Mathematics Commons^™

A Math Research Project Inspired By Twin Motherhood, Tiffany N. Kolba

Tiffany N Kolba

The phenomenon of twins, triplets, quadruplets, and other higher order multiples has fascinated humans for centuries and has even captured the attention of mathematicians who have sought to model the probabilities of multiple births. However, there has not been extensive research into the phenomenon of polyovulation, which is one of the biological mechanisms that produces multiple births. In this paper, I describe how my own experience becoming a mother to twins led me on a quest to better understand the scientific processes going on inside my own body and motivated me to conduct research on polyovulation frequencies. An overview of …

Using Three Fields Of Education Research To Frame The Development Of Digital Games, Michelle Zandieh, David Plaxco, Caro Williams-Peirce, Ashish Amresh

Ashish Amresh

No abstract provided.

The Feferman-Vaught Theorem, Mostafa Mirabi

Mostafa Mirabi

Alan Turing: The Man Behind The Machine, Christopher D. Goff

Christopher Goff

No abstract provided.

Alan Turing: The Man Behind The Machine, Christopher D. Goff

Christopher Goff

No abstract provided.

Alan Turing: The Man Behind The Machine, Christopher D. Goff

Christopher Goff

No abstract provided.

Musical Actions Of Dihedral Groups, Alissa S. Crans, Thomas M. Fiore, Ramon Satyendra

Alissa Crans

The sequence of pitches which form a musical melody can be transposed or inverted. Since the 1970s, music theorists have modeled musical transposition and inversion in terms of an action of the dihedral group of order 24. More recently music theorists have found an intriguing second way that the dihedral group of order 24 acts on the set of major and minor chords. We illustrate both geometrically and algebraically how these two actions are {\it dual}. Both actions and their duality have been used to analyze works of music as diverse as Hindemith and the Beatles.

The Philosophy Of Mathematics, Erin Wilding-Martin

Erin Wilding-Martin

The philosophy of mathematics considers what is behind the math that we do. What is mathematics? Is it some cosmic truth we discover, or is it created by humans? Do mathematical objects such as numbers and functions really exist, or are they just symbols we have invented? Two of the great debates in the history of mathematical philosophy center around ontology and epistemology. Where did mathematics come from? How do we know that it is true? Where did mathematics come from? Is it discovered or created? Ontological questions are concerned with the nature and status of mathematical objects. Some people …

Geometry: Drawing From The Islamic Tradition, Carol Bier

Carol Bier

Getting students involved in careful observation and analysis and encouraging their exploration of cultural forms of expression is an excellent means of introducing mathematical ideas. Geometric patterns abound in Islamic art and architecture. Exhibiting great ingenuity over the centuries, Muslim artists and craftsmen created beautiful patterns to adorn architectural monuments and exquisite objects. The Alhambra in Spain and the Taj Mahal in India offer the most famous examples of extraordinary patterns using brick and glazed tile, or carved and inlaid marble. Other examples of patterns are made using metal, wood, and fiber. Students may gain conceptual and theoretical understanding of …

Fibonacci Sequence And Orderliness As Observed In The Creations Of Allah, Mohd Rezuan Masran Mr.

Mr. Mohd Rezuan Masran

There are numerous verses in the Quran that encourage Muslims to observe the many creations of Allah. This article is an exploratory discuss ion on the observation of a sequence of numbers known as the Fibonacci sequence (also known as the Fibonacci numbers ) which can be observed in the creations of Allah. The history of Fibonacci sequence dated back to 1202 in the magnum opus of the Italian mathematician, Leonardo Pisano Fibonacci, entitled Liber Abaci ( Book of Calculation ). This article discusses verses in the Quran that encourage us to observe Allah’s creations. T here are many occurrences …

Los Modelos De Equilibrio General: La Revisión De Chancelier Y Una Crítica A Debreu Y Mckenzie, Rodrigo Lopez-Pablos

Lopez-Pablos, Rodrigo

A revision on general equilibrium theory from an entropic perspective. JEL CLASSIFICATION: D50, O21, Z19

Loss Of Vision: How Mathematics Turned Blind While It Learned To See More Clearly, Bernd Buldt, Dirk Schlimm

Bernd Buldt

To discuss the developments of mathematics that have to do with the introduction of new objects, we distinguish between ‘Aristotelian’ and ‘non-Aristotelian’ accounts of abstraction and mathematical ‘top-down’ and ‘bottom-up’ approaches. The development of mathematics from the 19th to the 20th century is then characterized as a move from a ‘bottom-up’ to a ‘top-down’ approach. Since the latter also leads to more abstract objects for which the Aristotelian account of abstraction is not well-suited, this development has also lead to a decrease of visualizations in mathematical practice.

Morphogrammatics Of Reflection, Rudolf Kaehr

Rudolf Kaehr

Turning back from the studies of morphogrammatics to some open questions of reflectional programming, the recountered problematics might be put into a different light and new methods of handling formal aspects of reflection and reflectionality shall be introduced. Albeit the use of light-metaphors, morphogrammatic reflection is not sketched along the paradigm of optical metaphors. Morphograms are presenting neither propositions nor perceptions able for mirroring (representation). Exercises in defining morphogrammatic retro-grade recursion and reflection schemata are continued from the paper “Sketches to Morphogrammatic Programming”.

