Final answer:
The programming paradigm that emphasizes abstraction, mathematical foundations, and the elimination of side effects and state changes is functional programming. Languages like ANSI SCHEME exemplify this approach, favoring immutable data structures and pure functions.
Step-by-step explanation:
The programming paradigm that focuses on abstraction to the level of mathematics and the elimination of side effects and state-based programming is functional programming. This paradigm treats computation as the evaluation of mathematical functions and avoids changing-state and mutable data. It is a declarative programming paradigm, which means programming is done with expressions or declarations instead of statements.
In functional programming languages like ANSI SCHEME and Haskell, functions are first-class citizens. This means that functions can be passed as arguments to other functions, returned as values from other functions, and assigned to variables. The aim is to make the coding process closer to mathematical functions to minimize bugs and improve clarity. Learning Python can introduce programming fundamentals, however, understanding functional programming requires a shift in thinking from more procedural languages like Python.
Another aspect of functional programming is that it favors immutable data structures and pure functions, which do not cause side effects outside their scope. This can lead to more predictable and testable code, which is a reason why this paradigm is valued in systems that need high reliability, such as in systems programming.