# Index
[Mathematical object](Mathematical%20object.md)
[[Primitive notion]]
[[Uniqueness]]
## Sub-Indices
[[Algebra (index)]]
[[Analysis (index)]]
[Geometry (index)](Geometry%20(index).md)
[Numbers (index)](Numbers%20(index).md)
[[Sets (index)]]
[[Statistics and Probability (index)]]
# Basic concepts
The topic that make up the [index](Mathematical%20Foundations%20(Index).md#Index) for this page are underlying concepts in _mathematical logic._ These concepts are the machinery that make everything in our (multi)[uni]verse possible.
## Mathematical symbols
### Quantifiers
Here we list _quantifiers_ used in mathematics and there meanings in rough ordere starting from the most common ones:
* $\forall$ ("for all")
* $\exists$ ("there exists")
* $\exists !$ ("there exists a unique")
%%# German-English Glossary of terms
* _entwicklungskoeffizienten_ - numerical factor resulting from a [[Change of basis]].
* _Randbedingung_ - boundary condition
* _spaltenvektoren_ - column vectors.%%
---
# Bibliography
[Altland, A. von Delft, J. _Mathematics for Physicists_, Cambridge University Press, 2019](Altland,%20A.%20von%20Delft,%20J.%20Mathematics%20for%20Physicists,%20Cambridge%20University%20Press,%202019.md)
[Aluffi, P., _Algebra: Chapter 0_, American Mathematical Society, 2009](Aluffi,%20P.,%20Algebra%20Chapter%200,%20American%20Mathematical%20Society,%202009.md)
[Ashcroft N. W., Mermin, N. D., _Solid State Physics_, Harcourt College Publishers, 1976.](Ashcroft%20N.%20W.,%20Mermin,%20N.%20D.,%20Solid%20State%20Physics,%20Harcourt%20College%20Publishers,%201976..md)
[Axler, S., Down With Determinants, _American Mathematical Monthly 102_, 1995.](Axler,%20S.,%20Down%20With%20Determinants,%20American%20Mathematical%20Monthly%20102,%201995..md)
[Axler S., Gerhing F.W., Ribet K.A. _Linear Algebra Done Right_, Springer. 2nd edition, 1997](Axler%20S.,%20Gerhing%20F.W.,%20Ribet%20K.A.%20Linear%20Algebra%20Done%20Right,%20Springer,%202nd%20edition,%201997.md)
[Barrington, D. M., _A Mathematical Foundation for Computer Science_, Kendall Hunt Publishing Company, Preliminary edition, 2019.](Barrington,%20D.%20M.,%20A%20Mathematical%20Foundation%20for%20Computer%20Science,%20Kendall%20Hunt%20Publishing%20Company,%20Preliminary%20edition,%202019..md)
[Boas M., _Mathematical Methods in the Physical Sciences_. John Wiley and Sons, 3rd edition, 2006.](Boas%20M.,%20Mathematical%20Methods%20in%20the%20Physical%20Sciences.%20John%20Wiley%20and%20Sons,%203rd%20edition,%202006..md)
[Brigham E. O., _The Fast Fourier Transform and Its Applications_, Prentice Hall, 1988.](Brigham%20E.%20O.,%20The%20Fast%20Fourier%20Transform%20and%20Its%20Applications,%20Prentice%20Hall,%201988..md)
[Brown, J. W., Churchill R. V., _Complex Variables and Applications_, McGraw Hill, 8th edition, 2009.](Brown,%20J.%20W.,%20Churchill%20R.%20V.,%20Complex%20Variables%20and%20Applications,%20McGraw%20Hill,%208th%20edition,%202009..md)
[Cherney D., Denton T., and Waldron A., _Linear Algebra_, 2013](Cherney%20D.,%20Denton%20T.,%20and%20Waldron%20A.,%20Linear%20Algebra,%202013..md)
[Griffiths D. J., _Introduction to Quantum Mechanics_, Pearson Prentice Hall, 2nd edition, 2005.](Griffiths%20D.%20J.,%20Introduction%20to%20Quantum%20Mechanics,%20Pearson%20Prentice%20Hall,%202nd%20edition,%202005..md)
[Hall, B., _Lie Groups Lie Algebras and Representations_, Springer, 2nd edition, 2015.](Hall,%20B.,%20Lie%20Groups%20Lie%20Algebras%20and%20Representations,%20Springer,%202nd%20edition,%202015..md)
[joshphysics (https://physics.stackexchange.com/users/19976/joshphysics), Trace of an operator matrix (Quantum computation and quantum information), URL (version: 2015-04-24): https://physics.stackexchange.com/q/104155](joshphysics%20Trace%20of%20an%20operator%20matrix%20(Quantum%20computation%20and%20quantum%20information),%20URL%20(version%202015-04-24).md)
