Mathematics Commons^™

Some Studies On Selected Stream Ciphers Analysis Fault Attack & Related Results., Subhadeep Banik Dr.

Doctoral Theses

Stream Ciphers are important Symmetric Cryptological primitives, built for the purpose of providing secure message encryption. As no formal security proofs exist, our confidence in these algorithms is largely based on the fact that intense cryptanalysis has been carried out over several years without revealing any weakness. This thesis makes some independent contributions to the cryptanalysis of a selection of stream ciphers.In this thesis, we take a closer look at two stream ciphers viz. RC4+ designed by Maitra et al. at Indocrypt 2008 and GGHN designed by Gong et al. at CISC 2005. Both these ciphers were designed as viable …

Book Review: How To Bake Pi: An Edible Exploration Of The Mathematics Of Mathematics, Darren B. Glass

Math Faculty Publications

If you think about it, mathematics is really just one big analogy. For one example, the very concept of the number three is an drawing an analogy between a pile with three rocks, a collection of three books, and a plate with three carrots on it. For another, the idea of a group is drawing an analogy between adding real numbers, multiplying matrices, and many other mathematical structures. So much of what we do as mathematicians involves abstracting concrete things, and what is abstraction other than a big analogy? [excerpt]

Counting On R-Fibonacci Numbers, Arthur Benjamin, Curtis Heberle

All HMC Faculty Publications and Research

We prove the r-Fibonacci identities of Howard and Cooper using a combinatorial tiling approach.

Teaching Algebra: A Comparison Of Scottish And American Perspectives, Brittany Munro

Undergraduate Honors Theses

A variety of factors influence what teaching strategies an educator uses. I analyze survey responses from algebra teachers in Scotland and Appalachia America to discover how a teacher's perception of these factors, particularly their view of mathematics itself, determines the pedagogical strategies employed in the classroom.

Mathematical Modeling And Optimal Control Of Alternative Pest Management For Alfalfa Agroecosystems, Cara Sulyok

Mathematics Honors Papers

This project develops mathematical models and computer simulations for cost-effective and environmentally-safe strategies to minimize plant damage from pests with optimal biodiversity levels. The desired goals are to identify tradeoffs between costs, impacts, and outcomes using the enemies hypothesis and polyculture in farming. A mathematical model including twelve size- and time-dependent parameters was created using a system of non-linear differential equations. It was shown to accurately fit results from open-field experiments and thus predict outcomes for scenarios not covered by these experiments.

The focus is on the application to alfalfa agroecosystems where field experiments and data were conducted and provided …

2015 Sonia Kovalevsky Math For Girls Day Program, Association For Women In Mathematics, Lincoln University Of Missouri, Donna L. Stallings

Math for Girls Day Documents

10th Annual Lincoln University Sonia Kovalevsky Math for Girls Day program on April 24, 2015.

Fostoria Intermediate Elementary School Family Math Night, Chelsea Nye

Honors Projects

This is a Family Math Night that was planned and held at Fostoria Intermediate Elementary School in Fostoria, Ohio. It includes the Research Questions, Literature Review, Proposed Activity, Methodology, and Expected Results as well as the Annotated Bibliography and Timeline for Completion from my research and planning. Following the Proposal are 20 mathematical activity or game lesson plans and direction sheets that were planned for the Family Math Night. There are 5 different mathematical activities or games for each grade level 3-6, each meeting a different domain in the Common Core State Standards. At the end there is two general …

Does Being Bilingual Make You Better At Math?, Enxhi Elezi

Honors Projects in Mathematics

The purpose of this study is to examine if there is any relationship between being bilingual, defined as speaking your native language at home and another language in school, and your mathematical ability. Data from the National Longitudinal Study of Adolescent Health was used to compare the math grades of students who were not born in the US and speak English, Spanish, or Other at home. Also, data from the Bryant University first year students was used to test if students who speak a different language at home have a higher mathematical average than their monolingual peers. Results show that …

Mathematical Modeling Of Trending Topics On Twitter, Jonathan S. Skaza

Honors Projects in Mathematics

Created in 2006, Twitter is an online social networking service in which users share and read 140-character messages called Tweets. The site has approximately 288 million monthly active users who produce about 500 million Tweets per day. This study applies dynamical and statistical modeling strategies to quantify the spread of information on Twitter. Parameter estimates for the rates of infection and recovery are obtained using Bayesian Markov Chain Monte Carlo (MCMC) methods. The methodological strategy employed is an extension of techniques traditionally used in an epidemiological and biomedical context (particularly in the spread of infectious disease). This study, which addresses …

Inside Out: Properties Of The Klein Bottle, Andrew Pogg, Jennifer Daigle, Deirdra Brown

