Optimal Separation on Two-Dimensional Arrays
By Jim Tao
Mathematics has always been important to me. When I was little, I liked to do mathematical puzzles out of a book I had bought from a catalog. I would think and ponder about these puzzles and discuss them with my family and friends. The answers were not straightforward, and I found the solutions interesting to read. Doing the puzzles, I discovered that mathematics is more than just a set of drills to memorize. It is a subject full of interesting, clever ideas . . . Gradually, I became more interested in proof-based mathematics, so I pursued it further in a research internship at CSULB. My mentor, Dr. Wen-Qing Xu, had published several articles in the field of error-correction coding theory. Since that field of mathematics does not require the use of calculus and other collegiate mathematical preparations, but it does involve serious mathematical arguments, so I decided to pursue research in this area. I studied the separation of symbols on two-dimensional arrays, and came up with formulas for the maximum separating distance in various cases. I wrote proofs of my results, and spent many, many days discussing them with my mentor and revising them over and over again. It was intense, grueling work, but in the end it paid off…