User contributions

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• 19:36, 2 October 2021 (diff | hist) . . (+265)‎ . . N User:IssaRice/Partial order summary table ‎ (Created page with "Let <math>(X, \leq)</math> be a partially ordered set. {| style="wikitable" |- ! Term !! Definition !! Must be in set? |- | Upper bound || || No |- | Maximal element || || Ye...")
• 21:41, 18 September 2021 (diff | hist) . . (+147)‎ . . N User:IssaRice/Reviews of undergraduate real analysis books ‎ (Created page with "==Tao, Analysis I and II== ==Rudin, Principles of Mathematical Analysis (Baby Rudin)== ==Pugh, Real Mathematical Analysis== ==Spivak, Calculus==")
• 18:54, 14 September 2021 (diff | hist) . . (+460)‎ . . N User:IssaRice/Lebesgue theory ‎ (Created page with "some questions for now: * why all the asymmetry in the usual definitions? [https://mathoverflow.net/questions/308856/why-is-lebesgue-measure-theory-asymmetric/308888] * why i...")
• 04:16, 12 September 2021 (diff | hist) . . (+865)‎ . . N User:IssaRice/One-dimensional wave equation ‎ (Created page with "why are people so bad at explaining this? * stein and shakarchi just say "We further assume that the force (or tension) coming from the right of the <math>n</math>th particle...")
• 01:48, 8 September 2021 (diff | hist) . . (+520)‎ . . N User:IssaRice/Fundamental theorem of calculus ‎ (Created page with "There's a typical picture of FTC1 that you see in places like Pugh's analysis book or 3Blue1Brown's video on FTC. This explanation makes sense, but I want point out a few diff...")
• 20:20, 27 July 2021 (diff | hist) . . (+1)‎ . . N User:IssaRice/Computability and logic/Diagonalization lemma (Yanofsky method) ‎ (Created page with ".")
• 02:57, 29 March 2021 (diff | hist) . . (+7)‎ . . N User:IssaRice/Linear algebra/A matrix is only similar to itself if and only if it is a scalar multiple of the identity matrix ‎ (Created page with "yo mayn")
• 04:17, 6 February 2021 (diff | hist) . . (+139)‎ . . N User:IssaRice/Linear algebra/Trace of matrix equals sum of eigenvalues ‎ (Created page with " ==See also== * https://machinelearning.subwiki.org/wiki/User:IssaRice/Linear_algebra/Determinant_of_matrix_equals_product_of_eigenvalues")
• 02:01, 4 February 2021 (diff | hist) . . (+65)‎ . . N User:IssaRice/Linear algebra/Determinant of matrix equals product of eigenvalues ‎ (Created page with "This is chapter 4 exercise 1.10 in ''Linear Algebra Done Wrong''.")
• 04:41, 24 December 2020 (diff | hist) . . (+77)‎ . . N User:IssaRice/Linear algebra/How to remember the projection formula ‎ (Created page with "yooo i keep forgetting this but i think i finally figured out a good mnemonic")
• 05:58, 15 December 2020 (diff | hist) . . (+440)‎ . . N User:IssaRice/Linear algebra/Rank of polynomial matrix is constant everywhere except possibly at finitely many points ‎ (Created page with "This is Corollary 6.2 in ''Linear Algebra Done Wrong''. I find the proof in the book pretty unclear, so I want to write up a clearer proof. Corollary statement: Let <math>A(...")
• 22:35, 13 November 2020 (diff | hist) . . (+607)‎ . . N User:IssaRice/Additivity of small risks ‎ (Created page with "Suppose you want to engage in some risky activities such as driving on the highway or swimming in the river, which have some small probability of resulting in death. It turns...")
• 20:37, 29 August 2020 (diff | hist) . . (+141)‎ . . N User:IssaRice/Analogous results between subfields of math ‎ (Created page with " ==See also== * https://machinelearning.subwiki.org/wiki/User:IssaRice/Subfield_of_math_as_study_of_concepts_preserved_under_transformation")
• 18:59, 25 August 2020 (diff | hist) . . (+373)‎ . . N User:IssaRice/Schröder–Bernstein theorem ‎ (Created page with "questions: * are the ancestor proof and the iterated partition proof actually different, or do they just look different on the surface? * what is the proof that uses axiom of...")
• 06:08, 24 May 2020 (diff | hist) . . (+338)‎ . . N User:IssaRice/Formalizing adjustment of epsilons ‎ (Created page with "I want to elaborate on a thing that shows up when proving part (a) of https://taoanalysis.wordpress.com/2020/05/24/exercise-5-6-1/ Actually, a similar thing appears in Tao's...")
