# User contributions

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- 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...")
- 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.")
- 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</...")
- 21:02, 3 December 2018 (diff | hist) . . (+346) . . N User:IssaRice/Understanding definitions (Created page with "{| class="sortable wikitable" |- ! Step !! Description !! Purpose !! Example |- | Type-checking and parsing || |- | Checking assumptions of objects introduced || Remove or alt...")
- 02:59, 1 December 2018
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**(+963)** . . N User:IssaRice/Tao's notation for limits (Created page with "Tao's notation for a limit is <math>\lim_{x\to x_0;\, x\in E} f(x)</math>. Can we write this in a more standard way? basically, if we give one additional definition, we have...") - 01:18, 1 December 2018 (diff | hist) . . (+414) . . N User:IssaRice/Colon-equals allows directionality (Created page with "For definitions, I prefer <math>:=</math> over other notations like <math>\equiv</math>, <math>\overset{\Delta}{=}</math>, and <math>\overset{\text{def}}{=}</math>. One reason...")
- 00:52, 1 December 2018
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**(+914)** . . N User:IssaRice/Proof that assumes the trick (Created page with "Many proofs in mathematics depend on one or two "tricks". Some proofs (or ways of writing the proof) seem to deliberately hide or assume the trick so that the proof, while val...") - 20:12, 30 November 2018
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**(+1,367)** . . N User:IssaRice/Reflections on working through Tao's Analysis (Created page with "Some thoughts I've had while working through Tao's ''Analysis I'' (and probably soon ''Analysis II''). * Notational pedantry: I like how Tao almost always introduces variable...") - 01:22, 28 November 2018
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**(+525)** . . N User:IssaRice/Chain rule proofs (Created page with "==Using Newton's approximation== Since <math>g</math> is differentiable at <math>y_0</math>, we know <math>g'(y_0)</math> is a real number, and we can write <math>g(y) = g(y...") - 02:52, 27 November 2018 (diff | hist) . . (+43) . . N Template:Collapsiblesolution (IssaRice moved page Template:Collapsiblesolution to Template:Collapsible solution) (current)
- 02:43, 27 November 2018 (diff | hist) . . (+133) . . N Template:Collapsible solution (Created page with "<div class="toccolours mw-collapsible mw-collapsed"> Expand to see solution: <div class="mw-collapsible-content">{{{1}}}</div> </div>")
- 02:20, 27 November 2018 (diff | hist) . . (+403) . . N User:IssaRice/Little o notation (Created page with " Can we write just <math>f \in o(g)</math> or <math>f = o(g)</math> or <math>f(x) \in o(g(x))</math> or <math>f(x) = o(g(x))</math>? In general we can't because for this not...")
- 22:21, 8 November 2018
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**(+641)** . . N Backpropagation derivation using Leibniz notation (Created page with "The cost function <math>C</math> depends on <math>w^l_{jk}</math> only through the activation of the <math>j</math>th neuron in the <math>l</math>th layer, i.e. on the value o...") - 05:21, 23 October 2018 (diff | hist) . . (+302) . . N User:IssaRice/Increasingly granular measuring stick (Created page with "Exercise 3.6.6 in Rosenthal's ''A First Look at Rigorous Probability Theory''. Theorem 5.5.9 (existence of least upper bound) and Proposition 5.4.14/exercise 5.4.5 in Tao's '...") (current)
- 18:43, 1 October 2018 (diff | hist) . . (+347) . . N User:IssaRice/Strength of a mathematical statement (Created page with " ==External links== * https://gowers.wordpress.com/2008/12/28/how-can-one-equivalent-statement-be-stronger-than-another/ (haven't read this yet) * https://gowers.wordpress.co...")
- 00:31, 22 September 2018
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**(+1,095)** . . N V-structure (Created page with "In graphical models, a '''v-structure''' is a set of three nodes in a graph such that there are two converging arrows and the tails of the arrows are not connected by an arrow...") - 06:47, 16 September 2018
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**(+2,378)** . . N User:IssaRice/Computability and logic/Decrement command in loop programs (Created page with "(started typing this up as a question for math SE, but I think I got it) Herbert Enderton’s ''Computability Theory: An Introduction to Recursion Theory'' defines a loop pro...") - 03:08, 15 September 2018
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**(+556)** . . N User:IssaRice/Computability and logic/First graph principle using a semirecursive relation (Created page with "This is about proposition 7.17 (first graph principle) in Boolos, Burgess, Jeffrey's ''Computability and Logic''. The proof in the book defines two functions as follows: :<m...") - 02:38, 15 September 2018
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**(+1,299)** . . N User:IssaRice/Computability and logic/Characteristic function of a semirecursive set (Created page with "What if we try to define a characteristic function for a semirecursive relation <math>S</math> as follows? :<math>\chi_S(x,y) = \begin{cases}1 & \text{if }S(x,y) \\ 0 & \text...") - 22:57, 14 September 2018
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**(+805)** . . N User:IssaRice/Computability and logic/Comparison of concepts in computability theory (Created page with "{| class="sortable wikitable" |- ! Set !! Intuitive meaning !! In terms of characteristic function |- | Primitive recursive set || || The characteristic function (which must b...") - 19:09, 6 September 2018 (diff | hist) . . (+309) . . N User:IssaRice/Computability and logic/Summary table of sets in computability (Created page with "{| class="sortable wikitable" |- ! Set !! Enumerable? !! Recursive? !! Primitive recursive? !! Recursively enumerable/semirecursive? |- | Set of natural numbers || Yes || Yes...")
- 18:13, 3 September 2018
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**(+504)** . . N User:IssaRice/Belief propagation two coins and a bell example (Created page with "This is an example that illustrates belief propagation in a simple polytree. The situation is given by Pearl (though he doesn't use it as an example of belief propagation). Th...") - 04:53, 3 September 2018 (diff | hist) . . (+314) . . N User:IssaRice/Belief propagation and cognitive biases (Created page with "* "Several cognitive biases can be seen as confusion between probabilities and likelihoods, most centrally base-rate neglect." [https://www.greaterwrong.com/posts/tp4rEtQqRshP...")
- 21:11, 1 September 2018 (diff | hist) . . (+490) . . N User:IssaRice/Type checking Pearl's belief propagation notation (Created page with "this is all from Judea Pearl's ''Probabilistic Reasoning in Intelligent Systems'', chapter 4. Pearl writes expressions like "<math>\lambda(x)</math>" and "<math>\pi(x)</math>...")
- 20:56, 24 August 2018 (diff | hist) . . (+293) . . N User:IssaRice/Aumann's agreement theorem (Created page with "Hal Finney's example <math>\begin{array}{c|rrrrrr} & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ 3 & 4 & 5 & 6 & 7 & 8 &...")
- 22:45, 13 August 2018
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**(+1,376)** . . N User:IssaRice/Minus notation in game theory (Created page with "In game theory, <math>s_{-i}</math> is a shorthand for <math>(s_1,\ldots,s_{i-1},s_{i+1},\ldots,s_n) \in S_1 \times \cdots \times S_{i-1} \times S_{i+1} \times \cdots \times S...")

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