Thinking Matters Symposium Archive

A Klein Bottle is a two-dimensional manifold in mathematics that, despite appearing like an ordinary bottle, is actually completely closed and completely open at the same time. The Klein Bottle, which can be represented in three dimensions with self-intersection, is a four dimensional object with no intersection of material. In this presentation we illustrate some topological properties of the Klein Bottle, use the Möbius Strip to help demonstrate the construction of the Klein Bottle, and use mathematical properties to show that the Klein Bottle intersection that appears in ℝ3 does not exist in ℝ4. Introduction: Topology

Mathematical Explorations Of Card Tricks, Timothy R. Weeks

Senior Honors Projects

In this project, we explore various mathematical topics as they apply to an assortment of card tricks. We will focus on an examination of theorems applied to the manipulation of cards in an attempt to prove why certain card tricks work. These theorems utilize abstract algebra, probability, number theory, and combinatorics. Many tricks can be explained this way, instead of singularly by sleight of hand or other “magical” methods. We will rigorously prove the theorems and principles that explain these concepts, focusing primarily on the card tricks and examples presented in Mathematical Card Magic by Colm Mulcahy (2013).

Possible Bias In Asset Valuations: An Application Of The Fraud Risk Triangle To Divorce Cases, Jennifer Tomasetti

Honors Projects in Accounting

No abstract provided.

Armstrong Calculus, Michael Tiemeyer, Jared Schlieper

Mathematics Open Textbooks

Authors' Description:

An open-source textbook for calculus.

The text is mostly an adaptation of two other excellent open- source calculus textbooks: Active Calculus by Dr. Matt Boelkins of Grand Valley State University and Drs. Gregory Hartman, Brian Heinold, Troy Siemers, Dimplekumar Chalishajar, and Jennifer Bowen of the Virginia Military Institute and Mount Saint Mary's University. Both of these texts can be found at http://aimath.org/textbooks/approved-textbooks/.

The authors of this text have combined sections, examples, and exercises from the above two texts along with some of their own content to generate this text. The impetus for the creation of this text …

My Math Gps: Elementary Algebra Guided Problem Solving, Jonathan Cornick, G Michael Guy, Karan Puri

Open Educational Resources

My Math GPS: Elementary Algebra Guided Problem Solving is a textbook that aligns to the CUNY Elementary Algebra Learning Objectives that are tested on the CUNY Elementary Algebra Final Exam (CEAFE). This book contextualizes arithmetic skills into Elementary Algebra content using a problem-solving pedagogy. Classroom assessments and online homework are available from the authors. In a paper to appear in PRIMUS, this textbook and accompanying pedagogy showed significant increases in learning outcomes.

Hurwitz's Theorem, Marianna Malek

Masters Essays

No abstract provided.

On Pi Day, A Serving Of Why We Need Math, Darren B. Glass

Math Faculty Publications

Today, our Facebook feeds will be peppered with references to Pi Day, a day of celebration that has long been acknowledged by math fans and that Congress recognized in 2009. Every high schooler learns that pi is the ratio of the circumference of a circle to its diameter and that its decimal expansion begins 3.14 and goes on infinitely without repeating. [excerpt]

Generic Constructions Of Different Cryptographic Primitives Over Various Public Key Paradigms., Sumit Kumar Pandey Dr.

Doctoral Theses

In this thesis, we study the generic construction of some cryptographic primitives over various public key paradigms like traditional Public Key Cryptosystems and Identity Based Cryptosystems. It can be broadly divided into two categories1. Generic construction of some highly secure cryptographic primitives from less secure cryptographic primitives, and2. Generic construction of some complex cryptographic primitives from basic cryptographic primitives. Mathematical tools provide a way to achieve cryptographic functionality like confidentiality, authentication, data-integrity, non-repudiation etc., but in the case of complex cryptographic functionality like achieving confidentiality and authentication at the same time or confidentiality, authentication and non-repudiation at the same time …

Some Conjugacy Problems In Algebraic Groups., Anirban Bose Dr.

Doctoral Theses

In this thesis we address two problems related to the study of algebraic groups and Lie groups. The first one deals with computation of an invariant called the genus number of a connected reductive algebraic group over an algebraically closed field and that of a compact connected Lie group. The second problem is about characterisation of real elements in exceptional groups of type F4 defined over an arbitrary field. Let G be a connected reductive algebraic group over an algebraically closed field or a compact connected Lie group. Let ZG(x) denote the centralizer of x ∈ G. Define the genus …

A Mathematician's Villanelle, Gizem Karaali

Pomona Faculty Publications and Research

No abstract provided.

My Finite Field, Matthew Schroeder

Journal of Humanistic Mathematics

A love poem written in the language of mathematics.

Improving University Students' Perception Of Mathematics And Mathematics Ability, Shelly L. Wismath, Alyson Worrall

Numeracy

Although mathematical and quantitative reasoning skills are an essential part of adult life in our society, many students arrive at post-secondary education without such skills. Taking a standard mathematics course such as calculus may do little to improve those skills. Using a modification of the Tapia & Marsh questionnaire, we surveyed 62 students taking a broad quantitative reasoning course designed to develop quantitative skills, with respect to two broad attitudinal areas: students’ perception of their own ability, confidence and anxiety, and their perception of the value of mathematics in their studies and their lives. Pre- to post-course comparisons were done …

Letters To Joel, David J. Stucki, Joel M. Stucki

Mathematics Faculty Scholarship

A professor and his students answer his brother’s question: Is mathematics art?

