In addition to covering the basic concepts of mathematical logic and the fundamental material on completeness, compactness, and incompleteness, it devotes significant space to thorough introductions ...

Random set theory is a fascinating branch of mathematics that amalgamates techniques from topology, convex geometry, and probability theory. Social scientists routinely conduct empirical work with ...

Discover how groundbreaking research on infinities is reshaping our understanding of mathematics and challenging traditional ...

It’s an idea straight out of the schoolyard: that you might one day accidentally count so high that you break the laws of ...

Familiarity with a rigorous treatment of mathematics (through definitions, theorems and proofs) is expected. Students must know basics of linear algebra (matrix multiplication, geometric ...

Some of the notes are designed to remove misunderstandings such as are constantly met with in debates on the relativity theory. Others give alternative mathematical treatments of various points ...

Concepts and methods of mathematical game theory. Nim and combinatorial games ... Zero-sum games, maxmin strategies. Extensive games with information sets, behaviour strategies, perfect recall.

Fuzzy mathematics, a concept proposed by L.A. Zadeh in 1965, introduces the idea of fuzzy sets, emphasizing elements' degrees of membership in certain classes as potentially infinite. Over decades, ...