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Here are some words of explanation, advice, and motivation from past students:
Dear future combinatorics students:
This semester you will learn about combinatorics, or "advanced counting"! Combinatorics is really just a way to count different things and prove that you are right, which sounds a little silly, but it's really not. It's actually quite fun and I think anyone that has an appreciation for math will enjoy this course.
For me, this class was different than any math class I had taken previously. I was familiar with classes where the professor gave many equations and proofs of those equations with the expectation students could apply them. This class was a little different in that I did not feel as overwhelmed with equations and theories, but the math was just as important. However, I will say that in this class more than any other I have taken, lecture is so important and it is even more important to understand the material day to day.
I think that the most important thing I took away from this class and hope you do as
well, is that this class teaches you how to think more mathematically. Instead of worrying about memorizing equations you will
worry about what the equations actually mean, and why you are learning them. All of the topics we discussed in this class at first
seemed so weird, but the more material we covered the more interesting it became. This class was intimidating at first, but for
me, this class gave me a whole new perspective on math and I really enjoyed it. I hope you do too!
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This course was one of the most interesting courses I have even taken here. Be prepared for a
semester filled with fun, learning and opportunity. The first two words are pretty self explanatory but this course gave me the
opportunity to excel in mathematics. It was challenging enough to give myself a chance to take my understanding of the material
to the next level. I found all the topics of this course quite interesting so I enjoyed working hard in this course and learning
new concepts.
The course is geared to a different type of thinking that has not been seen in any previous
math course. The thinking used is sort of like more creative thinking rather than concrete. The term combinatorics in my mind
means the ways in which you can count anything. You could be talking about numbers, sets of numbers, objects, or even elephants.
Combinatorics is just the methods and ways in which certain things can be assorted and accounted for and there are a wide range of
methods that can be used to arrive at any specific conclusion.
The most interesting part of this course was the presentations of different
homework problems. I thought that presenting problems to the class gave the presenter and also the students a better
understanding of the material. There are so many ways to solve problems and hearing a different method from someone else can
really make one think differently about something. Overall this is a great course to take and I hope you all enjoy this class as
much as my classmates and I did this past semester. I wish you the best of luck.
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Combinatorics studies different ways to count objects, while the main goal of this topic of mathematics is to investigate the
best, or most intelligent, way to count. When dealing with a group of finite objects, combinatorics helps count the different
arrangements of these objects, and eventually enumerate, or list, the properties of these arrangements. After a semester of
studying combinatorics, you will find a better way to count things from cutting a cube of cheese into 16 smaller cubes, to how
many different poker hands are full houses. You will finally be able to beat your friends at poker while eating 16 identically
shaped pieces of cheese.
One of my best experiences in this class was researching an outside topic of my choice, and making a
poster on the subject. As a musician, I choose to research the relationship between rhythm and combinatorics. Using methods that
I had learned throughout the semester, I was able to find a formula for the number of ways we hear certain time signatures for a
given number of beats. As a result of my research, I am able to recognize how similar time signatures can be used in completely
different ways. This experience has made me both listen to and play music differently. Not only was it interesting to
investigate my topic, but upon looking at other peoples research at our poster session, I learned a lot about other combinatorial
problems dealing with gin rummy, connect four, and chess that were very interestingly researched.
Overall, this class was extremely interesting. If you are at all interested in how we can
intelligently count any group of finite objects than you will have a blast in this class.
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Dear incoming Combinatorics class,
Upon registering for this class, many of you probably weren't really sure what exactly
combinatorics is. However, by the end of the semester, you'll be able to answer this question easily due to the multitude of
times you are asked ``Combina-what''? My simple answer to my friends who continually ask this question is, ``It's counting.'' Sounds
easy enough, right?
Throughout this semester, you'll expand your definition of counting tremendously. You'll begin with the
basics: permutations and combinations. From here, you'll realize that there is much more to these two words than you thought.
You'll learn different interpretations of games as well as various principles that will help you visualize these interpretations.
You'll also learn how to combinatorially prove something. That is, you'll break down a set into something you're familiar with
and analyze the familiar set so that it gives you a representation of the more complicated model. In doing so, it is very easy to
visualize what is occurring in your proof.
Another central topic that you'll discuss is the various uses of some important
sequences of numbers such as the Fibonacci and Catalan numbers. You'll first learn how to visualize these sequences using
pictures. This is their combinatorial interpretation. Then you'll analyze these sequences and learn how to determine some of
their different properties, such as their generating functions and recurrence formulas. Properties such as these are useful
because they allow us to more easily prove different facts about a certain sequence.
As you can see, there is much more to
combinatorics than solely ``counting''. It is a conglomeration of analysis and interpretation of games, sequences and numbers in
general. This class will force you to use a different perspective when looking at the subject of mathematics. If you embrace
this fact early, you should be fine. Good luck!
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