Discrete Probability
COMPSCI 230 Discrete Math
April 9, 2015
COMPSCI 230 Discrete Math
Discrete Probability
April 9, 2015
1 / 18
Outline
1
Conditional Probability Functions
2
Bayesian Inference and the Monty Hall Problem
3
Random Variables and Probability
The Substitution Model
COMPSCI 230 Discrete Math
January 27, 2015
COMPSCI 230 Discrete Math
The Substitution Model
January 27, 2015
1 / 12
Announcements
Grades for homework 1 available on Sakai
Homework 1 papers available in class today
Collecting homewor
Even More Racket
COMPSCI 230 Discrete Math
January 22, 2015
COMPSCI 230 Discrete Math
Even More Racket
January 22, 2015
1 / 14
Outline
1
Even More Racket
Expressions and Functions
Numbers
COMPSCI 230 Discrete Math
Even More Racket
January 22, 2015
2 / 14
Racket
COMPSCI 230 Discrete Math
January 20, 2015
COMPSCI 230 Discrete Math
Racket
January 20, 2015
1 / 24
Announcements
Homework 2 is due January 27
Make sure you have the book
Readings for Thursday consolidate
COMPSCI 230 Discrete Math
Racket
January
Racket
COMPSCI 230 Discrete Math
January 15, 2015
COMPSCI 230 Discrete Math
Racket
January 15, 2015
1/7
Outline
1
.
From Algorithm to Racket Code
RPM Revisited
COMPSCI 230 Discrete Math
Racket
January 15, 2015
2/7
From Algorithm to Racket Code
RPM Revisit
Multiplication and Racket
COMPSCI 230 Discrete Math
January 13, 2015
COMPSCI 230 Discrete Math
Multiplication and Racket
January 13, 2015
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Announcements
Homework 1 due on January 20.
Start early!
Clicker registration is online
Working out kinks w
MATH 242
Written HW1
Due Feb 9, 2017
PLEASE SUBMIT THESE TWO PROBLEMS IN CLASS (NOT VIA EMAIL). SHOW ALL
YOUR WORK! GOOD LUCK!
NAME:
1. (10 pts.) Use Gaussian Elimination (with matrices and row operations) and back-substitution
to solve the following syst
Course Schedule
NUMN 402
Fall 2016
*Please note there may be additional required readings posted on Blackboard for certain content areas
*Dates for presentation of specific content and assignments due are subject to change. Students will be notified in ad
CASE WESTERN RESERVE UNIVERSITY
FRANCES PAYNE BOLTON SCHOOL OF NURSING
Fall 2016
COURSE NUMBER:
COURSE TITLE:
NUMN 410
Health Assessment for the Advanced Generalist Nurse
COURSE DESCRIPTION:
This course uses a comprehensive, system-by-system, patient-cent
Math 313/515, Spring 2005
Jerry L. Kazdan
Homework Set 3, Due Thursday, Feb. 3, 2005
(Late papers will be accepted until 4 PM on Fri., Feb. 4)
All of these problems are from our text by Strang (3rd edition). I believe you will nd them
both short and routi
Exam 1
Math 609
March 18, 2004
Jerry L. Kazdan
1:30 2:50
Directions This exam has two parts, the rst is short answer (6 points each) while the second
has traditional problems (12 points each). Closed book, no calculators but you may use one
3 5 card with
Math 313/515, Spring 2005
Jerry L. Kazdan
Homework Set 2, Due Thursday, Jan. 27, 2005
d).
e).
f).
1 1
1 1
1 2
1 1
2 2
1 1
0 1 1 1
1 0
2?
0 1
1 0
1 0
a).
b).
c).
1. Which of the following sets of vectors are bases for
2. For which rea
Math 313/515, Spring 2005
Jerry L. Kazdan
Homework Set 4, Due Thursday, Feb. 10, 2005
(Late papers will be accepted until 4 PM on Fri., Feb. 11)
All but the last of these problems are from our text by Strang (3rd edition).
1. Strang, p. 92-93, #7, #9, #13
Math 313/515, Spring 2005
Jerry L. Kazdan
Homework Set 2, Due Thursday, Jan. 27, 2005
1. Which of the following sets of vectors are bases for R2 ?
a). cfw_(0, 1), (1, 1)
b). cfw_(1, 0), (0, 1), (1, 1)
c). cfw_(1, 0), (1, 0
d). cfw_(1, 1), (1, 1)
e). cfw_(
Math 313/515, Spring 2005
Jerry L. Kazdan
Homework Set 5, Due Thursday, Feb. 17, 2005
(Late papers will be accepted until 4 PM on Fri. Feb. 18)
1. a) With the usual Euclidean norm in Rn show that for any vectors X , Y :
X +Y
2
+ X Y
2
=2 X
2
+2 Y
2
.
Geom
Math 313/515, Spring 2005
Jerry L. Kazdan
Homework Set 6, Due Thursday, Feb. 24, 2005
(Late papers will be accepted until 4 PM on Fri. Feb. 25)
1. Strang p. 180 #1, 2, 14
2. Strang p. 180 #4, 5
3. Strang p. 181 #10, 11, 17
4. Strang p. 182 #21, 22
5. Stra
Prime Numbers
COMPSCI 230 Discrete Math
January 29, 2015
COMPSCI 230 Discrete Math
Prime Numbers
January 29, 2015
1 / 13
Outline
1
Prime Numbers
The Sieve of Eratosthenes
Racket Implementation with Lists
More on Primes
COMPSCI 230 Discrete Math
Prime Numb
Expectation and Hashing
COMPSCI 230 Discrete Math
April 16, 2015
COMPSCI 230 Discrete Math
Expectation and Hashing
April 16, 2015
1 / 13
Outline
1
Associative Storage and Retrieval
2
Hash Tables
3
Probabilistic Analysis of Hashing
COMPSCI 230 Discrete Mat
Expectation and Hashing
COMPSCI 230 Discrete Math
April 14, 2015
COMPSCI 230 Discrete Math
Expectation and Hashing
April 14, 2015
1 / 12
Outline
1
Expectation
2
Repeated Bernoulli Trials
3
Associative Storage and Retrieval
COMPSCI 230 Discrete Math
Expect
Discrete Probability
COMPSCI 230 Discrete Math
April 7, 2015
COMPSCI 230 Discrete Math
Discrete Probability
April 7, 2015
1 / 24
Outline
1
Compound Events and Joint Probability Functions
2
Conditional Probabilities and Independence
3
Bayess Theorem and Re
Logic
COMPSCI 230 Discrete Math
February 24, 2015
COMPSCI 230 Discrete Math
Logic
February 24, 2015
1 / 12
Bertrand Russell, 1872-1970
Logic
1
2
3
4
Why Logic
Propositional Logic
Predicate Logic
Euclids Elements
Euclid, circa 300 B. C.
The Times Higher Ed
Discrete Probability
COMPSCI 230 Discrete Math
April 2, 2015
COMPSCI 230 Discrete Math
Discrete Probability
April 2, 2015
1 / 21
Outline
1
A Warning about Quantiers
2
Probability and Intuition: The Monty Hall Problem
3
Discrete Probability
COMPSCI 230 Dis
Proof Continued
COMPSCI 230 Discrete Math
March 24, 2015
COMPSCI 230 Discrete Math
Proof Continued
March 24, 2015
1 / 18
Proof
1
Some Good Proofs
2
Direct Proofs
3
Mathematical Induction
COMPSCI 230 Discrete Math
Proof Continued
March 24, 2015
2 / 18
Theo