Math

• 
  Google News: Math

• Bellevue discusses new high-school math books - Seattle Times

  7 Nov 2009 | 1:16 am

  Bellevue discusses new high-school math booksSeattle TimesHave an opinion on the best way to teach math? The Bellevue School District will hold two community meetings next week on the proposed adoption of new

• Creekside High merit semifinalist counts math, acting among her passions - Florida Times-Union

  6 Nov 2009 | 9:05 pm

  Creekside High merit semifinalist counts math, acting among her passionsFlorida Times-UnionMott says she loves math and plans to double major in engineering and physics. "Math has always been my favorite subject," she said. and more »

• Russia's Conquering Zeros - Wall Street Journal

  6 Nov 2009 | 5:55 pm

  Russia's Conquering ZerosWall Street JournalDecades before, in the Soviet Union, math placed a premium on logic and consistency in a culture that thrived on rhetoric and fear; it required highly and more »

• A Math Geek's Ride to the High Court in Landmark Patent Fight - The American Lawyer

  6 Nov 2009 | 5:06 pm

  ReutersA Math Geek's Ride to the High Court in Landmark Patent FightThe American LawyerBernie Bilski and Rand Warsaw were just a couple of "math geeks for hire" from Pittsburgh when they applied for a patent in 1997. U.S. top court to hear business method patent caseReutersall 19 news articles »

• Michigan to offer incentives to math, science teachers - The Detroit News

  6 Nov 2009 | 2:52 pm

  The Bay City Times - MLive.comMichigan to offer incentives to math, science teachersThe Detroit NewsDetroit -- Michigan will be one of the first states to participate in a national program that encourages math and science teachers to work in urban school $16.7M grant to train Mich. science, math teachersChicago TribuneGrant to boost Mich. teachersDetroit Free PressGranholm touts 'blockbuster' partnership with Kellogg FoundationMichigan MessengerWLNS -Michigan Radio -The Bay City Times - MLive.comall 19 news articles »

• 
  Topix: Math

• Kids skip school to watch Yankees parade down Canyon of Heroes

  7 Nov 2009 | 4:25 am

  Fans cheer down Broadway for the World Series Champion New York Yankees during the parade.

• Schools recognized with achievement awards

  7 Nov 2009 | 4:23 am

  Several schools across north-central and northwest Kansas have been recognized for their students' performance on the state assessment tests this past spring.

• Bobcats gain TRD title - roanoke.com

  7 Nov 2009 | 4:20 am

  Radford scores 13 points in the fourth quarter to rally for the victory. By Ray Cox A 381-1672 "I think Giles will be right back here next week." Matthew Saunders Radford coach on next week''s tournament play Radford's Dontae Carter tries to run the ball up field against Giles.

• Vikings celebrate district crown - roanoke.com

  7 Nov 2009 | 4:20 am

  Burt Torrence strode into the giggling, jostling postgame huddle and shoved the Blue Ridge District trophy into the hands of his waiting team.

• Sawmill operator welcomes lower power bills

  7 Nov 2009 | 4:13 am

  Large industrial facilities such as Fraser Papers in Plaster Rock welcomed the news of lower power rates from the proposed sale of NB Power's generation assets and power grid to Hydro-Quebec. Paul McKinley, manager of Fraser Papers sawmill operations in Canada and the United States, said the Plaster Rock mill, which has been idle for nine months ...

• 
  ScienceDaily: Mathematics News

• Professor Sees 70 Percent Chance For Yankees To Win 2009 World Series

  27 Oct 2009 | 11:00 pm

  A mathematician who has applied mathematical modeling techniques to elucidate the dynamics of run scoring in baseball has computed the probability of the Yankees and Phillies winning the World Series. He also has computed the most deserving of Major League Baseball's prestigious 2009 Most Valuable Player (MVP) and Cy Young awards.

• How Low Doses Of Radiation Can Cause Heart Disease And Stroke

  23 Oct 2009 | 2:00 am

  A mathematical model constructed by researchers predicts the risk of cardiovascular disease (heart attacks, stroke) associated with low background levels of radiation. The model shows that the risk would vary almost in proportion with dose. Results are consistent with risk levels reported in previous studies involving nuclear workers.

