I think you have quite a wrong idea aobut things. There are many forms of "mathematical finance" that do NOT require a Ph.D. and there are many forms of mathematical biology or pharmacokinetics that might well require a Ph.D.dankshu said:I'm guessing it depends on how many factors/how unpredictable a subject is, what is it really? What makes mathematical finance so rigorous- requiring a phd in math/finance- while something like systems biology or pharmacokinetics only requires knowledge up to linear algebra?
Mathematical modeling is the process of creating a mathematical representation of a real-world system or phenomenon. It involves using mathematical equations and data to simulate and predict the behavior of the system.
There are several types of mathematical modeling, including deterministic modeling, stochastic modeling, and agent-based modeling. Deterministic modeling uses precise mathematical equations to describe a system, while stochastic modeling incorporates randomness and uncertainty into the equations. Agent-based modeling involves simulating the behavior of individual agents within a larger system.
The difficulty of a mathematical modeling method depends on the complexity and characteristics of the system being modeled. Deterministic models may be more difficult to create and analyze if the system is highly nonlinear or has many variables. Stochastic models can be challenging due to the need to incorporate randomness and uncertainty into the equations. Agent-based models can be difficult to validate and interpret because of the complex interactions between individual agents.
The type of mathematical modeling used depends on the specific goals and characteristics of the system being modeled. Deterministic models are best suited for systems with well-defined equations and known variables. Stochastic models are useful for systems that involve randomness and uncertainty. Agent-based models are suitable for systems with complex interactions between individual agents.
Mathematical modeling is a simplified representation of a real-world system and may not capture all the complexities and nuances of the system. The accuracy of a mathematical model also depends on the quality and quantity of data used to create it. Additionally, some systems may be too complex to model accurately with current mathematical techniques.