Rutgers Young Scholars Program in Discrete Mathematics

Student Comments about the Program

July 2004

Elissa Ball 16, Sleepy Hollow HS, Tarrytown, NY

"The Rutgers Young Scholars Program in Discrete Mathematics has been a wonderful new experience for me. I liked being surrounded by others who share my interest in math. The course work was very different form anything I'd ordinarily be exposed to. The very first week we did graph theory, a field that I had never even heard of before, but that I found very interesting and was glad to have opportunity of learning. Furthermore, applications of graph theory kept coming up during the following weeks. Robotics was also great, especially since it gave us hands on experience. Lastly, fractals and chaos theory were a topic that I had heard of before coming here. Thus, for the first three weeks I was looking forward to learning more about a topic that already fascinated me. Having such high expectations, there was a good chance that I would be disappointed with the class. However, instead, I think I m even more interested in chaos theory and fractals than I was before."

Pauline Barkin 15, Union County Magnet HS, Scotch Plains NJ

"YSP introduced discrete mathematics, a new field to me. Before, I entered this program, I never would have conceived of fascinating algorithms, fractals, or graph theory. I was expecting this program to be "Brain Teaser Camp" , but it is much more, I learned useful applications of math. I never knew that fractals appeared in nature, and self similarity occurred in the human kidney, let alone what a fractal was, I was introduced to the mathematics behind games. I would not have covered the topics in school. While all of the information is new to me, I enjoyed the challenge. Being with people who have the same interest as me adds to the educational entertainment of YSP. I was informed of Bio-informatics which is now an occupation that interests me. YSP made a great impression on my mathematical knowledge."

Farah Fenelus 16, East Orange Campus HS, East Orange NJ

"The Discrete Mathematics program of 2004 was very well planned program. Through this program, I was introduced to a whole new world in mathematics and applied math. The professors had incredible knowledge of what they were teaching and were very much prepared. The applied mathematics introduced to me has taught me to be more open-minded, in other words & to think outside the box. I would definitely recommend this program to anyone with a passion of Math."

Mary Germino 16, Immaculata HS Somerville NJ

"I was very satisfied with the math content of this program. It was very comprehensive and complete, and at just the right level of difficulty. A lot of the math will serve me well in the math contests I often take - especially the combinatorics, number theory, and problem solving. Some material I had been previously introduced to, but never in the depth of this program. I think I learned more in a month here than in a year of high school math. I found everything very interesting, and will probably remember quite a bit, thanks to the reinforcement of the fun homework problems. The professors were great, and provided us with valuable notes. I'm glad I came."

George Hayward 14, Philip Exeter Academy Exeter NH

"I was very new to Discrete Math when I entered the RYSP. I also was worried because my mathematical background was just algebra and some geometry and at 14 I was the youngest of the group. However through the guidance of our very good professors I began to get a taste of Discrete Math. I learned a number of mathematical techniques that help me in geometry, algebra and general problem solving. I learned how fractals existed in nature, how to program robots, how to find the shortest path in a network, chaos theory and much more. I would recommend this program to anyone who loves mathematics, because not only do you learn things that aren't really taught in high school but also you begin to see the beauty of mathematics."

James Kong 16, Middlesex Academy HS, Edison NJ

"The math subjects high school students are exposed to in their normal courses pales in comparison to the eye-opening experience that the Rutgers Young Scholars program offers. From combinatorics to graph theory to fractals and chaos, the program drastically changed my view of the field of mathematics.

When I applied to the Young Scholars Program, I expected it to be simply a course in advanced math. I expected the program to push me ahead of the other students simply because I would have learned more material. I did not expect the over-whelming and contagious enthusiasm our professors had for math. I did not expect graph theory and the myriad of practical application it can be used to model. I did not expect the guest speakers on the forefront of their fields to be speaking to us high school students. Never before had I seen so many frontiers or applications of mathematics.

