Mathematics Commons^™

How I Got Gnarly, Rudy Rucker

SWITCH

The article describes how Rudy Rucker’s curious interest in celluar automata led to his career in mathematical computer science at San José State University. After conducting interviews on the theory of cellular automata as a freelance writer, he felt compelled to be involved in this great intellectual revolution in computer-aided experimental mathematics. Committed to reinventing himself, Rucker's interactions with mathematicians inspired him to write “Mind Tools”, a book that surveys mathematics from the standpoint that is information. After publishing his book, in 1987, he was eventually offered a position at SJSU in the Mathematics and Computer Science department. With assistance …

Tests Of Random Number Generators Using Ising Model Simulations, Paul D. Coddington

Northeast Parallel Architecture Center

Large-scale Monte Carlo simulations require high-quality random number generators to ensure correct results. The contrapositive of this statement is also true – the quality of random number generators can be tested by using them in large-scale Monte Carlo simulations. We have tested many commonly used random number generators with high precision Monte Carlo simulations of the 2-d Ising model using the Metropolis, Swendsen-Wang, and Wolff algorithms. This work is being extended to the testing of random number generators for parallel computers. The results of these tests are presented, along with recommendations for random number generators for high-performance computers, particularly for …

Data Compression Based On The Cubic B-Spline Wavelet With Uniform Two-Scale Relation, S. K. Yang, C. H. Cooke

Mathematics & Statistics Faculty Publications

The aim of this paper is to investigate the potential artificial compression which can be achieved using an interval multiresolution analysis based on a semiorthogonal cubic B-spline wavelet. The Chui-Quak [1] spline multiresolution analysis for the finite interval has been modified [2] so as to be characterized by natural spline projection and uniform two-scale relation. Strengths and weaknesses of the semiorthogonal wavelet as regards artificial compression and data smoothing by the method of thresholding wavelet coefficients are indicated.

Secure Trapdoor Hash Functions Based On Public-Key Cryptosystems, Gary R. Greenfield, Sarah Agnes Spence

Department of Math & Statistics Technical Report Series

In this paper we systematically consider examples representative of the various families of public-key cryptosystems to see if it would be possible to incorporate them into trapdoor hash functions, and we attempt to evaluate the resulting strengths and weaknesses of the functions we are able to construct. We are motivated by the following question:

Question 1.2 How likely is it that the discoverer of a heretofore unknown public-key cryptosystem could subvert it for use in a plausible secure trapdoor hash algorithm?

In subsequent sections, our investigations will lead to a variety of constructions and bring to light the non-adaptability of …

Vr Products, P.D. Quick

SWITCH

The article is an analysis of the author’s experience testing several virtual reality items at Siggraph, an annual convention displaying computer machinery and interactive technology products. The author explains each device and how they work, the company behind the invention, as well as how it can help with future technological advancements. Several products are explained in more depth; the i-Glasses by Virtual I/O, Red Planet by Virtual World Entertainment Inc., Venturer S-2 by Thomson Entertainment Systems, and several more. Each item explores virtual reality in differing ways such as interactive video games, more user-friendly 3D modeling, and virtual movie theater …

Virtual Celluoid, Switch Staffs

SWITCH

The article is an analysis of the author’s research pertaining to films relating to or containing the concept of virtual reality. The author lists several films such as Johnny Mnemnonic, Virtuosity, The Net, and Disclosure and provides a brief synopsis and review of each movie. Each film explains the concept of virtual reality through differing plots and methods such as cyberspace, progressive software, and artificial intelligence. The author also gives their own insight into and ratings of the films, explaining what they think is the most relatable in terms of overall storyline as well as how realisticly the movie portrays …

An Object Oriented Implemtation Of Fractal Image Compression, Darrell Burkhead

Masters Theses & Specialist Projects

The technique of Fractal Image Compression, although new, has been described in several ways. Thus far, all descriptions of this compression algorithm read by the author have been in procedural form. The purpose of this paper is to present the Fractal Image Compression algorithm in an object-oriented form and to point out the advantages of this organization. The main advantages of taking an object-oriented approach to this problem are flexibility and maintainability. Different aspects of this algorithm are handled by different objects, thereby allowing for easy customization and testing of each part. Another advantage of this approach is that the …

Mathematics From The Viewpoint Of Science In Context, Johan Deklerk

ACMS Conference Proceedings 1995

This is the first of a series of papers presented over several years by deKlerk exploring the notion of how mathematics might be taught from a Christian perspective. In this paper, he introduces the notion of context as the basis for such an approach. He then discusses seven contexts a teacher can employ.

