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• 08:02, 25 April 2019 (diff | hist) . . (+131)‎ . . N User:IssaRice/Computability and logic/List of important distinctions in mathematical logic ‎ (IssaRice moved page User:IssaRice/Computability and logic/List of important distinctions in mathematical logic to User:IssaRice/Computability and logic/Some important distinctions and equivalences in introductory mathematical logic) (current)
• 18:03, 17 April 2019 (diff | hist) . . (+2,052)‎ . . N Abstracting sensory data in Solomonoff induction ‎ (Created page with "One potential misconception one might have about Solomonoff induction is the degree to which one "abstracts" the sensory information that Solomonoff induction is "allowed...")
• 16:56, 17 April 2019 (diff | hist) . . (+662)‎ . . N Proportion of valid programs view of Solomonoff induction ‎ (Created page with "'''Proportion of valid programs view of Solomonoff induction''' is one of several ways of viewing the deterministic variant of Solomonoff induction. This view roughly says...")
• 00:12, 16 April 2019 (diff | hist) . . (+1,252)‎ . . N Equivalence of random coinflips view and minimal programs view ‎ (Created page with "Two of the several ways of viewing the deterministic variant of Solomonoff induction are: * The "random coinflips view": Given a monotone Turing machine, we feed the machine...")
• 02:26, 31 March 2019 (diff | hist) . . (+60)‎ . . N Variants of Solomonoff induction ‎ (Created page with "This page lists some '''variants of Solomonoff induction'''.")
• 20:25, 25 March 2019 (diff | hist) . . (+118)‎ . . N User:IssaRice/Computability and logic/Computability of the uncountable ‎ (Created page with "* http://jdh.hamkins.org/alan-turing-on-computable-numbers/ * stillwell's reverse mathematics, p. 77 * Hay 2007, p. 31")
• 22:08, 24 March 2019 (diff | hist) . . (+422)‎ . . N User:IssaRice/Computability and logic/Bounded computation trick ‎ (Created page with "Instead of saying "compute this thing" you can say "compute this thing for <math>n</math> steps", then let <math>n</math> vary. This trick makes the computation bounded, which...")
• 19:51, 21 March 2019 (diff | hist) . . (+493)‎ . . N Solomonoff induction ‎ (Created page with "'''Solomonoff induction''' is an idealized method of sequence prediction. ==Variants== There are many variants of Solomonoff induction that seem to all turn out essentially...")
• 19:35, 20 February 2019 (diff | hist) . . (+695)‎ . . N User:IssaRice/Computability and logic/List of possibilities for completeness and decidability ‎ (Created page with "{| class="sortable wikitable" |- ! Decidable logic? !! Complete logic? (semantic completeness) !! Decidable theory? !! Complete theory? (negation-completeness) !! Example or p...")
• 07:21, 17 February 2019 (diff | hist) . . (+43)‎ . . N Hunting for Simpson's paradox ‎ (IssaRice moved page Hunting for Simpson's paradox to Recognizing Simpson's paradox) (current)
• 22:37, 10 February 2019 (diff | hist) . . (+617)‎ . . N User:IssaRice/Computability and logic/Some important distinctions and equivalences in introductory mathematical logic ‎ (Created page with "This page lists some important distinctions in introductory mathematical logic. * completeness: semantically complete (complete logic; the topic of the completeness theorem)...")
• 02:56, 10 February 2019 (diff | hist) . . (+228)‎ . . N User:IssaRice/Computability and logic/Eliezer Yudkowsky's Löb's theorem puzzle ‎ (Created page with "original link: https://web.archive.org/web/20160319050228/http://lesswrong.com/lw/t6/the_cartoon_guide_to_l%C3%B6bs_theorem/ current LW link: https://www.lesswrong.com/posts/...")
• 20:56, 9 February 2019 (diff | hist) . . (+299)‎ . . N User:IssaRice/Computability and logic/Logic versus theory ‎ (Created page with "Many terms in mathematical logic apply to both logics and to theories. In these cases, the terms mean different things depending on what object it applies to. {| class="wikit...")
