# User contributions

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- 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
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**(+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
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**(+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
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**(+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
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**(+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
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**(+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
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**(+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
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**(+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
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**(+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
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**(+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
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**(+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...") (current)
- 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
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**(+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
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**(+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...") - 18:11, 18 December 2018 (diff | hist) . . (+131) . . N User:IssaRice/Computability and logic/ (Created page with "Index of pages in this directory: {{Special:PrefixIndex/User:IssaRice/Computability_and_logic/ | hideredirects=1 | stripprefix=1}}") (current)
- 07:07, 18 December 2018 (diff | hist) . . (+17) . . N User:IssaRice/Computability and logic/Function versus algorithm (Created page with "write this later.") (current)
- 06:58, 18 December 2018 (diff | hist) . . (+442) . . N User:IssaRice/Computability and logic/Index and program (Created page with "In computability theory, if we have some numbering <math>\varphi_0, \varphi_1, \varphi_2, \ldots</math> of computable partial functions then...") (current)
- 06:47, 18 December 2018
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**(+525)** . . N User:IssaRice/Computability and logic/Diagonalization out of a class (Created page with "'''Diagonalization out of a class''' is a trick used to define a function that is not in a given list of functions. Let <math>C</math> be some class of total functions. If we...") - 06:33, 18 December 2018 (diff | hist) . . (+27) . . N User:IssaRice/Computability and logic/S–m–n theorem (Created page with "The '''s–m–n theorem'''")
- 06:32, 18 December 2018 (diff | hist) . . (+62) . . N User:IssaRice/Computability and logic/Uniformity in computability theory (IssaRice moved page User:IssaRice/Computability and logic/Uniformity in computability theory to User:IssaRice/Computability and logic/Uniformity) (current)
- 06:26, 18 December 2018 (diff | hist) . . (+86) . . N User:IssaRice/Uniformity in computability theory (IssaRice moved page User:IssaRice/Uniformity in computability theory to User:IssaRice/Computability and logic/Uniformity in computability theory) (current)
- 06:26, 18 December 2018 (diff | hist) . . (+90) . . N User:IssaRice/Summary table of sets in computability (IssaRice moved page User:IssaRice/Summary table of sets in computability to User:IssaRice/Computability and logic/Summary table of sets in computability) (current)
- 06:25, 18 December 2018 (diff | hist) . . (+99) . . N User:IssaRice/Characterization of recursively enumerable sets (IssaRice moved page User:IssaRice/Characterization of recursively enumerable sets to User:IssaRice/Computability and logic/Characterization of recursively enumerable sets) (current)
- 06:25, 18 December 2018 (diff | hist) . . (+98) . . N User:IssaRice/Characteristic function of a semirecursive set (IssaRice moved page User:IssaRice/Characteristic function of a semirecursive set to User:IssaRice/Computability and logic/Characteristic function of a semirecursive set) (current)
- 06:25, 18 December 2018 (diff | hist) . . (+98) . . N User:IssaRice/Comparison of concepts in computability theory (IssaRice moved page User:IssaRice/Comparison of concepts in computability theory to User:IssaRice/Computability and logic/Comparison of concepts in computability theory) (current)
- 06:24, 18 December 2018 (diff | hist) . . (+104) . . N User:IssaRice/First graph principle using a semirecursive relation (IssaRice moved page User:IssaRice/First graph principle using a semirecursive relation to User:IssaRice/Computability and logic/First graph principle using a semirecursive relation) (current)
- 06:24, 18 December 2018 (diff | hist) . . (+86) . . N User:IssaRice/Decrement command in loop programs (IssaRice moved page User:IssaRice/Decrement command in loop programs to User:IssaRice/Computability and logic/Decrement command in loop programs) (current)
- 04:32, 18 December 2018
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**(+1,243)** . . N User:IssaRice/Computability and logic/Characterization of recursively enumerable sets (Created page with "Let <math>S</math> be a set of natural numbers. The following are all equivalent. {| class="sortable wikitable" |- ! Property !! Emphasis |- | The elements of <math>S</math>...") - 23:07, 17 December 2018 (diff | hist) . . (+149) . . N User:IssaRice/Computability and logic/Uniformity (Created page with "Some resources on computability will talk about something holding "uniformly". I haven't seen a page that defines this clearly, so here's my attempt.")
- 22:34, 17 December 2018 (diff | hist) . . (+57) . . N User:IssaRice/taking inf and sup separately (IssaRice moved page User:IssaRice/taking inf and sup separately to User:IssaRice/Taking inf and sup separately) (current)
- 22:25, 17 December 2018 (diff | hist) . . (+310) . . N User:IssaRice/Taking inf and sup separately (Created page with "This page describes a trick that is sometimes helpful in analysis. ==Satement== Let <math>A</math> and <math>B</math> be bounded subsets of the real line. Suppose that for e...")
- 06:25, 9 December 2018 (diff | hist) . . (+175) . . N User:IssaRice/Adverb negative adjective (Created page with "* "absolutely divergent" to mean "''not'' absolutely convergent" * "recursively inseparable" to mean "''not'' recursively separable"")
- 19:38, 7 December 2018
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**(+1,464)** . . N User:IssaRice/Tiers of learning in mathematics (Created page with "{| class=sortable wikitable" |- ! Name !! Description |- | Computation-based || The material is taught, but proofs of the main results are not covered. Example: high school/fr...") - 04:21, 5 December 2018 (diff | hist) . . (+305) . . N User:IssaRice/Conjunction of subset statements versus Cartesian product subset statement (Created page with "This is exercise is from Tao's ''Analysis I'' (exercise 3.5.6) and from Munkres's ''Topology'' (exercise 1.1.2(k)–(l)). The exercise is to consider the sets <math>A,B,C,D</...")

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