Some heuristics about elliptic curves

We give some heuristics for counting elliptic curves with certain properties. In particular, we re-derive the Brumer-McGuinness heuristic for the number of curves with positive/negative discriminant up to $X$, which is an application of lattice-point counting. We then introduce heuristics (with refinements from random matrix theory) that allow us to predict how often we expect an elliptic curve $E$ with even parity to have $L(E,1)=0$. We find that we expect there to be about $c_1X^{19/24}(\log X)^{3/8}$ curves with $|\Delta|<X$ with even parity and positive (analytic) rank; since Brumer and McGuinness predict $cX^{5/6}$ total curves, this implies that asymptotically almost all even parity curves have rank 0. We then derive similar estimates for ordering by conductor, and conclude by giving various data regarding our heuristics and related questions

Paid Sick Days and Restaurant Jobs: The Evidence from San Francisco

In February 2007, San Francisco implemented the nation's first paid sick days law, allowing all workers within the city to earn a minimum amount of paid sick leave. Restaurants are among the employers least likely to provide sick leave benefits, absent such a requirement. Therefore, if minimum paid leave standards affect the number of jobs available, we would expect to see that impact most clearly in the food service industry.The data show that the job market in restaurants and bars has been stronger in San Francisco than in the state of California as a whole in every year since the sick days law passed

Teaching the YouTube generation: exploring the benefits of an interactive teaching approach in sustainable product design

This paper presents findings from a doctoral study, which investigated effective methods for teaching social sustainability within product design courses in British and Irish universities. Specifically exploring, how to foster a holistic understanding of the social aspects of sustainable product design amongst undergraduate and postgraduate students, through design thinking. Perceived relevance is considered as a fundamental aspect in enabling students to engage deeply with sustainability [1]. Authors [2;3;4] note that 'Net Generation' learners have specific learning preferences that can be targeted in order to improve the students learning experience. Through the careful design of materials which build upon the students tendency towards visual learning and seeking increase relevance and motivation, by offering opportunities for collaborative learning and learning through discovery. Three 'Rethinking Design' workshops were designed and developed as part of a doctoral study to introduce students to the wider social aspects of sustainability and these were conducted in five universities in Britain and Ireland. The workshops featured visually rich audio visual introductions followed by collaborative group based mind mapping activities, which were successful in fostering deep learning by facilitating learning through discovery, critical reflection, peer learning and creativity leading to an exploration of design thinking solutions

Washington's Working Women

The lingering impacts of recession highlight the central importance of women's work to family economic survival - but also the gulf that still separates women's earnings from men's, and the need for new policies that promote healthy workplaces and healthy families

The Straight Facts on Social Security

Social Security is the bedrock of economic security for millions of children, as well as working and retired Americans.Social Security benefits are progressive, replacing half the earnings for a low wage worker, one-third for median wage earners, and one-quarter for high wage workers. Social Security has almost eliminated poverty among the elderly, thanks to lifetime retirement benefits, annual cost of living increases, and family benefits

Towards an understanding of the social aspects of sustainability in product design: teaching HE students in the UK and Ireland through reflection and peer learning

This paper presents findings from a doctoral study, which investigated effective methods for teaching social sustainability within product design courses in British and Irish universities. This paper explores approaches for encouraging students to explore the social aspects of sustainable product design through workshops specifically designed to foster deep learning through collaboration, discovery and critical reflection. The importance of deep learning is reflected in both the sustainable design education (O’Rafferty et al., 2008, Griffith and Bamford, 2007) and education for sustainability literature (Warburton, 2003) as important to an understanding of the holistic and complex nature of sustainability. Three 'Rethinking Design' workshops were designed and developed as part of the doctoral main study to introduce students to the wider social aspects of sustainability and these were conducted in five universities in Britain and Ireland. The workshops were developed to foster principles that encourage students to adopt deep learning methods, taking into account the specific learning preferences of the current generation of students to enhance motivational factors such as relevance, appropriate teaching materials and opportunities for collaborative learning. The workshops were tested amongst 150 undergraduate and postgraduate students and found to be successful in fostering deep learning by facilitating learning through discovery, critical reflection, peer learning and creativity leading to an exploration of design thinking solutions