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diff --git a/documentation/research/math.md b/documentation/research/math.md new file mode 100644 index 000000000..72629ab74 --- /dev/null +++ b/documentation/research/math.md @@ -0,0 +1,298 @@ +# Statistics + +1. https://www.statisticsdonewrong.com/ + +# Topology + +1. [ELEMENTARY APPLIED TOPOLOGY](https://www.math.upenn.edu/~ghrist/notes.html) + +# Library + +1. https://github.com/ZacharyPatten/Towel + +# Polynomials + +1. https://en.wikipedia.org/wiki/Horner%27s_method + +# Chaos Theory + +1. http://ncase.me/attractors/ + +# Number Theory + +1. https://en.wikipedia.org/wiki/Dual_number +1. https://en.wikipedia.org/wiki/Division_algebra +1. [Division algebras](https://www.youtube.com/watch?v=3BZyds_KFWM&list=PLNxhIPHaOTRZMO1VjJcs7_3dgyJ2qU1yZ) +1. https://www.quantamagazine.org/the-octonion-math-that-could-underpin-physics-20180720 +1. http://illustratedtheoryofnumbers.com/ +1. [Topology of Numbers](http://pi.math.cornell.edu/~hatcher/TN/TNpage.html) + +# Quaternions + +1. [APPLICATION OF DUAL QUATERNIONS ON SELECTED PROBLEMS](https://otik.uk.zcu.cz/bitstream/11025/28563/1/phd_Application%20of%20dual%20quaternions%20on%20selected%20problems.pdf) +1. https://www.3dgep.com/understanding-quaternions/ + +# _Compendium of resources_ + +1. https://github.com/llSourcell/learn_math_fast +1. https://www.algorithm-archive.org/ +1. [3b1b featured creators #1](https://www.youtube.com/watch?v=VcgJro0sTiM) +1. [An infinite descent into pure mathematics](https://infinitedescent.xyz/) +1. https://hackernoon.com/be-a-better-programmer-with-these-40-mathematics-courses-d8ca48a2f8a2 +1. https://www.intmath.com/ +1. https://en.wikipedia.org/wiki/Graduate_Texts_in_Mathematics + +# Bézier curves + +1. https://cormullion.github.io/blog/2018/06/21/bezier.html +1. https://pomax.github.io/bezierinfo/ +1. https://99designs.com/blog/engineering/math-draw-vector-curves/ +1. https://medium.freecodecamp.org/nerding-out-with-bezier-curves-6e3c0bc48e2f +1. https://pomax.github.io/bezierinfo/#curvature +1. https://raphlinus.github.io/curves/2018/12/28/bezier-arclength.html +1. https://astiopin.github.io/2019/01/04/qbez-parabola.html +1. http://dlacko.org/blog/2016/10/19/approximating-bezier-curves-by-biarcs/ +1. https://bosker.wordpress.com/2013/11/13/beyond-bezier-curves/ + +# Number systems + +1. https://en.wikipedia.org/wiki/Negative_base + +# Discrete mathematics + +1. [Notes on Discrete Mathematics](http://www.cs.yale.edu/homes/aspnes/classes/202/notes.pdf) +1. [The system of integer functions, an efficient version of discrete mathematical analysis](https://arxiv.org/abs/1710.00676) +1. [Computing the Continuous Discretely: Integer-Point Enumeration in Polyhedra](http://math.sfsu.edu/beck/papers/ccd.pdf) +1. [Discrete Mathematics: An Open Introduction](http://discrete.openmathbooks.org/dmoi2/frontmatter.html) + +# Linear Algebra + +1. [Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares](https://web.stanford.edu/~boyd/vmls/vmls.pdf) +1. [Linear Algebra Done Wrong.](http://www.math.brown.edu/~treil/papers/LADW/LADW.html) +1. [Linear Algebra Done Right](http://linear.axler.net/) +1. [Down with Determinants!](http://www.axler.net/DwD.html) +1. https://github.com/jacobbogers/blasjs +1. https://graphicallinearalgebra.net/ +1. [Wild Linear Algebra](https://www.youtube.com/watch?v=yAb12PWrhV0&list=PLIljB45xT85BhzJ-oWNug1YtUjfWp1qAp &&& https://www.youtube.com/watch?v=nJdWFoliRnc&list=PLIljB45xT85DF5G-Hq0xPsVUnR5_wJRSw) +1. https://github.com/ferreiradaselva/mathc +1. http://www.fast.ai/2017/07/17/num-lin-alg/ +1. https://github.com/bluemathsoft/bm-linalg +1. [The Matrix Cookbook](https://www.math.uwaterloo.ca/~hwolkowi/matrixcookbook.pdf) +1. https://dhruvp.netlify.com/2018/12/31/matrices/ +1. https://www.nalgebra.org/ +1. http://immersivemath.com/ila/index.html +1. [Linear Logic and Linear Algebra](http://www.cs.bham.ac.uk/~drg/bll/steve.pdf) +1. https://www.math3ma.com/blog/matrices-probability-graphs +1. [Essence of linear algebra](https://www.youtube.com/watch?v=fNk_zzaMoSs&list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab) +1. https://www.dhruvonmath.com/2018/12/31/matrices/ +1. http://blog.ezyang.com/2019/05/a-short-note-about-functional-linear-maps/ +1. https://www.math3ma.com/blog/matrices-as-tensor-network-diagrams +1. [Convolution is outer product](https://arxiv.org/abs/1905.01289) +1. [Graphical Calculus for products and convolutions](https://arxiv.org/abs/1903.01366) + +# Category Theory + +1. [Abstract and Concrete Categories: The Joy of Cats](http://katmat.math.uni-bremen.de/acc/acc.pdf) +1. https://bartoszmilewski.com/ +1. [YOW! Lambda Jam 2018 - Mark Hopkins -All of Basic Category Theory](https://www.youtube.com/watch?v=9u1q3lH7VbE) +1. [Categorifying cardinal arithmetic](http://www.math.jhu.edu/~eriehl/arithmetic.pdf) +1. https://bartoszmilewski.com/2014/10/28/category-theory-for-programmers-the-preface/ +1. [Elements of ∞-Category Theory](http://www.math.jhu.edu/~eriehl/elements.pdf) +1. [Category Theory: A Gentle Introduction](https://www.logicmatters.net/resources/pdfs/GentleIntro.pdf) +1. [Applied Category Theory (@ MIT 2019)](https://www.youtube.com/playlist?list=PLhgq-BqyZ7i5lOqOqqRiS0U5SwTmPpHQ5) +1. https://jvns.ca/blog/2019/03/26/what-are-monoidal-categories/ +1. [Daniela Sfregola - A Pragmatic Introduction to Category Theories - Code Mesh 2017](https://www.youtube.com/watch?v=8XGFFMPHG0o) +1. [Seven Sketches in Compositionality: An Invitation to Applied Category Theory](http://xahlee.info/math/i/category_theory_brendan_fong_david_spivak_2018-03.pdf) + +# Direct Logic + +1. [Strong Types for Direct Logic](https://drive.google.com/file/d/1relKFB4aOMD2VZHM9qj3wWMXOq-q2AJr/view) + +# Geometric Algebra | Clifford Algebra + +1. https://slehar.wordpress.com/2014/03/18/clifford-algebra-a-visual-introduction/ +1. [Vectors and Beyond: Geometric Algebra and its Philosophical Significance](http://www.tara.tcd.ie/bitstream/handle/2262/61825/Vectors%20and%20Beyond%20as%20Printed.pdf?sequence=1&isAllowed=y) +1. [Let's remove Quaternions from every 3D Engine](http://marctenbosch.com/quaternions/) +1. [Geometric Algebra Playlist](https://www.youtube.com/playlist?list=PLLvlxwbzkr7igd6bL7959WWE7XInCCevt) +1. https://github.com/wolftype/versor +1. [Exploring Physics with Geometric Algebra, Book 1](http://peeterjoot.com/archives/math2015/gabookI.pdf) +1. [Joan Lasenby on Applications of Geometric Algebra in Engineering](https://www.youtube.com/watch?v=ikCIUzX9myY) +1. https://www.amazon.com/Geometric-Algebra-Computer-Graphics-Vince/dp/1846289963 +1. https://www.amazon.com/Geometric-Algebra-Computer-Science-Revised/dp/0123749425 +1. https://www.amazon.com/Space-Time-Algebra-David-Hestenes/dp/3319184121 +1. https://www.amazon.com/Introduction-Clifford-Algebras-Spinors/dp/0198782926 +1. https://gist.github.com/pervognsen/b204bf31af0809af078617af1609c8b8 +1. [Fundamentals of Grassmann Algebra](http://www.terathon.com/gdc12_lengyel.pdf) +1. https://github.com/chakravala/Grassmann.jl + +# Abstract Algebra + +1. https://gowers.wordpress.com/2011/11/20/normal-subgroups-and-quotient-groups/ +1. [Abstract Algebra: Theory and Applications](http://abstract.ups.edu/) +1. [Group Theory](http://birdtracks.eu/version9.0/GroupTheory.pdf) +1. [VISUAL GROUP THEORY](http://web.bentley.edu/empl/c/ncarter/vgt/index.html) +1. [THE GEOMETRY OF REFLECTION GROUPS](http://people.mpim-bonn.mpg.de/geordie/mpg.pdf) +1. https://kubuszok.com/2018/algebras-we-love/ +1. [Notes