Aaron Snook
EECS 203 Discrete Mathematics
Spring 2015, University of Michigan, Ann Arbor
Date: June 22, 2015
Extra Credit
Problem Double-deck Pinochle.
Problem Part a.
P20
Note that the number of hands can be written as the number of solutions to i=1 xi =
EECS 203: Discrete Mathematics
Spring 2015
Discussion 2 Notes
1. Exercise 1.8.7
Prove the triangle inequality, which states that if x and y are real numbers, then |x|+|y|
|x + y|
Solution
A proof by cases!
a) Case I: x 0, y 0 Then |x| + |y| = x + y and |
*EXAM 1*
EECS 203
Spring 2015
Name (Print):
_
uniqname (Print): _
Instructions. You have 110 minutes to complete this exam. You may have one page of notes
(8.5x11.5 two-sided) but may not use any other sources of information, including electronic
devices,
Aaron Snook
EECS 203 Discrete Mathematics
Spring 2015, University of Michigan, Ann Arbor
Date: June 16, 2015
Homework 6
Problem 5.1 P40.
Base case: Distributive laws dictate that (A1 A2 ) B = (A1 B) (A2 B) (and of course (A1 ) B =
(A1 B).
Inductive step:
Aaron Snook
EECS 203 Discrete Mathematics
Spring 2015, University of Michigan, Ann Arbor
Date: June 14, 2015
Homework 6
Problem 6.5 P32.
There are 6 ways to place the start of the AAA, and 5!/2! ways to place the rest (we divide by 2 since the
order of th
Discussion 5
EECS 203
Spring 2015
Problem 1
Suppose that armies A and B are two generals in the Civil War, and have an enemy that
you would like to face off against. Both of you have rather small forces. However, you have
a network of spies that is able t
Discussion 5
EECS 203
Spring 2015
Proof(?) that f (S T ) = f (S) f (T ):
(1)f (S T ) = cfw_b B | a S T such that f (a) = b Definition
(2) = cfw_b B | a such that a S T f (a) = b Rewording
(3) = cfw_b B | a such that a S a T f (a) = b Definition of
(4) =
Group assignment 3 A practice exam
EECS 203
Spring 2015
Name (Print):
uniqname (Print):
Name (Print):
uniqname (Print):
Name (Print):
uniqname (Print):
General Instructions
This is a group assignment that is posted as a LaTeX file. You are to answer the q
Aaron Snook
EECS 203 Discrete Mathematics
Spring 2015, University of Michigan, Ann Arbor
Date: June 1, 2015
Homework 3
Problem 2.1 P14.
Problem 2.1 P18.
One example is A = cfw_ and B = cfw_, cfw_.
Problem 2.1 P42.
Problem 2.1 P42a.
There is a real number
Aaron Snook
EECS 203 Discrete Mathematics
Spring 2015, University of Michigan, Ann Arbor
Date: May 12, 2015
Solutions for EECS 203 HW1
Problem 1.3 P52.
p = (p|p)
p
T
F
p|p
F
T
p q = (p|q) (where denotes our earlier construction; a long way to write this i
Discussion 5
EECS 203
Spring 2015
Problem 1
Prove that in any set of 6 people, where any two people either know each other or do not,
that there is a set of 3 people that all know each other or all do not.
First, just come up with sets of 6 people and cre
EECS 203: Discrete Mathematics
Spring 2015
Discussion 3 Notes
1. Exercise 2.3.40a
Let f be a function from the set A to the set B. Let S and T be subsets of A.
Show that f (S T ) = f (S) f (T ).
Solution:
f (S T ) = cfw_f (a)|a S T
= cfw_f (a)|a S a T
=
EECS 203: Discrete Mathematics
Spring 2015
Discussion 1 Notes
1. Exercise 1.3.30
Show that (p q) (p r) (q r) is a tautology.
Solution:
To be a tautology, the given expression must be TRUE for all possible values p, q, and
r. The most straight forward appr
Aaron Snook
EECS 574 Computational Complexity
Fall 2013, University of Michigan, Ann Arbor
Date: May 12, 2015
Solutions for EECS 203 HW1
Problem 1.1 P14.
