Topics to be covered
Counting
Basic
Principles
Multiplication
Addition
Permutations
Combinations
Basic
principles
Multiplication
principle
If an activity can be performed in k
successive steps,
Topics to be covered
Binomial Theorem
Pascals Triangle
and Combinatorial
Identities
At first glance the expression (a+b)n does not have much to do
with combinations
In fact, we can obtain the formula
Topics to be Covered
Basic Probability Rules (Reminded)
The Law of Total Probability
Bayes Theorem
Basic Rules for Probability Reminder
1.
1.
Range of
of Values
Values 0 P( A) 1
Range
2.
2.
Complement
Topics to be covered
Inclusion-Exclusion
Examples
Permutations
Combinations
Principle
Inclusion-Exclusion
Principle
Let Ai be a set
A1 A2 A1 A2 A1 A2
A1 A2 A3 A1 A2 A3 A1 A2 A1 A3 A2 A3 A1 A2 A3
A1 A
Topics to be Covered
Orders of Growth (Briefly)
Big Oh Notation
Omega Notation
Theta Notation
Master Theorem
Divide-and-Conquer Recurrence Relations
1
Orders of Growth
Complexity: the amount of time a
Topics to be Covered
Master Theorem
General Case
1
Master Theorem Example
3
Solve the following problem using Master Theorem:
T(n) = 2T(n/2) + n log n
Solution
Consider the recurrence:
T(n) = aT(n/b)
Topics to be covered
Pigeonhole Principle
Fibonacci Numbers
Pigeonhole Principle
The Pigeonhole Principle
is
also known as
Dirichlet
Shoe
Drawer Principle
Box Principle
2
Pigeonhole Principle
The Pi
Topics to be covered
Basics of Counting
Tree Diagrams
Lexicographic Order
Tree Diagrams
Counting problems can be solved using Tree
Diagrams.
[A tree consists of a root, and a number of
branches leav
Topics to be Covered
Master Theorem
General Case
1
Master Theorem - Recall
A Generic Recursion Tree
Determining the final T(n)
Summing the expressions (internal nodes and
leaves), we have
log b n 1
T
Topics to be Covered
Sample space and events
Finite probability spaces
Conditional Probability
Independent Events
Introduction to
discrete probability
An experiment is a process that yields an
outcome
Topics to be Covered
Orders of Growth (Briefly)
Big Oh Notation
Omega Notation
Theta Notation
Master Theorem
Divide-and-Conquer Recurrence Relations
1
Orders of Growth
Complexity: the amount of time a
Topics to be Covered
Master Theorem
General Case
1
Master Theorem - Recall
A Generic Recursion Tree
Determining the final T(n)
Summing the expressions (internal nodes and
leaves), we have
log b n 1
T
Topics to be Covered
Probability Tree
Bayes Theorem
The new probability of B, P(B|A) is called the
posterior probability, posterior to A occurring. We
would have information on the prior probability o
Topics to be Covered
Master Theorem
General Case
1
Master Theorem Example
3
Solve the following problem using Master Theorem:
T(n) = 2T(n/2) + n log n
Solution
Consider the recurrence:
T(n) = aT(n/b)
NOVEMBER 11, 2016
If primary key already exists in data file then you must choose your own primary key
when importing. However, when the data file that youre importing doesnt have the
primary key colu
MGMT
2004
WEEK 2- September 12, 2016
1. First Assignment (Chat a lot tutorial): due September 20 @noon
NB.
Change the name in all files from data/datafile to solution so you can
differentiate between
WEEK 11
Why do a query before a report?
(3Cs)
Expression in database are equivalent to formulas in excel. They are user-defined.
Close all tabs before doing lookup wizard! Also close excel file before
MGMT 2004
WEEK 3- September 19, 2016
(Grade Book Exercise contd)
If you are doing a look-up true (for Vlookup) it must be in ascending order.
Start with the lowest value in each range. Lookup true re
MGMT 2004
BEST PRACTICES
Come to class
Buy the textbook
Organize your storage device by course and within course by week
No eating in the lab
MARKUP VS MARGIN
Markup is a percentage of cost. [It can b
WEEK 9
October 31, 2016
Click refresh on pivot table to update data from calculations
in the pivot table.
Q7: Sum, Average for the stock will be the same because it is
the same one unit of stock.
F
Identify four problems to be avoided when conducting a Performance Appraisal.
The Performance Appraisal is used to evaluate or test the performance of an employee on the
job. This information can be u
ERD Diagram
Customer
Item
Rents
Customer
Payment
makes
Assumptions.
M:N
Each customer rents MAX many items.
Each item is rented by MAX many customers.
Each customer rents MIN zero items.
Each item is
E-R Approach to Database Design
The Appropriate Rules to be applied are:
For 1:M relationships
we take the primary key from the table on the ONE side and copy it to the table on the MANY side.
For 1:1
COMP3161 - Solution to question 4
Question:
Find the highest grade for CS51T.
Which tables are we interested in?
In this case it is only the Enrol table.
Step 1: Find the grades that are less than the
COMP3161
Semester 2 2015/2016
Lecture 0: Introduction
Lecturer: Mr. Kevin Miller
Aim
This course aims to introduce students to the principles
behind Database Management Systems. Students will
gain pra
Introduction to
Database Management
Systems
Kevin Miller
1
Motivation
Organisations are increasingly aware of the importance of
information in the solution of their problems.
Because of decreasing cos
Data Modeling
Which data to include in the database
1
Aim of Data Modelling
Form a model of the enterprise so that the data are
accurate and useful.
Yet another form of abstraction.
First and most imp