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Mathematical Induction – again

Sassafras leaves, Fredericksburg, VaTeaching the course titled Theoretical Foundations of Computing always presents the problem of (re)introducing studentens to the application and use of the Principle of Mathematical Induction. This link is to one discussion that I think will be helpful to my students.

  • Section 1.6 Proof by Induction
    “The Principle of Mathematical Induction is a method of proof normally used to prove that a proposition is true for all natural numbers 1,2,3,…            , although there are many variations of the basic method.  The method is particularly important in discrete mathematics, and one often sees theorems proven by induction in areas like computer science.  The technique is so intuitive and familiar that it sometimes is used without reference to its use.    For example, suppose someone tells you they are going to color the natural numbers 1,2,3, …   with some color and that the number 1 will be colored blue, and that if a given number is colored blue, then the next number will also be colored blue.   Is there any doubt in your mind that all the numbers will be colored blue?  Of course not.  This is the induction axiom.   And the good thing is you don’t have to proof it.  It is an axiom”
    (tags: induction recursion)
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2011 09 05 ernie Teaching Comments (0) Permalink

Some ideas about Green Machines

Sign to river access, Fredericksburg, VaI came across this article through The Chronicles of Higher Education. It seemed interesting and thoughtful o I posted it on Facebook. It got a few comments mostly affirming the article but some that seemed to take offense at it. I don’t understand why it was offensive to some folks. The information in the article was cited or referenced, not too much opinion, and I didn’t get a sense of any accusatory remarks.

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2011 09 03 ernie Commentary Comments (0) Permalink

Photos from APtBS show with the Kills

APtBS poster europe 2011

Collection  of photos from the show in NY, August 8, 2011
(tags: aptbs ny photos)
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2011 08 31 ernie A Place to Bury Strangers Comments (0) Permalink

An agglomeration of vim links

Crossing Brooklyn Bridge, Brooklyn, NY

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2011 08 30 ernie Teaching Comments (0) Permalink

Geeks Guide to Getting Almost Anything Free

Azalea plants in the snow, back yard,Home, Falmouth, VA This came to me via Stumbleupon.

  • The Geek’s Guide to Getting Almost Anything for Free | MintLife Blog |… – StumbleUpon
    “Does it pay to be Internet savvy? Yes. In more ways than many people imagine. Sure, the Internet is a great way to research just about anything you could ever want to know about; and it’s an outstanding communication, marketing, and entertainment tool. But the Internet can also save you a boatload of money. And we’re not just talking 10 cents off here and there. We’re talking free (and nearly free) stuff.”
    (tags: free guide)
2011 08 26 ernie About the Internet and the Web
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Make and Makefile tutorials

Maple Blossoms, back yard,Home, Falmouth, VA

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2011 08 24 ernie Teaching Comments (0) Permalink

Blekko Search and Accelerating Peer-reviewed Science links from the Scout Report

Maple Blossoms, back yard,Home, Falmouth, VA

  • blekko | slashtag search
    ‘New search engines are released all the time, and occasionally a new one is worth checking out. Blekko is a new customizable search engine that helps users stay away from spam, content farms, and malware. Blekko draws on the power of the slashtag in order to organize websites and search results around specific topics. The slashtag is a tool designed to filter search results, and it helps visitors only search high quality sites that are vetted by a team of experts. This version of Blekko is compatible with all operating systems. ‘ – scout report
    (tags: web2.0 search internet web tools)
  • PLoS ONE : accelerating the publication of peer-reviewed science
    “The Public Library of Science (PLoS) ONE is a peer-reviewed, open-access and online publication that publishes articles from all the branches of science and medicine. Their progressive decision not to limit papers based on subject matter “facilitates the discovery of the connections between papers whether within or between disciplines” and allows for a richer site. Visitors will find that one of the unique features of the site is the ability to rate the quality of the articles published. Any registered user can rate the articles, and anybody can become a registered user. The “For Readers” tab near the top of the homepage has a link to “Guidelines for Rating”, which provides visitors with the three rating categories, and their scales, one to five. The categories are “Insight”, “Reliability” and “Style”, and comments are also allowed to accompany the article. Visitors should not miss the link to “Collections”, under the “Browse Articles” tab. . – Scout report
    (tags: research online web2.0 internet)
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2011 08 13 ernie Interesting Web Sites
Searching and Researching
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Agglomeration on or near 2011-08-09

Leaves in a soap dish in front garden, home, falmouth, va

The next two are from  Scout Report
  • DuckDuckGo
    “You may have played “duck duck goose” growing up, but have you used “DuckDuckGo” yet? It’s a new search engine that is geared towards those folks browsing the web who are looking for a general, all-purpose way to search for materials online. DuckDuckGo doesn’t track users like some search engines, and there’s even a “Goodies” section. In this section, users can personalize their search homepage, learn about their syntax commands, and also find out information about their keyboard shortcuts. This version is compatible with all operating systems. “
    (tags: web internet search web2.0 reference)
  • Aardvark
    “Recently purchased by Google, the Aardvark site is a great way to get quick answers to questions large and small. Visitors can type in their question into the text box on the Aardvark site, and the site will find just the right person to answer the question. Users are encouraged to send questions via Twitter or email as well, and it will generally take just a few minutes to get an answer. Essentially, Aardvark sends out these questions to people in a users’ network who are available via IM or email in order to find a suitable response. The site also includes sample questions and contact information. This version is compatible with all operating systems.”
    (tags: web internet search web2.0 reference)
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2011 08 09 ernie agglomeration
Interesting Web Sites
Music
Searching and Researching
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A link for inexpensive glasses & You Tube of Lynn’s fiddle class at Augusta

Fall leaves, Beech tree, home, falmouth, va

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2011 07 24 ernie agglomeration
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View du jour – July 23, 2011

Hibiscus in the front garden at 8 AM. I took these pics this morning before it got too hot. The plant has bloomed for several years and puts out very large flowers. The bugs always get to them very early; maybe before they bloom.  They’re really nice.

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2011 07 23 ernie view du jour Comments (0) Permalink