calculus, so we’ll skip it.”

19
Proof by terror
When intimidation fails…
20
Proof by lack of interest
“Does anyone really want to see this?”
21
Proof by illegibility
22
Proof by logic
“If it is on the problem sheet, then it must be true!”
23
Proof by majority rule
“Only to be used if general agreement is impossible.”
24
Proof by clever variable choice
“Let A be the number such that this proof works…”
25
Proof by tessellation
“This proof works the same as the last.”
26
Proof by divine word
“…And the Lord said, ‘Let it be true,’ and it was true.”
27
Proof by stubbornness
“I don’t care what you say-it is true!”
28
Proof by simplification
“This proof reduces to the statement 1+1=2.”
29
Proof by hasty generalization
“Well, it works for 17, so it works for all real numbers.”
30
Proof by deception
“Now everyone turn their backs…”
31
Proof by supplication
“Oh please, let it be true.”
32
Proof by poor analogy
“Well, it’s just like…”
33
Proof by avoidance
Limit of proof by postponement as it approaches infinity
34
Proof by design
If it’s not true in today’s math, invent a new system in which it is.
35
Proof by authority
“Well, Ruth Kraus says it’s true, so it must be!”
36
Proof by intuition
“I just have this gut feeling…”
]]>Its coefficients are found as a solution of system of linear equations:

Code example:

def fib(n): if n == 0: return 0 elif n == 1: return 1 else: return fib(n-1) + fib(n-2)]]>

Welcome to WordPress. This is your first post. Edit or delete it, then start writing!

]]>- 22 free tools for data visualization and analysis – Computerworld – Here’s a rundown of some of the better-known options, many of which were demonstrated at the Computer-Assisted Reporting (CAR) conference last month. Others are not as well known but show great promise. They range from easy enough for a beginner (i.e., anyone who can do rudimentary spreadsheet data entry) to expert (requiring hands-on coding). But they all share one important characteristic: They’re free. Your only investment: time.

- List of resources: Article text extraction from HTML documents | My tech blog. – Following up to my overview of article text extractors, Iâ€ll try to compile a list of research papers, articles, web APIs, libraries and other software that I encountered during my research.
- A Short History of Markov Chain Monte Carlo – We attempt to trace the history and development of Markov chain Monte Carlo (MCMC) from its early inception in the late 1940â€s through its use today. We see how the earlier stages of Monte Carlo (MC, not MCMC) research have led to the algorithms currently in use. More importantly, we see how

the development of this methodology has not only changed our solutions to problems, but has changed

the way we think about problems. - Scraper – Chrome Web Store – Scraper is a simple data mining extension for Google Chromeâ„¢ that is useful for online research when you need to quickly analyze data in spreadsheet form.To use it: highlight a part of the webpage you’d like to scrape, right-click and choose “Scrape similar…”. Anything that’s similar to what you highlighted will be rendered in a table ready for export, compatible with Google Docsâ„¢.

- The Ideal Large Scale Learning Class Â« Machine Learning (Theory) – At NIPS, Andrew Ng asked me what should be in a large scale learning class. After some discussion with him and Nando and mulling it over a bit, these are the topics that I think should be covered.

There are many different kinds of scaling. - 10 Rules That Govern Groups â€” PsyBlog – Much of our lives are spent in groups with other people: we form groups to socialise, earn money, play sport, make music, even to change the world. But although groups are diverse, many of the psychological processes involved are remarkably similar.

Here are 10 insightful studies that give a flavour of what has been discovered about the dynamics of group psychology. - Graphing/Charting Data on Web Pages: JavaScript Solutions – Effective data visualization allows users to easily understand and consume otherwise complex, boring information. Plotting your data can serve as a replacement to tabular data, and is also a great way to add practical graphics to your web page or application. There are a variety of ways you can plot data on-the-fly â€“ but in this article weâ€ll focus on 10 excellent JavaScript solutions to graphing/charting data that allow you to process data client-side. Youâ€ll also find a link to one of the demonstration pages of the script so that you can see it in action.
- Bertandâ€s paradox [R details] – Some may have had reservations about the â€œrandomnessâ€ of the straws I plotted to illustrate Bertrandâ€s paradox. As they were all going North-West/South-East. I had actually made an inversion between cbind and rbind in the R code, which explained for this non-random orientation. Above is the corrected version, which sounds â€œmore randomâ€ indeed. (And using wheat as the proper, if weak, colour!) The outcome of a probability of 1/2 has not changed, of course. Here is the R code as well:
- www.unifyingtheories.org – Unifying Theories of Programming deals with program semantics. It shows how denotational semantics, operational semantics and algebraic semantics can be combined in a unified framework for the formal specification, design and implementation of programs and computer systems.

