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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 (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...") (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 (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...")
• 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 (diff | hist) . . (+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 (diff | hist) . . (+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 (diff | hist) . . (+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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