• Eleven Genetic Variations Linked To Type 2 Diabetes

  19 Oct 2009 | 2:00 pm

  Mathematicians have developed powerful new tools for winnowing out the genes behind some of humanity's most intractable diseases.

• Math Modeling Predicts Unknown Biological Mechanism Of Regulation

  19 Oct 2009 | 5:00 am

  A team of scientists have demonstrated -- for the first time -- that mathematical models created from data obtained by DNA microarrays, can be used to correctly predict previously unknown cellular mechanisms. This brings biologists a step closer to one day being able to understand and control the inner workings of the cell as readily as NASA engineers plot the trajectories of spacecraft today.

• New Mathematical Model More Accurately Diagnoses Acute Heart Failure In Emergency Rooms

  19 Oct 2009 | 5:00 am

  Researchers have developed the first mathematical model in cardiology and emergency medicine to more quickly and reliably diagnose acute heart failure in emergency room patients. Research findings have been shown to help physicians diagnose AHF with greater accuracy.

• 
  Scientific American - Math

• Happy (2 5 x 3 - 1)th birthday to Martin Gardner

  21 Oct 2009 | 9:45 am

  Longtime Scientific American columnist Martin Gardner turns 95 Wednesday, and a profile in Tuesday's New York Times honors the mathematical proselytizer who, tireless as ever, marks the milestone himself with the publication of a new book. [More]

• Mathematician sees a Yankees-Dodgers World Series, but don't pop that bubbly yet

  15 Oct 2009 | 2:35 pm

  The National League Championship Series gets under way this evening when the Los Angeles Dodgers host the Philadelphia Phillies, and tomorrow the American League follows suit as the Los Angeles Angels of Anaheim visit the New York Yankees. [More]

• Bird Moves: Dancing with the Starlings

  15 Oct 2009 | 8:00 am

  Researchers have long assumed that humans were the only animals that could dance--even our close primate relatives cannot keep a steady beat or be taught to move to a rhythm. But new evidence shows that birds can dance, revealing that the mysterious ability could be a by-product of vocal learning.Aniruddh Patel of the Neurosciences Institute, Adena Schachner of Harvard University and their colleagues studied several birds, among them a cockatoo that dances to the Backstreet Boys’ “Everybody.” When Patel sped up or slowed down the song, the bird adjusted its moves to match…

• Pirate Economics?: Captain Hook Meets Adam Smith

  12 Oct 2009 | 6:00 am

  Will Turner : “If we can outrun her, we can take her. We should turn and fight.” Captain Jack Sparrow : “Why fight when you can negotiate?” [More]

• More Animals Seem to Have Some Ability to Count

  15 Sep 2009 | 6:00 am

  Scientists have been skeptical of claims of mathematical abilities in animals ever since the case of Clever Hans about 100 years ago. The horse, which performed arithmetic and other intellectual tasks to delighted European audiences, was in reality simply taking subconscious cues from his trainer. Modern examples, such as Alex the African grey parrot, which could count up to six and knew sums and differences, are seen by some as special cases or the product of conditioning.Recent studies, however, have uncovered new instances of a counting skill in different species, suggesting that…

• 
  NYT: Mathematics

• For Decades, Puzzling People With Mathematics

  19 Oct 2009 | 9:00 pm

  Martin Gardner is the world’s best-known recreational mathematician, and has probably introduced more people to the joys of math than anyone in history.

• Sluggish Results Seen in Math Scores

  14 Oct 2009 | 9:00 pm

  Test results suggest that the nation will not come close to the goal of bringing all children to proficiency by 2014.

• U.S. Math Tests Find Scant Gains Across New York

  14 Oct 2009 | 9:00 pm

  New York State’s fourth and eighth graders made no notable progress on federal math exams this year.

• Prizes Aside, the P-NP Puzzler Has Consequences

  7 Oct 2009 | 9:00 pm

  The solving of a grand math challenge in the fields of theoretical computer science and complexity theory has garnered interest, but no real answers.

