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Articles 1 - 6 of 6
Full-Text Articles in Set Theory
Belonging, Lawrence M. Lesser
Discordium Mathematica - A Symphony In Aleph Minor, Vijay Fafat
Discordium Mathematica - A Symphony In Aleph Minor, Vijay Fafat
Journal of Humanistic Mathematics
How did Mathematics arise? Who created it? Why is it subject to Godel’s Incompleteness Theorems? And what does all this have to do with Coleridge’s poem, “Kubla Khan”, and “The Person from Porlock”? Here is a complete mythology of Mathematics set in an epic poetry format, fusing thoughts and verses from Western religions and Eastern mysticism… Those with immense patience and careful reading shall reap the fruit… (best read on a large screen or in printed form)
Combinatorial Polynomial Hirsch Conjecture, Sam Miller
Combinatorial Polynomial Hirsch Conjecture, Sam Miller
HMC Senior Theses
The Hirsch Conjecture states that for a d-dimensional polytope with n facets, the diameter of the graph of the polytope is at most n-d. This conjecture was disproven in 2010 by Francisco Santos Leal. However, a polynomial bound in n and d on the diameter of a polytope may still exist. Finding a polynomial bound would provide a worst-case scenario runtime for the Simplex Method of Linear Programming. However working only with polytopes in higher dimensions can prove challenging, so other approaches are welcome. There are many equivalent formulations of the Hirsch Conjecture, one of which is the …
My Finite Field, Matthew Schroeder
My Finite Field, Matthew Schroeder
Journal of Humanistic Mathematics
A love poem written in the language of mathematics.
The Mathematical Landscape, Antonio Collazo
The Mathematical Landscape, Antonio Collazo
CMC Senior Theses
The intent of this paper is to present the reader will enough information to spark a curiosity in to the subject. By no means is the following a complete formulation of any of the topics covered. I want to give the reader a tour of the mathematical landscape. There are plenty of further details to explore in each section, I have just touched the tip the iceberg. The work is basically in four sections: Numbers, Geometry, Functions, Sets and Logic, which are the basic building blocks of Math. The first sections are a exposition into the mathematical objects and their …
Proof Without Words: Alternating Sums Of Odd Numbers, Arthur T. Benjamin
Proof Without Words: Alternating Sums Of Odd Numbers, Arthur T. Benjamin
All HMC Faculty Publications and Research
Proof for alternating sums of odd numbers in two figures.