MATH 491/691: ALGORITHMS AND THEIR COMPUTATIONS PRELIMINARY REPORT 1. OVERVIEW This preliminary report investigates the use of computational to investigate mathematical conjectures, which is the overal theme of the class. Unlike the two main projects, in this report you will outline a project that you may or may not later commit to. The goal is to think about the scope and feasibility of a proposed computation. 2. F ORMAT The report should discussed and written as a team collaboration. It should be written with latex, and each report should contain the following sections. 2.1. Introduction. Introduce the problem or conjecture that you will decribe a computational approach towards investigating. Describe the relevance of this problem or conjecture, and describe why it is of interest. For instance, could this problem be used to gain insight or used directly in any applications, would it provide insight into any abstract ideas, or are there relevant generalizations? Are there known solutions are partial solutions to this problem? 2.2. Computational approach. Outline a computational approach that could be used to investigate this problem or conjecture. What resources would you need to perform this computation? This may include publicly available software or tools, and hardware that you may or may not have access to. How much computation would you expect to be necessary, e.g., do you expect the necessary computations would take seconds, hours, days, years, several lifetimes...? 2.3. Comparison with known results. To effectively use computation to investigate mathematics, it is common to compare preliminary calculations with known results in order to verify the computation. Describe how you might do this. 2.4. Conclusion/Discussion. Is the computation you described feasible within the constraints of a semester-long class? If not, what time-frame and additional resources and skills would be necessary? 2.5. References. Include relevant citations. E-mail address: snpolloc@math.tamu.edu D EPARTMENT OF M ATHEMATICS , T EXAS A&M U NIVERSITY , C OLLEGE S TATION , T EXAS 77843 Date: August 17, 2015. 1