Lorentz Invariant Spacelike Surfaces Of Constant Mean Curvature In Anti-De Sitter 3-Space, 2015 University of Southern Mississippi

#### Lorentz Invariant Spacelike Surfaces Of Constant Mean Curvature In Anti-De Sitter 3-Space, Jamie Patrick Lambert

*Master's Theses*

In this thesis, I studied Lorentz invariant spacelike surfaces with constant mean curvature *H** *= *c** *in the anti-de Sitter 3-space H^{3}_{1}(*−c*^{2}) of constant curvature *−c*^{2}. In particular, I construct Lorentz invariant spacelike surfaces of constant mean curvature *c** *and maximal Lorentz invariant spacelike surfaces in H^{3}_{1}(*−c*^{2}). I also studied the limit behavior of those constant mean curvature *c** *surfaces in H^{3}_{1}(*−c*^{2}). It turns out that they approach a maximal catenoid in Minkowski 3-space E^{3}_{1} as *c** **→** *0. The limit maximal catenoid is Lorentz invariant in ...

Gait Transition Dynamics Are Modulated By Experimental Protocol, 2015 University of Connecticut - Storrs

#### Gait Transition Dynamics Are Modulated By Experimental Protocol, Mohammad Abdolvahab, Jason Gordon

*Mohammad Abdolvahab*

No abstract provided.

Evaluation Of A Family Of Binomial Determinants, 2015 Pennsylvania State University

#### Evaluation Of A Family Of Binomial Determinants, Charles Helou, James A. Sellers

*Electronic Journal of Linear Algebra*

Motivated by a recent work about finite sequences where the n-th term is bounded by n^2, some classes of determinants are evaluated such as the (n − 2) × (n − 2) determinant ∆_n=\det [ (x_i+j \choose i-1)] for n \geq 1, where n, k, h, i, j are integers, (x_k) is a sequence of indeterminates over C and ( A \choose B ) is the usual binomial coefficient. It is proven that D_n=1 and ∆_n=(-1)^{ (n-2)(n-3)/2}.

Some Properties Of The Exchange Operator With Respect To Structured Matrices Defined By Indefinite Scalar Product Spaces, 2015 Ateneo de Manila University

#### Some Properties Of The Exchange Operator With Respect To Structured Matrices Defined By Indefinite Scalar Product Spaces, Hanz Martin C. Cheng, Roden Jason David

*Electronic Journal of Linear Algebra*

The properties of the exchange operator on some types of matrices are explored in this paper. In particular, the properties of exc(A,p,q), where A is a given structured matrix of size (p+q)×(p+q) and exc : M ×N×N → M is the exchange operator are studied. This paper is a generalization of one of the results in [N.J. Higham. J-orthogonal matrices: Properties and generation. SIAM Review, 45:504–519, 2003.].

Gödel’S Second Incompleteness Theorem, 2015 Indiana University - Purdue University Fort Wayne

#### Gödel’S Second Incompleteness Theorem, Bernd Buldt

*Philosophy Faculty Presentations*

Slides for the third tutorial on Gödel's incompleteness theorems, held at UniLog 5 Summer School, Istanbul, June 24, 2015

Gödel’S First Incompleteness Theorem, 2015 Indiana University - Purdue University Fort Wayne

#### Gödel’S First Incompleteness Theorem, Bernd Buldt

*Philosophy Faculty Presentations*

Slides for the second tutorial on Gödel's incompleteness theorems, held at UniLog 5 Summer School, Istanbul, June 24, 2015

Fixed Points, Diagonalization, Self-Reference, Paradox, 2015 Indiana University - Purdue University Fort Wayne

#### Fixed Points, Diagonalization, Self-Reference, Paradox, Bernd Buldt

*Philosophy Faculty Presentations*

Slides for the first tutorial on Gödel's incompleteness theorems, held at UniLog 5 Summer School, Istanbul, June 24, 2015

Guest Editorial: Risk – Mathematical Or Otherwise, 2015 University of Montana

#### Guest Editorial: Risk – Mathematical Or Otherwise, Egan J. Chernoff

*The Mathematics Enthusiast*

No abstract provided.

