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 nicf.net
Quantum Field Theory III - Perturbation Theory and Feynman Diagrams | Nicolas James Marks Ford
| | www.preposterousuniverse.com
Energy Conservation and Non-Conservation in Quantum Mechanics - Sean Carroll
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| | [AI summary] The text discusses the implications of quantum mechanics and the concept of expected energy in quantum systems. It highlights the difference between the average energy of a quantum state and the energy of the system post-measurement, emphasizing that the former is a statistical average while the latter is determined by the measurement outcome. The discussion also touches on the broader context of quantum theory, including the role of measurement and the probabilistic nature of quantum states. Additionally, it references the importance of energy in physical processes and the connection to classical thermodynamics, suggesting that while quantum mechanics provides a framework for understanding energy at a fundamental level, classical concepts still...
| | nobsstats.com
Appendix F - Calculus tutorial - No Bullshit Guide to Statistics
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| | thenumb.at
Functions are Vectors
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| | [AI summary] This text provides an in-depth exploration of how functions can be treated as vectors, particularly in the context of signal and geometry processing. It discusses the representation of functions as infinite-dimensional vectors, the use of Fourier transforms in various domains (such as 1D, spherical, and mesh-based), and the application of linear algebra to functions for tasks like compression and smoothing. The text also touches on the mathematical foundations of these concepts, including the Laplace operator, eigenfunctions, and orthonormal bases. It concludes with a list of further reading topics and acknowledges the contributions of reviewers.
| | mathscholar.org
Is modern science socially constructed and forever tentative? « Math Scholar
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| [AI summary] The article discusses the intersection of science and philosophy, highlighting the importance of empirical evidence and the scientific method in advancing knowledge. It critiques postmodern science studies for lacking scientific rigor and credibility, referencing the Sokal hoax as a key example. The piece also touches on the contributions of non-Western societies to science and the need for diversity in the scientific community. Ultimately, it concludes that while philosophical reflection has value, it should not replace the empirical foundation of scientific research.