• 00:31, 9 February 2019 (diff | hist) . . (+214)‎ . . N User:IssaRice/Computability and logic/Entscheidungsproblem ‎ (Created page with "'''Entscheidungsproblem''', also called '''Hilbert's decision problem''' is a problem in mathematical logic. ==Equivalent formulations== {| class="wikitable" |} ==See also=...")
• 02:03, 8 February 2019 (diff | hist) . . (+210)‎ . . N User:IssaRice/Computability and logic/Diagonalization lemma ‎ (Created page with " ==Rogers's fixed point theorem== Let <math>f</math> be a total computable function. Then there exists an index <math>e</math> such that <math>\varphi_e \simeq \varphi_{f(e)}...")
• 01:04, 7 February 2019 (diff | hist) . . (+431)‎ . . N User:IssaRice/Computability and logic/Expresses versus captures ‎ (Created page with "The ''expresses versus captures'' distinction is an important one in mathematical logic, but unfortunately the terminology differs wildly between different texts. The followin...")
• 08:53, 6 February 2019 (diff | hist) . . (+792)‎ . . N User:IssaRice/Multiplicative process ‎ (Created page with " ==Notes== * https://www.greaterwrong.com/posts/8jwAvGtrwvKHYgoC7/the-tails-coming-apart-as-a-strategy-for-success especially [https://www.greaterwrong.com/posts/8jwAvGtrwvKH...")
• 01:09, 1 February 2019 (diff | hist) . . (+374)‎ . . N User:IssaRice/Computability and logic/Theory ‎ (Created page with "In mathematical logic, '''theory''' has several related meanings. * theory as set of sentences * theory as set of sentences closed under deduction * theory as something with...") (current)
• 21:46, 30 January 2019 (diff | hist) . . (+1,059)‎ . . N User:IssaRice/Computability and logic/Intuitiveness and simplicity tradeoff ‎ (Created page with "In various places in computability and logic, there is a tradeoff between the intuitiveness of a formalization and its inherent simplicity. Some examples: * The more our ded...") (current)
• 03:39, 23 January 2019 (diff | hist) . . (+1,217)‎ . . N User:IssaRice/Computability and logic/Comparison of intuitive notions of computability and proof ‎ (Created page with "See Boolos/Burgess/Jeffrey, p. 185. {| class="sortable wikitable" ! !! Computability !! Mathematical proof |- | Intuitive notion || effectively computable/effectively calcula...")
• 03:48, 16 January 2019 (diff | hist) . . (+447)‎ . . N Variance ‎ (Created page with "The variance of a random variable <math>X</math> is defined as <math>\mathrm{Var}(X) := \mathbf E[(X - \mathbf EX)^2]</math>, where <math>\mathbf EX</math> is the expectatio...")
• 03:15, 16 January 2019 (diff | hist) . . (+25)‎ . . N Expected value ‎ (Redirected page to Expectation) (current)
• 03:04, 16 January 2019 (diff | hist) . . (+12)‎ . . N Expectation ‎ (Created page with "==Notation==")
• 05:51, 15 January 2019 (diff | hist) . . (+41)‎ . . N Category:Probability ‎ (Created page with "Pages about topics in probability theory.") (current)
• 05:39, 15 January 2019 (diff | hist) . . (+384)‎ . . N Disappearance of sample space ‎ (Created page with "In probability theory, the "orthodox approach" defines events, probability measure, random variable, etc., in terms of a sample space (often denoted <math>\Omega</math>). Howe...")
• 02:51, 15 January 2019 (diff | hist) . . (+258)‎ . . N List of sample space perspectives ‎ (Created page with "In probability theory, one can take several perspectives of what the sample space (often denoted <math>\Omega</math>) means. We record several of these here. * Possible world...")