What Can Education Learn From Real-World Communication Of Risk And Uncertainty?, 2015 University of Montana

#### What Can Education Learn From Real-World Communication Of Risk And Uncertainty?, David Spiegelhalter, Jenny Gage

*The Mathematics Enthusiast*

Probability is a difficult topic to teach, not least because it is rather unclear what it actually means. Modern risk communication has tackled general public incomprehension of probability statements by using the metaphor of ‘expected frequencies’ – for example, “of 100 people like you, we would expect 10 to have a heart attack or stroke in the next 10 years.” We show how these ideas can be taken into the classroom as the basis for teaching probability, using frequency tree diagrams as the fundamental representation. Empirical frequency trees can be used to summarise a series of classroom experiments, and then expected ...

Probability, Justice, And The Risk Of Wrongful Conviction, 2015 University of Montana

#### Probability, Justice, And The Risk Of Wrongful Conviction, Jeffrey S. Rosenthal

*The Mathematics Enthusiast*

We consider the issue of standards of proof in legal decisions from the point of view of probability. We compare ``balance of probabilities'' and ``beyond a reasonable doubt'' to the statistical use of p-values. We point out various fallacies which sometimes arise in legal reasoning. And we provide several examples of legal cases which involved probabilities, including some in which incorrect decisions were made and defendants were wrongfully convicted.

Risk: Mathematical And Otherwise, 2015 University of Montana

#### Risk: Mathematical And Otherwise, John Adams

*The Mathematics Enthusiast*

What role might mathematicians have to play in the management of risk? The idea of turning a risk, a possibility of loss or injury, into a “calculated” risk, a quantified probability of loss or injury, is one that has obvious appeal not just to statisticians and mathematicians – but to large numbers of others who would like to know the probability of failure before pursuing some intended course of action. Conclusion: even when risks can be calculated with great precision, they can only be used to inform judgment, but not substitute for it. And it matters who is making the judgment.

Worth The Risk? Modeling Irrational Gambling Behavior, 2015 University of Montana

#### Worth The Risk? Modeling Irrational Gambling Behavior, Matt Lane

*The Mathematics Enthusiast*

In math class, expected value is often used when deciding whether or not a game is worth playing. A common refrain is that games with negative expected value should be avoided. However, nearly all games of chance have a negative expected value, and a simple expected value analysis fails to explain why these games are so popular. In this article, we consider three psychological factors leading to irrational gambling behavior – the illusion of control, hypersensitivity to reward, and beginner’s luck – and explore how these factors affect an otherwise purely rational model of gambling behavior.

Understanding Risk Through Board Games, 2015 University of Montana

#### Understanding Risk Through Board Games, Joshua T. Hertel

*The Mathematics Enthusiast*

In this article, I describe a potential avenue for investigating individual’s understanding of and reactions to risk using the medium of board games. I first discuss some challenges that researchers face in studying risk situations. Connecting to the existing probabilistic reasoning literature, I then present a rationale for using board games to model these situations. Following this, I draw upon intuition and dual-process theory to outline an integrated theoretical perspective for such investigations. The article concludes with two vignettes demonstrating how this perspective might be used to analyze thinking about risk in a board game setting.

Developing Strategic And Mathematical Thinking Via Game Play: Programming To Investigate A Risky Strategy For Quarto, 2015 University of Montana

#### Developing Strategic And Mathematical Thinking Via Game Play: Programming To Investigate A Risky Strategy For Quarto, Peter Rowlett

*The Mathematics Enthusiast*

The Maths Arcade is an extracurricular club for undergraduate students to play and analyse strategy board games, aimed at building a mathematical community of staff and students as well as improving strategic and mathematical thinking. This educational initiative, used at several universities in the U.K., will be described. Quarto is an impartial game played at the Maths Arcade, in that there is one set of common pieces used by both players, and one where stalemates are a common outcome. While some students play without apparent direction until a winning opportunity appears, others adopt a more risky strategy of building ...

