The origins of mathematical abstraction

Designing for Mathematical Abstraction

ion and for the micro-evolution of mathematical knowledge can co-emerge.

Mathematical Abstraction of Object and Context

Reflective Abstraction in Advanced Mathematical Thinking

Our purpose in this chapter is to propose that the concept of reflective abstraction can be a powerful tool in the study of advanced mathematical thinking, that it can provide a theoretical basis that supports and contributes to our understanding of what this thinking is and how we can help students develop the ability to engage in it. To make such a case completely, it would be necessary to do...

Lightweight Abstraction for Mathematical Computation in Java

Many object-oriented programming languages provide type safety by allowing programmers to introduce distinct object types. In the case of Java, having objects as the sole abstraction mechanism also introduces a considerable or even prohibitive cost, especially when dealing with small objects over primitive types. Consequently, Java library implementations frequently avoid abstraction and are no...

The Mathematical Origins of 19 th Century Algebra of Logic ∗

Most 19th century scholars would have agreed to the opinion that philosophers are responsible for research on logic. On the other hand, the history of late 19th century logic clearly indicates a very dynamic development instigated not by philosophers, but by mathematicians. A central outcome of this development was the emergence of what has been called the “new logic”, “mathematical logic”, “sy...