• Israel Gelfand, Math Giant, Dies at 96

  7 Oct 2009 | 9:00 pm

  Dr. Gelfand’s pioneering work in many areas has proved crucial in quantum mechanics, M.R.I. imaging and CAT scans.

• 
  MathNotations

• THE OPEN-ENDED CONTEST PROBLEM AND SOLUTIONS

  Dave Marain

  4 Nov 2009 | 3:04 am

  As promised, here is the open-ended, rubric-based, holistically scored, performance-assessed, student-constructed first problem from MathNotation's Third Contest:1. A primitive Pythagorean triple is defined as an ordered triple of positive integers (a,b,c) in which a2 + b2 = c2 and the greatest common factor (divisor) of a, b and c is 1. If (a,b,c) form such a triple, explain why c cannot be an even integer.Comments(a) The content here is number theory. Is some of this covered in your district's middle school curriculum or beyond? More importantly, at what point do students begin to formulate…

• RESULTS OF THIRD MATHNOTATIONS CONTEST and OTHER NEWS...

  Dave Marain

  3 Nov 2009 | 6:00 am

  FINALLY -- THE RESULTS ARE IN!!I apologize for the delay in getting these results out. The participating schools have all been notified.NOTE: If any participating school did not receive an email from me, the advisor should email me. Also, if I misspelled anyone's name pls let me know and I'll correct it immediately!INITIAL COMMENTS ON CONTEST, ETC...MEAN SCORE: 5.6 PTS OUT OF 12TOPICS INCLUDED Number Theory, Geometric Sequences, Function Notation, Geometry, Discrete Math, Quadratic Functions, and Absolute Value Inequalities (advanced level)Twenty schools registered from around the world, but…

• A Rant, An Update and Model Problems for You

  Dave Marain

  12 Oct 2009 | 3:42 am

  And the seasons they go round and round And the painted ponies go up and down We're captive on the carousel of time We can't return we can only look behind From where we came And go round and round and round In the circle game...Oh, how I love Joni Mitchell's lyrics made famous by the inimitable Buffy Sainte-marie. Oh, how The Circle Game lyrics above describe my feelings about the state of U.S. math education. I feel I've been on this carousel forever. But I do believe that all is not hopeless. I do see promise out there despite all the forces resisting the changes needed to improve our…

• Another Sample Contest Problem - Counting...

  Dave Marain

  5 Oct 2009 | 3:29 am

  There is still time to register for the upcoming MathNotations Third Online Math Team Contest, which should be administered on one of the days from Mon October 12th through Fri October 16th in a 45-minute time period.Registration could not be easier this time around. Just email me at dmarain "at" "gamil dot com" and include your full name, title, name and full address of your school (indicate if Middle or Secondary School).Be sure to include THIRD MATHNOTATIONS ONLINE CONTEST in the subject/title of the email. I will accept registrations up to Fri October 9th (exceptions can always be…

• MathNotations Third Online Free Math Contest Update and Sample "Proof"

  Dave Marain

  4 Oct 2009 | 5:44 am

  There is still time to register for the upcoming MathNotations Third Online Math Team Contest, which should be administered on one of the days from Mon October 12th through Fri October 16th in a 45-minute time period. Registration could not be easier this time around. Just email me at dmarain "at" "gamil dot com" and include your full name, title, name and full address of your school (indicate if Middle or Secondary School). Be sure to include THIRD MATHNOTATIONS ONLINE CONTEST in the subject/title of the email. I will accept registrations up to Fri October 9th (exceptions can always be…

• 
  Math-U-See Blog

• Steve Interviewed on Prime Time America

  ethan

  21 Oct 2009 | 11:29 am

  Steve was recently interviewed by Paul Butler on Moody Radio’s “Prime Time America” You can listen to Steve’s segment “kids and math” on Paul Butler’s blog. Despite years of federally funded education initiatives, a recent study by the NAEP reports that our children are still performing poorly in basic mathematics. Steve Demme is the Founder, President and Author of Math U See. He helps us understand why our kids are struggling and what we can do about it. In this feature, Mr. Demme mentions the first step in helping our children improve in math is to…

