Physical Sciences and Mathematics Commons^™

An Introduction To The Algebra Revolution, Art Bardige

Numeracy

Bardige, Art. 2022. The Algebra Revolution: How Spreadsheets Eliminate Algebra 1 to Transform Education; (Bookbaby) 135 pp. UNSPSC 55111505.

The Algebra Revolution: How Spreadsheets Eliminate Algebra 1 to Transform Education argues that Algebra 1 can be eliminated by teaching mathematics through spreadsheets. Such a change would eliminate the greatest roadblock to student achievement.

Applied Analysis For Learning Architectures, Himanshu Singh

USF Tampa Graduate Theses and Dissertations

Modern data science problems revolves around the Koopman operator Cφ (or Composition operator) approach, which provides the best-fit linear approximator to the dynamical system by which the dynamics can be advanced under the discretization. The solution provided by Koopman in the data driven methods is in the sense of strong operator topology, which is nothing better then the point-wise convergence of data (snapshots) in the underlying Hilbert space. Chapter 2 provides the details about the aforementioned issues with essential counter-examples. Thereafter, provable convergence guarantee phenomena is demonstrated by the Liouville weighted composition operators Af,φ over the Fock space by providing …

Classification Of Finite Topological Quandles And Shelves Via Posets, Hitakshi Lahrani

USF Tampa Graduate Theses and Dissertations

The objective of this dissertation is to investigate finite topological quandles and topological shelves. Precisely, we give a classification of both finite topological quandles and topological shelves using the theory of posets. For quandles with more than one orbit, we prove the following Theorem.

Proposition 0.0.1. Let X be a finite quandle with n orbits X₁, ... , X_n. Then any right continuous poset on X is n-partite with vertex sets X₁, ... , X_n.

For connected quandles, we prove the following Theorem.

Theorem 0.0.2. There is no T …

Rational Functions Of Degree Five That Permute The Projective Line Over A Finite Field, Christopher Sze

USF Tampa Graduate Theses and Dissertations

Rational functions over a finite field Fq induce mappings from the projective line P1(Fq) to itself. Rational functions that permute the projective line are called permutation rational functions (PRs). The notion of permutation rational functions is a natural extension of the permutation polynomials which have been studied for over a century. Recently, PRs of degrees up to four have been determined. This dissertation is a project aimed at determining PRs of degree five.

Rational functions of degree five (excluding those that are equivalent to polynomials) are divided into five cases according to the factorization of their denominators. Our main results …