jtth + mathematics   56

Simplifying calculus by assuming linearity « Casting Out Nines
Last semester I stumbled upon an approach for teaching the concept of the derivative, and later the integral, that worked surprisingly well with my students. It stems from a realization I had that much of what students see when they first learn about derivatives has very little to do with understanding what a derivative is. The typical approach to introducing the derivative throws students directly into the trickiest possible case: a smooth nonlinear curve, and we want to calculate the slope of a tangent line to this curve at a point. To do this, we have to bring in a lot of “stuff”: average rates of change, tables of sequences of average rates of change, and in a vague and non-rigorous sort of way the notion of a limit. It’s this “stuff” that confuses students — not because it’s hard, but because maybe it’s not suited for their first contact with the idea of the derivative. Maybe we need to build their intuition first.
mathematics  education 
january 2010 by jtth
Linear Algebra textbook home page
The text Linear Algebra is free for downloading, It covers the material of a first undergraduate Linear Algebra course. You can use it either as a main text, as a supplement to another text, or for independent study.
free  education  books  book  math  mathematics  algebra  linear  linearalgebra 
may 2009 by jtth
Wolfram Blog : Droste Effect with Mathematica
Take a look at this Demonstration using the original Droste box artwork. But much more interesting results can be achieved when you get complex analysis involved. M.C. Escher was the first to popularize applying conformal mapping to images, but with computers we can easily apply the same ideas to photographs, to get results like this:
tutorial  programming  math  mathematics  photography  photo  images  mathematica  droste 
april 2009 by jtth
Backpropagation
The project describes teaching process of multi-layer neural network employing backpropagation algorithm. To illustrate this process the three layer neural network with two inputs and one output,which is shown in the picture below, is used:
programming  computer  tutorial  math  network  ai  mathematics  computerscience  algorithm  algorithms  neural  networks  neuralnetworks  nn  ann  machinelearning  backpropagation 
december 2008 by jtth
10 Easy Arithmetic Tricks - The List Universe
Math can be terrifying for many people. This list will hopefully improve your general knowledge of mathematical tricks and your speed when you need to do math in your head.
arithmetic  cheatsheet  lists  mathematics  learning  maths  interesting  reference  howto  math 
september 2008 by jtth
PARI/GP Development Headquarters
PARI/GP is a widely used computer algebra system designed for fast computations in number theory (factorizations, algebraic number theory, elliptic curves...), but also contains a large number of other useful functions to compute with mathematical entities such as matrices, polynomials, power series, algebraic numbers etc., and a lot of transcendental functions. PARI is also available as a C library to allow for faster computations.
science  software  programming  computer  tools  linux  math  mathematics  opensource  education  development  language  library  academic  theory  number  system  calculator  algebra  C  cas  number_theory  pari-gp  gp  matematica  number-theory 
august 2008 by jtth
BBC NEWS | Health | Brain's counting skill 'built-in'
Humans have an in-built ability to do mathematics even if they do not have the language to express it, a research team has suggested.
science  psychology  neuroscience  research  brain  education  linguistics  english  mathematics  learning  language  bbc  2008 
august 2008 by jtth
Several Proofs of the Twin Primes Conjecture
Proof of Goldbach's Conjecture, the Prime Number Theorem, and Euclid's Logic Provide Proofs of the Twin Primes Conjecture. Proof of the Twin Primes Conjecture Provides Proof of Goldbach's Conjecture
math  proof  mathematics  goldbach  conjecture  goldbachconjecture  euclid  primes  prime  numbertheory  number  theory 
july 2008 by jtth
What Every Computer Scientist Should Know About Floating-Point Arithmetic
This paper presents a tutorial on those aspects of floating-point that have a direct impact on designers of computer systems. It begins with background on floating-point representation and rounding error, continues with a discussion of the IEEE floating-p
programming  floating-point  reference  floating  point  cs  math  computing  computerscience  academic  development  documentation  document  engineering  optimization  numerical  numbers  number  model  mathematics  manual  science  sun  statistics  technology  theory  useful 
april 2008 by jtth
SAGE: Open Source Mathematics Software
"Building the Car Instead of Reinventing the Wheel"
math  python  software  opensource  programming  tools  Mathematics 
december 2007 by jtth
Sparkline PHP Graphing Library
Sparklines are "intense, simple, wordlike graphics" so named by Edward Tufte. In lieu of a more detailed introduction, Professor Tufte's site has an early release of a chapter on sparklines.