• Math-U-See Student Wins Google SketchUp Contest

  ethan

  13 Oct 2009 | 2:11 pm

  We recently received this email from proud parent and wanted to share it with you. Dear Steve, one of your students - Matthew Notaro - won the 2009 Google SketchUp Kid’s Digital Design Contest and was honored by the Howe brothers - Popular Science’s 2009 Inventors/Invention of the year. Your Math program was a direct result to his success. In 7th grade he got so bogged down by Saxon Math’s overkill review and drill he spent over 2 hours a day per lesson and slid farther and farther behind. We finally listened to some friends and ordered your intro DVD. Math U See’s…

• I Love U

  ethan

  1 Oct 2009 | 12:28 pm

  A happy mom sent me this the other day and I just had to share it. This is Cole. He is my 11 year old (6th grade) son. For 4 years we have stressed, cried, and begged the school to help figure out what was going on with him. They kept saying ADHD (surprise!) But after being tested twice he still wasn’t diagnosed ADHA. I started pushing for him to be tested for dyslexia. But, Ky doesn’t do that. I finally had him tested myself and guess what? Momma was right! But KY doesn’t recognize dyslexia as a LD so rather than fight the system I pulled Cole out and began homeschooling.

• Great Pre Calculus Testimony

  ethan

  26 Aug 2009 | 2:00 pm

  I was browsing a forum today and someone asked the question “Does home schooling affect a student’s chances of getting into college?” here is one of the responses. Home schooling most definitely affects a student’s chances of getting into a good university. In most cases, it improves their chances. Most home school materials and curricula are designed for use by the parent who is not an expert in every subject. I’m taking Pre Calculus this year, and my mom barely got through high school algebra. We use a home school math curriculum called Math U See. It is a…

• How Does Math-U-See Fit?

  ethan

  21 Aug 2009 | 10:43 am

  Guest post from Miriam Homer. Miriam has authored several of the Math-U-See books, has been a teacher and is a Pennsylvania homeschool evaluator. ************************************************ photo from lillarkie/ / CC BY-ND 2.0 Homeschool books and magazines often suggest that you choose curriculum to fit the teaching methods and philosophy you prefer. Did you ever wonder how Math-U-See fits with different methods of homeschooling? Here is an interesting list. How does Math-U-See fit with the Charlotte Mason approach? The lessons are short and free of “twaddle.” There are…

• 
  Wild About Math

• History and trajectory of Mathematica

  Sol

  6 Nov 2009 | 5:24 pm

  Today’s Wolfram Alpha Blog is the first in a series of videos and transcripts from Stephen Wolfram’s keynote address at the International Mathematica User Conference 2009. From the Wolfram Blog entry: Future Mathematica features, new directions for Wolfram|Alpha, and how the two Wolfram technologies will be integrated were highlights of Stephen Wolfram’s keynote address at the International Mathematica User Conference 2009. This first video gives a quick history of Mathematica from its roots going back to 1981. I’m looking forward to hints about future features.

• MMM #38: We have a winner!

  Sol

  30 Oct 2009 | 10:31 am

  Random.org selected Ken Lareau as the winner for MMM #38. Congratulations, Ken! Here’s what the problem was: Prove or disprove: The product of any four consecutive integers is always one less than a perfect square. Don’t assume the integers are all positive. Here’s Ken’s solution: The above conjecture is true. The domain can be simplified a bit by noting two things: 1) If there are both positive and negative integers in the product, then since they’re consecutive, 0 has to be present, meaning the product is 0, which is one less than 1, a perfect square. 2) If all the…

• How much would you pay for a 146 year old Math book?

