Developing Mathematics Enrichment Workshops for Middle School Students: Philosophy and Sample Workshops

This paper describes our approach to organizing enrichment activities using advanced mathematics topics for diverse audiences of middle school students. We discuss our philosophy and approaches for the structure of these workshops, and then provide sample schedules and resource materials. The workshops cover activities on the following topics: Graphing Calculators; The Chaos Game; Statistical Sampling; CT Scans–the reconstruction problem; The Platonic and Archimedean solids; The Shape of Space; Symmetry; The Binary Number System and the game of NIM; Graph Theory: Proof by Counterexample

Analyzing the Gender Gap on an Entrance Exam for Mathematically Talented Students

We investigate the qualifying entrance exam for the University of Minnesota Talented Youth Mathematics Program (UMTYMP), a five-year accelerated program covering high school- and undergraduate-level mathematics. The exam is used to assess the computational, numerical reasoning, and geometric skills of hundreds of fifth-, sixth-, and seventh-grade students annually. It has accurately identified qualified students in past years, but female participants consistently have had lower overall scores. Based on our belief that they are equally well qualified, in 2011 we began an extensive investigation into the structure and content of the exam to determine the possible sources for these differences. After gathering and analyzing data, we made relatively modest changes in 2012 which essentially eliminated the gender bias on one version of the entrance exam, increasing the percentage of females who qualified. The other unmodified versions in 2012 exhibited the typical gender difference from previous years. We continue to analyze the possible reasons for the gender differences while monitoring the overall student performance upon entering the Program

The mechanism of the Einstellung (set) effect: A pervasive source of cognitive bias

Copyright @ The Authors 2010The eye movements of expert players trying to solve a chess problem show that the first idea that comes to mind directs attention towards sources of information consistent with itself and away from inconsistent information. This bias continues unconsciously even when the player believes he is looking for alternatives. The result is that alternatives to the first idea are ignored. This mechanism for biasing attention ensures a speedy response in familiar situations but it can lead to errors when the first thought that comes to mind is not appropriate. We propose that this mechanism is the source of many cognitive biases from phenomena in problem solving and reasoning, to perceptual errors and failures in memory

Risk, Uncertainty, and the Perceived Threat of Terrorist Attacks: Evidence of Flight-to-Quality

© 2013 World Scientific Publishing Company and Midwest Finance Association. Information provided by the US Department of Homeland Security regarding potential terrorist attacks significantly affects US Treasury securities markets. When the government announces heightened terror alert levels, investors\u27 perceptions of risk increase and investors purchase 1-month and 1-year Treasury bills and 3-year, 5-year, 7-year, and 10-year US Treasuries in a flight-to-quality episode. Partial anticipation of increased threat level announcements is stronger than the anticipation of announcements regarding the federal funds rate during the 10 days prior to an announcement

Quantum cat maps with spin 1/2

We derive a semiclassical trace formula for quantized chaotic transformations of the torus coupled to a two-spinor precessing in a magnetic field. The trace formula is applied to semiclassical correlation densities of the quantum map, which, according to the conjecture of Bohigas, Giannoni and Schmit, are expected to converge to those of the circular symplectic ensemble (CSE) of random matrices. In particular, we show that the diagonal approximation of the spectral form factor for small arguments agrees with the CSE prediction. The results are confirmed by numerical investigations.Comment: 26 pages, 3 figure

Testing Wagner’s law versus the Keynesian hypothesis for GCC countries

© 2020 Informa UK Limited, trading as Taylor & Francis Group. This paper examines the relationship between real GDP and government spending for the six Gulf Cooperation Council (GCC) countries. Linear Granger causality tests in the time and frequency domains provide moderate support for Wagner’s law in four countries and weak support for the Keynesian model in two countries. In contrast, asymmetric nonlinear causality tests in the frequency domain support Wagner’s law in five countries, while some form of the Keynesian hypothesis is valid in all six GCC countries. Our results illustrate the importance of using nonlinear, asymmetric models to examine causal relationships

Capacitance fluctuations causing channel noise reduction in stochastic Hodgkin-Huxley systems

