The theory of extremal graphs is a fascinating area of combinatorics, focused on analyzing the limits and optimal structures of graphs under certain constraints. Questions such as “what is the minimum number of edges needed to ensure a given property?” or “how can we characterize the graphs that reach these limits?” are central to this … Read more
IN BRIEF Algorithm: a sequence of steps to transform input data into output data. Mathematics and computer science work in symbiosis. An algorithm is essential in computer programming. Structuring the steps to solve a problem. The principles of algorithmics include assertions and a clear objective. Algorithms are fundamental for numerical calculation and applications. Mastering algorithms … Read more
IN BRIEF Machine learning for cosmological analysis. Correction of detection biases of weak lenses. Use of algorithms for astrophysical parameter estimation. Introduction to ensemble methods. Estimations of biases related to galaxy properties. Applications of AI in the quest for the infinite. Use of optimal transport algorithms in cosmology. Machine learning in astronomy and biomedicine. In … Read more
IN SHORT Modern cryptography: Securing transactions and generating trust. Mathematical problems: Use of unsolved problems, such as the factorization of large numbers. History: Cryptographic system RSA developed by Ronald Rivest and his colleagues in 1977. Applications: Computer programs derived from cryptographic protocols. Prime numbers: Essential for research in cryptography. Encoding function: Encryption keys validated by … Read more
IN BRIEF Use of mathematics to model complex systems. Neural networks and their mathematical foundations. Statistics to analyze and interpret data. Supervised learning and parameter tuning. Modern theories to predict chaotic phenomena. Applied mathematics in operational research. Influence on education and mathematics teaching. Optimization of learning methods through mathematics. Data security via mathematical approaches. Mathematics … Read more