[Jech, T., _Set Theory_, Springer, 3rd edition, 2002.](Jech,%20T.,%20Set%20Theory,%20Springer,%203rd%20edition,%202002..md)
[Jänich K., _Topology_. Translated by Silvio Levy, Springer-Verlag 1984](Jänich%20K.,%20Topology.%20Translated%20by%20Silvio%20Levy,%20Springer-Verlag,%201984.md)
[Kuttler K., _Elementary Linear Algebra_, 2021.](Kuttler%20K.,%20Elementary%20Linear%20Algebra,%202021..md)
[Marcolli M., The notion of space in mathematics, general audience lecture, sponsored by Revolution Books, Berkeley, 2009.](Marcolli%20M.,%20The%20notion%20of%20space%20in%20mathematics,%20general%20audience%20lecture,%20sponsored%20by%20Revolution%20Books,%20Berkeley,%202009..md)
[McGreevy, John. A., Physics 212A Lecture Notes, Fall 2015.](McGreevy,%20John.%20A.,%20Physics%20212A%20Lecture%20Notes,%20Fall%202015..md)
[Munkres, J. R., _Topology_, Prentice Hall, 2nd Edition, 2000.](Munkres,%20J.%20R.,%20Topology,%20Prentice%20Hall,%202nd%20Edition,%202000..md)
[Nielson, M. A., Chuang, I. L. _Quantum Computation and Quantum Information_, Cambridge University Press, 2010](Nielsen,%20M.%20A.,%20Chuang,%20I.%20L.%20Quantum%20Computation%20and%20Quantum%20Information,%20Cambridge%20University%20Press,%202010.md)
Bartle R., Sherbert D., _Introduction to Real Analysis_
.pdf)
Gradshteyn I. S., Ryzhik I. M. _Table of Integrals, Series, and Products_
.pdf)
Hall, Brian. _Quantum Theory for Mathematicians_
%20-%20Quantum%20Theory%20for%20Mathematicians%20(2013,%20Springer-Verlag%20New%20York)%20-%20libgen.lc.pdf)
Horn R. A., Johnson C. A., _Matrix Analysis_
.pdf)
Fraleigh, J. B, Katz, V. J. _A First Course in Abstract Algebra_
.pdf)
Brychkov, Y. A., Prudnikov A. P. _Integral Transforms of Generalized Functions_
.pdf)
Engel, E., Dreizler, R. M., _Density Functional Theory - An Advanced Course_
%20-%20Density%20Functional%20Theory_%20An%20Advanced%20Course%20(2011,%20Springer-Verlag%20Berlin%20Heidelberg)%20-%20libgen.lc.pdf)
Dullemond K., Peeters, K. _Introduction to Tensor Calculus_
.pdf)
Hatcher. A. _Algebraic Topology_
Istratescu, V. I. _Inner Product Structures: Theory and Application_
%20-%20Inner%20Product%20Structures_%20Theory%20and%20Applications%20(1987,%20Springer%20Netherlands)%20-%20libgen.lc.pdf)
Bernstein D. S. _Matrix Mathematics: Theories, Facts and Formulas_
%20-%20libgen.lc.pdf)
Schollwöck, U. _Formalismus 1_, T2: Quantenmechanik Lecture Notes, Winter 2019/2020 (German)
Murayama H., MH2801: Complex Methods for the Sciences
Fomenko A. T., Mischenko A. S., _A Short Course in Differential Geometry_, Cambridge Scientific Publishers 2009
%20-%20libgen.lc.pdf)
Choquet Bruhat Y., Dewitt Morette C., _Analysis, Manifolds, and Physics Part 1: Basics_, Elsevier 1996
%20-%20libgen.lc.pdf)
Thorpe, J. A., _Elementary Topics in Differential Geometry_, Springer-Verlag 1979
%20-%20libgen.lc.pdf)
Schollwöck, U. Homework 0, Quantum Mechanics 1 (German) (2019/2020)
[Schollwöck, U. Homework 1, Quantum Mechanics 1 (German) (2019-2020)](Schollwöck,%20U.%20Homework%201,%20Quantum%20Mechanics%201%20(German)%20(2019-2020).md)
Streater R. F., Wightman A. S. _PCT Spin and Statistics and All That_, Princeton University Press, 2000
%20-%20libgen.lc.pdf)
Orloff, J., Lecture Notes, MIT 18.04 _Complex Variables with Applications_
Arken G. B., _Mathematical methods for Physicists_
%20-%20libgen.lc.pdf)
Halmos P. R. _Naive Set Theory_
%20-%20libgen.lc.pdf)
Suppes P. _Axiomatic Set Theory_
%20-%20libgen.lc.pdf)
Halmos, P.R., _Finite-Dimensional Vector Spaces,_ Springer (1974)
%20-%20libgen.lc.pdf)
Courant R., Hilbert D., _Methods of Mathematical Physics_ Vol. I,
%20-%20libgen.lc.pdf)
[von Neumann J., _Mathematical Foundations of Quantum Mechanics_. Translated by Robert T. Beyer. Princeton University Press, 2018.](von%20Neumann%20J.,%20Mathematical%20Foundations%20of%20Quantum%20Mechanics.%20Translated%20by%20Robert%20T.%20Beyer.%20Princeton%20University%20Press,%202018..md)