• 21:06, 8 May 2020 (diff | hist) . . (+606)‎ . . N User:IssaRice/Monte Carlo tree search ‎ (Created page with "(from a long time ago) what i don't understand about monte carlo tree search: for the final action selection, at least two sources (https://www.youtube.com/watch?v=Fbs4lnGLS8...") (current)
• 20:43, 13 April 2020 (diff | hist) . . (+653)‎ . . N User:IssaRice/Faulty mathematical induction proof example ‎ (Created page with "Consider the following "proof": <blockquote style="border: 1px solid black; padding: 10px;"><p>'''Proposition.''' Let <math>b,c</math> be positive integers. Then <math>bc > b...")
• 09:20, 30 March 2020 (diff | hist) . . (+209)‎ . . N User:IssaRice/Metric space completion ‎ (Created page with "https://web.archive.org/web/20170329045035/https://math.unm.edu/~crisp/courses/math402/sol-hwk1.pdf https://www.rose-hulman.edu/~bryan/lottamath/complete.pdf http://www.math...") (current)
• 23:23, 4 March 2020 (diff | hist) . . (+1,438)‎ . . N User:IssaRice/Random variable switching trick ‎ (Created page with "i'm not sure what to call this, so i've temporarily given it a name, "Random variable switching trick". in reinforcement learning, the value of a state, <math>v_\pi(s)</math>...")
• 06:15, 4 March 2020 (diff | hist) . . (+2,011)‎ . . N User:IssaRice/Changes to the return after adding a constant to rewards ‎ (Created page with "This is a combination of exercises 3.15 and 3.16 in the 2nd edition of Sutton and Barto. For a continuing task, the new return is <math>G'_t = (R_{t+1} + c) + \gamma(R_{t+2}...") (current)
• 22:47, 12 February 2020 (diff | hist) . . (+95)‎ . . N User:IssaRice/Ergodicity ‎ (Created page with " ==See also== * https://machinelearning.subwiki.org/wiki/User:IssaRice/Multiplicative_process")
• 08:04, 8 February 2020 (diff | hist) . . (+830)‎ . . N User:IssaRice/List of mathematical difficulties ‎ (Created page with "This pages lists some of the concepts in math that I had the most difficulty with. * material implication (introductory sources don't even mention the deduction theorem...) *...")
• 07:13, 7 February 2020 (diff | hist) . . (+951)‎ . . N User:IssaRice/Metropolis–Hastings algorithm ‎ (Created page with "without exception, every single explanation i have seen so far of this absolutely sucks. like, not just "most really suck, and some suck a little". literally everything just s...")
• 20:13, 5 February 2020 (diff | hist) . . (+337)‎ . . N User:IssaRice/Pareto distribution ‎ (Created page with " I still don't know how this is derived, but here's how to make sense of the 80/20 rule: What does it mean to say that the top 20% own 80% of the wealth? It means that <math...")
• 18:46, 5 February 2020 (diff | hist) . . (+494)‎ . . N User:IssaRice/Chi-squared distribution ‎ (Created page with "start at "Consider a binomial random variable Y" on http://www.stat.yale.edu/Courses/1997-98/101/chigf.htm -- I really like the derivation for the binomial case. you can clear...") (current)
• 03:35, 5 February 2020 (diff | hist) . . (+398)‎ . . N User:IssaRice/Gamma distribution ‎ (Created page with "https://www.youtube.com/watch?v=Qjeswpm0cWY ok, so given a poisson process, instead of asking the time until the next occurrence, we can ask for the total time taken until n...")
• 00:57, 5 February 2020 (diff | hist) . . (+121)‎ . . N User:IssaRice/Exponential distribution ‎ (Created page with "this is the only derivation that makes any sense to me: https://neurophysics.ucsd.edu/courses/physics_171/exponential.pdf")
• 23:55, 4 February 2020 (diff | hist) . . (+199)‎ . . N User:IssaRice/List of probability distributions ‎ (Created page with "List of distributions that make sense to me: * uniform * bernoulli * binomial * geometric * beta List of distributions that i don't understand: * exponential * pareto * gam...")
• 23:43, 4 February 2020 (diff | hist) . . (+795)‎ . . N User:IssaRice/Beta distribution ‎ (Created page with "the derivation given here is simple enough to understand: https://web.stanford.edu/class/archive/cs/cs109/cs109.1176/lectureHandouts/15%20Beta.pdf the one thing i don't reall...")
• 19:50, 26 January 2020 (diff | hist) . . (+1,175)‎ . . N User:IssaRice/Moral public goods example ‎ (Created page with "working out the general optimal tax for the example given in https://www.greaterwrong.com/posts/pqKwra9rRYYMvySHc/moral-public-goods each noble has utility function <math>u(x...")
• 03:29, 24 January 2020 (diff | hist) . . (+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 (diff | hist) . . (+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 (diff | hist) . . (+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...")
• 07:51, 15 January 2020 (diff | hist) . . (+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 (diff | hist) . . (+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 (diff | hist) . . (+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 (diff | hist) . . (+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 (diff | hist) . . (+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 (diff | hist) . . (+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 (diff | hist) . . (+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 (diff | hist) . . (+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 (diff | hist) . . (+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 (diff | hist) . . (+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")

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