In algebra, letters are used when numbers are not known. Algebraic terms, such as \(2s\) or \(8y\), leave the multiplication signs out. So rather than \(2 \times s\), write \(2s\), and rather than \(8 ...

Algebraic expressions can be simplified by collecting like terms. Positive like terms are often written before the negative like terms. When grouping the like terms together, the order does not matter ...

Semigroups, algebraic structures defined by a set equipped with an associative binary operation, are a cornerstone within modern algebra. Their study encompasses both abstract theoretical development ...

In so-called Kripke-type models, each sentence is assigned either to true or to false at each possible world. In this setting, every possible world has the two-valued Boolean algebra as the set of ...

Students of Grade 7 were given a test followed by individual interviews; at the end of Grade 8 the same students were subject to an analogous test and interviews. Each student had to simplify certain ...

Eric Larson and Isabel Vogt have solved the interpolation problem — a centuries-old question about some of the most basic objects in geometry. Some credit goes to the chalkboard in their living room.

How can the behavior of elementary particles and the structure of the entire universe be described using the same mathematical concepts? This question is at the heart of recent work by the ...