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This primer on mathematics formalisation provides a rapid, hands-on introduction to proof verification in Lean. After a quick introduction to Lean, the basic techniques of human-readable formalisation are introduced, illustrated by simple examples on maps, induction and real numbers. Subsequently, typical design options are discussed and brought to life through worked examples in the setting of simplicial complexes (a higher-dimensional generalisation of graph theory). Finally, the book demonstrates how current research in algebraic and geometric topology can be formalised by means of suitable abstraction layers. Informed by the author's recent teaching and research experience, this book allows students and researchers to quickly get started with formalising and checking their proofs. The core material of the book is accessible to mathematics students with basic programming skills. For the final chapter, familiarity with elementary category theory and algebraic topology is recommended.

Mathematical logic --- Algebraic geometry --- Algebraic topology --- Differential topology --- Computer architecture. Operating systems --- algebra --- topologie (wiskunde) --- informatica --- wiskunde --- logica --- geometrie --- topologie --- Automatic theorem proving --- Demostració automàtica de teoremes --- Programes d'ordinador --- Computer programs.

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This book gathers selected papers presented at the Fourth International Conference on Mechatronics and Intelligent Robotics (ICMIR 2020), held in Kunming, China, on May 22-44, 2020. The proceedings cover new findings in the following areas of research: mechatronics, intelligent mechatronics, robotics and biomimetics; novel and unconventional mechatronic systems; modeling and control of mechatronic systems; elements, structures and mechanisms of micro- and nano-systems; sensors, wireless sensor networks and multi-sensor data fusion; biomedical and rehabilitation engineering, prosthetics and artificial organs; artificial intelligence (AI), neural networks and fuzzy logic in mechatronics and robotics; industrial automation, process control and networked control systems; telerobotics and human-computer interaction; human-robot interaction; robotics and artificial intelligence; bio-inspired robotics; control algorithms and control systems; design theories and principles; evolutional robotics; field robotics; force sensors, accelerometers and other measuring devices; healthcare robotics; kinematics and dynamics analysis; manufacturing robotics; mathematical and computational methodologies in robotics; medical robotics; parallel robots and manipulators; robotic cognition and emotion; robotic perception and decisions; sensor integration, fusion and perception; and social robotics.

Mechatronics --- Robotics --- Mecatrònica --- Robòtica --- Intel·ligència artificial --- Ciència cognitiva --- Mètodes de simulació --- Processament de dades --- Sistemes autoorganitzatius --- Aprenentatge automàtic --- Demostració automàtica de teoremes --- Intel·ligència artificial distribuïda --- Intel·ligència computacional --- Sistemes adaptatius --- Tractament del llenguatge natural (Informàtica) --- Raonament qualitatiu --- Representació del coneixement (Teoria de la informació) --- Sistemes de pregunta i resposta --- Traducció automàtica --- Visió per ordinador --- Xarxes neuronals (Informàtica) --- Xarxes semàntiques (Teoria de la informació) --- Agents intel·ligents (Programes d'ordinador) --- Programació per restriccions --- Vida artificial --- Enginyeria robòtica --- Cibernètica --- Autòmats --- Robòtica en medicina --- Robots --- Robots industrials --- Automatització --- Teoria de màquines --- Microelectrònica en mecànica --- Enginyeria mecànica --- Microelectrònica --- Sistemes microelectromecànics

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Mathematical linguistics. --- Computational linguistics. --- Automatic language processing --- Language and languages --- Language data processing --- Linguistics --- Natural language processing (Linguistics) --- Applied linguistics --- Cross-language information retrieval --- Mathematical linguistics --- Multilingual computing --- Algebraic linguistics --- Linguistics, Mathematical --- Information theory --- Computational linguistics --- Data processing --- Statistical methods --- Mathematical models --- Lingüística matemàtica --- Lingüística computacional --- Lingüística --- Teoria de la informació --- Glossemàtica --- Gramàtica de dependències --- Lingüística aplicada --- Processament de la parla --- Traducció automàtica

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Spherical functions. --- Euclidean algorithm. --- Algorithm of Euclid --- Continued division --- Division, Continued --- Euclid algorithm --- Euclidian algorithm --- Euclid's algorithm --- Algorithms --- Number theory --- Functions, Spherical --- Spherical harmonics --- Transcendental functions --- Spheroidal functions --- Funcions esferoïdals --- Algorismes --- Algorisme d'Euclides --- Algoritmes --- Àlgebra --- Algorismes computacionals --- Algorismes genètics --- Anàlisi numèrica --- Funcions recursives --- Programació (Matemàtica) --- Programació (Ordinadors) --- Teoria de màquines --- Traducció automàtica --- Funcions harmòniques

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Translanguaging (Linguistics) --- Teachers --- Science --- Training of. --- Study and teaching. --- Science education --- Scientific education --- Teacher education --- Teacher training --- Teachers, Training of --- Linguistics --- Multilingualism --- Ensenyament científic --- Lingüística aplicada --- Lingüística --- Aprenentatge integrat de continguts i llengües estrangeres --- Lingüística computacional --- Lingüística contrastiva --- Lingüística forense --- Llengües d'especialitat --- Traducció automàtica --- Educació científica --- Ensenyament de la ciència --- Ensenyament --- Ensenyament de la química --- Educació STEM