Thursday, June 7, 2018

Statistical and Mathematical Methods for Data Science

Statistical and Mathematical Methods for Data Science
Credit Hours: 3
Prerequisites: None

Date : 7 June 2018

Course Contents:

Probability basics (axioms of probability,

conditional probability,

random variables,

expectation, independence,

etc.), (Ignored)

multivariate distributions,

Maximum a posteriori and maximum likelihood estimation;


introduction to concentration bounds,

laws of large numbers,

central limit theorem,

minimum mean - squared error estimation,

confidence intervals;

Linear algebra:
Vector spaces,

Projections (will also cover the least regression),

linear transformations,

singular value decomposition (this substitute for PCA),

eigen decomposition,

power method;

Matrix calculus with Lagrange Multipliers,


gradient descent,

coordinate descent,

introduction to convex optimization.

Teaching Methodology: Lectures, Problem based learning

Course Assessment:
Sessional Exam, Home Assignments, Quizzes, Project, Presentations, Final Exam

Reference Materials
1. Probability and Statistics for Computer Scientists, 2nd Edition, Michael Baron
2. Linear Algebra and Its Applications, 5th Edition, David C. Lay and Steven R. Lay
3. Introduction to Linear Algebra, 5th Edition, Gilbert Strang
4. Probability for Computer Scientists, online Edition, David Forsyth.

Friday, March 9, 2018

Tawanai Solar Module Rates updated.


Price List

Solar Module Prices 10 March 2018

Solar Module Rates 27 October 2017

UK’s top development official visits Pakistan

UK’s Department for International Development Permanent Secretary Matthew Rycroft visited Pakistan to see first-hand how DFID programmes were changing lives. During his visit to DFID’s largest overseas programme, Rycroft met with Adviser to the Prime Minister on Finance, Revenue and Economic Affairs Miftah Ismail, Dr Aisha Ghouls Pasha, Punjab’s finance Minister and other senior provincial ministers.

Friday, September 15, 2017

Why are marketing information systems necessary? What are some examples?

Khawar Nehal
Khawar Nehal, works at Applied Technology Research Center
What I understand are CRMs. Customer Relationship Management systems.
These are required to track what discussions and paper work has been exchanged between customers and the company representatives.
This avoids having the customer repeating themselves.
Usually not mentioned, but the success of a CRM depends on top management commitment, so I tell my clients that if the CEO is going to poke around the CRM at least 15 minutes per day, then the results for the company shall be very good.
It is a good way to make the company customer oriented.
Employees can put in everything related to customers, policies and other information into the CRM, but it is better to stay relevant to the customer’s needs and use the CRM appropriately.
A good example is SugarCRM and other CRMs which can integrate well with a lot of other applications which might be considered for organizations.
Benefits include :
Better client relationships.
Improved ability to cross-sell.
A well-implemented CRM system can replace manual processes that create significant organizational inefficiencies. But CRM systems don't just create efficiency by reducing the use of inefficient processes.
Thanks to the ability of popular CRM platforms to integrate with other systems, such as marketing automation tools, the efficiencies of CRM can enable companies to interact with customers in ways that they wouldn't have the resources to otherwise.
Greater staff satisfaction.
The more knowledge your employees have the more empowered and engaged they are. Having an accurate and up-to-date CRM that everyone uses and has acces to helps employees solve client problems. Doing so makes employees and clients happy.
Most importantly : Increased revenue and profitability.But this comes at the commitment of the top management of the company to look regularly inside the CRM. From my experience. Without this, the CRM becomes just another waste of resources with no one caring what is done with it.
Also the CRMs are able to make real time reports which are call dashboards or business intelligence nowdays.
The marketing information system is defined as : (in wikipedia)
A marketing information system (MkIS) is a management information system (Management information system - Wikipedia) (MIS) designed to support marketing (Marketing - Wikipedia) decision making (Decision-making - Wikipedia). Jobber (2007) defines it as a "system in which marketing data is formally gathered, stored, analysed and distributed to managers (Management - Wikipedia) in accordance with their informational needs on a regular basis." In addition, the online business dictionary defines Marketing Information System (MkIS) as "a system that analyzes and assesses marketing information, gathered continuously from sources inside and outside an organization or a store."
Furthermore, "an overall Marketing Information System can be defined as a set structure of procedures and methods for the regular, planned collection, analysis and presentation of information for use in making marketing decisions." (Kotler, at al, 2006)
So it is similar to the new term CRM which is common now.

