15.053 vs. 15.058
We asked Tim, the MIT beaver, to help
out, but he is busy doing other
important things for MIT. Besides,
Professor Orlin, who teaches 15.053 and
15.058, doesn’t own the copyright to
drawings or pictures of him.
Hi. My name is Amit. And my
friend who looks a lot like me is
Mita. We are both MIT beavers.
We’re here to tell you about the
differences between 15.053 and
15.058. If you aren’t sure which
one to take, we hope that this
presentation will help you.
Amit and Mita are quite
right. I also vouch for their
honesty and knowledge.
Mita
Amit
Tim
We’ll be joined by some
friends who will also
help provide some help.
You will meet them
soon.
You may be wondering why cartoon characters
are giving you this information. It turns out
that Professor Orlin likes us a lot and uses us to
explain a variety of things. Most students don’t
mind, and it’s always a pleasure for us. By the
way, we don’t give the lectures, although we do
give some tutorials.
I’m Stan the
stegosaurus.
I can’t wait to meet
all of the friends.
Amit
Stan
Mita
Hi, I’m Ella the owl.
Before listing
differences between
15.053 and 15.058,
we will list some of
the similarities. You
can see them on the
white board on the
next slide.
Ella
I’m Tom the Turkey.
I peeked ahead. The subjects do look very
similar.
It looks like a great subject for anyone who
wants to see mathematics used in the “real
world **.”
** For students at MIT, the real world is defined to
be the set of places that are not MIT. For faculty
and graduate students, the real world is anything
outside of academia. By the way, optimization is
very useful for decision making at MIT too.
Tom
As Professor Orlin often says,
“Optimization is everywhere.” People
want the best value for the cost;
manufacturers want to produce the best
quality for a given cost of production.
Students (and everyone else) want to
use their time as efficiently as possible.
Financial engineers want to maximize
return for a given level of risk. Engineers
want optimal designs. Yada Yada Yada.
Ella
Wow! Does this mean that I
can optimize my life after
taking 15.053 or 15.058?
No, but it would be so cool if you could.
The techniques from 15.053 and 15.058 are
useful mostly in business (or engineering)
decision making where there is a lot of
available data and where the value of
making better decisions is high.
Occasionally, it can be really useful for
smaller or more personal decisions. By the
end of the course, students will get a good
sense where the optimization methods in
the subject can be applied, and where it is
not so useful to apply them.
Tom
On the much smaller white
board to the right, I’ve listed
the key differences between
15.053 and 15.058.
I still don’t understand why there
are two subjects? How much linear
algebra is needed? Does it make a
big difference? Why not combine
the two courses into a single
course?
Ella
Tom
There are really two
reasons for having
two closely related
but different
subjects. First of all,
we needed a new
number for
graduate students
so that they can
obtain graduate
credit.
The other reason relates to
“efficiency of learning”. Some
students are very comfortable with
the use of matrix notation and its
relationship to solving linear systems.
They often learn more efficiently if
the lectures and readings rely on the
use of matrix algebra. 15.058 is
better for these students.
Other students have not had linear
algebra, or have had it but prefer to
learn optimization without much
matrix notation. 15.053 is better for
these students.
So, the goal is to optimize
the efficiency of learning. I
like that.
I like the way that the size of
the white board was
optimized so that we had
room to say what we wanted.
Ella
Stan
Tom
But how can undergraduates
who have had linear algebra
know which subject to take?
Are they permitted to take
15.053 if they have had linear
algebra? Can they take 15.058
if they only know some linear
algebra?
Students really only need to know
the first 1/3 of a linear algebra
subject. In order to take 15.058,
they should be facile with that
material. I think that the best way
for students to judge is for them to
check out the topics in linear
algebra that will be used. They are
listed on the next slide. More
detail is available on Professor
Orlin’s website.
Do we have to keep using
these name cards
underneath our drawings?
Ella
Tom
Stan
List of topics from linear algebra
• Working with matrices
–
–
–
–
matrix addition
matrix multiplication
the transpose of a matrix
Identity matrices and
permutation matrices
• Abstract properties of
matrices
– linear independence (and linear
dependence) of columns
and of rows
– rank of a matrix
• Solving systems of equations
– elementary row operations
– Gauss-Jordan elimination for
solving a system of equations
– Determining the inverse of a
matrix
– Determining when a systems of
equations has a solution
Here is a rule of thumb
for undergraduates
deciding between
15.053 and 15.058. If
you are relatively
comfortable with the
concepts on the
previous slide, you
know enough to take
15.058. But it’s also
OK to take 15.053
Another rule of
thumb is the
following: if you
have had 18.06 (or
another linear
algebra course) and
if you obtained a B
or better, you will
learn more from
15.058 than from
15.053.
Another rule of thumb is that
you will be really happy with
either 15.053 or 15.058.
They are both great courses.
Also, they are a great way to
learn about business analytics
and operations research.**
What are thumbs?
Do thumbs have
rules?
Tom
Ella
Stan
** This promotional
support was paid
for by “Cartoon characters
for 15.053 and 15.058.”
Some final comments
We hope you found
these slides helpful. If
you still need more
information on the
differences between
15.053 and 15.058,
you can contact
Professor Orlin via
email at
jorlin@mit.edu.
Amit
I’ll finish with a factoid on
the names of the 15.053
and 15.058. 15.053 was
renamed “Optimization
methods in Management
Science” less than 10 years
ago. But Professor Orlin
originally wanted to use
the name “Optimization
methods in Operations
Research” because he
refers to himself as a
Professor of Operations
Research. But he was
talked into using the term
Management Science so
that it would be the same
as the name of the major.
So, when 15.058 was created,
Professor Orlin decided to call it
“Optimization methods in
Operations Research.” It sounds
as though the distinction
between names for 15.053 and
15.058 are meaningful, but it’s
not. Management Science is a
synonym for Operations
Research.
Mita
Wait! Before you go, I’ll
introduce you to my other
15.053 and 15.058 friends.
Here they are:
•
Cathy, the catculating cat.
•
Nooz, the most trusted
name in fox, and
•
McGraph, a dog who
really Excels in making
charts and graphs.
We all look
forward to
seeing you soon!
Cathy
Stan
Nooz
McGraph
These cartoon characters and the others in this presentation were
drawn by Liana Moskowitz for Professor Orlin. The copyrights for
all cartoon characters in this presentation belong to James Orlin