# User contributions

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- 03:29, 24 January 2020
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**(+2,104)** . . N User:IssaRice/Poisson distribution (Created page with "Let X be the number of letters received in a day. If the letters arrive indenpendently blah blah blah, it should be clear that X has a Poisson distribution. Let's say you get...") (current) - 05:42, 17 January 2020
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**(+637)** . . N User:IssaRice/Linear algebra/Properties preserved under various operations to a matrix (Created page with "properties to discuss: {| class="sortable wikitable" |- ! Operation !! Preserved properties !! Properties not necessarily perserved |- | Elementary operation: swapping rows...") - 09:11, 15 January 2020
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**(+1,539)** . . N User:IssaRice/Linear algebra/Singular value decomposition (Created page with "the stupid textbooks don't tell you anything about SVD!!!! i think it's super helpful to look at all the ''wrong'' things one might say about SVD... we need to un-knot all tho...") - 08:00, 15 January 2020 (diff | hist) . . (+247) . . N User:IssaRice/Math resources I like (Created page with "* Terence Tao's notes and books * Tim Gowers's blog (especially intro logic) * Evan Chen's infinite napkin * mathematicalmonk's youtube videos * Vipul's notes * abstractmath.o...") (current)
- 07:51, 15 January 2020
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**(+1,063)** . . N User:IssaRice/Linear algebra/Geometry of linear transformations (Created page with "There are various "geometric properties" that transformations can have, such as "[https://en.wikipedia.org/wiki/Isometry preserves lengths]", "[https://en.wikipedia.org/wiki/C...") - 21:52, 14 January 2020
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**(+1,403)** . . N User:IssaRice/Self-sampling assumption with large reference class in sleeping beauty (Created page with ""Unlike SIA, SSA ''is'' dependent on the choice of reference class. If the agents in the above example were in the same reference class as a trillion other observers, then the...") - 00:05, 14 January 2020
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**(+1,916)** . . N User:IssaRice/Convex function (Created page with "a function <math>f : \mathbf R \to \mathbf R</math> is often defined to be convex if <math>f(tx + (1-t)y) \leq tf(x) + (1-t)f(y)</math> for all <math>x,y \in \mathbf R</math>...") (current) - 03:42, 8 January 2020
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**(+736)** . . N User:IssaRice/Scoring rule (Created page with "how can we formalize the idea of a rule for scoring predictions? ==first pass== we can start with a list <math>s_1,\ldots,s_n</math> of statements. each statement makes a ye...") - 10:34, 7 January 2020 (diff | hist) . . (+354) . . N Quantities defined for a random variable that depend only on the distribution (Created page with "Some quantities defined for a random variable, such as expected value and entropy (as well as quantities defined in terms of those, such as variance), depend only...")
- 10:06, 7 January 2020 (diff | hist) . . (+84) . . N User:IssaRice/Dual space of vector space of polynomials (IssaRice moved page User:IssaRice/Dual space of vector space of polynomials to User:IssaRice/Linear algebra/Dual space of vector space of polynomials) (current)
- 09:45, 7 January 2020
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**(+1,527)** . . N User:IssaRice/Linear algebra/Dual space of vector space of polynomials (Created page with "Given a vector space <math>V</math>, its dual space <math>V'</math> is the set of all linear functionals <math>V \to \mathbf F</math>, i.e. all linear functions that "evaluate...") - 05:40, 1 January 2020
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**(+2,422)** . . N User:IssaRice/Generators and relations of dihedral groups (Created page with "problem II.2.5 (p. 57) in Aluffi's Algebra: Chapter 0. As suggested by the hint, take <math>x</math> to be a reflection through the center and some vertex, and <math>y</math>...") - 02:39, 28 December 2019
