Introduction to Quantum Mechanics Fundamentals of Machine Learning (desirable)

To give the student a new perspective on data analysis (textbases, experiment results, questionnaires) that facilitates creativity for research in multidisciplinary fields. To this end, a non-classical probabilistic model is introduced to explain phenomena considered "anomalous" or not "rational" in the traditional literature (e.g. Tversky and Shafir). These mathematical models are non-Boolean logic-based, with a final structure that allows the use of conventional tools in quantum mechanics, which is why we usually call them "quantum-like."

1. Why do we need non-classical probabilistic formalisms in data analysis and modelling? Paradoxes in experiments, main concepts in broader probabilistic paradigms, and research opportunities. 2. A first approximation into this subject: Experiments in cognition. Disjunction effect. Conjunction fallacy. Probability interference. 3. Some account of Mathematical tools: Lattices and Logic (Classical vs. Quantum). Hilbert space tools (States, Gleason's theorem, and non-unitary system evolution). 4. An interesting line: Concepts composition and vectorial text embedding in NLP (BERT, GPT4): Contexts, individual mental spaces, and collective spaces. 5. Some fun with Game Theory: Decision Making and Strategic games with incomplete information. 6. Some other possible excursions: 6.1 Formal Concept Analysis 6.2 Simplicial complex lattices: Chaotic dynamical attractors 6.3 Second quantization -from scratch- in social applications 6.4 Implementation on Quantum Computers .

- Focus on applying the introduced models in various multidisciplinary applications: finance, health, risk management, geostrategy, ecosystems, or conflict management, through the student's choice of their deliverables. - Conducting experiments and games in the classroom to understand and evaluate the concepts. - Use of mathematical models as simple as possible: the Hilbert spaces used are of finite dimension so that the spectra of the operators are eigenvalues, avoiding the introduction of projection valued sigma-measures and Finite Lattices. - Different analytical perspectives are presented: probabilistic/algebraic to allow understanding of the subject. - Links with other fields of knowledge will be established to allow the development of multidisciplinary research. - Text embedding (BERT. GPT4) - Formal Concept Analysis - Simplicial complexes in signal processing and chaotic dynamical attractors.