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Presentation videos : Why learn Physics by yourself.

This site in other languages : French − Russian

About html display of symbols / wrong links

(I need help for several tasks : some only require to be a good internet user ; for others I need translators. Please write me if you can help either for free or as a small job - but do not expect US or west european salaries, thanks)

1.1. Introduction
to the foundation of mathematics

1.2. Variables, sets, functions and operations

1.3. Form of theories: notions, objects and meta-objects

1.4. Structures of mathematical systems

1.5. Expressions and definable structures

1.6. Connectives

1.7. Classes in set theory

1.8. Bound variables in set theory

1.9. Quantifiers

1.10. First axioms of set theory

1.11. Set generation principle

1.2. Variables, sets, functions and operations

1.3. Form of theories: notions, objects and meta-objects

1.4. Structures of mathematical systems

1.5. Expressions and definable structures

1.6. Connectives

1.7. Classes in set theory

1.8. Bound variables in set theory

1.9. Quantifiers

1.10. First axioms of set theory

1.11. Set generation principle

2.1. Tuples, families

2.2. Boolean operators on families of sets

2.3. Products, graphs and composition

2.4. Uniqueness quantifier

2.5. The powerset axiom

2.6. Injectivity and inversion

2.7. Properties of binary relations on a set ; ordered sets

2.8. Canonical bijections

2.9. Equivalence relations and partitions

2.10. Axiom of choice

2.11. Galois connections

2.2. Boolean operators on families of sets

2.3. Products, graphs and composition

2.4. Uniqueness quantifier

2.5. The powerset axiom

2.6. Injectivity and inversion

2.7. Properties of binary relations on a set ; ordered sets

2.8. Canonical bijections

2.9. Equivalence relations and partitions

2.10. Axiom of choice

2.11. Galois connections

3.1. Mathematical theories and the Completeness Theorem

3.2. How mathematical theories develop

3.3. Morphisms of relational systems and concrete categories

3.4. Algebras

3.5. Products of systems

3.6. Integers and recursion (new, May 2015)

3.7. Second-order theories (updated, May 2015)

3.8. Formalizations of Arithmetic

3.9. Non-standard models of Arithmetic

3.10. The Incompleteness Theorem

More philosophical notes : About the powerset axiom

3.2. How mathematical theories develop

3.3. Morphisms of relational systems and concrete categories

3.4. Algebras

3.5. Products of systems

3.6. Integers and recursion (new, May 2015)

3.7. Second-order theories (updated, May 2015)

3.8. Formalizations of Arithmetic

3.9. Non-standard models of Arithmetic

3.10. The Incompleteness Theorem

More philosophical notes : About the powerset axiom

(List of texts on algebra)

The Galois
connection between structures and permutations (Automorphisms, Invariants)

Introduction to categories

Monoids and groups

Actions of monoids and groups

Introduction to the foundations of geometry

Introduction to categories

Monoids and groups

Actions of monoids and groups

Introduction to the foundations of geometry

What is geometry

Structures and permutations in the plane

Affine geometry

Beyond affine geometry

Euclidean geometry

The completeness of first-order geometry

Structures and permutations in the plane

Affine geometry

Beyond affine geometry

Euclidean geometry

The completeness of first-order geometry

General formalization tools (draft)

Polymorphisms and invariants

Relational clones

(To be continued - see below drafts)

Polymorphisms and invariants

Relational clones

(To be continued - see below drafts)

Monotone Galois connections (adjunctions)

Upper and lower bounds, infimum and supremum

Complete lattices

Fixed point theorem

Transport of closure

Preorder generated by a relation

Finite sets

Generated equivalence relations, and more

Well-founded relations

Dimensional analysis : Quantities and real numbers - incomplete draft text of a video lecture I wish to make on 1-dimensional geometry

Introduction to inversive geometry

Duality systems and theories

Affine geometry

Introduction to topology

Vector spaces in duality

Axiomatic expressions of Euclidean and Non-Euclidean geometries

Cardinals

Well-orderings and ordinals (with an alternative to Zorn's Lemma).

Introduction to inversive geometry

Duality systems and theories

Affine geometry

Introduction to topology

Vector spaces in duality

Axiomatic expressions of Euclidean and Non-Euclidean geometries

Cardinals

Well-orderings and ordinals (with an alternative to Zorn's Lemma).

Pythagorean
triples (triples of integers (a,b,c) forming the sides of a
right triangle, such as (3,4,5))

Resolution of
cubic equations

Philosophical
proof of consistency of the Zermelo-Fraenkel axiomatic system
(Requires to have read Part 1 with philosophical aspects)

I wrote large parts of the Wikipedia article on Foundations
of mathematics (September 2012 - because until then,
other authors focused on the more professional and technical
article Mathematical
logic instead; the Foundations of mathematics article is
more introductory, historical and philosophical) and improved
the one on the completeness
theorem.

Research teams and centers : Europe - North America - Other

Publications
- Blogs - Organizations
- Mailing
lists - Software
- Other

Criticism of the academic system

Criticism of the academic system

List of
physics theories that will progressively link to other
pages presenting each theory. The main presentations of
physics theories already available here are

- Geometric expression of Markov processes
- Quantum physics : quantum states and measurements - notes on the articulations between quantum and classical physics (wave/particle duality, conservation of energy)
- Interpretations of quantum physics
- Problems with the de Broglie-Bohm interpretation
- The Many-worlds interpretation
- The Mind makes collapse interpretation
- Notes on decoherence and interpretations of quantum physics
- A mind/mathematics dualistic foundation of physical reality written for the fqxi essay contest, where the "community" of participants are unfortunately idiots, making their average mutual ratings senseless
- Special
Relativity Theory (still incomplete, will need more developments on geometry; relativistic mechanics not written yet)

- Tensors.
- General relativity:

An
exploration of physics by dimensional analysis : telling a
lot of fundamental physics and the amplitudes of diverse effects
mainly by multiplying quantities. Some sections have been
moved to separate pages:

The speed of light and astronomical distancesSolved physics problems (for now just one thing about gravitation)

The energy of nuclear reactions ; The radius of nuclei

Electromagnetism

The gravitational constant

Effects of General Relativity

The parameters of the atomic structure

The compressibility of condensed matter

The speed of the sound in condensed matter

Temperature(to be continued)

On the world's failures to steer itself properly : a very long analysis of the stakes of the future and how they are often improperly considered in essays of 2014's contest "How should humanity steer the future", with a few sections in separate pages: Links against psychiatry