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**(+1,103)** . . N User:IssaRice/Linear algebra/Determinant as signed volume of transformation (Created page with " Let <math>f : \mathbf R^n \to \mathbf R^n</math> be some function (not necessarily linear) and let <math>\Omega \subseteq \mathbf R^n</math> be some region in space. we will...") - 23:36, 18 October 2019
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**(+1,748)** . . N User:IssaRice/Boundedness theorem for continuous functions (Created page with "There are two typical proofs of the boundedness theorem: * one uses just the least upper bound property * the other uses some sequences machinery (Bolzano-Weierstrass theorem...") (current) - 22:11, 5 October 2019
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**(+1,264)** . . N User:IssaRice/AI safety/Possibility of act-based agents (Created page with " "If a predictor can predict a system containing consequentialists (e.g. a human in a room), then it is using some kind of consequentialist ma...") - 21:58, 5 October 2019 (diff | hist) . . (+116) . . N User:IssaRice/AI safety/List of critiques of iterated amplification (Created page with "{| class="sortable wikitable" ! Critique !! Links making this critique !! Paul's response !! Resolution status |- |}")
- 20:38, 4 October 2019 (diff | hist) . . (+291) . . N User:IssaRice/AI safety/History of Paul Christiano's views (Created page with "https://www.greaterwrong.com/posts/9zpT9dikrrebdq3Jf/will-humans-build-goal-directed-agents/comment/JzYRLCdjxD2Cuqfgu -- i'd like to get the date ranges for each of these view...") (current)
- 08:13, 27 September 2019 (diff | hist) . . (+451) . . N User:IssaRice/AI safety/Bostrom writing style (Created page with ""I think there is a possible culture where people say a bunch of inside-view things, and run with speculations all the time, and another possible culture where people mostly o...") (current)
- 20:59, 7 September 2019
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**(+527)** . . N User:IssaRice/Implementation details in math (Created page with "ideas similar to software engineering's "implementation details" come up quite often in math, when we are constructing/defining certain objects: * constructing number systems...") (current) - 20:52, 7 September 2019 (diff | hist) . . (+37) . . N User:IssaRice/AI safety/Intelligence amplification (Created page with "https://nickbostrom.com/cognitive.pdf") (current)
- 03:44, 7 September 2019
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**(+2,674)** . . N User:IssaRice/AI safety/Issa's stupid questions about AI safety (Created page with "* there's a bunch of different considerations that people talk about (like different takeoff scenarios, comparisons to nuclear arms control, etc.) and it's unclear to me how t...") - 00:41, 6 September 2019 (diff | hist) . . (+236) . . N User:IssaRice/AI safety/Whole brain emulation (Created page with "==Different kinds of WBE== * hi-fi * lo-fi ==Distinction between magically obtaining and the expected ways of obtaining== ==Timelines== * how many years to WBE under a "de...")
- 01:01, 3 September 2019 (diff | hist) . . (+115) . . N User:IssaRice/AI safety/Asymmetry of risks (Created page with "https://www.greaterwrong.com/posts/aPwNaiSLjYP4XXZQW/ai-alignment-open-thread-august-2019/comment/moZS7T7gGYnTxkqDJ") (current)
- 00:56, 3 September 2019
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**(+537)** . . N User:IssaRice/AI safety/Distribution of AI failures leading up to AGI (Created page with "'''Distribution of AI failures leading up to AGI''' refers to how many and how severe AI-related failures are, in the period leading up to AGI. Each "failure event" has sever...") - 00:47, 3 September 2019 (diff | hist) . . (+117) . . N User:IssaRice/AI safety/ (Created page with "Index of pages in this directory: {{Special:PrefixIndex/User:IssaRice/AI_safety/ | hideredirects=1 | stripprefix=1}}") (current)
- 22:47, 2 September 2019 (diff | hist) . . (+221) . . N User:IssaRice/AI safety/Comparison of terms related to agency (Created page with "{| class="wikitable" ! Term !! Opposite |- | Agent || |- | Optimizer, optimization process || |- | consequentialist || |- | expected utility maximizer || |- | goal-directed, g...")
