Ricerc@Sapienza

Results are presented abut a professional development workshop based on the ABN Method for learning mathematics (N = 27), conducted in Talca, Chile, for Pre-K and Primary in-service teachers (children from 4 to 7 years of age in charge). The workshop is aimed at nursery school teachers and first grade teachers. The ABN Method is based on the significant learning of the decimal number system and on the complete domain of operations and their properties, which are learned and assimilated at the same time by children from the early stages of teaching.

We investigate the average number of representations of a positive integer as the sum of k + 1 perfect k-th powers of primes. We extend recent results of Languasco and the third author, which dealt with the case k = 2 and k = 3, respectively. We use the same technique to study the corresponding problem for sums of just k perfect k-th powers of primes.

Multistage launch vehicles of reduced size, such as "Super Strypi" or "Sword", are currently investigated for the purpose of providing launch opportunities for microsatellites. This work proposes a general methodology for the accurate modeling and performance evaluation of launch vehicles dedicated to microsatellites. For illustrative purposes, the approach at hand is applied to the Scout rocket, a micro-launcher used in the past. Aerodynamics and propulsion are modeled with high fidelity through interpolation of available data.

I investigate the construction of the mathematical concept of quaternion from a methodological and heuristic viewpoint to examine what we can learn from it for the study of the advancement of mathematical knowledge. I will look, in particular, at the inferential microstructures that shape this construction, that is, the study of both the very first, ampliative inferential steps, and their tentative outcomes—i.e. small ‘structures’ such as provisional entities and relations.

I argue that the construction of representation theorems is a powerful tool for creating novel objects and theories in mathematics, as the construction of a new representation introduces new pieces of information in a very specific way that enables a solution for a problem and a proof of a new theorem. In more detail, I show how the work behind the proof of a representation theorem transforms a mathematical problem in a way that makes it tractable and introduces information into it that it did not contain at the beginning of the process.

In this paper I examine the heuristic view of mathematics focussing on an updated version of it. I discuss how the seminal work of Lakatos has been improved under several respects and I point at four issues that are particularly relevant for the philosophy of mathematics and mathematical practice from a heuristic point of view: 1. the quest for a method of discovery (§ 2); 2. the construction of heuristic procedure, that is rational and inferential ways of producing a hypothesis to solve a problem (§ 3); 3. the nature of mathematical objects (§ 4); 4.

The book offers an interdisciplinary perspective on finance, with a special focus on stock markets. It presents new methodologies for analyzing stock markets’ behavior and discusses theories and methods of finance from different angles, such as the mathematical, physical and philosophical ones. The book, which aims at philosophers and economists alike, represents a rare yet important attempt to unify the externalist with the internalist conceptions of finance.

The nature of the data of financial systems raises several theoretical and methodological issues, which not only impact finance, but have also philosophical and methodological implications, viz. on the very notion of data. In this paper I will examine several features of financial data, especially stock markets data: these features pose serious challenges to the interpretation and employment of stock markets data, weakening the ‘myth of data’. In particular I will focus on two issues: (1) the way data are produced and shared, and (2) the way data are processed.

The view from outside on finance maintains that we can make sense of, and profit from, stock markets’ behavior, or at least few crucial properties of it, by crunching numbers and looking for patterns and regularities in certain sets of data. The basic idea is that there are general properties and behavior of stock markets that can be detected and studied through mathematical lens, and they do not depend so much on contextual or domain-specific factors.

The view from inside maintains that not only to study and understand, but also to profit from financial markets, it is necessary to get as much knowledge as possible about their internal ‘structure’ and machinery. This view maintains that in order to solve the problems posed by finance, or at least a large part of them, we need first of all a qualitative analysis. Rules, laws, institutions, regulators, the behavior and the psychology of traders and investors are the key elements to the understanding of finance, and stock markets in particular.