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• 20:00, 15 July 2019 (diff | hist) . . (+1,651)‎ . . N Shattering ‎ (Created page with "Let <math>\mathcal H</math> be a class of functions from <math>\mathcal X</math> to <math>\{0,1\}</math>, called a hypothesis class. Let <math>S = \{p_1, \ldots, p_n\} \subset...")
• 20:28, 12 July 2019 (diff | hist) . . (+651)‎ . . N User:IssaRice/Computability and logic/Rogers fixed point theorem using Sipser's notation ‎ (Created page with "Sipser's textbook presents the recursion theorem, but not the fixed point theorem. Here is one way to state the fixed point theorem using Sipser's notation. '''Theorem''' (Fi...")
• 07:24, 6 July 2019 (diff | hist) . . (+864)‎ . . N User:IssaRice/Isometry in metric spaces ‎ (Created page with "when playing around with metric spaces, one might notice that certain metric spaces can be "modeled" by other metric spaces. For instance, let <math>X = \{1,2,3\}</math> be a...")
• 07:09, 6 July 2019 (diff | hist) . . (+438)‎ . . N User:IssaRice/Construction of the real numbers ‎ (Created page with "something that i have seen clarified ''exactly once'' is why constructing the real numbers (for instance via dedekind cuts or equivalence classes of cauchy sequences of ration...")
• 04:24, 6 July 2019 (diff | hist) . . (+1,143)‎ . . N User:IssaRice/Adherent point and limit point ‎ (Created page with "Let <math>(X,d)</math> be a metric space, let <math>E</math> be a subset of <math>X</math>, and let <math>x_0\in X</math> be a point. * there exists a sequence <math>(x_n)_{n...")
• 03:42, 5 July 2019 (diff | hist) . . (+210)‎ . . N User:IssaRice/Subfield of math that is best for introducing proofs ‎ (Created page with "==Real analysis== Pros: Cons: ==Linear algebra== Pros: Cons: ==Abstract algebra== Pros: Cons: ==Computability and logic== Pros: Cons: ==Discrete math== Pros: Con...")
• 21:50, 27 June 2019 (diff | hist) . . (+531)‎ . . N User:IssaRice/Linear algebra/Linear transformation vs matrix views ‎ (Created page with "Given an <math>m\times n</math> matrix <math>A</math> we can define a linear map <math>T : \mathbf R^n \to \mathbf R^m</math> by <math>T(x) = Ax</math>. Given a linear map <m...")
• 00:46, 25 June 2019 (diff | hist) . . (+1)‎ . . N User:IssaRice/Logical inductor construction ‎ (Created page with ".")
• 00:09, 19 June 2019 (diff | hist) . . (+1,230)‎ . . N User:IssaRice/Computability and logic/Sipser's quine in Python ‎ (Created page with "Michael Sipser's ''Introduction to the Theory of Computation'' describes a quine using Turing machines. Here is an implementation of the machine ''SELF''. <pre>TAPE = "" de...")
• 05:38, 10 June 2019 (diff | hist) . . (+2,281)‎ . . N User:IssaRice/Subsets of the reals that can define their own convergence ‎ (Created page with "(probably not very important) Something that has bugged me about the Cauchy sequence construction of the reals is that in the definition of Cauchyness/convergence, a rational...")
• 02:34, 7 June 2019 (diff | hist) . . (+440)‎ . . N User:IssaRice/Linear algebra/Rank ‎ (Created page with "<math>T : V \to W</math> <math>A</math> is m by n matrix * <math>\dim \operatorname{range} T</math> * dimension of row space of <math>A</math> * dimension of column space of...")
• 22:18, 1 June 2019 (diff | hist) . . (+2,063)‎ . . N User:IssaRice/Extreme value theorem ‎ (Created page with "Working through the proof in Pugh's book by filling in the parts he doesn't talk about. Let <math>M = \sup\{f(x) : x \in [a,b]\}</math> and <math>X = \{x \in [a,b] : \sup V_x...")
• 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)

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