Why Have I Chosen the ESE 554 Course?

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This was the question that our professor asked us at the beginning of the first class.  I remember one guy saying honestly that he just needed three credits to complete his registration.  I was afraid that if my professor asked me, my answer would not be sophisticated, and I would say something about my interest in mathematics and computers, as the other guys did.  If my English were better, I would honestly admit that the list of courses for the spring semester was really too limited and most of us did not have any other choice.  However, I would add that if I had had the choice, I would have chosen the ESE 554 anyway, because my friends recommended it as a course where I would not have problems with my English.

As one can see, our answers were not connected with the subject of the course itself.  We meant different things: certain circumstances, our preferences, all other things, except for the subject of the course.  My understanding is only a few students knew exactly what the course is about, that is why an acquaintance of mine dropped the course after the first class.  I believe my experience will help other students to avoid some frustration if they register for ESE 554 Computational Models for Computer Engineers.

While registering for the course, students encounter the following course definition:
This course covers mathematical techniques and models used in the solution of computer engineering problems.  The course heavily emphasizes computer engineering application.  Topics covered include set theory, relations, functions, graph theory and graph algorithms, and algebraic structures.

When I read it for the first time, I assumed that we would be dealing with some software, which would be used for practical models design.  It turned out we could do it on our own; however, there were no assignments for the class.  This was my first disappointment.

According to the course definition, we had to study some theoretical topics, like Set and Graph theory, etc.  I have a rich mathematical background, and I was sure that the additional knowledge obtained in this course would help me in my work.  However, it turned out that Graph Theory is so huge that it requires a several-volume textbook.  It is impossible to present the full theory in one volume.  The same can be said about Combinatorics – a small course section that was not even mentioned in the course definition.  A variety of problems solved through Combinatorics is so wide that it is difficult even to enumerate them.  I realized that at the end of the course I would get an idea only about the fundamentals of these theories.  This is when I was disappointed a second time.

Studying these fundamentals we have learned that although all the course sections are separate mathematical theories, in reality, not only do they use the same methods but also they are closely related.  Also, all of these sections are parts of Discrete Mathematics.  I was convinced that the knowledge of these fundamentals of Discrete Mathematics is the necessary condition for studying Computer Science and becoming a software designer.  It is obvious that the students whose major is Computer Science will use these fundamentals to delve deeper into Discrete Mathematics.  However, my major is Electrical Engineering.  If I do not use the obtained knowledge, I will soon forget most of it.  Does it mean that I wasted my time studying the fundamentals of Discrete Mathematics in ESE 554 course, if my major is not Computer Science?

The answer is ‘no’. There are several reasons for registering for ESE 554, even if you are not going to continue to study Discrete Mathematics.  Let us remember that, according to the astonishing study of a primitive tribe in Brazil, even words may limit ideas.  If someone has no word for a number, he may have no notion of what that number means.  Due to the ESE 554 course, not only do the students obtain words, but also the fundamental concepts of Discrete Mathematics.  It is possible that some of the students will soon forget even the names of the theorems they studied, but they will never forget these concepts.  Moreover, being acquainted with methods of solution of the problems considered in the course allows students to develop their intuition that might come in handy for their ability to solve problems in other fields.

As an example of the application of the obtained knowledge for real life, let us consider the question asked at the beginning of this paper.  From Graduate Student Guide to Electrical & Computer Engineering one can learn that ESE 554 is one of seven core courses.  According to the degree requirements, three out of these seven must be selected.  The number of the selections from seven taken three at a time is the number of combinations:

                                                                                7!

C(7,3) =  ----------- = 35

      3!*4!

The number of the selections which include ESE 554 is

                                                                                 6!

C(6,2) =  ----------- = 15

      2!*4!

Suppose I am choosing the core courses at random.  Then the possibility that I encounter ESE 554 equals 42.9%.  It is easy to calculate that if I exclude the courses which I do not like from the list of the core one by one, the possibility to select ESE 554 will be increasing in this order – 50%, 60%, 75%, and so on.  One can see that it is difficult to skip the ESE 554 even if you make a random selection of courses.

As for me, I think the earlier a student registers for ESE 554 the better his progress in other subjects will be.

 

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