Improving The Teaching Of Mathematics, David S. Moore

ACMS Conference Proceedings 1995

No one concerned about the teaching of college mathematics--and few mathematicians who are not concerned--can have missed the movement to reform teaching in the mathematical sciences at all levels. The teaching of any active branch of knowledge, like the church, is of course "reforming and ever to be reformed." Calls to modernize what we offer students are always with us. What is striking about the current reform movement is not only its momentum but the fact that it centers on pedagogy rather than on content. We ought, say the reformers, to radically alter our style of teaching. My purpose in …

Experimenting With The Calculus Laboratory Setting, Glen Van Brummelen

ACMS Conference Proceedings 1995

Reform of post-secondary mathematics education, particularly introductory calculus, is becoming commonplace across North America. Although there are many varieties of reform, most can be placed within the philosophical camp of social constructivism. According to this movement, mathematical knowledge is constructed in an interactive way through instructor-student and inter-student dialogue, rather than built in an axiomatic sense such as the "new math" of 20 years ago, or in the reductionistic, algorithmic sense dominant in secondary and introductory college mathematics. While I hold serious concerns about the relativizing of mathematical knowledge that occurs when social constructivism is adopted as a philosophy of …

What Does A Computer Program Mean? An Introduction To Denotational Semantics, Gene B. Chase

ACMS Conference Proceedings 1995

This paper is for mathematicians who are curious about how topology is being used to prove computer programs correct. Those advanced parts have been limited to Sections III, V, and VI, and they are marked by a [clock symbol]. By contrast, sections II, IV, and VII are suitable as a companion to existing textbooks in a Computer Science course such as Organization of Programming Languages, the course CS 8 as described in Curriculum [1979]. Perhaps in a first reading you might read just those sections.

Among many books and articles on the semantics, or meaning, of computer languages, …

Using Data To Develop Mathematical Methods, Philip R. Carlson

ACMS Conference Proceedings 1995

An analysis of ordered pairs and their scatter plots leads to interesting questions related to mathematical modeling. Some statistical methods suggest ways to approach this analysis of the ordered pairs. Both high school and college methods are illustrated in this paper.

The 25 Greatest Mathematicians, Robert Brabenec

ACMS Conference Proceedings 1995

Many have tried to determine the greatest mathematicians in history. The purpose of this paper is to consider making such a list, along with some criteria to consider in making a rank order of these mathematicians.

Mathematical And Theological Beliefs: A Cognitive Science Perspective, Ron Benbow

ACMS Conference Proceedings 1995

In recent years, research studies have shown that control decisions and processes, beliefs about the nature of mathematics, attitudes, and other affective variables have enormous impact on the mathematical performance of students. This paper gives an overview of the research on mathematical beliefs and reviews some work done in Christian education relating to theological beliefs. It then compares the two.

Parallel Processing In The Undergraduate Curriculum, William E. Toll

ACMS Conference Proceedings 1995

No abstract provided.

Drawing The Boundaries: Mathematical Statistics In Twentieth-Century America, Patti W. Hunter

ACMS Conference Proceedings 1995

No abstract provided.

A Course In Mathematical Recreations, Richard Laatsch

ACMS Conference Proceedings 1995

No abstract provided.

The Intermediate Value Theorem, Dale Varberg

ACMS Conference Proceedings 1995

The Intermediate Value Theorem (a continuous function on an interval assumes all values between any two of its values) is one of the big theorems of calculus. Yet the theorem is absent or briefly mentioned in most calculus textbooks. The theorem deserves better as we intend to show by listing ten picturesque consequences that we think could enliven any calculus course.