• 00:35, 15 January 2019 (diff | hist) . . (+736)‎ . . N User:IssaRice/Subfield of math as study of concepts preserved under transformation ‎ (Created page with "See https://terrytao.wordpress.com/2010/01/01/254a-notes-0-a-review-of-probability-theory/ for an articulation of the general idea. Many of the examples are from Tao's post....")
• 16:59, 10 January 2019 (diff | hist) . . (+1,515)‎ . . N User:IssaRice/Distribution of X over Y ‎ (Created page with "A distribution of <math>X</math> over <math>Y</math> is any function <math>f : Y \to X</math>. Examples: * A probability distribution over a finite sample space is a distrib...")
• 20:00, 9 January 2019 (diff | hist) . . (+878)‎ . . N User:IssaRice/Computability and logic/K is recursively enumerable ‎ (Created page with "<math>K := \{x : x \in W_x\}</math> ==Proofs== ===Finding a partial recursive function that enumerates ''K''=== This proof is from Enderton.<ref>Herbert Enderton. ''Computa...")
• 23:49, 8 January 2019 (diff | hist) . . (+130)‎ . . N User:IssaRice/Linear algebra/Change of basis example in two dimensions ‎ (Created page with "This example comes from [https://www.youtube.com/watch?v=P2LTAUO1TdA&index=12&list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab this video].")
• 22:20, 6 January 2019 (diff | hist) . . (+903)‎ . . N User:IssaRice/Linear algebra/Matrix of a linear transformation ‎ (Created page with "==Notation== Axler writes <math>\mathcal M(T, (v_1,\ldots, v_n), (u_1, \ldots, u_m))</math>. Axler never abbreviates bases, although if he did, the notation would look like <...") (current)
• 17:28, 6 January 2019 (diff | hist) . . (+624)‎ . . N User:IssaRice/Linear algebra/Riesz representation theorem ‎ (Created page with "Let's take the case where <math>V = \mathbf R^n</math> and the inner product is the usual dot product. What does the Riesz representation theorem say in this case? It says tha...")
• 15:34, 6 January 2019 (diff | hist) . . (+762)‎ . . N User:IssaRice/Linear algebra/Invertible equals expressible as change of coordinate matrix ‎ (Created page with "Let <math>T : \mathbf F^n \to \mathbf F^n</math>. We want to write <math>T</math> as a change of coordinate matrix, i.e. as <math>[I]_\beta^{\beta'}</math> for some appropriat...")
• 23:31, 2 January 2019 (diff | hist) . . (+475)‎ . . N User:IssaRice/Linear algebra/Classification of operators ‎ (Created page with "Let <math>V</math> be a finite-dimensional inner product space, and let <math>T : V \to V</math> be a linear transformation. {| class="sortable wikitable" |- ! Operator name...")
• 21:35, 2 January 2019 (diff | hist) . . (+324)‎ . . N User:IssaRice/Linear algebra/List of matrix products ‎ (Created page with "{| class="sortable wikitable" |- ! Product name !! Matrix notation !! Linear transformation/basis notation |- | || <math>QDQ^{-1}</math> where <math>Q</math> is invertible and...")
• 21:29, 2 January 2019 (diff | hist) . . (+91)‎ . . N User:IssaRice/Properties of a list of vectors and their images ‎ (IssaRice moved page User:IssaRice/Properties of a list of vectors and their images to User:IssaRice/Linear algebra/Properties of a list of vectors and their images) (current)
• 21:28, 2 January 2019 (diff | hist) . . (+70)‎ . . N User:IssaRice/Type checking vector spaces ‎ (IssaRice moved page User:IssaRice/Type checking vector spaces to User:IssaRice/Linear algebra/Type checking vector spaces) (current)
• 21:28, 2 January 2019 (diff | hist) . . (+68)‎ . . N User:IssaRice/Outline of linear algebra ‎ (IssaRice moved page User:IssaRice/Outline of linear algebra to User:IssaRice/Linear algebra/Outline of linear algebra) (current)
• 21:27, 2 January 2019 (diff | hist) . . (+122)‎ . . N User:IssaRice/Linear algebra/ ‎ (Created page with "Index of pages in this directory: {{Special:PrefixIndex/User:IssaRice/Linear_algebra/ | hideredirects=1 | stripprefix=1}}") (current)
• 05:43, 2 January 2019 (diff | hist) . . (+1,177)‎ . . N User:IssaRice/Mental representations in mathematics ‎ (Created page with "I think people don't talk enough about mental representations of objects in math, and I think it's horrible! This is closely related to how people don't talk enough about thei...")
