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.
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