CSCI 103 Algorithms and Problem Solving
Tutorial Exercise 1
October - December 2016
Introduction to Problem Solving
Pseudocode and Flowcharts
Tutorial Exercise 1
Objectives
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MAS212 Linear Algebra I Lecture Notes
Francis J. Wright, 2004
11. Orthogonality
Contents
Inner Products and Norms
Real Symmetric Matrices
Eigenvalues and Eigenvectors of Real Symmetric Matrices
Ortho
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B.Sc. EXAMINATION BY COURSE UNIT
MAS212 Linear Algebra I
Monday 26 April 2004, 10:00 am 12:00 noon
The duration of this examination is 2 hours.
This paper has two sections and you should attempt both
B.Sc. EXAMINATION BY COURSE UNIT
MAS212 Linear Algebra I
Monday 8 May 2006, 2:30 pm 4:30 pm
The duration of this examination is 2 hours.
This paper has two sections and you should attempt both section
B.Sc. EXAMINATION BY COURSE UNIT
MAS212 Linear Algebra I
Thursday 12 May 2005, 2:30 pm 4:30 pm
The duration of this examination is 2 hours.
This paper has two sections and you should attempt both sect
B.Sc. EXAMINATION BY COURSE UNITS
MAS212 Linear Algebra I
Tuesday 8 May 2007, 2:30 pm 4:30 pm
The duration of this examination is 2 hours.
This paper has two sections and you should attempt both secti
Queen Mary
University of London
BSc Degree by Course Units
MAS 212 LINEAR ALGEBRA I
30th April 2003
2.30pm - 4.30pm
Duration 2 hours.
This paper has two Sections and you should attempt both Sections.
This paper is not to be removed from the Examination Halls
UNIVERSITY OF LONDON
279 0091 ZB
BSc degrees and Diplomas for Graduates in Economics, Management, Finance and the
Social Sciences, the Diplom
This paper is not to be removed from the Examination Halls
UNIVERSITY OF LONDON
279 004a ZB
990 004a ZB
996 D04a ZB
BSc degrees and Diplomas for Graduates in Economics, Management, Finance and the Soc
COMPLETE FAMILIES OF STATISTICS
Def: Assume that f ( t ) is the family of pdfs (pmfs) for the statistic T ( X ) , (which is
random variable). The family is called complete if E g (T ) = 0 implies that
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FAMILIES OF DISTRIBUTIONS
Parametric Families: Functional form indexed by parameters (e.g. , 2 ) Each
member has a specific value for each parameter.
Exponential Family: A family of pdfs or pmfs is ca
POINT ESTIMATION
Def: A point estimator is any function W ( X 1 ,.X n ) of a sample.
So, any statistic is a point estimator but in order to be useful, estimators must have
good properties. We will stu
BAYESIAN ESTIMATION
Assumptions:
Classical Inference: Parameters are constants that are unknown. They are
estimated from samples of data. The estimators are random variables.
Bayesian Inference: Param
ANCILLIARY STATISTICS
Def: A statistic S ( X ) whose distribution is not a function of is an ancillary statistic.
Consider the situation where S is the minimal sufficient statistic for and the dim ( S
PRINCIPLES OF DATA REDUCTION
1. Def: Likelihood Function: If f ( x ) is the pdf (pmf) of X = ( X 1 , X n ) and we
observe X = x , the likelihood function of is L ( x ) = f ( x ) .
2. Def: Likelihood P
PRINCIPLES OF DATA REDUCTION
Goal: Make inferences about a parameter(s) in a family using a sample X i , i = 1,.n .
Data Reduction: Functions of the data called statistics may summarize all the inform
RATIO OF LIKELIHOODS AS SUFFICIENT STATISTICS
Given two pdfs (or pmfs) f o ( x ) , f1 ( x ) and propose a statistic, S =
f1 ( x )
fo ( x )
(the ratio of
likelihoods) for a single observation. The two
MINIMAL SUFFICIENT STATISTICS
If a statistic is sufficient, then so is an augmented statistic S ' ( S ,T ) . Since the goal is
to summarize information concisely, we desire to work with minimal suffic
PROPERTIES OF A RANDOM SAMPLE
Background Concepts:
Def: The random variables X i ,i = 1,.n are called a random sample of size n from the
population f ( x ) if X i ,i = 1,.n are mutually independent ra
USEFUL INEQUALITIES AND IDENTITIES
Numerical Inequalities:
Lemma 1: Let a,b be positive numbers and p,q be positive numbers greater than 1
satisfying:
1 1
1
1
+ = 1 , then a p + b q ab
p q
p
q
Holders
Examiners commentaries 2008
Examiners commentary 2008
05A Mathematics 1
Specific comments on questions Zone B
Question 1
The demand equation for a good is q(2p + 3) = 8 and the supply equation is q 2p
Examiners commentaries 2008
Examiners commentary 2008
32 Management science methods
Specific comments on questions Zone A
Section A
Answer one question from this section and not more than one
further
Lecture 5
Linked Lists
CSCI 103 Algorithms & Problem Solving
October December 2016
Topics
What are linked lists ?
Create List
Insert Node
Delete Node
Traversing a Linked List
Doubly Linked List
CSCI 1
CSCI103 Algorithm and Problem Solving
Lecture Exercises 6
Lecture Exercises 6
Stacks and Queues
Question 1: Stacks
(a) The figure below shows a stack S implemented using a linked list.
Stack S
2
count
Lecture 2
Pseudocode and Flowcharts
CSCI 103 Algorithms & Problem Solving
October December 2016
Topics
Flowchart
Pseudocode
Using Flowchart and Pseudocode
Basic Data Types
Basic Data Structures
Modula
CSCI 103 Algorithms and Problem Solving
Tutorial Exercises 2
Tutorial Exercises 2
October December 2016
More on Problem Solving
Sorting and Searching
Objectives
After the completion of these exercise