Nonsingular acyclic M-matrices whose
inverse is also acyclic

In this talk, we present the
characterization of the acyclic M-matrices whose inverse shares the same
underlying tree. We discuss a possible extension. Several illustrative examples
are provided.

Ayman Badawi has taught in mathematics departments for more than 25 years at institutions such as Emory & Henry College, Virginia, USA; the University of Tennessee-Knoxville, USA; and Birzeit University, West Bank, Palestine. His area of research is in commutative algebra and his teaching interests are linear algebra, abstract algebra, number theory, discrete math, calculus, differential equations, math for architects, geometry, graph theory and business math.

On Generalizations of Valuation Domains

Let R be an integral domain with quotient field K. In this talk, we survey many generalizations of valuation domains. For example: Pseudo-valuation domains as in [5]; Almost-valuation domains as in [1]; Pseudo-almost-valuation domains as in [3]; Almost-pseudo-valuation domain as in [4]. Let n ≥ 1. Then Anderson and Badawi [2] recently introduced n-Pseudo-valuation domains, n-valuation domains, and pseudo-n-valuation domains.

[1] D. D. Andersonand M. Zafrullah, AlmostBezoutdomains, J. Algebra 142(1991), 285–309.

[2] D. F. Andersonand A. Badawi, n-Pseudo-valuationdomains (in preparation).

[3] A. Badawi, On pseudo-almostvaluationdomains, Comm. Algebra 35(2007), 1167-1181.

[4] A. Badawiand E. Houston, Powerfulideals, stronglyprimaryideals, pseudo-valuation do-mains, andconducivedomains, Comm. Algebra 30(2002), 1591–1606.

[5] J. R. Hedstromand E. G. Houston, Pseudo-valuationdomains, Pacific J. Math. 75(1978), 137–147.

Araceli Queiruga-Dios obtained her Ph.D. in Mathematics at the University of Salamanca (Spain) when she was working for a telecommunications multinational company. Her major field of research is public key cryptography, together with educational tools and mathematical applications for engineering students. She is Professor at theDepartment of Applied Mathematics at the School of Industrial Engineering in the University of Salamanca. She has participated as coordinator and collaborator in several research projects at national and European level. She is co-author of over 50 papers, morethan 70 contributions to workshops and conferences, and 1 patent related to RSA parameters. She is currently the coordinator of the Erasmus+ project: RULES_MATH.

Conclusions from Rules_Math project: Changing methods, changing minds

As part of RULES-MATH Erasmus+ project, we have been working for 3 years about the establishment of rules for the assessment of mathematical competencies.

Mathematical teachers from 8 different countries have work together in this project: The Ankara HaciBayramVeli University (Turkey), the Slovak University of Technology in Bratislava (Slovakia), the Czech Technical University in Prague (Czech Republic), the University of Plovdiv PaisiiHilendarski (Bulgaria), the Spanish National Research Council (Spain), the Higher Institute of Engenharia de Coimbra (Portugal), the Technological University Dublin (Ireland), the Technical University of Civil Engineering of Bucharest (Romania), coordinated by the University of Salamanca.

Teaching mathematics to engineering students is training them in the use of several tools to solve engineering problems. Engineers do not need mathematics as their final goal. They need mathematics to solve mechanical, electric, or chemical problems. They need the applications of mathematics to their daily work. After this process of learning, we have to assess students. We need to know if they have acquired mathematical competencies: Thinking, reasoning, and modelling mathematically, posing and solving mathematical problems, representing mathematical entities, handling mathematical symbols and formalisms, communicating in, with, and about Mathematics, and making use of aids and tools for mathematical activity. All these competencies are the key to become an engineer.

During this session we will discuss about different procedures and activities that we propose to assess mathematical competencies: small projects, multiple choice tests, or “classical” problems. We do not suggest selecting only one option, is rather a selection of all of them.