Mathematics
Questions first.
Proofs in full.
Selected papers presented as questions, results, and complete manuscripts.
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01 / Original result
Min-Max Degree Optimization in Edge-Minimal Hall-Type Key Assignments
There are n people and m rooms. Any m people must be able to open all m rooms simultaneously, one room each. If the total number of keys is minimal, how should the keys be distributed so that the person carrying the most keys carries as few as possible?
Δ(m,n) = ⌈m(n−m+1)/n⌉ Question, result, and complete paper → -
02 / Study paper
Exploring Volumes Bounded by Implicit Surfaces: A Visual and Multivariate Calculus-Based Approach
A discussion of the volumes of an assortment of 3D shapes defined by implicit surfaces, using both analytical and numerical methods. We begin with foundational concepts in Multivariable Calculus including triple integrals, Jacobians, etc, laying the groundwork for exact volumes of classical shapes, such as spheres, ellipsoids and torus. For more complex surfaces, Monte Carlo estimation, an useful method for estimating volumes, is employed. We then explore parameter variations to demonstrate the efficiency and versatility of combining exact integration with computational methods.
Question, result, and complete paper →