Portal:Modern analysis
This is a topic offered by the mathematics department.
Modern analysis is also sometimes called "elementary analysis" or "real analysis", among many other similar synonyms.
Because the vocabulary for these course titles is not entirely standardized, this can often be confused with "graduate real analysis" which is sometimes called "measure theory and functional analysis". Please see the measure theory page for disambiguation.
Modern analysis is a part of the "foundations project" of mathematics, which constructs mathematical concepts from axioms. In particular, modern mathematics is constructed from the axioms of set theory, ZFC.
Once the real numbers are constructed from the axioms of ZFC, their properties are studied. Then various objects are constructed from real numbers, such as sequences, functions, and sequences of functions. Again the properties of these are studied.
This subject is required by nearly all mathematics departments for a degree in mathematics, and most of them require two semesters of the subject. It is of interest especially to theorists and pure mathematicians.
It constitutes what most mathematicians consider a primary branch of mathematics. Many further mathematics topics are founded on this subject.