①-based Infinity Computing: A New Computational Paradigm

Course description

①-based Infinity Computing: A New Computational Paradigm is a MOOC designed to provide university and high school students, PhD students, and professors with a concise introduction to the main ideas presented in the book Grossone Infinity Computing: A New Computational Paradigm Using Numerical Infinities and Infinitesimals, authored by Professor Sergeyev.

The course follows a progressive path from classical paradoxes and the limitations of traditional numeral systems to the Grossone methodology, positional numerals with infinite base, computability, and selected numerical applications. Each video identifies a central question, introduces the relevant concepts, and illustrates them through carefully selected examples.

Designed primarily for:

• university and high school students;

• PhD students;

• professors.

The course requires knowledge of English. Modules 1 and 2 require mathematics knowledge corresponding to the second-to-last year of high school. Module 3 requires knowledge corresponding to the first courses in mathematical analysis and computer science, while Module 4 requires basic knowledge in numerical analysis and optimization.

The MOOC develops knowledge and skills that enable learners to understand why infinity creates conceptual and computational difficulties in mathematics and science, explore classical paradoxes, distinguish mathematical objects from the numeral systems used to represent them, and understand both the methodological foundations and numerical applications of the Infinity Computing paradigm.

Learners will also be able to:

• explain the basic properties of the Infinite Unit Axiom and the numeral ① (Grossone);

• illustrate how infinite sets are measured within the proposed framework;

• interpret positional numerals containing finite, infinite, and infinitesimal parts;

• perform arithmetic operations with grossone-based infinite and infinitesimal numbers;

• understand the transition from infinite series to families of infinite sums and how the grossone-based paradigm addresses classical paradoxes;

• describe the new perspective on diagonalization and computability offered by this computational paradigm;

• identify representative applications of Infinity Computing in numerical analysis and optimization.

Objectives of the MOOC:

• provide a concise introduction to the main ideas of the Infinity Computing paradigm;

• explore the conceptual difficulties associated with infinity and the limitations of traditional numeral systems;

• introduce the Grossone-based methodology and positional numerals with infinite base;

• examine computability and infinite series from the grossone-based numerical perspective;

• present selected applications in numerical analysis and optimization;

• open new perspectives for students and professors interested in next-generation supercomputing, innovative numerical methods, and the foundations of mathematics and computer science.

Explore infinity from a new computational perspective and discover new horizons in mathematics and computer science.

Enroll now!

Author

Prof. Yaroslav D. Sergeyev

Yaroslav D. Sergeyev is Distinguished Professor at the University of Calabria, Italy, and Head of the Numerical Calculus Laboratory.

He is Editor-in-Chief of Springer’s journal Operations Research Forum.

He is the founder of the field of Infinity Computing and conducts research in global optimization, numerical and scientific computing, and the philosophy of computation.

He received numerous scientific awards including the International Constantin Carathéodory Prize, one of his most recent international research recognitions.