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Applied Mathematics Toolkit [Chen] - mklabgr - 09-13-2026 Applied Mathematics Toolkit: Modeling, Data, and Algorithms for Scientists and Engineers Authors: Nan Chen & Charlotte Moser Publisher: CRC Press / Chapman & Hall, Taylor & Francis Publication: forthcoming, 2026 ISBN: 978-1-041-23824-9 Summary Applied Mathematics Toolkit is designed as a modern, integrated introduction to the mathematical machinery needed to study complex scientific and engineering systems. Its central idea is that modeling, statistics, machine learning, dynamical systems, stochastic methods, and computation should not be learned as disconnected subjects. Real problems typically involve several simultaneously: a mathematical model may be incomplete, observations noisy, dynamics nonlinear, the state high-dimensional, and important quantities only partially observable. The book therefore develops these techniques as parts of a single problem-solving framework connecting models + data + algorithms. The scope is unusually broad.  After an introduction, the book develops separate toolkits for statistics, machine learning, dynamical systems, applied analysis, and stochastic mathematics. It then moves toward subjects that connect these areas: data assimilation, information theory and uncertainty quantification, causal inference, and reduced-order modeling. The latter topics are especially important for modern scientific computing because they address questions such as how to combine imperfect models with observations, quantify uncertainty in predictions, infer possible causal relationships from data, and replace extremely high-dimensional systems with computationally manageable approximations.   A major pedagogical feature is that the authors emphasize not merely formulas but why a method works, what assumptions it makes, when it should be used, and where it can fail. Concepts are introduced through relatively simple examples before moving to more complicated applications. Example code supports computational experimentation, while short companion “one concept–one example” videos of roughly 5–10 minutes are intended to build intuition and facilitate review. This makes the book suitable both as a university text and for self-study by scientists or engineers who want a working mathematical toolkit rather than a purely theoretical survey.   Contents at a glance Introduction Statistical Toolkit Machine Learning Toolkit Dynamical Toolkit Applied Analysis Toolkit Stochastic Toolkit Data Meets Models: An Introduction to Data Assimilation Information Theory and Uncertainty Quantification Causal Inference Reduced-Order Models BOOK