Biophysics is an interdisciplinary field that applies the principles and methods of physics to understand biological systems. It combines concepts from biology, physics, chemistry, mathematics, and computational science to explore the physical mechanisms underlying biological processes. Key areas of study in biophysics include: 1. **Molecular Biophysics**: Examines the physical properties of biomolecules such as proteins, nucleic acids, and lipids.

Medical physics is a multidisciplinary field that applies principles and techniques from physics to medicine, particularly in the diagnosis and treatment of diseases. It primarily focuses on the use of radiation and other physical principles in healthcare. Medical physicists work in various areas, including: 1. **Radiology**: They help in the safe and effective use of imaging technologies such as X-rays, MRI, CT scans, and ultrasound. They ensure that imaging studies are performed safely and produce high-quality images for diagnosis.

Applied geometry is a branch of geometry that focuses on the practical application of geometric principles and methods to solve real-world problems. It encompasses various fields and combines geometric concepts with tools from mathematics, engineering, computer science, and other disciplines. Some key areas where applied geometry plays an important role include: 1. **Computer Graphics**: Used extensively in rendering images, animations, and visual effects through modeling shapes, transformations, and perspective.

Applied mathematicians are professionals who utilize mathematical techniques and theories to solve real-world problems in various fields such as engineering, physics, economics, biology, computer science, and more. Their work involves developing mathematical models to represent complex systems and phenomena, analyzing data, and applying statistical methods to derive insights or make predictions. Key activities of applied mathematicians often include: 1. **Modeling:** Creating mathematical representations of real-world situations to analyze and predict outcomes.

Mathematical economics is a field that applies mathematical methods and techniques to represent economic theories, analyze economic problems, and derive economic relationships. It utilizes mathematical concepts such as calculus, linear algebra, and optimization to model economic behaviors and interactions quantitatively. The primary objectives of mathematical economics include: 1. **Modeling Economic Behavior**: Creating models that describe how individuals, firms, and markets behave under various conditions. This includes utility functions, production functions, and demand and supply models.

Mathematical finance is a field of applied mathematics that focuses on the mathematical modeling and analysis of financial markets and instruments. It integrates concepts from probability theory, statistics, differential equations, and stochastic calculus to understand and manage financial risks and to price financial derivatives. Key areas of mathematical finance include: 1. **Option Pricing**: Developing models to determine the fair value of options and other derivatives. The Black-Scholes model is one of the most famous examples.

Cool dude. Uses Stack Exchange: physics.stackexchange.com/users/31790/danielsank

Started at Google Quantum AI in 2014.

Has his LaTeX notes at: github.com/DanielSank/theory. One day he will convert to OurBigBook.com. Interesting to see that he is able to continue his notes despite being at Google.

Applied probability is a branch of probability theory that focuses on the application of probabilistic models and statistical techniques to solve real-world problems across various fields. It involves using mathematical tools and concepts to analyze and interpret random phenomena, make predictions, and inform decision-making under uncertainty. Key aspects of applied probability include: 1. **Modeling Real-World Situations**: Applied probability is used to create models that represent random processes or systems.

Information theory is a branch of applied mathematics and electrical engineering that deals with the quantification, storage, and communication of information. It was founded by Claude Shannon in his groundbreaking 1948 paper, "A Mathematical Theory of Communication." The field has since grown to encompass various aspects of information processing and transmission. Key concepts in information theory include: 1. **Information**: This is often quantified in terms of entropy, which measures the uncertainty or unpredictability of information content. Higher entropy indicates more information.

Inverse problems refer to a class of problems where one seeks to deduce unknown causes or parameters from observed effects or data. This is contrasted with direct problems, where the process is straightforward: given a set of inputs, one can directly compute the outputs. Inverse problems typically arise in fields such as physics, engineering, medical imaging, geophysics, and many other areas where one must infer the properties of a system from measured data.

Mathematical and theoretical biology is an interdisciplinary field that applies mathematical techniques and theoretical approaches to understand biological systems and processes. This area of research is diverse, encompassing various aspects of biology, from ecology and evolutionary biology to population dynamics, epidemiology, and cellular biology. ### Key Components: 1. **Mathematical Modeling**: - Researchers create mathematical models to describe biological processes. These models can take various forms, including differential equations, stochastic models, and discrete models.