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stuhlmueller + math   64

Tricki
"A Wiki-style site [..] intended to develop into a large store of useful mathematical problem-solving technique."
math  science  collab 
december 2011 by stuhlmueller
sympy
Open source Python library for symbolic mathematics.
python  math  algebra 
october 2011 by stuhlmueller
Video tutorials for the Coq proof assistant
Demonstrates how to use Coq in Emacs for machine-assisted theorem proving.
coq  math  logic  theorem-proving 
february 2011 by stuhlmueller
The capacity to be alone
A passage from Grothendieck’s memoir.
math  inspiration 
july 2010 by stuhlmueller
Topology via logic
Self-contained introduction to topology, approaching it as a way to study the logic of finite observations.
topology  math  compsci 
may 2010 by stuhlmueller
Information, Physics and Computation
Draft of an introduction to the research field at the interface between statistical physics, theretical computer science/discrete mathematics, and coding/information theory.
math  physics  information  compsci  book 
july 2009 by stuhlmueller
Metamath
Mathematics developed in complete detail from first principles, with absolute rigor (computer verified proofs).
math  logic 
july 2009 by stuhlmueller
Structure and Interpretation of Classical Mechanics
SICP style book on classical mechanics by Gerry Sussman and Jack Wisdom.
math  physics  programming  mechanics 
june 2009 by stuhlmueller
Mathematical undecidability and quantum randomness
"We demonstrate that the states of elementary quantum systems are capable of encoding mathematical axioms and show that quantum measurements are capable of revealing whether a given proposition is decidable or not within the axiomatic system."
math  quantum  physics 
december 2008 by stuhlmueller
Why Sets? (pdf)
Sets play a key role in foundations of mathematics and computer science. Why?
math  compsci  settheory 
november 2008 by stuhlmueller
Non-Uniform Random Variate Generation
Describes how to generate samples from different types of probability distributions.
math  probability  sampling 
october 2008 by stuhlmueller
Dirichlet Processes: Tutorial and Practical Course
Introduces Dirichlet processes and describe different representations of Dirichlet processes, including the Blackwell-MacQueen urn scheme, Chinese restaurant processes, and the stick-breaking construction.
dirichlet  bayes  math  video 
october 2008 by stuhlmueller
Advice to Younger Mathematicians (pdf)
The final chapter of the Princeton Companion to Mathematics.
math  research  advice 
september 2008 by stuhlmueller
Dempster-Shafer theory
A generalization of the Bayesian theory of subjective probability which does not require exact probabilities for each question of interest; can yield answers which contradict those arrived at using probability theory.
probabilitytheory  math  bayes 
september 2008 by stuhlmueller
Applied Statistics PhD Comprehensive Exam
"It should in theory be doable by someone with just a good introductory undergraduate course in statistics, including multiple regression."
statistics  math 
august 2008 by stuhlmueller
A Not-so-Characteristic Equation: the Art of Linear Algebra
Because most of math is just changing representations, visualization matters.
math  algebra  linear 
july 2008 by stuhlmueller
Fermat's Last Theorem
"The purpose of this blog is to present the story behind Fermat's Last Theorem and Wiles' proof in a way accessible to the mathematical amateur." — Start with "The Story So Far".
math  fermat  algebra  blog 
june 2008 by stuhlmueller
Proof Mining
The analysis of formalized proofs to obtain explicit bounds and convergence rates from proofs that, when expressed in natural language, appear to be nonconstructive.
proof  math  logic 
june 2008 by stuhlmueller
Inexact Graph Matching
Given a large (e.g. social or conceptual) network, applying graph matching to identify common structures (=subgraphs) might give us new vocabulary to talk about such networks.
graph  research  compsci  math 
may 2008 by stuhlmueller
Computational Category Theory
An implementation of concepts and constructions from category theory in the functional programming language Standard ML.
math  compsci  category  theory  ebook 
april 2008 by stuhlmueller
Wang Tile
"It is possible to translate any Turing machine into a set of Wang tiles, such that the Wang tiles can tile the plane if and only if the Turing machine will never halt. [..] In a sense, Wang tiles have computational power equivalent to that of a TM."
math  compsci  wang  egan  wikipedia 
april 2008 by stuhlmueller
Sometimes all functions are continuous
For functions from N to N, all reasonable models of computation are equivalent to Turing machines. At higher types, questions of representation become important, and it does matter which model of computation is used.
math  programming  compsci 
february 2008 by stuhlmueller
Interesting higher-order functionals
"Functionals are higer-order functions, i.e., functions that take functions as arguments or return them as results. [..] Understanding every next level of functionals requires new concepts and fresh ideas. We have not come very far."
math  programming  compsci 
february 2008 by stuhlmueller
Logical Systems - Peter Suber
Class covering different systems of logic, set theory, basic meta-math and recursive function theory.
logic  philosophy  math  course 
december 2007 by stuhlmueller
Infinite Ink: The Continuum Hypothesis
"There is no set whose size is strictly between that of the integers and that of the real numbers."
