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Combinatorics, Fall 2014
Letters to students of Combinatorics

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!

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.

As you have read or will read, this course is different. It requires patience, experimentation, understanding, and an open mind. There are no methodical ways to solve problems in this course, each problem is different in its own way. The key is to look at it from the right perspective. Understanding the tools given to you is extremely crucial; the interpretation of these tools will help you understand their strengths. Knowing when to use the appropriate method is important. It is more meaningful when you know what these tools actually do and even fascinating how elegantly they solve these problems.

I had a great experience with this course and I'm sure you will too. There are a lot great things to discover in this course and even more when you complete the research project. By the end, you will finally be able to appreciate combinatorics and understand what it really is. I hope you give it your all and I assure you that you will be greatly rewarded. I wish you all the best.

The course starts out simple and easy and then makes a hard left turn into a rigorous math course. My advice is to brace yourself for that, to any math major this should be what want to fell challenged. I would strongly advise going to all classes one of the positives of the course is that it sparks interest and a lot of that has to do with how the material is presented to us.

Making study groups is mandatory; by the end of the semester everybody left was in a study group or keeping in contact with someone else about problem sets. Math’s a team sport that’s why a lot of proofs have more than 1 name credited to them. Prof. Chris’s door is always open and he’s always willing to help through email or in office hours I strongly recommend taking advantage of opportunities to speak with him. Out of all the professors I have taken in Queens College he by far has the most extreme level of patience I have ever seen.

Some advice: Take pride in your project! Having the admiration of my fellow students and their interest in my work felt so rewarding that it made me want to continue my education.

Good luck!

Dear students,

You have registered this semester for an interesting and fun course. I was introduced to the terms combinatorics and permutations in probability so I thought the course COMBINATORICS was about counting different objects. However, my perspective changed as the semester progressed. It’s not only about counting but also deals with analysis and interpretation of sequences (Fibonacci), numbers (Catalan), games (chess) and many more interesting and fun topics. In this course, I was challenged to think as compared to other math classes which are mostly rote memorization.

The course culminates with a poster session which was a very enlightening. Each student chooses a topic, researches it and solves the chosen question using combinatorics. During this session I was able to see many other interesting applications of combinatorics in the real world. It opened my mind for the appreciation of combinatorics. It was amazing to see the numerous applications of the concepts of combinatorics—the concepts we learn inside a classroom, used to solve real life problems.

Dr. Hanusa is very passionate about the course. He is very easy going and is always available to assist students either in person or via email. He has high standards and expectations from every student.

All the best!!!!

And a letter to incoming Chinese students of combinatorics :)