Discrete Structures Journal

of Coleman Mulkerin


Week 1
Week 2
Week 3
Week 4
Week 5
Week 6
Week 7
Week 8
Week 9
Week 10
Week 12
Week 13
Week 14
Week 15
Week 16



Biography

Name

Coleman Mulkerin

Location

Sayre, PA

Intended Major

Computer Engineering

Other Interests

Reading: Blogs/Books, Science, Skepticism, Bowling, movies of any time period, and computers obviously



Discrete Structures - Week 7

Well we met on Monday this week in anticipation for the new professor. While we had alot of anecdotal and circumstantial evidence that the man existed and was in the building, we were not able to get observable evidence. At the end of class Haas saw him out side of the class, but he wasn't able to get him to come in. We have to wait yet another week...

The class started with a discussion of a problem. We explored just how much math can be done at a bagel shop. Most of the problem didn't cause us problems until the last part. We eventually hammered out and answer that was only off by 3... and we decided to just move on. This kind of problem lead to a lengthy discussion on passwords and what makes a strong password and what can we do to hack one. We came uncomfortably close to learning how to hack lab46 so we called it a day.

The Homework: Section 5 was tough but it was made easier by our discussions in class. It is tough in my mind to figure out what is a combination or permutation and whether repitition is allowed by I was able to slowly muddle through. Section 6 was really weird by I was able to hammer out what a lexicon order is. There other stuff in the chapter and the proof problems are a mystery rapped in a engima for me.

Exercises
- Ex 1 -
- Ex 2 -
- Ex 3 -
- Ex 4 -
- Ex 5 -
- Ex 6 -
- Ex 7 -
- Ex 8 -



Discrete Structures - Week 6

Today we got to class a few minutes late but the Haas was following us into the school so we weren't to worried. We expected to see the professor but he was MIA still. This is not good, because the later he gets here the harder it will be to transition. Next week we will have class on Monday if the teacher is here or if he is not we will have class on Tuesday.

The class was more of the same. People seemed to have absorbed the material pretty well which proves they mastered the arcane math of counting. We went over a couple problems, but we quickly moved on to the material in the upcoming sections.

One thing Professor Haas stressed was how these chapters relate to computer science. He went to an example of which I had no prior instructions on. Unix apparently can express a range of bit values using some syntax. It looked simple until Professor Haas himself was having a tough time expressing the simple example in the book. That unix course must have more meat in it than I had realized.

The Homework: I go behind on this weeks homework but I finally finished section 3 and 4. Section 3 was pretty easy to do. I have done those kind of problems before in Algebra courses. Section 4 was mostly new though I have used Pascal Triangles before. Knowing in depth why the triangle is like it is is a plus.

Exercises
- Ex 1 -
- Ex 2 -
- Ex 3 -
- Ex 4 -
- Ex 5 -
- Ex 6 -
- Ex 7 -
- Ex 8 -



Discrete Structures - Week 5

Today was another weird week. I made an hour commute into a 45 minute commute in order to get to class on time. When I get there Professor Haas was huddled over his laptop looking like he was ignoring the class. He pretty much was, but it was for good reason. The Lab46 server had gone down over night. I should of known it would happen. The server was doing weird things and kicking me off sometimes the night before. I settled down into my seat and waited for him to get done. Not being able to fiddle around in Lab46 was rough and I couldn't find much else to do.

Eventually we were able to get some class done. We discussed some of the properties of the summation and product symbols and how they relate to programming. Overall I think everybody understood the material when they could get past the crusty math exterior. Professor Haas decided to assign us something easier for next weak. The first 2 section on the chapter discussing Counting. Shouldn't be tough, but we'll see how hard the book tries to make it. We finished out the class discussing pigeons and were on our way.

Development:
I don't know what adjective to assign to the statement, but there is a development in the discrete structures class. Our intructor from abroad seems to have managed to get into this country. The transition from Haas to the new guy will be interesting and I hope it won't get to complicated. I have just gotten used to the general rythym of my school week and now who knows what kind of work we will be expected to do.

The Homework:
The homework was rather simple. It was kind of hard to create a variety of problems too. They were helpful in getting me to understand the material. They seem more like puzzles then math questions.

Exercises
- Ex 1 -
- Ex 2 -
- Ex 3 -
- Ex 4 -
- Ex 5 -
- Ex 6 -
- Ex 7 -
- Ex 8 -



Discrete Structures - Week 4

This week we were assigned the reading of Section 1 and 2 of Chapter 2. This section dealt with Set and their operations. I have begun to notice that this class deals with alot of stuff we already know, but just expresses it in a different way. Sets are easy enough on their face and actually seem to resemble the proposition stuff in their operations. The hard part comes forth when we talk about null sets and nested structures as we soon found out in class.

It all started with a simple question about a problem in the book. Professor Haas jumped up to the board and started to ask about ways to think of the solution. We began by thinging of the nested sets as almost like acess points or loops which would multiply the number of elements. Thie worked for the first problem but the second one started to give us problems. It had 4 elements and a nested nested element. The answer was 16 and we could only seem to come up withanswers like 10 and eventually 15. We struggled for a bit with people throwing out suggestions. One person even suggested to think of the nests as structures or classes.