Memristics: Memristors, Again? – Part Ii, How To Transform Wired ‘Translations’ Between Crossbars Into Interactions?, Rudolf Kaehr

Rudolf Kaehr

The idea behind this patchwork of conceptual interventions is to show the possibility of a “buffer-free” modeling of the crossbar architecture for memristive systems on the base of a purely difference-theoretical approach. It is considered that on a nano-electronic level principles of interpretation appears as mechanisms of complementarity. The most basic conceptual approach to such a complementarity is introduced as an interchangeability of operators and operands of an operation. Therefore, the architecture of crossbars gets an interpretation as complementarity between crossbar functionality and “buffering” translation functionality. That is, the same matter functions as operator and at once, as operand – …

Memristics: Memristors, Again?, Rudolf Kaehr

Rudolf Kaehr

This collection gives first and short critical reflections on the concepts of memristics, memristors and memristive systems and the history of similar movements with an own focus on a possible interplay between memory and computing functions, at once, at the same place and time, to achieve a new kind of complementarity between computation and memory on a single chip without retarding buffering conditions.

The Evolution And Discovery Of The Species Of Equality In Euclid’S Elements, Lee T. Nutini

Lee T Nutini

A look at the evidence for an additional and novel type of equality found in Euclid's Elements.

Sketch Of A Typology Of Abstract Memristic Machines, Rudolf Kaehr

Rudolf Kaehr

A typology of memristic machines is sketched. This sketch gives an overview and orientation to the paper “Towards Abstract Memristic Machines”. It also intents to propose a concise systematization of the newly introduced terms and strategies to memristics and morphogrammatics. This sketch is introducing four types of sign-use for four types of machines of fundamentally different paradigms: 1. semiotic, 2. monomorphic, 3. polymorphic and 4. bisimilar abstract machines. Further definitions of abstract machines have to be based on those graphematic notational systems. A realization of such constructions of abstract machines, in contrast to existing abstract machines of the theory of …

Towards Abstract Memristic Machines, Rudolf Kaehr

Rudolf Kaehr

No abstract provided.

From Universe To Polyverses, Rudolf Kaehr

Rudolf Kaehr

Some thoughts about the power of speculation behind important discoveries in mathematics, physics and computer science. The exercise shows that there is no need for a compulsory ultimate unifying universe. It is speculated that just this paradigm of a single ultimate universe is unmasking itself today as the main obstacle for further development in Western science and technology.

Morphogrammatics For Dummies: The Domino Approach, Rudolf Kaehr

Rudolf Kaehr

Dominoes, morphograms, cellular automata, memristics. Topics: possible continuation, coalitions, cooperations, substitution, morphic bisimilarity.

The Logic Of Bailout Strategies, Rudolf Kaehr

Rudolf Kaehr

Some thoughts about/of the logic, blend, chiasm and diamond of bailout strategies. Eliciting aspects of the maxim: “Without insurrection, no resurrection".

Diamond Semiotic Short Studies, Rudolf Kaehr

Rudolf Kaehr

A collection of papers on semiotics, polycontexturality and diamond theory

Creating A Warmer Environment For Women In The Mathematical Sciences And In Philosophy, Samantha Brennan, Rob Corless

Samantha Brennan

No abstract provided.

Diamond Theory Collections. A Collection Of Papers And Fragments Towards Diamond Theory 2007-2009, Rudolf Kaehr

Rudolf Kaehr

No abstract provided.

Double Cross Playing Diamonds, Rudolf Kaehr

Rudolf Kaehr

Understanding interactivity in/between bigraphs and diamonds Grammatologically, the Western notational system is not offering space in itself to place sameness and otherness necessary to realize interaction/ality. Alphabetism is not prepared to challenge the dynamics of interaction directly. The Chinese writing system in its scriptural structuration, is able to place complex differences into itself, necessary for the development and design of formal systems and programming languages of interaction. The challenge of interactionality to Western thinking, modeling and design interactivity has to be confronted with the decline of the scientific power of alpha-numeric notational systems as media of living in a complex …

Short Studies 2008. Adventures In Diamond Strategies Of Change(S), Rudolf Kaehr

Rudolf Kaehr

Modular Bolognese Paradoxes of postmodern education. A Tale of Fishes, Birds and Diamonds in Second-Order Epistemology Why it is useless to write about the mono-contexturality of alphabetism and digitalism Chez Maxime's Human rights in a polycontextural world Primary Thoughts to a Manifesto for Awareness Fashion Marketing Which Equality? How equal are equal human beings? Generalized Diamonds From monosemic to tectonic complementarity Diamond Disremption Diamond interpretation of the kenomic succession operation Diamond Web2.0? How social is social networking? Web Mobility Web computing between semiotic and kenomic spaces Double Cross Playing Diamonds Understanding interactivity in/between bigraphs and diamonds Morphogrammatics of Change A …

The Apostle Table - Part Iii - Incompetent Endogenous Response Intransitivity, David Randall Jenkins

David Randall Jenkins

The Apostle Table illustrates a New Testament encryption scheme revealed in the Book of Matthew. Specifically, the list of the twelve apostles in Matthew, 10:1-4, points to the Matthew, Chapters 8 and 9, disciple characterizations. The disciples metaphorically characterize the social choice theory aspect of the scripture writers' (ordered relations theory: social choice theory: welfare model) regression. The paper is written in two parts: I. The Exogenous Pressures; and, II. The Endogenous Response. Interestingly, the paper explains why the crucified Jesus could not get off the cross.

Actors, Objects, Contextures, Morphograms, Rudolf Kaehr

Rudolf Kaehr

Systematic and historic overview and critics of actor and object oriented programming.

From Dialogues To Polylogues, Rudolf Kaehr

Rudolf Kaehr

No abstract provided.

The Abacus Of Universal Logics, Rudolf Kaehr

Rudolf Kaehr

No abstract provided.