National Computer Science School Dr. James Curran James Curran is a senior lecturer and ARC Australian Research Fellow at the University of Sydney and the Research Leader in Language Technology at the Capital Markets Cooperative Research Centre. His research is in computational linguistics — the field of Artificial Intelligence involved in building computer systems that understand natural languages, like English and Chinese. James has a PhD in Informatics from the University of Edinburgh. He is currently researching statistical approaches to natural language processing ranging from theoretical and low-level component development through to high-level systems development in Question Answering and Information Extraction. James has been a Director of NCSS since 2001 and was recently included as one of Sydney's one hundred most influential people, published in the Sydney Morning Herald's 'the (sydney) magazine'. James enjoys Braeburn apples and bike riding. Dr. Tara has been a Director of NCSS since 2001. Dr. Tim Dawborn
Math Revision Resource Algebra Refresher A refresher booklet on Algebra with revision, exercises and solutions on fractions, indices, removing brackets, factorisation, algebraic frations, surds, transpostion of formulae, solving quadratic equations and some polynomial equations, and partial fractions. An interactive version and a welsh language version are available. Algebra Refresher - Interactive version An interactive version of the refresher booklet on Algebra including links to other resources for further explanation. Cwrs Gloywi Algebra An Algebra Refresher. Developing iPad Applications for Visualization and Insight - Download Free Content from Carnegie Mellon University
Category Theory Tutorial You don’t need to know anything about category theory to use Haskell as a programming language. But if you want to understand the theory behind Haskell or contribute to its development, some familiarity with category theory is a prerequisite. Category theory is very easy at the beginning. I was able to explain what a category is to my 10-year old son. You are given a polymorphic function imager that, for any function from Bool to any type r, returns a list of r. {-# LANGUAGE ExplicitForAll #-} imager :: forall r . Can you guess the implementation of imager? A category is a bunch of objects with arrows between them (incidentally, a “bunch” doesn’t mean a set but a more generall collection). Our usual intuition is that arrows are sort of like functions. Fig 1. h :: a -> b g :: b -> c f :: c -> d f . There is also an identity morphism for every object in a category, just like the id function: Fig 2. id :: a -> a id . f == f . id == f Functors in Hask are described by the type class Functor
A draft of a short introduction to topology A draft of a short introduction to topology One of my ongoing projects is to figure out how to explain topology briefly. For example, What is Topology?, putatively part 1 of a three-part series that I have not yet written parts 2 or 3 of yet. CS grad students often have to take classes in category theory. So a couple of years ago I wrote up a short introduction to topology for first-year computer science grad students and other people who similarly might like to know the absolute minimum, and only the absolute minimum, about topology. I started writing this shortly after my second daughter was born, and I have not yet had a chance to finish it. But I do think it will serve a useful function once it is finished, and that finishing it will not take too long. The current draft is version 0.6 of 2010-11-14. Please do send me corrections, suggestions, questions, advice, patches, pull requests, or anything else. [Other articles in category /math] permanent link
BetterExplained | Learn Right, Not Rote. Calculus Primer Calculus Tutorial The above graph where velocity = g • T (or v = 32 • T), is based on the derivative of the second graph equation d= ½ • g • t². Now, if we wanted to determine the distance an object has fallen, we calculate the "area under the curve". Yes, the "curve" in this case is a straight line but the principles of integral calculus still apply. If we calculated the sum of the orange, blue and red areas this would equal the distance fallen after 3 seconds. Area of a Right Triangle = ½ (base * height) = ½ (3 seconds * 96 feet per second) = 144 feet Now looking at the previous graph, we see that this is the precise distance after 3 seconds. If we wanted to find the distance fallen between 2 and 3 seconds, we calculate ALL the area from 0 to 3 seconds (144 feet) and then subtract the distance from 0 to 2 seconds: ½ (2 seconds * 64 feet per second) = 64 feet So, the distance fallen between 2 and 3 seconds is 144 - 64 = 80 feet. So how were we calculating these areas ? Integration the Easy Way (n+1)
How to Become a Pure Mathematician (or Statistician) Letters to a Young Math Teacher | Institute for Mathematics and Computer Science The following letter is extracted from the new book, Letters to a Young Math Teacher, by Gerald Rising and Ray Patenaude, which is available from Amazon.com and other sources. Gerry Rising is Distinguished Teaching Professor Emeritus at State University of New York at Buffalo where he co-founded the university’s Gifted Math Program for highly-qualified regional students in grades seven through twelve. Gerry Rising was for many years associated with IMACS activities and is a strong supporter of our work. Letter Seventeen: A Bag of Tricks Paul Rosenbloom enjoyed an international reputation as a senior mathematician when I joined his Minnemath Project at the University of Minnesota as his assistant director. In our very first conversation he told me that he considered teaching outside the classroom an important aspect of a mathematician’s life and he urged me to develop what he called “a bag of tricks” from which to draw math-related lessons for people of all ages. Now she wanted more.