
Grade (grader only):
Students UID:
Students Section Number:
University Honor Pledge:
I pledge on my honor that I have not given or received
any unauthorized as

CMSC 250
Fall 2016
Homework #5
Posted: 10-04-2016
Due: 10-11-2016
Students first and last name:
Grade (grader only):
Students UID:
Students Section:
University Honor Pledge:
I pledge on my honor that I have not given or received
any unauthorized assistanc

CMSC 250
Fall 2016
Homework #2
Posted: 09-06-2016
Due: 09-13-2016
Students first and last name:
Grade (grader only):
Students UID:
Students Section:
University Honor Pledge:
I pledge on my honor that I have not given or received
any unauthorized assistanc

CMSC 250
Fall 2016
Homework #8
Posted: 11-08-2016
Due: 11-15-2016
Students first and last name:
Grade (grader only):
Students UID:
Students Section Number:
University Honor Pledge:
I pledge on my honor that I have not given or received
any unauthorized as

CMSC 250
Fall 2016
Homework #3
Posted: 09-13-2016
Due: 09-20-2016
Students first and last name:
Grade (grader only):
Students UID:
Students Section:
University Honor Pledge:
I pledge on my honor that I have not given or received
any unauthorized assistanc

CMSC250
Homework 7
1. (25 points)
Due Date: October 31, 2012
We will use Mathematical Induction to prove that for n 1
n
4k + 1 = n(2n + 3) .
k=1
(a) Prove the base case.
Solution: Let n = 1. The summation gives
1
n
4k + 1 = 4 1 + 1 = 5 .
4k + 1 =
k=1
k=1

CMSC 250
Fall 2016
Homework #9
Posted: 11-15-2016
Due: 11-22-2016
Students first and last name:
Grade (grader only):
Students UID:
Students Section Number:
University Honor Pledge:
I pledge on my honor that I have not given or received
any unauthorized as