Constructivism, Mathematics Education And Christianity, Ted Watanabe

ACMS Conference Proceedings 1995

In this paper, I briefly describe what constructivism is and its implications in the field of mathematics education. I will then discuss what this epistemology may mean to Christians who are in the field of mathematics education

Statistics, Mathematics, And Teaching, David S. Moore

ACMS Conference Proceedings 1995

In discussing our teaching, we may focus on content, what we want our students to learn, or on pedagogy, what we do to help them learn. These two topics are of course related. In particular, changes in pedagogy are often driven in part by changing priorities for what kinds of things we want students to learn. It is nonetheless convenient to address content and pedagogy separately. Pedagogy, certainly the less specific of the two, is the topic of my second paper. This paper concerns content, and in particular contains one side of a conversation between a statistician and mathematicians …

The 25 Greatest Mathematicians, Robert L. Brabenec

ACMS Conference Proceedings 1995

No abstract provided.

Introduction (1995), David L. Neuhouser

ACMS Conference Proceedings 1995

Tenth ACMS Conference on Mathematics from a Christian Perspective

Table Of Contents (1995), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 1995

Tenth ACMS Conference on Mathematics from a Christian Perspective

Schedule (1995), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 1995

Tenth ACMS Conference on Mathematics from a Christian Perspective

Transitions In Masculinity And Hemingway's Developed "Code", Daniel Polk

Honors Theses

The "Hemingway Code" is much more than two words that fit nicely together for a scholar's usage; the words signify a much deeper championing of masculinity, almost a haunting presence. For Ernest Hemingway living life every day, every moment with its fullest masculine fervor, became an obsession, a never-ending quest to be at one with the attitude of never complaining, never crying out, panicking, thinking too much, or regretting. To live a manly life in a series of tactical victories, performed with steadfast ritualistic mannerisms, is to embody masculinity, and therefore the "Hemingway Code."

Discovery Of Integrity Relationships In Relational Databases, D. Harrier, D. C. St. Clair

Computer Science Technical Reports

The use of database management system integrity constraints has been a powerful tool in raising the quality of data within an application subject database. Unfortunately, the successful use of integrity constraints requires that the database administrator has implemented the constraint before data are inserted into the database.

The results of this research provide a methodology for discovering previously unknown integrity relationships in a relational database. The methodology uses the principles of knowledge discovery from the artificial intelligence community, and Quinlan's ID3 machine learning algorithm as the discovery tool. Experimental results are provided that demonstrate how the methodology can be applied.

Supereulerian Graphs And The Petersen Graph, Ii, Zhi-Hong Chen, Hong-Jian Lai

Scholarship and Professional Work - LAS

In this note, we verify two conjectures of Catlin in [J. Graph Theory 13 (1989) 465 - 483] for graphs with at most 11 vertices. These are used to prove the following theorem which improves prior results in [10] and [13]:

Let G be a 3-edge-connected simple graph with order n. If n is large and if for every edge 11.v E E(G), d(u) + d(v) 2 % - 2, then either G has a spanning eulerian subgraph or G can be contracted to the Petersen graph.

The Genus 22 Crossing Number Of K9, Adrian Riskin

Mathematics

Our main result is that a 1971 conjecture due to Paul Kainen is false. Kainen's conjecture implies that the genus 2 crossing number of K 9 is 3. We disprove the conjecture by showing that the actual value is 4. The method used is a new one in the study of crossing numbers, involving proof of the impossibility of certain genus 2 embeddings of Ks.

Mathematical And Theological Beliefs: A Cognitive Science Perspective, Ron Benbow

ACMS Journal 2004

In recent years, research studies have shown that control decisions and processes, beliefs about the nature of mathematics, attitudes, and other affective variables have enormous impact on the mathematical performance of students. This paper gives an overview of the research on mathematical beliefs and reviews some work done in Christian education relating to theological beliefs. It then compares the two.

Mathematics From The Viewpoint Of Science In Context, Johan Deklerk

ACMS Journal 2004

This is the first of a series of papers presented over several years by deKlerk exploring the notion of how mathematics might be taught from a Christian perspective. In this paper, he introduces the notion of context as the basis for such an approach. He then discusses seven contexts a teacher can employ.