rafaeldff + mathmatics   22

Bootstrap
Bootstrap is a curricular module for students ages 12-16, which teaches algebraic and geometric concepts through computer programming. At the end of the module, students have a completed workbook filled with word problems, notes and math challenges, as well as a videogame of their own design, which they can share with friends and family.

Our mission is to use students' excitement and confidence around gaming to directly apply algebra to create something cool.
education  math  programming  scheme  teaching  edtech  mathmatics  bootstrap  PLT  racket
july 2014 by rafaeldff
Philosophy and the practice of Bayesian statistics
A substantial school in the philosophy of science identi es Bayesian inference with
inductive inference and even rationality as such, and seems to be strengthened by the
rise and practical success of Bayesian statistics. We argue that the most successful
forms of Bayesian statistics do not actually support that particular philosophy but
rather accord much better with sophisticated forms of hypothetico-deductivism. We
examine the actual role played by prior distributions in Bayesian models, and the crucial
aspects of model checking and model revision, which fall outside the scope of Bayesian
con rmation theory. We draw on the literature on the consistency of Bayesian updating
and also on our experience of applied work in social science.
Clarity about these matters should bene t not just philosophy of science, but also
statistical practice. At best, the inductivist view has encouraged researchers to t and
compare models without checking them; at worst, theorists have actively discouraged
practitioners from performing model checking because it does not t into their frame-
work
paper  pdf  statistic  statistics  philosophy  Bayes  Bayesian  theory  analysys  BaeysianStatistics  AndrewGelman  CosmaRohillaShalizi  CosmaShalizi  mathmatics  math
may 2013 by rafaeldff
carlo angiuli (blog) » Blog Archive » Introduction
"I would like to approach them simultaneously and organically, in an attempt to motivate both [Category Theory and Programming Language Theory/Type Theory], and describe why they comprise a very useful view of the world (of mathematics and logic—is there another one?)."
introduction  tutorial  type  types  TypeSystem  math  mathmatics  CategoryTheory  PL  PLT  language  theory  formal  formalism
january 2013 by rafaeldff
QuickStart - scalala - Getting stated in Scalala in ten minutes - Google Code
"Cool, a Scala library for linear algebra. It's syntactically an internal DSL inspired by MATLAB."
scala  library  scalala  LinearAlgebra  math  mathmatics  DSL  internal  InternalDSL  project  OpenSource
june 2009 by rafaeldff
Proof Theory and Philosophy (pdf)
"First, propositional logic; second, quantifiers, identity and existence; third, modality and truth. In each part, the first chapter covers logical tools and techniques suited to the topic under examination. The second chapter both discusses the issues th
book  online  GregRestall  free  textbook  logic  philosophy  proof  ProofTheory  theory  modal  propositional  predicate  mathmatics  math  pdf
december 2006 by rafaeldff
Looking out for number one
The distribution of the first digit among many "everyday" domains of numbers is log((n+1)/n). This is due to the fact that these distributions are scale-invariant, and it can be proved that any scale-invariant distribution of a first digits is log((n+1)/n
article  interesting  story  math  mathmatics  statistic  statistics  stochastic  distribution  randomness  Newcomb  SimonNewcomb  number  numbers  digit
october 2006 by rafaeldff
Ars Mathematica » Blog Archive » Opinions of Category Theory
Mathematicians arguing whether Category Theory's hype exceeds it's usefulness. Some insight on the problems of over-abstraction (analogous to Peris' "Turing Tarpit" in CS); could be viewed as an argument against the One True Programming Language paradigm
math  mathmatics  CT  CategoryTheory  Category  theory  discussion  thread  blog  post  formal  formalism  system  abstraction  abstract  arsmathematica
july 2006 by rafaeldff
Dijkstra - Why Numbering should start at zero (EWD1019)
Include the lower bound to avoid unnatural edge cases and exclude the upper bound so that (x, x) represents an empty interval. Other nice properties are discussed.
dijkstra  notation  convention  language  design  arithmetic  number  natural  numbers  index  indices  bound  bounds  code  style  EWD  1019  EWD1019  edu  EdsgerDijkstra  essay  math  mathmatics
june 2006 by rafaeldff