  Sol

  29 Oct 2009 | 4:51 pm

  Every now and then I like to buy old Math books. I buy them on Ebay. Most of the books I buy are from the early 1900’s or the tail end of the 1800’s. Yesterday, I happened upon this book: Yes, it’s from 1863. Yes, I paid $6.50 for it and there was no shipping charge. What’s the book about? Beats me. I’m not quite sure what Analytical Arithmetic Antique College Math is. If you think you know, leave a comment. What condition is the book in? Dunno but for six and a half bucks I’m not complaining! ShareThis

• ‘Dismantling the calculus pyramid’ gets ton of views

  Sol

  29 Oct 2009 | 7:52 am

  A couple of days ago I posted a very brief article, Dismantling the calculus pyramid. The post has been seen 2,746 times, thanks mostly to being noticed by ‘timwiseman’ who posted a link to the article at Y Combinator Hacker News. The posting at Y Combinator has gotten 45 comments while, here, it’s gotten four comments. The conversation at Y Combinator is quite lively. Check it out. ShareThis

• Dismantling the calculus pyramid

  Sol

  27 Oct 2009 | 8:30 pm

  Here’s a quick 3 minute TED video by Mathemagician Arthur Benjamin. The topic: Benjamin’s idea about how to change Math education. He makes the point that Math education is like a pyramid with all classes (e.g. algebra, geometry, trigonometry) building up to calculus. But, he argues, calculus is not very useful to many of us in our ordinary lives. So, what should the pinnacle of the Math pyramid be? Watch the video and leave your comments. ShareThis

• 
  Ars Mathematica

• Bourbaki Archives

  Walt

  29 Oct 2009 | 3:19 am

  Via Peter Woit I see that there is a project to put the archives of Bourbaki online. These are the internal manuscripts that the group generated while writing their famous series of books.

• Class Weblog on Geometric Group Theory

  Walt

  15 Oct 2009 | 1:23 pm

  I just ran across an interesting weblog. Henry Wilton taught a course in the spring on geometric group theory, which is the use of topological techniques to prove theorems in group theory. He had his students write up the lecture notes for each lecture as a separate post on the class weblog, 392C Geometric Group Theory. I’m sorry that I didn’t find this site when the course was on-going. It would have been interesting to follow along with the class in real time.

• The thagomizer: science marches on.

  Walt

  7 Oct 2009 | 7:52 am

  The tail spikes of stegosauruses are known in palaeontology as the thagomizer. Yes, after the Far Side.

• Polish Virtual Library of Science

  Walt

  28 Sep 2009 | 2:03 pm

  The Polish Virtual Library of Science (which contains Banach’s book) has several other interesting mathematical works in English, French, German, and Polish. They have the archives for several journals, including Studia Mathematica. They also have several older but famous monographs, such as Zygmund’s Trigonometric Series.

• Théorie des opérations linéaires

  Walt

  28 Sep 2009 | 1:05 pm

  Stefan Banach’s famous monograph, Théorie des opérations linéaires, which gave birth to the field of Banach spaces, is available online.

• 
  Loren on the Art of MATLAB

• Calculus with Empty Arrays

  Loren

  4 Nov 2009 | 11:30 am

  MATLAB has had empty arrays since before I started using the program. When I started, the only size empty array was 0x0. When version 5 was released, empty arrays came along for the N-dimensional ride and got more shapely. Contents From the Newsgroup Dimensions Matter in MATLAB Empty Array Shapes Reference Got an Empty Question? Even relatively simple expressions involving empty arrays cause confusion from time to time, especially in concert with other rules in MATLAB (such as NaN values usually propagate from inputs to outputs). Let's play around a little with some empty arrays to get some…

• Dealing with Cells

  Loren

  21 Oct 2009 | 10:53 am

  A customer recently asked me this question at the MATLAB Virtual Conference. Contents Question about Summing Cell Rows Example Answer Cell Array Questions Question about Summing Cell Rows I was hoping you would cover cells some day. Here is a particular problem I was hoping to have a more elegant solutions for. A is a cell that has String (say names) in the first column, Numbers (say scores in tests 1 and 2) in the next two columns. Assume that each cell has only one value. Is there an easier way to calculate, say the sum of the two test scores than a for loop?Example Let's make some sample…

• Concatenating structs

  Loren

  15 Oct 2009 | 11:18 am

  From time to time, I get asked or see queries about how to concatenate two struct arrays to merge the fields. There's even a section in the documentation covering this topic. I thought I'd show it here to help people out. Contents Example Data mergeStruct Do You Need to Merge struct data? Example Data Suppose I've got some system for which I have collected information on a couple of individuals, including their names and ages. s1.name = 'fred'; s1.age = 42; s1(2).name = 'alice'; s1(2).age = 29;Later, I go back and collect the individual's heights (in cm).s2.height = 170; s2(2).height = 160;It…