on Computational Group Theory](https://www.math.colostate.edu/~hulpke/CGT/cgtnotes.pdf) + +# Logic + +1. http://openlogicproject.org/ + +# Calculus + +1. [Calculus BLUE](https://www.youtube.com/watch?v=Jes5jwLl1q8&list=PL8erL0pXF3JYm7VaTdKDaWc8Q3FuP8Sa7) +1. [Extending the Algebraic Manipulability of Differentials](https://arxiv.org/abs/1801.09553) +1. https://en.wikipedia.org/wiki/Fractional_calculus +1. https://medium.com/@notaredpanda/fractional-calculus-48192f4e9c9f +1. [EXTENDING THE ALGEBRAIC MANIPULABILITYOF DIFFERENTIALS](http://online.watsci.org/abstract_pdf/2019v26/v26n3a-pdf/4.pdf) +1. [Finite Calculus: A Tutorial for Solving Nasty Sums](https://www.cs.purdue.edu/homes/dgleich/publications/Gleich%202005%20-%20finite%20calculus.pdf) +1. http://jliszka.github.io/2013/10/24/exact-numeric-nth-derivatives.html + +# Octonion + +1. http://math.ucr.edu/home/baez/octonions/ + +# Differential Geometry + +1. [differential geometry reconstructed: a unified systematic framework](http://www.geometry.org/tex/conc/dgstats.php) +1. [Differential geometry reconstructed: a unified systematic framework](http://www.topology.org/tex/conc/dg.html) + +# Information Theory + +1. [Functional Bits: Lambda Calculus based Algorithmic Information Theory](https://tromp.github.io/cl/LC.pdf) + +# Graph Theory + +1. [Graph-Based Algorithms for Boolean Function Manipulation](http://mtv.ece.ucsb.edu/courses/ece156B_14/randy_obdd86.pdf) +1. [better geometry through graph theory](http://ideolalia.com/2018/08/28/artifex.html) + +# Division by Zero + +1. https://www.hillelwayne.com/post/divide-by-zero/ +1. https://www.1dividedby0.com/ + +# Partial Fractions + +1. https://jaydaigle.net/blog/calculus/easier-partial-fractions/ + +# Non-commutative Algebra + +1. [An Invitation to Noncommutative Algebra](https://arxiv.org/abs/1808.03172) + +# Lambda Calculus + +1. https://medium.com/@maiavictor/the-abstract-calculus-fe8c46bcf39c + +# _Software Library_ + +1. https://github.com/arguiot/TheoremJS +1. https://github.com/arguiot/Descartes + +# Set Theory + +1. [Set Theory and Algebra in Computer Science: A Gentle Introduction to Mathematical Modeling](https://pdfs.semanticscholar.org/d106/6b6de601c1d7d5af25af3f7091bc7ad3ad51.pdf) + +# Uncertainty Theory + +1. http://faculty.math.tsinghua.edu.cn/~bliu/ut.pdf +1. [An Introduction to the Mathematics of Uncertainty: including Set Theory, Logic, Probability, Fuzzy Sets, Rough Sets, and Evidence Theory](https://www.creighton.edu/fileadmin/user/CCAS/programs/fuzzy_math/docs/MOU.pdf) + +# Computational Geometry + +1. [CMPT 813: Computational Geometry (Fall 2011)](http://www.cs.sfu.ca/~binay/813.2011/) +1. https://www.johndcook.com/blog/2018/09/26/polygon-area/ +1. http://s2geometry.io/devguide/s2cell_hierarchy.html +1. http://alienryderflex.com/polygon/ +1. https://libigl.github.io/ + +# Finitism + +1. ["REAL" ANALYSIS Is A DEGENERATE CASE of DISCRETE ANALYSIS](http://sites.math.rutgers.edu/~zeilberg/mamarim/mamarimPDF/real.pdf) + +# Linear programming + +1. https://white.ucc.asn.au/2018/05/28/Optimizing-your-diet-with-JuMP.html + +# Combinatorics + +1. [Combinatorial Algorithms](http://www2.denizyuret.com/bib/kreher/donald1999combinatorial/combinatorialA.pdf) + +# Vector + +1. https://www.researchgate.net/publication/327989714_Coordinate_Free_Vector_Algebra_in_R2 + +# Knot theory + +1. [The Knot Book](http://math.harvard.edu/~ctm/home/text/books/adams/knot_book/knot_book.pdf) + +# Axiom + +1. [INTRODUCTION TO AXIOMATIC REASONING](http://www.math.harvard.edu/~mazur/papers/Axiomatic.pdf) + +# Differential equations + +1. [ELEMENTARY DIFFERENTIAL EQUATIONS](http://ramanujan.math.trinity.edu/wtrench/texts/TRENCH_FREE_DIFFEQ_I.PDF) +1. [Lecture Notes on Difference