Mathematica Militaris: Volume 25

Permanent URI for this collection


Recent Submissions

Now showing 1 - 4 of 4
  • Item
    Euler-Cauchy Undetermined Coefficients Exception
    (United States Service Academies, 2022) Fischer, George; Florio, Laurie
    In 2013 we stood up the Army Armament Graduate School at Picatinny Arsenal in New Jersey. All PhD students take Advanced Mathematics I and II. For the past eight years, we have taught the method of undetermined coefficients (UC) as a solutions technique for linear nonhomogeneous ordinary differential equations with constant coefficients whose nonhomogeneous terms are members of a short, but important, list (Kreyzsig, 2011). For this method to work, the derivatives of the nonhomogeneous term must form a closed set (Web references, 2021). Otherwise a more involved method, variation of parameters (VoP), is employed. This eighth time teaching, we noticed an exception to the rule for the implementation of the method of undetermined coefficients. Before jumping in with the exception, we introduce four topics that are useful in this problem, and that we also wish that all undergraduates would know. The first is why like powers of the variable, or like special functions, or the real part and the imaginary parts need to separately cancel each other out in order for an equation to be true over an open interval. The second is the set of functions that regenerate themselves, phoenix-like, upon differentiation. The third is avoiding division by zero, and when you can remove a singularity by multiplying both sides of the equation by the denominator. The fourth is the power law in derivatives.
  • Item
    Developing Critical Thinking Military Officers
    (United States Service Academies, 2022) Martinsen, Thor
    In May of 2020 the Joint Chiefs of Staff published guidance entitled Developing Today’s Joint Officers for Tomorrow’s Ways of War. In it they state, “To achieve intellectual overmatch against adversaries, we must produce the most professionally competent, strategic-minded, and critically thinking officers possible”. What then is critical thinking? These days many different definitions exist. The word critical comes from the Greek word kritikos, which pertains to judging or discerning. In the broadest sense, critical thinking involves objective analysis of facts to form a judgment. More specifically, critical thinking can be described as self-directed, self-disciplined, self-monitored, and self-corrective thinking.
  • Item
    Computational complexity reduction of deep neural networks
    (United States Service Academies, 2022) Im, Mee Seong; Dasari, Venkat R.
    Deep neural networks (DNN) have been widely used and play a major role in the field of computer vision and autonomous navigation. However, these DNNs are computationally complex and their deployment over resource-constrained platforms is difficult without additional optimizations and customization. In this manuscript, we describe an overview of DNN architecture and propose methods to reduce computational complexity in order to accelerate training and inference speeds to fit them on edge computing platforms with low computational resources.
  • Item
    Applying Data Analytics as an Alternative to Subjective Rankings of Players in Fantasy Basketball
    (United States Service Academies, 2022) Collins, Christopher
    Fantasy Basketball ranks secondly behind Fantasy Football for fantasy sports popularity (Statistica 2018), but trails substantially behind in total participation. The relatively small participation could ostensibly explain the dearth of research and analysis dedicated to the game. That explanation is refuted, however, by Fantasy Baseball which ranks third yet is the seminal fantasy game with a litany of historical analyses from the pioneers of fantasy sports. Within this void is a lack of academic rigor the other fantasy sports enjoy. Fantasy basketball enthusiasts and analysts are missing an opportunity to exploit a similar environment to collect, analyze, and assess game data. Fantasy basketball websites, nevertheless, try to fill in the gap in demand and cater to fantasy basketball devotees. These sites employ colloquially named “fantasy experts” who create and build player rankings with different qualitative and quantitative techniques to provide their audience a way to select players for their fantasy teams.