Giuseppe Peano

Giuseppe Peano (piˈɑːnoʊ; dʒuˈzɛppe peˈaːno; 27 August 1858 – 20 April 1932) was an Italian mathematician and glottologist. The author of over 200 books and papers, he was a founder of mathematical logic and set theory, to which he contributed much notation. The standard axiomatization of the natural numbers is named the Peano axioms in his honor. As part of this effort, he made key contributions to the modern rigorous and systematic treatment of the method of mathematical induction. He spent most of his career teaching mathematics at the University of Turin. He also wrote an international auxiliary language, Latino sine flexione ("Latin without inflections"), which is a simplified version of Classical Latin. Most of his books and papers are in Latino sine flexione, others are in Italian. Peano was born and raised on a farm at Spinetta, a hamlet now belonging to Cuneo, Piedmont, Italy. He attended the Liceo classico Cavour in Turin, and enrolled at the University of Turin in 1876, graduating in 1880 with high honors, after which the University employed him to assist first Enrico D'Ovidio, and then Angelo Genocchi, the Chair of calculus. Due to Genocchi's poor health, Peano took over the teaching of calculus course within two years. His first major work, a textbook on calculus, was published in 1884 and was credited to Genocchi. A few years later, Peano published his first book dealing with mathematical logic. Here the modern symbols for the union and intersection of sets appeared for the first time. In 1887, Peano married Carola Crosio, the daughter of the Turin-based painter Luigi Crosio, known for painting the Refugium Peccatorum Madonna. In 1886, he began teaching concurrently at the Royal Military Academy, and was promoted to Professor First Class in 1889. In that year he published the Peano axioms, a formal foundation for the collection of natural numbers. The next year, the University of Turin also granted him his full professorship.

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MATH-483: Gödel and recursivity

Gödel incompleteness theorems and mathematical foundations of computer science

Differential Equations: Part 2

Explores Peano's existence theorem, compactness properties, uniqueness of solutions, Ascoli-Arzela theorem, and ripeness in differential equations.

Vector Spaces and Convergence

Covers vector spaces, compact sets, convergence, continuity, and uniqueness theorems.

Giuseppe Peano

Mathematics

Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them.

Set theory

Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly concerned with those that are relevant to mathematics as a whole. The modern study of set theory was initiated by the German mathematicians Richard Dedekind and Georg Cantor in the 1870s. In particular, Georg Cantor is commonly considered the founder of set theory.