Equations](http://people.math.aau.dk/~matarne/11-imat/notes2011a.pdf) + +# Algebraic geometry + +1. http://nautil.us/issue/69/patterns/the-math-that-takes-newton-into-the-quantum-world +1. [Algebraic Geometry](http://www.mathematik.uni-kl.de/~gathmann/class/alggeom-2014/main.pdf) +1. https://en.wikipedia.org/wiki/Superformula + +# Physics + +1. https://www.researchgate.net/publication/309533409_Beyond_Einstein_non-local_physics +1. https://www.theoretical-physics.com/dev/index.html + +# Spherical trigonometry + +1. https://en.wikipedia.org/wiki/Haversine_formula + +# **Temp Cache** + +1. https://marginalrevolution.com/marginalrevolution/2018/05/one-parameter-equation-can-exactly-fit-scatter-plot.html +1. https://plato.stanford.edu/entries/mathematics-inconsistent/ +1. http://immersivemath.com/ila/index.html?m=1 +1. https://stacks.math.columbia.edu/ +1. http://www.gutenberg.org/ebooks/17384 +1. http://illustratedtheoryofnumbers.com/ +1. [Construction of the Transreal Numbers and Algebraic Transfields](http://www.iaeng.org/IJAM/issues_v46/issue_1/IJAM_46_1_03.pdf) +1. http://simit-lang.org/language +1. http://wykobi.com/tutorial0.html +1. https://pron.github.io/computation-logic-algebra +1. https://github.com/rossant/awesome-math +1. [Algebra, Topology, Differential Calculus, and Optimization Theory For Computer Science and Engineering](https://www.cis.upenn.edu/~jean/math-basics.pdf) +1. http://math.chapman.edu/~jipsen/structures/doku.php/ +1. http://stacks.math.columbia.edu/browse +1. https://bitworking.org/news/ga/2d +1. https://www.youtube.com/watch?v=OmJ-4B-mS-Y +1. https://www.youtube.com/watch?v=ZihywtixUYo +1. https://www.youtube.com/user/njwildberger +1. http://www.hedonisticlearning.com/posts/category-theory-syntactically.html +1. https://www.youtube.com/watch?v=EA1FFtTGAfw&list=PLSekr_gm4hWLRNHB5-sbajyUzN5tLOZmx +1. https://www.artofproblemsolving.com/wiki/index.php/Modular_arithmetic/Introduction +1. [Mathematics for Computer Science](https://courses.csail.mit.edu/6.042/spring17/mcs.pdf) +1. http://www.paultaylor.eu/ASD/foufct/ +1. https://probablydance.com/2017/08/05/intuitive-quaternions/ +1. [Toward the Unification of Physics and Number Theory](http://www.quantumgravityresearch.org/wp-content/uploads/2017/02/Toward-the-Unification-of-Physics2-1.pdf) +1. https://jeremykun.com/2014/03/13/programming-with-finite-fields/ +1. https://courses.cs.washington.edu/courses/cse590b/13au/ +1. http://magma.maths.usyd.edu.au/magma/ +1. [A VIEW OF MATHEMATICS](http://www.alainconnes.org/docs/maths.pdf) +1. [Introduction to Tensor Analysis and the Calculus of Moving Surfaces](https://www.amazon.com/gp/product/1461478669) +1. https://en.wikipedia.org/wiki/Wheel_theory +1. http://wordsandbuttons.online/interactive_guide_to_homogeneous_coordinates.html +1. https://a-guide-to-the-purescript-numeric-hierarchy.readthedocs.io/en/latest/index.html +1. http://blog.wolfram.com/2016/12/22/the-semantic-representation-of-pure-mathematics/ +1. https://www.youtube.com/watch?v=psSyM1zp82k +1. [Viviane Pons - Experimental pure mathematics using Sage - PyCon 2015](https://www.youtube.com/watch?v=3LZiZKgVjaU) +1. http://www.sagemath.org/ +1. [The axioms of constructive geometry](https://www.sciencedirect.com/science/article/pii/0168007295000052) +1. https://www.quora.com/What-is-it-like-to-understand-advanced-mathematics-Does-it-feel-analogous-to-having-mastery-of-another-language-like-in-programming-or-linguistics/answers/873950?share=1 +1. http://www.tricki.org/tricki/map +1. https://maxow.github.io/posts/computational-geometry-set-operations-on-polytopes.html +1. http://blog.robertelder.org/fast-multiplication-using-fourier-transform/ +1. [Graphical Models in a Nutshell](https://ai.stanford.edu/~koller/Papers/Koller+al:SRL07.pdf) + |