• Handling Discrete Data

  Loren

  9 Oct 2009 | 8:46 am

  Discrete data arise in many applications and the data may be numeric, or non-numeric, often referred to as categorical. Not all data are strictly numeric, and other characteristics can be pertinent or useful. You can use a variety of techniques and data representations in MATLAB for storing and manipulation discrete data. Contents Example: Periodic Table of Elements Discrete Data Representation Options logical String or Coded Integer nominal Array ordinal Array Integer Going All the Way Your Data or Experiment Example: Periodic Table of Elements The periodic table of elements provides a rich…

• October 14 - Virtual MATLAB Conference

  Loren

  5 Oct 2009 | 6:35 am

  We're having a MATLAB conference on October 14, in the virtual world. There'll be presentations, forums, chats, live discussion, etc. Please check out the event and join in the fun! Here's the presentation schedule to help you find what you'd like to participate in. I'm planning to attend some of the forums and listen to many of the talks, including ones focused on MATLAB for education. Hope to meet you there!

• 
  Homeschool Math Blog

• Review of Math Apprentice

  2 Nov 2009 | 2:46 am

  Math Apprentice is a new free website, meant to show students how math is used in real world. In the game, you are like an apprentice at various companies, applying your math skills to challenges similar to those encountered in the real world and real companies.Main Street - Click to enlargeTo begin, you click the button on the home page of the site that says "Explore the Math". Then choose your character, and you'll be on the main street (see screenshot above) . Then use arrow keys to move right or left, and click to select a company to visit.The companies you can visit are:Sweet Treat Cafe…

• Percentages with mental math

  1 Nov 2009 | 9:38 am

  (This is an older post that I have revised plus added a video to it.)In this article I want to explore some ideas for using MENTAL math in calculating percents or percentages.I have made this video of percent & mental math strategies as well:And here are the ideas:Find 10% of some example numbers (by dividing by 10).Find 1% of some example numbers (by dividing by 100).Find 20%, 30%, 40% etc. of these numbers.FIRST find 10% of the number, then multiply by 2, 3, 4, etc.For example, find 20% of 18. Find 40% of $44. Find 80% of 120.I know you can teach the student to go 0.2 × 18, 0.4 × 0.44,…

• Cell size and scale

  30 Oct 2009 | 8:40 am

  Just a neat link my hubby found this morning...http://learn.genetics.utah.edu/content/begin/cells/scale/You can zoom in to see these various things starting from a coffee bean and down to a skin cell, human egg, red blood cell, bacteria, viruses, hemoglobin, glucose and molecules, etc., all the way "down" to a carbon atom.In measuring scale, you go from millimeters (0.001 or 10-3m) to micrometers (0.000001 or 10-6m) to nanometers (0.000000001 or 10-9m) to picometers (0.000000000001 or 10-12m).

• American Math Challenge

  24 Oct 2009 | 1:35 pm

  The American Math Challenge is an online math challenge or "competition" where students aged 9-14 from across America can compete in a safe, multiplayer game environment.This is from the same folks as the World Math Day, if you happen to remember that.Students will have the task of answering as many correct questions as they can in 60 second mental arithmetic challenges LIVE, against other students. Or, they can also solve questions based on the national curriculum at their own pace.Why would you take part?It's about having fun with math. In fact, there's a good chance your students/children…

• Wolfram|Alpha homework day

  21 Oct 2009 | 5:48 am

  Today October 21st is a Wolfram|Alpha Homework Day. I am not quite sure myself what all this entails, but it is a LIVE interactive event on the web, revolving around what can be done with Wolfram|Alpha search engine.Here are some highlights (from the website) of what will be happening over there today: A special Homework Day Welcome from Stephen WolframA demonstration by a forward-looking elementary school teacher of lesson plans that use Wolfram|AlphaA conversation with the creator of "Shift Happens" about tech trends and their impact on educationA fun experiment with Wolfram|Alpha's mad…

• 
  About.com: Math

• Looking for a Career in Math?