php  sparklines  visualization  graphics  programming  tufte  web  utilities  usability  webdev  website  tool  analysis  communication  cool  informatics  mathematics  math  methods  plugins  presentation  services  scripting  script 
december 2007 by jtth
Documentation -
This is an official center for all documentation to NumPy and SciPy.
api  code  docs  library  mathematics  python  reference  research  statistics  science  tutorial  documentation  numpy  scipy 
october 2007 by jtth
[ wu :: riddles(intro) ]
WELCOME to [wu:riddles]! This is an archive of problems I've been collecting since the Spring of 2002. They come from many places, including word of mouth, college courses, books, and job interviews for hi-tech positions. Many are even written by members
puzzles  riddles  logic  math  games  fun  puzzle  technical  resources  mind  problem  problems  language  library  lists  gallery  enigma  computing  algorithms  brain  Geek  reference  mathematics 
september 2007 by jtth
SciPy -
SciPy (pronounced "Sigh Pie") is open-source software for mathematics, science, and engineering. It is also the name of a very popular conference on scientific programming with Python.
academia  application  code  coding  compsci  computation  computer  computers  computing  cs  lab  graphing  graphic  graph  freeware  free  framework  extension  engineering  developer  language  libraries  library  math  mathematics  maths  matrix  modeling  number  numbers  open  open-source  opensource  optimization  oss  package  plot  programming  python  research  resources  science  scientific  visualization  work  scripting  software  source  statistic  statistics  stats  tutorials  tools 
september 2007 by jtth
NPR: A Four-Dimensional Tribute to the Late Madeleine L'Engle
An actual tesseract is best described as a four dimensional cube...and is kind of confusing. So, in memory of L'Engle, we met up with Physicist David Morgan who took a little time out of his day to talk tesseracts with the BPP. Put your measley three-dime
tesseract  science  books  physics  video  education  geometry  4d  dimensions  layman  mathematics  math  literature 
september 2007 by jtth
R: Statistical Software for Psychology Research
Doing psychology research in R. Insane amount of material here. Insane.
r  howto  guide  tutorial  statistics  stats  math  maths  mathematics  introduction  intro  graph  graphing  graphics  information  reference  research 
september 2007 by jtth
Best Free Documentaries: Dangerous Knowledge - Full Documentary
In this one-off documentary, David Malone looks at four brilliant mathematicians - Georg Cantor, Ludwig Boltzmann, Kurt Gödel and Alan ... all » Turing - whose genius has profoundly affected us, but which tragically drove them insane and eventually led
blog  computers  brain  video  math  documentary  mathematics  science  documentaries  free  history 
september 2007 by jtth
The Countless Achievements of a Math Master - washingtonpost.com
f one is not a mathematician (and except for a few of you out there, who is?), it's going to be impossible to actually understand why Euler was such a great man. Other people will have to tell us, and we should probably believe them.
euler  science  mathematics  math  maths  achievement  biography 
june 2007 by jtth
Calculus Animations
A collection of various animations depicting various concepts of calculus.
calculus  animation  mathematica  math  mathematics  learning  learn 
march 2007 by jtth
What's Special About This Number?
A huge list of the importance of numbers from 0 to 9999.
number  numbers  math  mathematics  list 
february 2007 by jtth
Imagining the Tenth Dimension - A Book by Rob Bryanton
A mind-bending journing into m-theory, string theory, and a good visual primer into dimensionality.
animation  awesome  book  cool  flash  fun  Geek  humor  funny  interesting  math  image  mathematics  maths  philosophy  reference  physics  relativity  science  space  time  videos  visualization  weird 
july 2006 by jtth

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