Mathematical logic

Classical mathematics

In the foundations of mathematics, classical mathematics refers generally to the mainstream approach to mathematics, which is based on classical logic and ZFC set theory. It stands in contrast to other types of mathematics such as constructive mathematics or predicative mathematics. In practice, the most common non-classical systems are used in constructive mathematics. Classical mathematics is sometimes attacked on philosophical grounds, due to constructivist and other objections to the logic, set theory, etc., chosen as its foundations, such as have been expressed by L. E. J. Brouwer. Almost all mathematics, however, is done in the classical tradition, or in ways compatible with it. Defenders of classical mathematics, such as David Hilbert, have argued that it is easier to work in, and is most fruitful; although they acknowledge non-classical mathematics has at times led to fruitful results that classical mathematics could not (or could not so easily) attain, they argue that on the whole, it is the other way round. (Wikipedia).

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Introduction to Classical Physics

Physics is the grandaddy of the sciences! When those ancient dudes in togas were philosophizing about the way the universe works, they were setting the stage for what we now know of as physics, even though it didn't really get going until Galileo and Newton. Why should we study physics? Wh

From playlist Classical Physics

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Classical Mechanics | Lecture 1

(September 26, 2011) Leonard Susskind gives a brief introduction to the mathematics behind physics including the addition and multiplication of vectors as well as velocity and acceleration in terms of particles. This course is the beginning of a six course sequence that explores the theor

From playlist Lecture Collection | Classical Mechanics (Fall 2011)

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Classical Mechanics | Lecture 3

(October 10, 2011) Leonard Susskind discusses lagrangian functions as they relate to coordinate systems and forces in a system. This course is the beginning of a six course sequence that explores the theoretical foundations of modern physics. Topics in the series include classical mechani

From playlist Lecture Collection | Classical Mechanics (Fall 2011)

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Classical Mechanics | Lecture 7

(November 7, 2011) Leonard Susskind discusses the some of the basic laws and ideas of modern physics. In this lecture, he focuses on Liouville's Theorem, which he describes as one of the basis for Hamiltonian mechanics. He works to prove the reversibility of classical mechanics. This cour

From playlist Lecture Collection | Classical Mechanics (Fall 2011)

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Classical Mechanics | Lecture 5

(October 24, 2011) Leonard Susskind discusses different particle transformations as well as how to represent and analyze them using tools like the LaGrangian. This course is the beginning of a six course sequence that explores the theoretical foundations of modern physics. Topics in the s

From playlist Lecture Collection | Classical Mechanics (Fall 2011)

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Classical Mechanics | Lecture 10

(November 28, 2011) Leonard Susskind wraps up the lecture series by finishing his talk on particles and both electric and magnetic fields and how they relate to physics. This course is the beginning of a six course sequence that explores the theoretical foundations of modern physics. Topi

From playlist Lecture Collection | Classical Mechanics (Fall 2011)

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How to Get Classical Physics from Quantum Mechanics

We tend to think of Classical Physics as straightforward and intuitive and Quantum Mechanics as difficult and conceptually challenging. However, this is not always the case! In classical mechanics, a standard technique for finding the evolution equations for a system is the method of least

From playlist Quantum Mechanics

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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

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Classical Mechanics | Lecture 4

(October 17, 2011) Leonard Susskind discusses the some of the basic laws and ideas of modern physics. In this lecture, he focuses symmetry and conservation laws, including the principle of least action and Lagrangian methods. This course is the beginning of a six course sequence that expl

From playlist Lecture Collection | Classical Mechanics (Fall 2011)

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Five Stages of Accepting Constructive Mathematics - Andrej Bauer

Andrej Bauer University of Ljubljana, Slovenia; Member, School of Mathematics March 18, 2013 Discussions about constructive mathematics are usually derailed by philosophical opinions and meta-mathematics. But how does it actually feel to do constructive mathematics? A famous mathematician

From playlist Mathematics

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SHM - 16/01/15 - Constructivismes en mathématiques - Henri Lombardi

