Towards an Intelligent Tutor for Mathematical Proofs

Computer-supported learning is an increasingly important form of study since it allows for independent learning and individualized instruction. In this paper, we discuss a novel approach to developing an intelligent tutoring system for teaching textbook-style mathematical proofs. We characterize the particularities of the domain and discuss common ITS design models. Our approach is motivated by phenomena found in a corpus of tutorial dialogs that were collected in a Wizard-of-Oz experiment. We show how an intelligent tutor for textbook-style mathematical proofs can be built on top of an adapted assertion-level proof assistant by reusing representations and proof search strategies originally developed for automated and interactive theorem proving. The resulting prototype was successfully evaluated on a corpus of tutorial dialogs and yields good results.Comment: In Proceedings THedu'11, arXiv:1202.453

WARNING: Physics Envy May Be Hazardous To Your Wealth!

The quantitative aspirations of economists and financial analysts have for many years been based on the belief that it should be possible to build models of economic systems - and financial markets in particular - that are as predictive as those in physics. While this perspective has led to a number of important breakthroughs in economics, "physics envy" has also created a false sense of mathematical precision in some cases. We speculate on the origins of physics envy, and then describe an alternate perspective of economic behavior based on a new taxonomy of uncertainty. We illustrate the relevance of this taxonomy with two concrete examples: the classical harmonic oscillator with some new twists that make physics look more like economics, and a quantitative equity market-neutral strategy. We conclude by offering a new interpretation of tail events, proposing an "uncertainty checklist" with which our taxonomy can be implemented, and considering the role that quants played in the current financial crisis.Comment: v3 adds 2 reference

Large-Scale Asset Purchases by the Federal Reserve: Did They Work?

Discusses how the Federal Reserve faced the challenge to further ease the stance of monetary policy as the economic outlook deteriorated through LSAPs

Cultural corridors: An analysis of persistence in impacts on local development — A neo-Weberian perspective on South-East Europe

Culture matters for economic development. This postulate has been a main conceptual concern for “old” institutional economics (OIE) and has lately also been tested through neoclassically inspired econometric techniques. This conceptual foundation has been confirmed in several quantitative studies on developed countries, in particular cases from the USA, Germany, and Italy. In less developed regions with a wealth of cultural heritage, particularly in South-East Europe, this postulate is still an underexplored issue from the perspective of advanced econometric approaches. Our goal is to examine the impact of the so-called South-East European cultural corridors on welfare — and especially on total employment — at the local or regional level. Accounting for gross value added and sectoral specialization, we examine the effect of such corridors by considering the distance to a cultural corridor: namely, the East Trans-Balkan Road (crossing Romania, Bulgaria, and Greece) as an explanatory factor for regional development, particularly employment. Using the European University Institute (EUI) European Regional Dataset (ERD), as well as the geo-data from the Cultural Corridors of the South-East Europe website, we estimate a regression model using a 2SLS instrumental variable (IV) approach, with a pooled dataset at the NUTS 3 level (Eurostat) from 1980 to 2011. We then triangulate the results by using the distance to the cultural corridor concerned as a treatment effect in a propensity-score-matching and difference-in-differences exploratory analysis. The findings confirm the importance of distance to the cultural corridor under investigation as a strong predictor for local socio-economic development. The results further suggest that the slow evolution of culture over time is likely to lead to the gradual emergence of new geographical cultural centers and a new cultural path-dependence build-up of persistence chains