- 00:19, 1 September 2019
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**(+548)** . . N Bellman equation derivation (Created page with "Bellman equation for <math>v_\pi</math>. We want to show <math>v_\pi(s) = \sum_a \pi(a \mid s) \sum_{s',r} p(s',r\mid s,a) [r + \gamma v_\pi(s')]</math> for all states <math>...") - 01:54, 28 August 2019
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**(+2,010)** . . N User:IssaRice/Two envelopes problem (Created page with "https://en.wikipedia.org/wiki/Two_envelopes_problem {| class="wikitable" ! Step !! Wikipedia !! Formal version |- | 1 || I denote by ''A'' the amount in my selected envelope....") - 05:24, 20 August 2019
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**(+1,270)** . . N User:IssaRice/Computability and logic/Motivation for encoding (Created page with "The idea of numbering things/encoding things comes up a lot in computability and logic, but many books don't really seem to discuss why we do this in the first place (the answ...") - 18:09, 16 August 2019
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**(+3,164)** . . N User:IssaRice/Lebesgue number lemma and Tao's proof that sequential compactness implies covering compactness (Created page with "One typical statement of the Lebesgue number lemma is the following: Let <math>(X,d)</math> be a metric space, and let <math>Y</math> be a subset of <math>X</math>. Let <math>...") - 07:34, 15 August 2019
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**(+1,927)** . . N User:IssaRice/Linear algebra/Deriving projection formula and equivalent formulas for dot product (Created page with "This is based on the symmetry argument given in https://www.youtube.com/watch?v=LyGKycYT2v0 Let <math>u</math> and <math>v</math> be vectors. We want to figure out how to pro...") - 02:12, 14 August 2019
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**(+652)** . . N User:IssaRice/Summary of counting techniques (Created page with "Let <math>A</math> be a set with <math>n</math> elements, and let <math>B</math> be a set with <math>m</math> elements. {| class="wikitable" ! Description !! Set representing...") - 01:07, 14 August 2019
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**(+1,737)** . . N User:IssaRice/Linear algebra/Equivalent statements for injectivity and surjectivity (Created page with "Let <math>A</math> be an <math>m \times n</math> matrix. {| class="wikitable" ! Injective !! Surjective !! Bijective |- | <math>A</math> is injective || <math>A</math> is sur...") - 06:30, 10 August 2019
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**(+1,411)** . . N Translating informal probability statements to formal counterparts (Created page with "(inspired by how Aluffi explains universal properties in ''Algebra: Chapter 0'') I think probability is one of the fields in math where people who have learned the subject of...") - 04:12, 4 August 2019
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**(+1,059)** . . N User:IssaRice/Pythagorean theorem, law of cosines, angle between vectors, and inner product (Created page with "There is something peculiar about the dependency of the following concepts in math: * Pythagorean theorem * Law of cosines * Angle between two vectors * Dot product * Inner p...") - 03:59, 4 August 2019 (diff | hist) . . (+78) . . N User:IssaRice/Stringing together relations (IssaRice moved page User:IssaRice/Stringing together relations to User:IssaRice/Stringing together relations and binary operations) (current)
- 03:28, 3 August 2019
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**(+742)** . . N User:IssaRice/Stringing together relations and binary operations (Created page with "If <math>R</math> is a relation on a set <math>X</math>, and <math>x,y,z</math> are elements of <math>X</math>, we sometimes write <math>x \mathrel{R} y \mathrel{R} z</math> a...") - 21:11, 31 July 2019
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**(+771)** . . N Infinitely often and almost always (Created page with "Let <math>A_1, A_2, A_3, \ldots</math> be a sequence of events in some sample space <math>\Omega</math>. {| class="wikitable" |- ! perspective !! infinitely often !! almost a...") - 05:26, 30 July 2019
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**(+755)** . . N User:IssaRice/Linear algebra/Dual basis (Created page with "see p. 224 of https://terrytao.files.wordpress.com/2011/06/blog-book.pdf the following example is based on p. 115 of https://terrytao.files.wordpress.com/2016/12/linear-algeb...") - 22:54, 29 July 2019
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**(+1,480)** . . N User:IssaRice/Degree of polynomial (Created page with "Why is the definition of degree of polynomial what it is? First attempt: a polynomial like <math>a_n x^n + a_{n-1} x^{n-1} + \cdots + a_2 x^2 + a_1 x + a_0</math> should have...") (current) - 05:38, 25 July 2019 (diff | hist) . . (+367) . . N Lower semicomputable function (Created page with "A function <math>f : X \to \mathbf R</math> is lower semicomputable iff there exists a computable function <math>g : X \times \mathbf N \to \mathbf Q</math> such that: * for...")
- 20:00, 15 July 2019
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**(+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
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**(+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
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**(+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
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**(+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
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**(+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
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**(+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...")

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