math  infinity  settheory  complexity 
november 2007 by stuhlmueller
American Mathematical Society: Feature Column
Self-contained math columns on image compression, quantum computing, cryptography, game theory and other fun topics.
math  essays 
september 2007 by stuhlmueller
Analytic Combinatorics
Tries to provide a unified treatment of analytic methods in combinatorics. Might be important to know how to create "averages" of combinatorially exploding things.
math  combinatorics  algorithms  compsci 
september 2007 by stuhlmueller
Open Problem Garden
A collection of unsolved problems in mathematics.
math  research  problems 
july 2007 by stuhlmueller
Quantum Theory From Five Reasonable Axioms (Lucien Hardy)
The first four axioms are consistent with both quantum theory and classical probability theory. Axiom 5 (which requires that there exists continuous reversible transformations between pure states) rules out classical probability theory.
quantum  physics  math  probabilitytheory 
may 2007 by stuhlmueller
The Unreasonable Effectiveness of Mathematics in the Natural Sciences
If you recall that modern science is only about 400 years old, and that there have been from 3 to 5 generations per century, then there have been at most 20 generations since Newton and Galileo.
philosophy  math  science 
may 2007 by stuhlmueller
A map of mathematics
Diagram showing common mathematical structures and their relationships. From Max Tegmark's paper "Is 'the theory of everything' merely the ultimate ensemble theory?".
math  overview  tegmark  image 
april 2007 by stuhlmueller
The Nature of Code
Syllabus and notes from an ITP class called The Nature of Code, which focuses on "the programming strategies and techniques behind computer simulations of natural systems". Lots of good notes and Processing code examples.
programming  processing  compsci  math 
march 2007 by stuhlmueller
The Mizar Project
The Mizar project started around 1973 as an attempt to reconstruct mathematical language in a computer-oriented environment. The most important activity has been the development of a database for mathematics.
math  logic  programming  compsci  database 
march 2007 by stuhlmueller
Elegant Lisp Programs (Chaitin)
Call a program "elegant" if no smaller program has the same output. I.e., a LISP S-expression is defined to be elegant if no smaller S-expression has the same value. It is impossible to prove that any particular large program is elegant.
chaitin  gödel  math  copsci  lisp  programming 
march 2007 by stuhlmueller
Solomonoff Induction by Shane Legg (PDF)
Solomonoff ’s induction method is a theoretical model of what could be considered a perfect inductive inference system. Incomputable.
solomonoff  induction  prediction  ai  math 
march 2007 by stuhlmueller
Category theory - Wikipedia, the free encyclopedia
Deals in an abstract way with mathematical structures and relationships between them. A category consists of a class of objects, a class of morphisms (structure-preserving mappings between structures) and a binary operation (composition of morphisms).
math  category  theory  compsci 
march 2007 by stuhlmueller
PCP theorem - Wikipedia, the free encyclopedia
Implies that every arbitrarily long proof for any statement in propositional logic can be formalized (in polynomial time), so that one can check whether it is correct or not by only reading a constant number of letters from it!
proof  logic  math  theorem  pcp 
march 2007 by stuhlmueller
Fixed-point theorem - Wikipedia, the free encyclopedia
A fixed-point theorem is a result saying that a function F will have at least one fixed point (a point x for which F(x) = x), under some conditions on F that can be stated in general terms. Results of this kind are amongst the most useful in mathematics.
math  theorem  compsci 
march 2007 by stuhlmueller
Nash equilibrium - Wikipedia, the free encyclopedia
If each player has chosen a strategy and no player can benefit by changing his strategy while the other players keep theirs unchanged, then the set of strategy choices constitutes a Nash equilibrium. Nash equilibria must exist for all finite games.
math  game-theory  economics 
february 2007 by stuhlmueller
An Introduction to Kolmogorov Complexity and Its Applications
The idea behind Kolmogorov complexity: a good measure of the complexity of an object is the length of the shortest computer program which will construct that object. From this basic idea a variety of insights and powerful techniques have been developed.
kolmogorov  math  compsci 
february 2007 by stuhlmueller
Goodstein's theorem - Wikipedia, the free encyclopedia
Theorem : Every Goodstein sequence eventually terminates at 0. Unprovable in Peano arithmetic. In contrast to the Collatz conjecture, Goodstein's theorem has been proven using the axioms of set theory.
math  theorem  compsci 
february 2007 by stuhlmueller
Collatz conjecture - Wikipedia, the free encyclopedia
Will a certain number sequence (n even: n/2; n odd: 3n+1) always end the same way, regardless of the starting number? Unsolved conjecture.
collatz  compsci  math  reference 
february 2007 by stuhlmueller
Principle of indifference - Wikipedia, the free encyclopedia
If n possibilities are indistinguishable, then each possibility should be assigned the probability 1/n. For continuous variables, the principle of indifference does not indicate which variable is to have a uniform epistemic probability distribution.
math  philosophy  probabilitytheory 
february 2007 by stuhlmueller
The Unknowable by Gregory J. Chaitin
Chaitin compares and contrasts Gödel's, Turing's and his own work in a straight-forward manner using Lisp.
