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Full-Text Articles in Physical Sciences and Mathematics
The Last Digits Of Infinity (On Tetrations Under Modular Rings), William Stowe
The Last Digits Of Infinity (On Tetrations Under Modular Rings), William Stowe
Celebration of Learning
A tetration is defined as repeated exponentiation. As an example, 2 tetrated 4 times is 2^(2^(2^2)) = 2^16. Tetrated numbers grow rapidly; however, we will see that when tetrating where computations are performed mod n for some positive integer n, there is convergent behavior. We will show that, in general, this convergent behavior will always show up.
Category Theory And Universal Property, Niuniu Zhang
Category Theory And Universal Property, Niuniu Zhang
Honors Theses
Category theory unifies and formalizes the mathematical structure and concepts in a way that various areas of interest can be connected. For example, many have learned about the sets and its functions, the vector spaces and its linear transformation, and the group theories and its group homomorphism. Not to mention the similarity of structure in topological spaces, as the continuous function is its mapping. In sum, category theory represents the abstractions of other mathematical concepts. Hence, one could use category theory as a new language to define and simplify the existing mathematical concepts as the universal properties. The goal of …
Patterns, Symmetries, And Mathematical Structures In The Arts, Sarah C. Deloach
Patterns, Symmetries, And Mathematical Structures In The Arts, Sarah C. Deloach
Honors College Theses
Mathematics is a discipline of academia that can be found everywhere in the world around us. Mathematicians and scientists are not the only people who need to be proficient in numbers. Those involved in social sciences and even the arts can benefit from a background in math. In fact, connections between mathematics and various forms of art have been discovered since as early as the fourth century BC. In this thesis we will study such connections and related concepts in mathematics, dances, and music.