- 20 Fresh JavaScript Data Visualization Libraries – There are plenty of JavaScript libraries out there for rendering your otherwise plain and boring numerical data into beautiful, interactive, and informative visualizations. The beauty of using JavaScript for data visualization is that, if created correctly, your data will be highly accessible (usually via HTML tables). A long time ago (2008), I wrote about JavaScript solutions for graphing and charting data and this article revisits the topic with twenty more JavaScript libraries that you can use to bring your data to life.
- Function Point Analysis – The purpose of this article is to provide an introduction to Function Point Analysis and its application in non-traditional computing situations. Software engineers have been searching for a metric that is applicable for a broad range of software environments. The metric should be technology independent and support the need for estimating, project management, measuring quality and gathering requirements. Function Point Analysis is rapidly becoming the measure of choice for these tasks.
- Interactive visualization of Mixture of Gaussians, the Law of Total Expectation, and the Law of Total Variance – The laws of total expectation and variance hold for any probability distribution, but are illustrated here with a Gaussian mixture, which is amenable to a nice visual decomposition.<br />

<br />

This demo probably needs Firefox or Chrome to work. - Top 10 uncracked codes – Although the internet has spawned a multi-billion dollar industry in creating and cracking codes, crypologists have yet to solve some of the oldest riddles.
- StockTwits – StockTwits® is an open, community-powered idea and information service for investments. Users can eavesdrop on traders and investors, or contribute to the conversation and build their reputation as savvy market wizards. The service takes financial related data and structures it by stock, user, reputation, etc.
- Mathematics VSI: Further Reading – On this website I have written several mathematical discussions, informal but mostly aimed at a more experienced audience than the projected audience for Mathematics VSI. (I had in mind first-year mathematics undergraduates at Cambridge.) A full index appears here . In the not too distant future, I shall write some less advanced material, and also recommend other websites.

Q: Are there any areas of mathematics that are known to be impossible to formalise in terms of set theory?

A:Â Yes — set theory.

It’s funny ’cause it’s true!

]]>- Book Review – The Information – By James Gleick – NYTimes.com – The universe, the 18th-century mathematician and philosopher Jean Le Rond dâ€Alembert said, â€œwould only be one fact and one great truth for whoever knew how to embrace it from a single point of view.â€ James Gleick has such a perspective, and signals it in the first word of the title of his new book, â€œThe Information,â€ using the definite article we usually reserve for totalities like the universe, the ether â€” and the Internet. Information, he argues, is more than just the contents of our overflowing libraries and Web servers. It is â€œthe blood and the fuel, the vital principleâ€ of the world. Human consciousness, society, life on earth, the cosmos â€” itâ€s bits all the way down.
- www.andrew.cmu.edu/user/awodey/preprints/fold.pdf – In the present work, we generalize the entire arrangement from propositional to ï¬rst-order logic. Boolean algebras are replaced by Boolean categories presented by theories in ï¬rst-order logic, and spacesof models are replaced by topological groupoids of models and their isomorphisms. A duality between the resulting categories of syntaxand semantics, expressed ï¬rst in the form of a contravariant adjunction, is established by homming into a common dualizing object, nowSets, regarded once as a boolean category, and once as a groupoid equipped with an intrinsic topology.
- First-Order Logical Duality.pdf – “â€¦an extension of Stone Duality for Boolean Algebras from classical propositional logic to classical first-order logic. The leading idea is, in broad strokes, to take the traditional logical distinction between syntax and semantics and analyze it in terms of the classical mathematical distinction between algebra and geometry, with syntax corresponding to algebra and semantics to geometry.”
- Tim Berners-Lee on the next Web | Video on TED.com – 20 years ago, Tim Berners-Lee invented the World Wide Web. For his next project, he’s building a web for open, linked data that could do for numbers what the Web did for words, pictures, video: unlock our data and reframe the way we use it together.