Risk Education: A Worldview Analysis Of What Is Present And Could Be, 2015 University of Montana

#### Risk Education: A Worldview Analysis Of What Is Present And Could Be, Gale L. Russell

*The Mathematics Enthusiast*

Risk, risk analysis, risk management and risk-based decision-making are ubiquitous ideas in the modern world. Consequently, risk education is emerging as a new field of research. However, just as the defining of risk and what it entails is a contested topic, so too is the field of risk education research open to many possible approaches. In this paper notions of risk, particularly as they play out in research on risk education, are analyzed (within an ethical space) using a theoretical framework based on the Traditional Western and an Indigenous worldview. Through this analysis, along with the identification of the kinds ...

Risks Worth Taking? Social Risks And The Mathematics Teacher, 2015 University of Montana

#### Risks Worth Taking? Social Risks And The Mathematics Teacher, Ami Mamolo, Laura Elizabeth Pinto

*The Mathematics Enthusiast*

In this article, we explore notions of risk as perceived or experienced by individuals involved in mathematical education. We present this exploration in the form of vignettes, each illustrating a form of risk: a parent’s reaction to classroom “propaganda”; a teacher trying to do justice by her students; a teacher confronted by his administration; and a college professor who believes university policy to be unjust. Each vignette sheds light on areas in which teacher education may offer additional support in fostering the mathematical knowledge, pedagogical sensitivity, and social awareness required to foster, what are in our view, much needed ...

Risky Research Business: Mathematics Education Research On The Margins, 2015 University of Montana

#### Risky Research Business: Mathematics Education Research On The Margins, Erika C. Bullock

*The Mathematics Enthusiast*

Although we would like to believe that decisions about what research to conduct and how to conduct it are based solely on researcher interest and societal need, the reality is that external political and disciplinary factors do play a role. Scientifically based research (SBR) is one example of external political pressures that shape researcher choice both directly and indirectly. Additionally, disciplines like mathematics education operate under hidden curricula that have the potential to marginalize particular research foci. The purpose of this paper is to consider the implications of such a narrow focus on a young mathematics education researcher’s choices ...

Risk As An Explanatory Factor For Researchers’ Inferential Interpretations, 2015 University of Montana

#### Risk As An Explanatory Factor For Researchers’ Inferential Interpretations, Rink Hoekstra

*The Mathematics Enthusiast*

Logical reasoning is crucial in science, but we know that this is not something that humans are innately good at. It becomes even harder to reason logically about data when there is uncertainty, because there is always a chance of being wrong. Dealing with uncertainty is inevitable, for example, in situations in which the evaluation of sample outcomes with respect to some population is required. Inferential statistics is a structured way of reasoning rationally about such data. One could therefore expect that using well-known statistical techniques protects its users against misinterpretations regarding uncertainty. Unfortunately, this does not seem to be ...

Risk And Decision Making: The “Logic” Of Probability, 2015 University of Montana

#### Risk And Decision Making: The “Logic” Of Probability, Manfred Borovcnik

*The Mathematics Enthusiast*

Risk is a hot topic. There is an international trend to use examples of risk or the concept of risk in the early teaching of probability. It enriches the problems, it widens the contexts, and it motivates the students to learn probability. This paper illustrates the notion of risk as a multi-faceted concept. The diverse perceptions start with language where risk is used in very different ways. The overlap of risk and hazard is not restricted to the technical context of safety and reliability; Knight’s seminal work on risk and uncertainty has its definite impact on today’s perception ...

A Cognitive Framework For Normative Reasoning Under Uncertainty, And Reasoning About Risk, And Implications For Educational Practice, 2015 University of Montana

#### A Cognitive Framework For Normative Reasoning Under Uncertainty, And Reasoning About Risk, And Implications For Educational Practice, Sylvia Kuzmak

*The Mathematics Enthusiast*

Clarifying what is normative or appropriate reasoning under various circumstances provides a valuable reference for guiding what should be taught, and, in contrast, what should not be. This paper proposes a cognitive framework for viewing normative reasoning and behavior under uncertainty, including the applying of knowledge of probability and statistics in real world situations; and identifies implications for educational practice. Factors relevant to normative reasoning under uncertainty that are addressed within the framework include: risk of misapplying statistics knowledge, involvement of mathematical and non-mathematical reasoning, knowledge of real world domains and situation/application detail, and existence of expert consensus. The ...