Problem 14a.
r q
Problem 14c.
p r
Problem 14f.
r qp
Problem 1.1 P22.
Problem 22a.
If you do not wash
11/18/13
Complex Experimental and Factorial Designs
Lot of independent variables
why? 1.) Economy (limit it to single study, done at once)
2.) Can test non-linear trend & we can test interaction effects (synonymous with
moderation.) <-specific hypothes
Memory and Valgrind
Int *p;
*p +=1;
Error: integer goes up by 4 bits not one, if we just do +=, we're now pointing to a random part of that
integer.
Int *p = NULL:
*p+=1;
Error: segmentation fault, you're incrementing a value that's NULL
#include <cstdlib
Problem Set 10 solutions
Section 9.1
#18 How many vertices does a full 5-ary tree with 100 internal vertices have?
#20 How many leaves does a full 3-ary tree with 100 vertices have?
#22 A chain letter starts when a person sends a letter to five others. Ea
Behavior
Resting
Foraging
Locomotion
Standing
Binky
Elimination
Grooming
Sniffing
Description
The animal is stationary, crouched or stretched, and mostly unmoving except for the twitch
of the nose. The animal may be sleeping or simply staying in such a po
Grading Rubric: Assignment #5 - (18% of Final Grade)
Assignment Component
Final Paper/Project Proposal
Abstract
Should be concise and specific (no longer than 120 words)
Follows abstract guidelines from APA manual
Points
/5
/10
Introduction
Describe the p
GRADING RUBRIC: Assignment 3 Data Analysis (13% of final grade 130 points)
Component
Introduction paragraph
Include a brief description of the overall study, what the main research question(s) of the
ANES data are, and what this assignment will address
D
Name: _ Section: _
GRADING RUBRIC
Assignment 2- Comparing Popular Press Reports and Journal Articles
10% of final grade 100 points
4-6 pages
Research Design Components - Sample & Design (from Media Article)
- The identity and sources of participants
- Sam
AAPTIS 331: FINAL PAPER GUIDELINES
Sections 006 & 007
Due Wednesday April 17 by 5pm Paper Outline
turn in as forum post via ctools and in hard copy to me in section
Paper Outline
The paper outline will consist of two parts: a research question, and a work
1. Rosen 5.2.16
Prove that the first player has a winning strategy for the game of Chomp if the initial board is two
squares wide, that is, a 2 n board.
-If the Player1(the first player) chomps the far right bottom cookie as his first move, then player 1
1.) Rosen 9.5.58
the relation R between bracelet is (B1, B2) where B1 and B2 are bracelets that belong to R iff B2 can
be obtained from B1 by rotating it or rotating it and then reflecting it.
a.) Show that R is an equivalence relation.
We know R is refle
Using memories
What values should we apply if we want to write 0x12 to memory location 0x044?
What values should we apply if we want to read memory location 0x44?
Cells
4-bit words
r e d o c e d _ _ _ _ _
_
_
memory array 256bits (16x16)
_mux/demux OE C
Using memories
What values should we apply if we want to write 0x12 to memory location 0x044?
What values should we apply if we want to read memory location 0x44?
Cells
4-bit words
r e d o c e d _ _ _ _ _
_
_
memory array 256bits (16x16)
_mux/demux OE C
Laser problem
We want to measure distance with a laser-based measurement device (you can buy these fairly cheaply by the way). The idea is you shoot a laser at a target and you measure how long it took for the light to get back to you. Weve got two input
Go
A[3:0]
B[3:0]
State Machine
X, Y, Z
4-bit Multiplier Data Path
Zero
Done
Out[7:0]
0000 A[3:0] 4 X RA: 8-bit register 0000000 8
0 1
B[3:0] 4 RB: 4-bit register Y
For RA and RB 0 Hold 1 Load 2 Shift Right 3 Shift Left
4
8 RB[0]
RB=zero? zero
Shift Regist