[Oppenheim A. V., Willsky A. S., Nawab S. H., _Signals and Systems_, Prentice Hall, 1996.](Oppenheim%20A.%20V.,%20Willsky%20A.%20S.,%20Nawab%20S.%20H.,%20Signals%20and%20Systems,%20Prentice%20Hall,%201996..md)
[Wasserman, L., _All of Statistics - A Concise Course in Statistical Inference_, Springer, 2003.](Wasserman,%20L.,%20All%20of%20Statistics%20-%20A%20Concise%20Course%20in%20Statistical%20Inference,%20Springer,%202003..md)
[Weisstein, Eric W. "Boxcar Function."" From MathWorld--A Wolfram Web Resource](Weisstein,%20Eric%20W.%20Boxcar%20Function.%20From%20MathWorld--A%20Wolfram%20Web%20Resource.md)
[Weisstein, Eric W. "Heaviside Step Function." From MathWorld--A Wolfram Web Resource.](Weisstein,%20Eric%20W.%20Heaviside%20Step%20Function.%20From%20MathWorld--A%20Wolfram%20Web%20Resource..md)
[Weisstein, Eric W. "Sign." From MathWorld--A Wolfram Web Resource](Weisstein,%20Eric%20W.%20Sign.%20From%20MathWorld--A%20Wolfram%20Web%20Resource.md)
[Weisstein, Eric W. "Space."" From MathWorld--A Wolfram Web Resource.](Weisstein,%20Eric%20W.%20Space.%20From%20MathWorld--A%20Wolfram%20Web%20Resource..md)
[Woit, Peter. _Quantum Theory, Groups and Representations: An Introduction_, Springer, 2017](Woit,%20Peter.%20Quantum%20Theory,%20Groups%20and%20Representations%20An%20Introduction,%20Springer,%202017.md)
#MathematicalFoundations
#MathematicalFoundations/Algebra/AbstractAlgebra
#MathematicalFoundations/Algebra/AbstractAlgebra/Algebras
#MathematicalFoundations/Algebra/AbstractAlgebra/GroupTheory
#MathematicalFoundations/Algebra/AbstractAlgebra/GroupTheory/Groups
#MathematicalFoundations/Algebra/AbstractAlgebra/RepresentationTheory
#MathematicalFoundations/Algebra/AbstractAlgebra/GroupTheory/Lie/LieGroups
#MathematicalFoundations/Algebra/AbstractAlgebra/GroupTheory/Lie/LieGroups/Algebras
#MathematicalFoundations/Algebra/AbstractAlgebra/LinearAlgebra
#MathematicalFoundations/Algebra/AbstractAlgebra/LinearAlgebra/VectorSpaces
#MathematicalFoundations/Algebra/AbstractAlgebra/LinearAlgebra/Operators
#MathematicalFoundations/Algebra/AbstractAlgebra/LinearAlgebra/Operators/Matrices
#MathematicalFoundations/Algebra/AbstractAlgebra/LinearAlgebra/MultiLinearAlgebra
#MathematicalFoundations/Algebra/AbstractAlgebra/LinearAlgebra/MultiLinearAlgebra/Tensors
#MathematicalFoundations/Analysis
#MathematicalFoundations/Analysis/Functions
#MathematicalFoundations/Analysis/Integrals
#MathematicalFoundations/Analysis/Functionals/Integrals/IntegralTransforms
#MathematicalFoundations/Analysis/GeneralizedFunctions
#MathematicalFoundations/Analysis/Functions/Functionals
#MathematicalFoundations/Analysis/Derivatives
#MathematicalFoundations/Analysis/ComplexAnalysis
#MathematicalFoundations/Analysis/ComplexAnalysis/Integrals
#MathematicalFoundations/Analysis/ComplexAnalysis/Functions
#MathematicalFoundations/Analysis/DifferentialEquations/OrdinaryDifferentialEquations
#MathematicalFoundations/Analysis/DifferentialEquations/PartialDifferentialEquations
#MathematicalFoundations/Analysis/FourierAnalysis
#MathematicalFoundations/Analysis/FourierAnalysis/Integrals
#MathematicalFoundations/Analysis/VectorAnalysis
#MathematicalFoundations/Analysis/VectorAnalysis/Derivatives
#MathematicalFoundations/Analysis/VectorAnalysis/Integrals
#MathematicalFoundations/Geometry
#MathematicalFoundations/Geometry/DifferentialGeometry
#MathematicalFoundations/Geometry/Topology
#MathematicalFoundations/SetTheory
#MathematicalFoundations/Numbers
#MathematicalFoundations/Numbers/Combinatorics
#MathematicalFoundations/StatisticsAndProbability/ProbabilityDistributions
#MathematicalFoundations/StatisticsAndProbability/ProbabilityDistributions/DiscreteProbabilityDistributions
#MathematicalFoundations/StatisticsAndProbability/ProbabilityDistributions/ContinuousProbabilityDistributions
#MathematicalFoundations/StatisticsAndProbability
#MathematicalFoundations/SignalProcessing
#Bibliography
#index