5,047 research outputs found
Dynamic Web Tools for Trigonometry
In the last 20 years, computer technology having mathematical capability has been developed, improved, and become widely available, but textbook presentations are still largely free of any discussion that might require technology. Technology could be used in mathematical instruction for student drill and practice, for instructor demonstrations that promote conceptual understanding, or for the exploration of mathematical ideas, but software is often designed to be pedagogically generic, leaving its use to the creativity of the instructor. Technological solutions for local machines can be quite extensive, but cost and time constraints then limit availability for student use. The internet has the capability to provide mathematical instruction at all hours and in all places, with little financial investment by the student. This article describes the issues encountered and addressed by the author as he attempted to include self-authored web-based instructional units into a traditional trigonometry class.
This paper was published in issue 5/6, volume 18, of the International Journal of Continuing Engineering Education and Life-Long Learning, distributed by Inderscience. DOI: 10.1504/IJCEELL.2008.022175. Original article: http://www.inderscience.com/search/index.php?action=record&rec_id=22175&prevQuery=&ps=10&m=or\u3
Robust Computer Algebra, Theorem Proving, and Oracle AI
In the context of superintelligent AI systems, the term "oracle" has two
meanings. One refers to modular systems queried for domain-specific tasks.
Another usage, referring to a class of systems which may be useful for
addressing the value alignment and AI control problems, is a superintelligent
AI system that only answers questions. The aim of this manuscript is to survey
contemporary research problems related to oracles which align with long-term
research goals of AI safety. We examine existing question answering systems and
argue that their high degree of architectural heterogeneity makes them poor
candidates for rigorous analysis as oracles. On the other hand, we identify
computer algebra systems (CASs) as being primitive examples of domain-specific
oracles for mathematics and argue that efforts to integrate computer algebra
systems with theorem provers, systems which have largely been developed
independent of one another, provide a concrete set of problems related to the
notion of provable safety that has emerged in the AI safety community. We
review approaches to interfacing CASs with theorem provers, describe
well-defined architectural deficiencies that have been identified with CASs,
and suggest possible lines of research and practical software projects for
scientists interested in AI safety.Comment: 15 pages, 3 figure
Harnessing a Refinement Theory to Compute Loop Functions
AbstractWe consider a while loop on some space S and we are interested in deriving the function that this loop defines between its initial states and its final states (when it terminates). Such a capability is useful in a wide range of applications, including reverse engineering, software maintenance, program comprehension, and program verification. In the absence of a general theoretical solution to the problem of deriving the function of a loop, we explore engineering solutions. In this paper we use a relational refinement calculus to approach this complex problem in a systematic manner. Our approach has many drawbacks, some surmountable and some not (being inherent to the approach); nevertheless, it offers a way to automatically derive the function of loops or an approximation thereof, under some conditions
Summer Jobs Connect: Building Sustainable Banking and Savings Programs in Summer Youth Employment
Across the country, municipal Summer Youth Employment Programs (SYEPs) provide hundreds of thousands of young people, often from low-income communities, with short-term work experience and a regular paycheck. Building off this existing, widespread infrastructure and connection to young people, the Citi Foundation and the Cities for Financial Empowerment Fund (CFE Fund) saw an opportunity to connect young workers to bank accounts and targeted financial education, turning this large-scale youth employment program into a linchpin for building long-term positive financial behaviors. More broadly, Summer Jobs Connect (SJC) demonstrates how banking access efforts can be embedded in municipal infrastructure, a core goal of the CFE Fund's national Bank On initiative
Application-tailored Linear Algebra Algorithms: A search-based Approach
In this paper, we tackle the problem of automatically generating algorithms
for linear algebra operations by taking advantage of problem-specific
knowledge. In most situations, users possess much more information about the
problem at hand than what current libraries and computing environments accept;
evidence shows that if properly exploited, such information leads to
uncommon/unexpected speedups. We introduce a knowledge-aware linear algebra
compiler that allows users to input matrix equations together with properties
about the operands and the problem itself; for instance, they can specify that
the equation is part of a sequence, and how successive instances are related to
one another. The compiler exploits all this information to guide the generation
of algorithms, to limit the size of the search space, and to avoid redundant
computations. We applied the compiler to equations arising as part of
sensitivity and genome studies; the algorithms produced exhibit, respectively,
100- and 1000-fold speedups
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