That day I was walking along
the beach at Zandvoort; the sky was filled solid with white clouds and several seagulls were gliding in the gentle wind.
As I walked I thought about
myself and asked a funny question of God. I asked,
“Well, just where do I stand in the great scheme of things, how do I rate?”
Just then the sky opened up
and a strong beam of sun shone squarely on a seagull above me
and towards the sea, about
120 feet away.
The gull was white but
now all that I could see was a massive, golden array of rippled muscles forming his chest, back, and left wing.
As his wings gracefully moved,the muscles continued to shine brightly in the newly forming blue sky;
and with great freedom and command of his world,
he flew off.
And I thought to myself,
so that’s it, I’m no better than a lowly gull.
Contact Dan DuPort at
ON YOUR NEXT VACATION
Expect good company surfing,
and good company fishing, too.
But expect a few delays along the road,
and to sometimes have a hard time finding your way.
It goes without saying, the local culture will abound
and it will amaze you.
All making for some great story telling back at the office.
So you think that you....
So you think that you’re
where you are now because
when you think about every
turn you took, you think
“if only I’d done that instead”,
then things would be different, things would be a lot better.
When in fact, you really did the that that you thought you should have done. If you did something different, you would still be sitting here thinking about why you should’ve done something else.
A different that. And that’s just because there is no real difference between the this and that of where you’ve been; you’d be in the same place now regardless of which prior choices you have made.
That is, if you take all the yous that you could have been, all the ones gotten by making the different choices, and then consider all that
is common to all these yous;
then that is the you of which I speak.
So you see, you could be no
different from the way you
are now.
There's a lot that's not right. If you let any of it disturb you, you miss the point of it.
The bright side relies on your recognition of it; not your submission to it.
Learning is tough because, while a little knowledge that you're missing
can often bridge large gaps, it is not accessible to you -
for if it was, you would reach out and grasp it.
And no one else can provide it,
because no one but you knows exactly what you
know and don't know.
This is why we have few friends in our neighborhoods,
just acquaintances and strangers.
Pickwick’s Umbrella
In London, half of the days have some rain. The weather forecaster is correct 2/3 of the
time, i.e., the probability that it rains, given
that she has predicted rain, and the
probability that it does not rain, given that she has predicted that it won’t rain, are both
equal to 2/3. When rain is forecast, Mr.
Pickwick takes his umbrella. When rain is not forecast, he takes it with probability 1/3.
Can you find
(a) the probability that Pickwick has no umbrella, given that it rains.
(b) the probability it doesn’t rain, given that he brings his umbrella.
This problem appears in
K. L. Chung, Elementary Probability Theory With Stochastic Processes, 3rd ed. (New York:
Springer-Verlag, 1979), p. 152
NOTE: You may not assume that the probability that she predicts rain is 1/2 or that the probability that she predicted rain given that it rains is 2/3; however, you need that, so prove it first.
HINT: Show that for any two events R & F such that a = P(R|F) = P(~R|~F)
P(F) = 1 - (a +P(R)) ,
1 - 2a
a ≠ ½ and under the further constraints that place the RHS between 0 and 1 inclusive.
When P(R) = ½ a drops out of the RHS and P(F) = ½ .
Like a train whose length spans your entire journey,
with doors wide open at each station, the river sometimes fails to move you.
If you continually see the same shoreline,
check that you are on the boat.
At least look at your ticket.
When opening it, ENABLE EDITING and ENABLE CONTENT
Note that the graphing tool uses VBA routines that are not supported on Apple products.
For years I've been asking myself if there are better ways of teaching Quantitative Business Methods, and in particular, Linear Programming, as I came to realize that many students lacked algebraic skills that were necessary in its study. Even those with good algebraic skills would be distracted because of the algebra involved, and those with poor skills would turn away in predestined failure. This led me to the creation of interactive Excel workbooks which allow the student to study linear programming without much algebra, or skill in Excel. They are ideal for a student who has forgotten math and for a student that is weak in it.
Chapter1i.xls can be used for your first few classes in a QBM course. You can work it into your own materials, or use it as a sole text for a short introduction to LP. I am open to your critique, suggestions for enhancements and also additional favorite exercises you'd like added in.
The series of interactive workbooks forms a complete interactive course text that takes the student by the hand to understand theory and develop skill. The workbooks are written in such a way that the student can work entirely autonomously, or ideally work in a class room lab with resident help from an instructor, class monitor, or peers. Alternately, a standard course can be conducted where the students work in harmony. Homework and self-tests can be done in the workbooks and emailed in for correction and grading, minimizing the time spent in course administration.
The content is written from the point of view of a mathematician, and covers the content of many standard recently written textbooks like the works of Ragsdale, Taylor, and Anderson / Sweeny / Williams. However, it is more foundational, interactive and avoids algebra.
Chapter1i.xls can be used as a stand-alone introduction to Linear Programming, without follow through. It consists of 23 worksheets, including self-tests, and exercises. It presents 2 variable LP in a simple manner using a graphing tool that I built in VBA which allows the student to input an objective function and (up to 8) constraints; the model is automatically graphed and the student can move the objective function iso-line and any of the constraint lines around the graph, to pin-point a model solution or do sensitivity analysis.
Each worksheet contains small interactive exercises that the student performs as part of the learning. These help guide the student through the concepts. There are also self-tests which are easy modeling problems that build the student’s confidence, as well as beginning exercises. Later exercises border on sensitivity analysis and prepare the student for Chapter2i.xls
Chapter2i presents the 4 aspects of LP: Shadow Price, Reduced Cost, Range of Optimality, and Range of Feasibility. These are introduced and illustrated using the 2 variable models. Sensitivity analysis is introduced and almost simultaneously, the training wheels are taken away and the student is introduced to solving models using the Excel solver, and interpreting the solver sensitivity reports. In Chapter3i.xls, setting up and solving N variable models is presented along with the analysis of accompanying Excel sensitivity reports. Reports from other solvers are also presented.
The first three chapters can be completed in 10 to 20 hours, depending on the student level and depth of study. The next chapters cover the standard fare up to and including the linear models associated with networks. There are eight chapters in all, enough for a course in the linear programming part of quantitative business methods.
Let me finish by saying that I have used this material for two separate courses, and each time got results that were 30% to 50% better than the results that I achieved previously via lecturing and using the standard texts.
