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International Conference on Mathematics and its Applications in Science and Engineering (ICMASE 2020), on-line conference. July 9-10, 2020. 10 páginas, 10 figuras. ; Due to the Bologna Accord, the teaching of mathematics has undergone importantchanges. Some of the most visible modifications have been the need to complementthe traditional teaching-learning process with practical, real-life cases and thepossibility to reinforce the introduction and usage of key concepts throughmathematical software.Nowadays, there exist many computational packagesdealing with mathematics, some of the best-known being Mathematica and Matlab.However, although they are very complete and powerful, they demand the use ofcommercial licences, which can be a problem for some education institutions orin the cases where students desire to use the software in an unlimited number ofdevices or to access from several of them simultaneously.In this article, we show how to apply GeoGebra and WolframAlpha to the processof teaching Calculus to first-year university students.While GeoGebra is aninteractive geometry, algebra, statistics, and calculus application available both asan online resource and a native application in Windows, macOS, and Linux systems,WolframAlpha is a computational knowledge engine developed by a subsidiaryof Wolfram Research, the company behind Mathematica. However, unlike thatproduct, WolframAlpha can be accessed by any individual as a web service free ofcharge. One of the key aspects of WolframAlpha is the possibility to use naturallanguage and Mathematica syntax for requesting computations, which allows usersto benefit from a large amount of Mathematica resources.Being able to use GeoGebra and WolframAlpha as web services withoutdownloading and installing software is another important advantage, as it avoidsthe need to have adminstrator rights to use those computational engines, whichtypically represents a problem in education centres where lab computers arelocked so students cannot inadvertently install malware that can compromise theuniversity's network.As the best way to show a topic in mathematics is to provide examples,this contribution focuses on the main topics associated to a first-year Calculus class (limits, continuity, derivatives, curve interpolation and integrals), providingexamples with GeoGebra and WolframAlpha for the computations and concreteexamples used in actual Calculus classes. ; This work was supported in part by the Ministerio de Economía, Industria y Competitividad (MINECO), in part by the Agencia Estatal de Investigación (AEI), in part by the Fondo Europeo de Desarrollo Regional (FEDER, UE) under Project COPCIS, Grant TIN2017-84844-C2-1-R, and in part by the Erasmus+ program of the European Union under grant 2017-1-ES01-KA203-038491(RULES_MATH). Víctor Gayoso Martínez would like to thank CSIC Project CASP2/201850E114 for its support.

CSIC SCIENTIFIC CHALLENGES: TOWARDS 2030 VOLUME 10 DIGITAL & COMPLEX INFORMATION Challenge 5 ; The exponential deployment and popularization of Internet access ( the so- called democratization of Internet access ) facilitated by the proliferation of the technological devices with connecting capabilities, has driven to the growth of the cyberspace, which has changed our society dramatically. Al- though this change has provided a large number of benefits, it has also gener- ated a number of risks and threats that often go unnoticed. An obvious chal- lenge would be minimizing such risks and threats through scientific research in order to improve the security of the digital information, thus contributing to enhance users ' trust in the digital society. Research will be carried out on the design of methods for ensuring the confi- dentiality, integrity and availability of information, as transversal require- ments for digital security. Key challenging points are identified regarding the storage of data, the communication of information over networks, and the processing of data on hardware devices. To secure the storage of data, cryp- tographic protocols and algorithms will be developed taking into account fun- damental aspects of authentication, lightweight cryptography and post-quan- tum cryptography. To guarantee the security of communications over networks, dodging the threat of quantum computing, quantum key distribu- tion will be improved by means of new protocols and technological develop- ments. For the secure processing of data on hardware devices, microelectronics developments of secure computing systems and hardware roots of trust will be investigated, looking for a European technological sovereignty. Addressing this challenge and achieving its goals will ensure that digital ap- plications will be used in a trustworthy and secure way. The experience and previous achievements of the groups involved in this chal- lenge show their ability to succeed in reaching results which will contribute to the progress of basic science, and to the development of new technologies and novel applications which will have a remarkable impact in many aspects of our society.