chaitin  gödel  turing  math  compsci  lisp 
january 2007 by stuhlmueller
Complexity Theory: A Modern Approach / Sanjeev Arora and Boaz Barak
Draft of a textbook on computational complexity theory. Basic complexity classes, lower bounds for concrete computational models and more advanced topics.
compsci  complexity  theory  algorithms  math 
january 2007 by stuhlmueller
Quantum Mechanics for CS people
Quantum mechanics is what you would inevitably come up with if you started from probability theory, and then said, let's try to generalize it so that the "probabilities" can be negative numbers.
quantum  physics  math 
january 2007 by stuhlmueller
A Course in Combinatorial Optimization (PDF)
Combinatorial optimization algorithms solve problems that are believed to be hard in general, by exploring the usually-large solution space. Combinatorial optimization algorithms achieve this by reducing the effective size of the space.
math  compsci 
january 2007 by stuhlmueller
The Evolution of Cybernetics
A Journal by Simon Funk
blog  ai  math  compsci 
january 2007 by stuhlmueller
Project Euler
Project Euler is a series of challenging mathematical/computer programming problems that will require more than just mathematical insights to solve.
math  programming  compsci 
january 2007 by stuhlmueller
Mathe für Informatiker 2, SS 2005, Real Video-Aufzeichnungen
Analysis: Folgen, Reihen, Differentialrechnung, Integrale.
math  compsci  video 
december 2006 by stuhlmueller
Mathe für Informatiker 3, WS 2005/06, Real Video-Aufzeichnungen
Stochastik, lineare Algebra.
math  compsci  video 
december 2006 by stuhlmueller
MIT OpenCourseWare | Mathematics
Lecture notes, assignments, tests, solutions from courses taught at MIT.
math  education  learning  lectures  mit 
december 2006 by stuhlmueller
An Intuitive Explanation of Fourier Theory
Fourier theory is pretty complicated mathematically. But there are some beautifully simple holistic concepts behind Fourier theory which are relatively easy to explain intuitively.
math  fourier 
december 2006 by stuhlmueller
MIT OpenCourseWare | Mathematics | 18.06 Linear Algebra
These video lectures of Professor Gilbert Strang teaching 18.06 were recorded live in the Fall of 1999.
math  video  algebra  mit  lectures  *informative 
december 2006 by stuhlmueller
Unprovability of Friendly AI by Shane Legg
"Trying to prove that an AI is friendly is hard, trying to define “friendly” is hard, and trying to prove that you can’t prove friendliness is also hard. Although it is not the desired possibility, I suspect that the latter is actually the case."
friendliness  ai  dallemolle  research  math 
september 2006 by stuhlmueller
Gödel's Theorem and Information
If a theorem contains more information than a given set of axioms, then it is impossible for the theorem to be derived from the axioms. This suggests that the incompleteness phenomenon discovered by Gödel is natural and widespread [..].
gödel  math  compsci  information  logic 
september 2006 by stuhlmueller
Is there an Elegant Universal Theory of Prediction? by Shane Legg (PDF)
Appears to prove that beyond a moderate level of complexity the development of powerful artificial intelligence algorithms can only be an experimental science.
ai  prediction  math  singularity  dallemolle 
september 2006 by stuhlmueller
Halting problem - Wikipedia, the free encyclopedia
Alan Turing proved in 1936 that a general algorithm to decide for all program-input pairs whether a program will halt or run forever cannot exist.
compsci  turing  wikipedia  math  algorithms 
september 2006 by stuhlmueller
Gödel's incompleteness theorems - Wikipedia, the free encyclopedia
For any consistent formal theory that proves basic arithmetical truths, it is possible to construct an arithmetical statement that is true but not provable in the theory. That is, any consistent theory of a certain expressive strength is incomplete.
math  logic  wikipedia  reference 
september 2006 by stuhlmueller
Löb's theorem - Wikipedia, the free encyclopedia
In a theory with Peano arithmetic, for any formula P, if it is provable that "if P is provable then P", then P is provable.
math  logic  goedel  wikipedia 
september 2006 by stuhlmueller
Kolmogorov complexity - Wikipedia, the free encyclopedia
The Kolmogorov complexity of an object such as a piece of text is a measure of the computational resources needed to specify the object.
wikipedia  math  information  compression  compsci 
september 2006 by stuhlmueller
What is Solomonoff Induction?
Solomonoff induction is a mathematically rigorous, idealized form of induction, that is, predicting what will happen in the future based on prior experiences.
algorithms  statistics  compsci  math 
august 2006 by stuhlmueller
VC dimension - Wikipedia, the free encyclopedia
The VC dimension (for Vapnik Chervonenkis dimension) is a measure of the capacity of a statistical classification algorithm.
wikipedia  algorithms  learning  math 
august 2006 by stuhlmueller
Bayesian inference - Wikipedia, the free encyclopedia
Bayesian inference is statistical inference in which evidence or observations are used to update or to newly infer the probability that a hypothesis may be true.
statistics  bayes  wikipedia  math 
august 2006 by stuhlmueller

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