Category: Mathematics
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Signals and Statistics of Medical Imaging
Chapter 1: Setting the Stage: Probability Theory and Random Variables in Medical Imaging 1.1: Introduction to Probability and Random Variables: Bridging the Gap Between Theory and Medical Imaging. This section will introduce the fundamental concepts of probability theory, including sample spaces, events, probability axioms, conditional probability, and independence. It will then bridge the gap to…
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Flow Architect: The Foundations of Fluid Dynamics
Chapter 1: Introduction: The Grand Challenge of Fluid Dynamics and Its Computational Solution 1.1 The Ubiquity and Importance of Fluid Dynamics: From Microscopic to Astrophysical Scales Fluids are everywhere. The air we breathe, the water we drink, the blood coursing through our veins, and even the molten rock deep within the Earth – all are…
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Magnetic Resonance Imaging: A Dive into its Physics
Chapter 1: The Quantum Underpinnings: A Journey into Nuclear Spin and Magnetic Moments 1. The Intrinsic Angular Momentum: Demystifying Nuclear Spin and its Quantization At the heart of nuclear magnetic resonance (NMR) lies a fundamental property of atomic nuclei known as nuclear spin. Unlike the classical notion of a spinning top, nuclear spin is an…
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Fermat’s Last Theorem (FLT)
What is Fermat’s Last Theorem? Fermat’s Last Theorem (FLT) is one of the most iconic and enduring mathematical problems in history. The theorem itself states that there are no positive integers x, y, and z that can satisfy the equation x^n + y^n = z^n for any integer value of n greater than 2. This…