• 01:43, 2 January 2019 (diff | hist) . . (+283)‎ . . N User:IssaRice/Linear algebra/Properties of a list of vectors and their images ‎ (Created page with "Let <math>V</math> and <math>W</math> be two finite-dimensional vector spaces, let <math>T : V \to W</math> be a linear transformation, and let <math>v_1, \ldots, v_n</math> b...")
• 23:28, 1 January 2019 (diff | hist) . . (+323)‎ . . N User:IssaRice/Computability and logic/K (set of natural numbers) ‎ (Created page with "In computability theory, the set <math>K</math> is defined as <math>K := \{x : x \in W_x\}</math>, where <math>W_0, W_1, \ldots</math> is a standard numbering of recursively e...") (current)
• 21:22, 1 January 2019 (diff | hist) . . (+573)‎ . . N User:IssaRice/Linear algebra/Type checking vector spaces ‎ (Created page with "If <math>V</math> is an arbitrary vector space, it does not in general make sense to ask whether <math>v \in V</math> is a string of numbers. If <math>v \in \mathbf R^n</math...")
• 22:36, 26 December 2018 (diff | hist) . . (+1,094)‎ . . N User:IssaRice/Linear algebra/Outline of linear algebra ‎ (Created page with "==Two approaches to linear algebra== * Coordinate-based approach: looks at concrete matrices, more emphasis on computation, works a lot in the standard basis. If linear algeb...")
• 21:54, 23 December 2018 (diff | hist) . . (+1,411)‎ . . N User:IssaRice/Computability and logic/Model as the representation and as that which is represented ‎ (Created page with "From the preface (written by Jesús Mosterín) of María Manzano's ''Model Theory'' (p. ix): <blockquote>In ordinary language, as well as in scientific language the word ''mo...")
• 20:01, 21 December 2018 (diff | hist) . . (+294)‎ . . N User:IssaRice/Computability and logic/Intended interpretation versus all interpretations ‎ (Created page with "Something I have found tricky in mathematical logic is that some theorems/propositions apply to just the intended/standard interpretation (structure), while others are about a...")
• 05:49, 21 December 2018 (diff | hist) . . (+284)‎ . . N User:IssaRice/Computability and logic/Gödel's completeness theorem ‎ (Created page with "I'm confused about the following framing: "The completeness theorem says that, if a bunch of sentences is consistent in the sense of not entailing a contradiction [in a standa...")
• 05:17, 21 December 2018 (diff | hist) . . (+111)‎ . . N User:IssaRice/Computability and logic/Semantic completeness ‎ (Created page with "Semantic completeness is sometimes written as: if <math>T \models \phi</math>, then <math>T \vdash \phi</math>.")
• 05:13, 21 December 2018 (diff | hist) . . (+988)‎ . . N User:IssaRice/Computability and logic/Models symbol ‎ (Created page with "The "models" symbol, <math>\models</math> is used for several purposes in mathematical logic. * If <math>\mathfrak A</math> is a structure/interpretation and <math>\phi</math...")
• 05:04, 21 December 2018 (diff | hist) . . (+659)‎ . . N User:IssaRice/Computability and logic/Least search operator ‎ (Created page with "The '''least search operator''', '''minimzation operator''', or '''μ-operator''' is used in computability theory to define new functions. The least search operator allows us...")

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