Henri Lombardi (LMB, Université de Franche-Comté), « Foundations of Constructive Analysis, Bishop, 1967 : une refondation des mathématiques, constructive, minimaliste et révolutionnaire »

From playlist Les constructivismes mathématiques - Séminaire d'Histoire des Mathématiques

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Quantum Field Theory as the Language of Physics by Nathan Seiberg

ICTS at Ten ORGANIZERS: Rajesh Gopakumar and Spenta R. Wadia DATE: 04 January 2018 to 06 January 2018 VENUE: International Centre for Theoretical Sciences, Bengaluru This is the tenth year of ICTS-TIFR since it came into existence on 2nd August 2007. ICTS has now grown to have more tha

From playlist ICTS at Ten

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Lecture 1 | The Theoretical Minimum

(January 9, 2012) Leonard Susskind provides an introduction to quantum mechanics. Stanford University: http://www.stanford.edu/ Stanford Continuing Studies: http://continuingstudies.stanford.edu/ Stanford University Channel on YouTube: http://www.youtube.com/stanford

From playlist Lecture Collection | The Theoretical Minimum: Quantum Mechanics

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Why Momentum in Quantum Physics is Complex

In classical physics, we are used to calculating an object's momentum by multiplying its mass by its velocity. But how do we deal with momentum in Quantum Mechanics, where we commonly deal with wave functions? A wave function is a mathematical function that contains all the information we

From playlist Quantum Physics by Parth G

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Homotopy Type Theory: what can logic do for homotopy theory? - Peter Lumsdaine

Peter Lumsdaine Homotopy Type Theory: what can logic do for homotopy theory? Institute for Advanced Study; Member, School of Mathematics October 4, 2013 For more videos, visit http://video.ias.edu

From playlist Mathematics

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Olivia Caramello - 3/4 Introduction to Grothendieck toposes

This course provides an introduction to the theory of Grothendieck toposes from a meta-mathematical point of view. It presents the main classical approaches to the subject (namely, toposes as generalized spaces, toposes as mathematical universes and toposes as classifiers of models of firs

From playlist Olivia Caramello - Introduction to Grothendieck toposes

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Exact instanton summation in O(3) non-linear sigma model by Sergei Lukyanov

PROGRAM: INTEGRABLE SYSTEMS IN MATHEMATICS, CONDENSED MATTER AND STATISTICAL PHYSICS ORGANIZERS: Alexander Abanov, Rukmini Dey, Fabian Essler, Manas Kulkarni, Joel Moore, Vishal Vasan and Paul Wiegmann DATE : 16 July 2018 to 10 August 2018 VENUE: Ramanujan Lecture Hall, ICTS Bangalor

From playlist Integrable​ ​systems​ ​in​ ​Mathematics,​ ​Condensed​ ​Matter​ ​and​ ​Statistical​ ​Physics

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Equilibrium spatio-temporal correlations of conserved quantities....by Abhishek Dhar

PROGRAM: INTEGRABLE SYSTEMS IN MATHEMATICS, CONDENSED MATTER AND STATISTICAL PHYSICS ORGANIZERS: Alexander Abanov, Rukmini Dey, Fabian Essler, Manas Kulkarni, Joel Moore, Vishal Vasan and Paul Wiegmann DATE : 16 July 2018 to 10 August 2018 VENUE: Ramanujan Lecture Hall, ICTS Bangalore

From playlist Integrable​ ​systems​ ​in​ ​Mathematics,​ ​Condensed​ ​Matter​ ​and​ ​Statistical​ ​Physics

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Quantum Mechanics 1.1: Introduction

In this video I provide some motivation behind the development of quantum mechanics, kicking off a new series on everything you've been wondering about quantum mechanics! Twitter: https://twitter.com/SciencePlease_

From playlist Quantum Mechanics

Related pages

David Hilbert | Mathematics | L. E. J. Brouwer | Foundations of mathematics | Intuitionism | Classical logic | Finitism | Ultrafinitism