For me, mathematics is no longer a defined matrix dominated by computers. It is no longer an endless field of arcane theory. The Young Scholars Program has shown me that mathematics is a beautiful and incredibly useful study of our universe."

Esther Kwak 15, Stuyvesant HS, Manhattan NY

"My experience at Young Scholars has opened up a new window of learning. One topic of mathematic that I truly enjoyed was "Robotics" . The professors were enjoyable and pleasure to work with. The mathematic I learned here added and extended my knowledge. This experience was truly a life affecting event. I would definitely attended this program again given the opportunity."

Paul Leybov 15 Fair Lawn HS, Fair Lawn NJ

"The math I was exposed to at the Rutgers Young Scholars Program was a type of math that I had never seen before. The math topics that were covered here were very different from what I am used to seeing at school. I like this very much because school is not challenging. The math here was also more interesting because it had many real life applications, as in the topics covered in combinatorics and other topics. The homework presentations were useful because I was presented with different solutions for problems, which gave me a better understanding of the subject matter. I liked that we were shown different methods for proving theorems, like induction and contradiction, and for approaching complex problems where it is not obvious how to solve them. The YSP at Rutgers opened me up to a whole new field that I did not know existed and now like very much."

Jonathan Ma 17, Parsippany Hiss HS, Parsippany NJ

"Previously as a math student, I have only been exposed to "textbook" style teaching methods and topics, of reading and repetition. However at the YSP I was exposed to new, more active teaching methods as well as new, interesting math topics like graph theory and fractals. The program has left an indelible mark on myself as a math student, as I have not only learned more math but methods of thinking and problem solving."

Vikrum Modi 16, Ridgewood HS, Ridgewood NJ

"I have thought of a truly remarkable essay, but the margins of this page are too small to contain it. (misquotation of Fermat)

The Rutgers YSP program was an extensive tour of discrete mathematics comprised of several introductory courses on topics ranging from graph theory and algorithms to combinatorics and chaos. Each week's material built upon that of the previous week, integrating the courses to make the program more complete. Proofs often combined a variety of methods, including induction, combinatorics, and algebraic methods. Although each day was filled with new theorems and definitions with little repetition, there was even more of an emphasis on problem solving and processes. After lectures, problem sets required the use of clever approaches that were sometimes difficult to find but drew only from what had been learned until that point. This was one of the best aspects of the program since regular high school classes do not always force more creative thinking. Professors were always available for further questions on breaks and encouraged independent discoveries of patters and theorems. YSP had a permanent influence in this way."

Puja Patel 16, Hightstown HS, Hightstown NJ

"The instructors were great. They were well prepared as well as organized with notes etc. The math we were exposed to was not something you get in the classroom. It was unique yet very vital to real life. The real-life applications were interesting. The fact that we had time allocated for homework was also very convenient and helped us learn more. The material was in depth and will be helpful in future endeavors. I enjoyed the classroom time of program."

Nick Sawyer 16, North Plainfield HS, North Plainfield NJ

"Looking back on the last four weeks I've spent at Rutgers Young scholars program, I wonder, Was this program worth my time? Of course, it takes a millisecond for me to answer, and the answer is yes. Four weeks of intense mathematics sessions have exponentially increased my knowledge of the world of mathematics. To me, discrete mathematics is a building block necessary for future continuation of study in mathematics. It involves the basics, used to build more complex theorems, which in the end, have led mathematics like Euler to their greatest conclusions. The lessons included previously unknown problem-solving methods, new ways to observe and analyze equations, and an overall increase in mathematics comprehension. The professors, well-experienced in their field and accustomed to student environment, often provided helpful advice for solving homework questions. Fellow students also pooled their efforts on such problems, allowing others to share the solutions and learn the new tactics used. Thus, through the combined increase in knowledge, understanding, and method, the Rutgers Young Scholars Program has provided an ideal environment for augmenting mathematical interest and perhaps spawning a new group to succeed and improve on the great mathematicians of yesterday and today. "

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