I was confused with there answers and started to consult the book. I came across a equation that just seemed to simple. It said the power set had 2^n elements with n being the number of elements of the original. It seemed to work with all the answers in the back of the book so I meekly raised my hand and explained what I saw. It was then the Haas realized we were dealing with Power Sets and that they were a strictly defined function. This made the answers much simpler to find. Professor Haas said he was glad that we were trying to solve the problem in our own weird way though and was very happy with the work we did.

The Homework:

The Program: This came mostly from my desire to learn how to make class structures again. I decided to make at least a Set structure that I could use in future program. The Set just consists of an array but the advantage is that I can use the class and do operation with simple phrases like "A + B" to make a union of the A and B set. The only hitch I found was in the creation of the print statement in the class definition. I put it instead in my program code. The code itself is just a program that takes in an input of 2 Sets in order to do operations on them. So far it can do Unions, Intersection, and difference.

Exercises
- Ex 1 -
- Ex 2 -
- Ex 3 -
- Ex 4 -
- Ex 5 -
- Ex 6 -
- Ex 7 -
- Ex 8 -
- Prog .h -
- Prog .cpp -



Discrete Structures - Week 3

After two weeks of confusion, I finally was confortable with both the lectures times and the homework to follow. The lecture was mostly about what of we read were we responsible for to learn. Turns out half of what we did was not to important or would not show up until years later unexpectedly. Would of liked to now that before hand :). He pointed out 1.6 on Proofs as being an important section. I am going to have to study that more in the future as it was one of the harder parts of the chapter.

We also looked at a quirky programming language called proglog. More out of curiousity probably than anything else. I was interesting to see a programming language with a much different format. I could see how it could be useful in specific application. We also looked into the language lisp. It had scary formating and seemed to completly different from conventional language. I have to check it out sometime.

The homework this week was alot easier and it was not just because of the shorter number of problems. I knew this time not to write it out and word but to do it in notepad/nano. I tried to pick a variety of problems, but it was tempting sometimes to pick ones that looked easy. They tended however to be the ones that were more complicated.

Prob 5 of Section 1 was pretty simple though I had some trouble with all of the brackets. (A member of a group of a group of a group....)

Prob 22 of Section 1 was another set question but had the confusion of have the null set. Apparently Null is always part of a Power set but not used in all of the sets of the power set.

Prob 1 of Section 2 was a problem where we had to convert expression with unions, intersection, etc symbols into english form. I noticed that much of the same rules of logic operators parallel the rules of set operation. I hope the analogy doesn't get me into a trap later...

Prob 26 of Section 2 was one I had to do by virtue of my love for Venn Diagrams. I am a spatial thinker and Venn diagrams really bring things into focus. Some of these were a challenge though particularly the last with it's many negations.

I was going to do a program even though one wasn't assigned. I am itching to code some more because the last one was fun to do. It ended up being a busy weekend though with 2 reports. Maybe next week.

PS. I am having to much trouble with permissions. Something I am not getting I suppose. I'll try to fix it.

PSS. I realized I was short on the number of problems done so I did 4 more.

Exercises

  - Ex1.php -
  - Ex2.php -
  - Ex3.php -
  - Ex4.php -
  - Ex5.php -
  - Ex6.php -
  - Ex7.php -
  - Ex8.php -


Discrete Structures - Week 2

Week 2 turned out to be much like what week 1 should of been. We went over the syllabus and Professor Haas way of teaching a class which can only be described as laid back. It remains to be seen whether I can thrive in the kind of structure or if I need someone pushing me.

The rest of the period was devoted to getting me up to speed with all the technology elements of the class. It turns out that I had a general experience with most of it, but just needed a few the details of the programs provided. The journal that I am writing in now is structured in php. I have heard about php, but never get into using it. From what I have seen it looks like a very useful programming language. The IRC channel is alot like others I have used so I was able to hop right into using it though it's not getting used much yet.

Homework was much more of a hassle. Because I was not there for the first class I was behind on the reading. I had to study all of chapter 1, do 8 of the exercises, and make a program in one weekend. Granted I should of spread the work load out but it kind of crept up on me. Oh well, it is behind me now. On the good side, the program was fun to do. It could use some work in terms of effeciency, but not bad for an hours work.

One particular thing that was hard for me in studying the book was trying to unlearn some of my previous experience with Boolean Logic. I used + instead of v and * instead of ^. I also negated things with a line over the top of the variable or whole expression. I ended up trying to convert the expressions in my head most of the time. I guess this is one case where high school classes actually hinder college classes with more sophistication.

Hopefully next week I spread things out

Exercises

  - Ex1.php -
  - Ex2.php -
  - Ex3.php -
  - Ex4.php -
  - Ex5.php -
  - Ex6.php -
  - Ex7.php -
  - Ex8.php -
  - prog1.php -


Discrete Structures - Week 1

Week 1 was a particularly odd week. Not only had I missed the first class due to a scheduling conflict, but I found out that the rest of the class was still almost as confused as I was. Having looked at the notes of a classmate to see what I missed, I new that I was at least comfortable with the material to date. Granted it's the first day, but it's a good start.

The class I actually attended was light on content, but understandably so. We had to flesh out the schedule. I was pleased to see the class displayed a little more initiative then some of the glaze eyed classmates in my other classmates. We hammered out an amazing schedule of 1 face time meeting with some internet instruction on the side to supplement.

Here is hoping that our intended Professor doesn't show up to ruin all our hard fought compromise.

Exercises

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