Metalogic | Formal languages | Formal systems
A formal system is an abstract structure used for inferring theorems from axioms according to a set of rules. These rules, which are used for carrying out the inference of theorems from axioms, are the logical calculus of the formal system. A formal system is essentially an "axiomatic system". In 1921, David Hilbert proposed to use such a system as the foundation for the knowledge in mathematics. A formal system may represent a well-defined system of abstract thought. The term formalism is sometimes a rough synonym for formal system, but it also refers to a given style of notation, for example, Paul Dirac's bra–ket notation. (Wikipedia).
Reactive Systems use a high-performance software architecture. They are resilient under stress, and their reactive design allows them to scale elastically to meet demand. The reactive design approach allows the creation of more complex, more flexible systems and forms the basis for some of
From playlist Software Engineering
Quantum Mechanics -- a Primer for Mathematicians
Juerg Frohlich ETH Zurich; Member, School of Mathematics, IAS December 3, 2012 A general algebraic formalism for the mathematical modeling of physical systems is sketched. This formalism is sufficiently general to encompass classical and quantum-mechanical models. It is then explained in w
From playlist Mathematics
There is a great deal of confusion about the term 'grammar'. Most people associate with it a book written about a language. In fact, there are various manifestations of this traditional term: presecriptive, descriptive and reference grammar. In theoretical linguistics, grammars are theory
From playlist VLC107 - Syntax: Part II
Linear Algebra - Lecture 10 - Homogeneous Linear Systems
In this lecture, we define "homogeneous" linear systems, and discuss how to find the solutions to these systems in parametric vector form.
From playlist Linear Algebra Lectures
Type Systems - Vladimir Voevodsky
Vladimir Voevodsky Institute for Advanced Study November 21, 2012
From playlist Mathematics
Writing a Formal Business Letter
In this video, you’ll learn more about writing a formal business letter. Visit https://www.gcflearnfree.org/business-communication/how-to-write-a-formal-business-letter/1/ for our text-based lesson. This video includes information on: • The format and structure of business letters • Uses
From playlist Communication in the Workplace
Formal Definition of a Function using the Cartesian Product
Learning Objectives: In this video we give a formal definition of a function, one of the most foundation concepts in mathematics. We build this definition out of set theory. **************************************************** YOUR TURN! Learning math requires more than just watching vid
From playlist Discrete Math (Full Course: Sets, Logic, Proofs, Probability, Graph Theory, etc)
Operating system for beginners || Operating system basics
An operating system (OS) is system software that manages computer hardware, software resources, and provides common services for computer programs. Time-sharing #operating_systems schedule tasks for efficient use of the system and may also include accounting software for cost allocation o
From playlist Operating System
Mathematical modeling of evolving systems
Discover the multidisciplinary nature of the dynamical principles at the core of complexity science. COURSE NUMBER: CAS 522 COURSE TITLE: Dynamical Systems LEVEL: Graduate SCHOOL: School of Complex Adaptive Systems INSTRUCTOR: Enrico Borriello MODE: Online SEMESTER: Fall 2021 SESSION:
From playlist What is complex systems science?
Séminaire Bourbaki - 21/06/2014 - 3/4 - Thomas C. HALES
Developments in formal proofs A for mal proof is a proof that can be read and verified by computer, directly from the fundamental rules of logic and the foundational axioms of mathematics. The technology behind for mal proofs has been under development for decades and grew out of efforts i
From playlist Bourbaki - 21 juin 2014
Fabian Immler, Carnegie Mellon University Formal mathematics and a proof of chaos Formal proof has been successfully applied to the verification of hardware and software systems. But formal proof is also applicable to mathematics: proofs can be checked with ultimate rigor and one can bui
From playlist Fall 2019 Kolchin Seminar in Differential Algebra
Séminaire Bourbaki - 21/06/2014 - 4/4 - Thierry COQUAND
Théorie des types dépendants et axiome d'univalence Cet exposé sera une introduction à la théorie des types dépendants et à l'axiome d'univalence. Cette théorie est une alternative à la théorie des ensembles comme fondement des mathématiques. Guidé par une interprétation d'un type comme u
From playlist Bourbaki - 21 juin 2014
Foundations of Mathematics and Homotopy Theory - Vladimir Voevodsky
Vladimir Voevodsky Institute for Advanced Study March 22, 2006 More videos on http://video.ias.edu
From playlist Mathematics
Institute for Advanced Study November 17, 2006 Karl Sigmund (University of Vienna) Solomon Feferman (Stanford University) More videos on http://video.ias.edu
From playlist Kurt Gödel Centenary
3 - Kick-off afternoon : Thomas Hales, Formalizing the proof of the Kepler Conjecture
Thomas Hales (University of Pittsburgh): Formalizing the proof of the Kepler Conjecture
From playlist T2-2014 : Semantics of proofs and certified mathematics
What if Current Foundations of Mathematics are Inconsistent? | Vladimir Voevodsky
Vladimir Voevodsky, Professor, School of Mathematics, Institute for Advanced Study http://www.ias.edu/people/faculty-and-emeriti/voevodsky In this lecture, Professor Vladimir Voevodsky begins with Gödel's second incompleteness theorem to discuss the possibility that the formal theory of f
From playlist Mathematics
First Author Interview: AI & formal math (Formal Mathematics Statement Curriculum Learning)
#openai #math #imo This is an interview with Stanislas Polu, research engineer at OpenAI and first author of the paper "Formal Mathematics Statement Curriculum Learning". Watch the paper review here: https://youtu.be/lvYVuOmUVs8 OUTLINE: 0:00 - Intro 2:00 - How do you explain the big pub
From playlist Applications of ML
Live CEOing Ep 28: Proofs in the Wolfram Language
Watch Stephen Wolfram and teams of developers in a live, working, language design meeting. This episode is about Proofs in the Wolfram Language.
From playlist Behind the Scenes in Real-Life Software Design
Univalent Foundations Seminar - Steve Awodey
Steve Awodey Carnegie Mellon University; Member, School of Mathematics November 19, 2012 For more videos, visit http://video.ias.edu
From playlist Mathematics