Voltage-dependent ion channels determine the electric properties of axonal cell membranes. They not only allow the passage of ions through the cell membrane but also contribute to an additional charging of the cell membrane resulting in the so-called capacitance loading. The switching of the channel gates between an open and a closed configuration is intrinsically related to the movement of gating charge within the cell membrane. At the beginning of an action potential the transient gating current is opposite to the direction of the current of sodium ions through the membrane. Therefore, the excitability is expected to become reduced due to the influence of a gating current. Our stochastic Hodgkin-Huxley like modeling takes into account both the channel noise -- i.e. the fluctuations of the number of open ion channels -- and the capacitance fluctuations that result from the dynamics of the gating charge. We investigate the spiking dynamics of membrane patches of variable size and analyze the statistics of the spontaneous spiking. As a main result, we find that the gating currents yield a drastic reduction of the spontaneous spiking rate for sufficiently large ion channel clusters. Consequently, this demonstrates a prominent mechanism for channel noise reduction.Comment: 18 page

Double Exponential Instability of Triangular Arbitrage Systems

If financial markets displayed the informational efficiency postulated in the efficient markets hypothesis (EMH), arbitrage operations would be self-extinguishing. The present paper considers arbitrage sequences in foreign exchange (FX) markets, in which trading platforms and information are fragmented. In Kozyakin et al. (2010) and Cross et al. (2012) it was shown that sequences of triangular arbitrage operations in FX markets containing 4 currencies and trader-arbitrageurs tend to display periodicity or grow exponentially rather than being self-extinguishing. This paper extends the analysis to 5 or higher-order currency worlds. The key findings are that in a 5-currency world arbitrage sequences may also follow an exponential law as well as display periodicity, but that in higher-order currency worlds a double exponential law may additionally apply. There is an "inheritance of instability" in the higher-order currency worlds. Profitable arbitrage operations are thus endemic rather that displaying the self-extinguishing properties implied by the EMH.Comment: 22 pages, 22 bibliography references, expanded Introduction and Conclusion, added bibliohraphy reference

On the lease rate, convenience yield and speculative effects in the gold futures market

By examining data on the gold forward offered rate (GOFO) and lease rates over the period 1996- 2009, we conclude that the convenience yield of gold is better approximated by the lease rate than the interest-adjusted spread of Fama & French (1983). Using the latter quantity, we study the relationship between gold leasing and the level of COMEX discretionary inventory and exhibit that lease rates are negatively related to inventories. We also show that Futures prices have increasingly exceeded forward prices over the period, and this effect increases with the speculative pressure and the maturity of the contracts

Risks, alternative knowledge strategies and democratic legitimacy: the conflict over co-incineration of hazardous industrial waste in Portugal.

The decision to incinerate hazardous industrial waste in cement plants (the socalled ‘co-incineration’ process) gave rise to one of the most heated environmental conflicts ever to take place in Portugal. The bitterest period was between 1997 and 2002, after the government had made a decision. Strong protests by residents, environmental organizations, opposition parties, and some members of the scientific community forced the government to backtrack and to seek scientific legitimacy for the process through scientific expertise. The experts ratified the government’s decision, stating that the risks involved were socially acceptable. The conflict persisted over a decade and ended up clearing the way for a more sustainable method over which there was broad social consensus – a multifunctional method which makes it possible to treat, recover and regenerate most wastes. Focusing the analysis on this conflict, this paper has three aims: (1) to discuss the implications of the fact that expertise was ‘confiscated’ after the government had committed itself to the decision to implement co-incineration and by way of a reaction to the atmosphere of tension and protest; (2) to analyse the uses of the notions of ‘risk’ and ‘uncertainty’ in scientific reports from both experts and counter-experts’ committees, and their different assumptions about controllability and criteria for considering certain practices to be sufficiently safe for the public; and (3) to show how the existence of different technical scientific and political attitudes (one more closely tied to government and the corporate interests of the cement plants, the other closer to the environmental values of reuse and recycling and respect for the risk perception of residents who challenged the facilities) is closely bound up with problems of democratic legitimacy. This conflict showed how adopting more sustainable and lower-risk policies implies a broader view of democratic legitimacy, one which involves both civic movements and citizens themselves