Wednesday, September 13, 2017

Infinities explained

Definition of Zero and Infinity to solve dividing

by zero and managing infinity.
By : Khawar Nehal
Date : 19 March 2014.
Copyright : 19 March 2014. All rights reserved.
If you wish to share this article, please link directly to it on or
Modified to explain some more indeterminate forms. 23 March 2014.
When I was in class 8 I was thinking about infinite points in a line. Then
infinite lines in a plane.
If I divided the points with the number of lines in a plane, then I was getting
one point per line.
So I thought for many days about how to define it “correctly.”
Then I came up with infinity being the number of points between the number
0 and 1 in a line.
This included the point on the number 1. It became the points from (0..1]
then the next infinite points became (1..2] skipping the point located exactly
on 1.
So the number of points on a line bacame (2 (infinity) + 1). The +1
representing the point located on zero. 2 x infinity because the number line
went to positive and negative directions.
There are some cases where the theoritical physicists need to divide by zero
or infinity. The sometimes are not sure when to divide and when not to. There
are many types of infinities. So the one I am defining shall be called I
( Capital letter I). Zero shall be denoted with Z (Capital Z).
I is one of the infinities from all the various infinities. And Z is one of the
many zeros.
To define this Z and I correctly, I needed to define it in some other term than
zero and infinity.
So I tried and after many years was able to do so. I learned about limits in
Class 11 and in a few years I was able to define Z and I in terms of something
I selected the number 1 to define and tried many ways to avoid using a zero
and infinity.
This is the magic formula I finally arrived at.
Z = limit ( 1 / 1 – x ) where x approaches 1.
This Z shall be the size of one point on the number line.
So the number of points from (0..1] = I
I = 1 / Z
Number of points on a line = 2(I)
+ 1
Number of points on a plane = (2(I)
+ 1 )
Number of points in 3D space = (2(I)
+ 1 )
Finally you can divide by zero and multiply by infinity. You just need to
select the correct zero or infinity based on my definition before doing so.
So 1 / Z = I
( 1 / Z )
= I
This shall explain why some limits converge and some diverge.
A famous mathematician named George Cantor tried to convert these number
into a concept of cardinality.
In simplified terms.
The number of natural numbers = I. Without the Zero.
Number of integers = 2I + 1 (Including the zero)
Number of fractions with integers in numerator and denominator =
(2I + 1)
This means the number of fractions are equal to the number of
Number of real numbers based on base 10. I numbers on both sides of the
decimal point = (10)
(2I +1).
That is a lot of real numbers.
Number of real numbers based on base 2 (binary).
I numbers on both sides of the decimal point = (2)
(2I +1).
That is a lot of real numbers.
So according to my method, the number of base 10 real numbers is a LOT
more than binary real numbers.
The great thing about this method compared to the existing attempts at
managing infinity is that it can create a small number when dividing or
multiplying by infinity or zero.
Here are some examples.
2I / I = 2
1 / Z = I
2 / Z = 2I
This you gotta see.
I / I = 1
Z / Z = 1
The last two lines shall solve a lot of issues in maths.
From Wikipedia
and other branches of
mathematical analysis
, limits involving algebraic operations are
often performed by replacing subexpressions by their limits; if the expression obtained after this
substitution does not give enough information to determine the original limit, it is known as an
indeterminate form
The most common indeterminate forms are denoted 0/0, ∞/∞, 0
∞, 0
∞, 1
and ∞
These indeterminate forms are solved by my method as follows :
Z/Z = 1
I/I = 1
Z x I = 1
= 1
I – I = Z
= 1
= 1
Some more to clarify
I – 2(I) = -I
I / Z = I x I
Z / I = Z x Z = Z
I x Z = 1 = One.
If you really want to know about a larger number then the normal infinities,
then ask me for my definitions of the “Infinital” and “Beyond Infinital.”
An example is the issue of solving the following
In my system, the first one looks like
(-Z^2)/(Z) which means the limit of the first is -Z = Negative zero.
For the second looks like
( 4(I^2) – 5I ) / (1-3(I^2)) which is close to 4(I^2) / -3(I^2).
So the limit for the second is 4/-3 = negative 4/3
If you need more definitions,
please email me on