The Finite Embeddability Property For Some Noncommutative Knotted Varieties Of Rl And Drl, Riquelmi Salvador Cardona Fuentes

Electronic Theses and Dissertations

Residuated lattices, although originally considered in the realm of algebra providing a general setting for studying ideals in ring theory, were later shown to form algebraic models for substructural logics. The latter are non-classical logics that include intuitionistic, relevance, many-valued, and linear logic, among others. Most of the important examples of substructural logics are obtained by adding structural rules to the basic logical calculus FL. We denote by ������ � the varieties of knotted residuated lattices. Examples of these knotted rules include integrality and contraction. The extension of �� by the rules corresponding to these two equations is …

Two Compact Incremental Prime Sieves, Jonathan P. Sorenson

Scholarship and Professional Work - LAS

A prime sieve is an algorithm that finds the primes up to a bound n. We say that a prime sieve is incremental, if it can quickly determine if n+1 is prime after having found all primes up to n. We say a sieve is compact if it uses roughly √n space or less. In this paper, we present two new results.

• We describe the rolling sieve, a practical, incremental prime sieve that takes O(n log log n) time and O(√n log n) bits of space.

• We also …

Factorial Growth Rates For The Number Of Hyperbolic 3-Manifolds Of A Given Volume, Christian Millichap

Faculty Publications

The work of Jørgensen and Thurston shows that there is a finite number N(v) of orientable hyperbolic 3-manifolds with any given volume v. In this paper, we construct examples showing that the number of hyperbolic knot complements with a given volume v can grow at least factorially fast with v. A similar statement holds for closed hyperbolic 3-manifolds, obtained via Dehn surgery. Furthermore, we give explicit estimates for lower bounds of N(v) in terms of v for these examples. These results improve upon the work of Hodgson and Masai, which describes examples that grow exponentially fast with v …

Mathematics Education In A Multilingual And Multicultural Environment, Anjum Halai, Richard Barwell

Book Chapters / Conference Papers

No abstract provided.

The Impact Of Math Anxiety In The Primary Grades, Amanda R. Anderson-Mix

Mathematics Graduate Theses

Math anxiety is an increasingly common occurrence among individuals when working with mathematical concepts. While researching math anxiety the author came across common gender stereotypes implying: women do not perform as well as men in the field of mathematics, women experience a much higher level of math anxiety than men, and most women do not appreciate performing mathematical tasks. Although the concept of math anxiety is an interesting topic to the author, it's important to look deeper than simply the question, “What is math anxiety?” Seeing these stereotypical assumptions that women have higher math anxiety levels, it made this author …

A Survey On Reverse Carleson Measures, Emmanuel Fricain, Andreas Hartmann, William T. Ross

Department of Math & Statistics Faculty Publications

This is a survey on reverse Carleson measures for various Hilbert spaces of analytic functions. These spaces include the Hardy, Bergman, certain harmonically weighted Dirichlet, Paley-Wiener, Fock, model (backward shift invariant), and de Branges-Rovnyak spaces. The reverse Carleson measure for backward shift invariant subspaces in the non-Hilbert situation is new.

Mathematics In Contemporary Society Chapter 4, Patrick J. Wallach

Open Educational Resources

Mathematics in Contemporary Society is the textbook that corresponds to MA-321, the course of the same name. The course is designed to provide students with mathematical ideas and methods found in the social sciences, the arts, and in business. Topics will include fundamentals of statistics, scatterplots, graphics in the media, problem solving strategies, dimensional analysis, mathematics in music and art, and mathematical modeling. EXCEL is used to explore real world applications.

The textbook was posted in weekly installments:

• Chapter 1
• Chapter 2
• Chapter 3
• Chapter 4
• Chapter 5
• Chapter 6
• Chapter 7
• Chapter 8
• Chapter 9
• Chapter 10
• Chapter 11 …

Mathematics In Contemporary Society Chapter 2, Patrick J. Wallach

Open Educational Resources

Mathematics in Contemporary Society is the textbook that corresponds to MA-321, the course of the same name. The course is designed to provide students with mathematical ideas and methods found in the social sciences, the arts, and in business. Topics will include fundamentals of statistics, scatterplots, graphics in the media, problem solving strategies, dimensional analysis, mathematics in music and art, and mathematical modeling. EXCEL is used to explore real world applications.

The textbook was posted in weekly installments:

• Chapter 1
• Chapter 2
• Chapter 3
• Chapter 4
• Chapter 5
• Chapter 6
• Chapter 7
• Chapter 8
• Chapter 9
• Chapter 10
• Chapter 11