  6 Nov 2009 | 5:40 am

  The American Mathematical Society (AMS) has an oustanding career section for those interested in pursuing careers in mathematics. Not only will you find the job listings but you'll also find a wealth of information pertaining to early prep., issues great advice for new PHDs and programs. If you haven't visited the AMS site before, it's well worth a bookmark.Looking for a Career in Math? originally appeared on About.com Mathematics on Friday, November 6th, 2009 at 13:40:20.Permalink | Comment | Email this

• Scientific Notation Worksheets

  3 Nov 2009 | 5:14 am

  Check out the scientific notation worksheets with answers on the 2nd page of the PDF. After all, practice makes perfect, or at least improves learning!Not sure about Scientific Notation? It's really just a method of writing very large or very small numbers in a form of shorthand. Scientists developed this method many years ago to provide them with a method to save time by easily representing numbers by using less characters. See more.Scientific Notation Worksheets originally appeared on About.com Mathematics on Tuesday, November 3rd, 2009 at 13:14:47.Permalink | Comment | Email this

• What Can We Learn From Martin Gardner?

  31 Oct 2009 | 1:00 am

  The year was 1956, Martin Gardner who had never taken a math course since high school left his job with Humpty Dumpty and began writing recreational math for Scientific American. Mr. Gardner just turned 95 and has now published 70 books! He has probably turned more people on to the joy of math than anyone else! Why? Because he makes math fun! "He has turned thousands of children into mathematicians, and thousands of mathematicians into children." Ronald Graham, University of California. Many teachers use Gardner's puzzles as part of the problem solving in their math program. Making math fun…

• Singapore Math

  28 Oct 2009 | 8:04 am

  Why is it that this tiny country scores so high in mathematics? Is it their curriculum? Is it their superior approach to teaching math? Do Singapore students actually have superior ability? Something they're doing is working and it sure would be nice to know just what is working. Other countries could certainly learn from and benefit from whatever it is that is working there, I would think. Note: The Singapore Math Curriculum and the actual core math curriculum/program used in Singapore are NOT the same. As a result of Singapore's success, the Singapore Math Curriculum is getting a great deal…

• Order of Operations

  26 Oct 2009 | 4:16 am

  The order of operations is taught usually in the 7th grade and is used immensely for many grades beyond. Usually the problem with teaching the order of operations is that it becomes a task for memory. Hence, it's more important that students understand why there is order. Be sure to use manipulatives and basic questions when starting out with the order of operations. Here are some great basic worksheets to start with.See also, how to solve the classic algebra age problem questions that tend to appear in most math text books.Order of Operations originally appeared on About.com Mathematics on…

• 
  Let's Play Math

• Quotable

  Denise

  5 Nov 2009 | 5:15 pm

  “Let’s give the governor a break,” says Williams College mathematician Edward Burger. “If nothing else, he’s encouraging math education.” — Carl Bialik Coincidental Obscenity Deemed Extremely Dubious

• Math Teachers at Play #19

  Denise

  1 Nov 2009 | 8:50 am

  Check out the new math carnival to discover plenty of great fun for all ages: Math Teachers at Play #19 Are you wondering where MTAP #18 went? Here’s the story (contest-winning entry from Lisa Downing), and we’re sticking to it! “The Odds were at odds with the Evens. It never seemed fair to them that two Odds made an Even but two Evens didn’t make an Odd…” [Click over to MTaP #19 to read more.]

• New Blog: 19 & Still Alive

  Denise

  28 Oct 2009 | 8:17 am

  [Graphite drawing by Niner.] Niner (pronounced Neener), who takes the photos for my blog header — which reminds me, we’re about due for a new one of those… — has started a new blog. She calls it 19 & Still Alive, because “the world doesn’t end when you’re 16 if you don’t go to Prom or don’t get your driver’s license. (I never went to Prom, and I didn’t go through Driver’s ED until 17, but I’m alive, amazingly.)” There won’t be any math there, or at least I don’t expect to see any; the blog will be mostly her rambling thoughts…

• Algebra: A Problem in Translation

  Denise

  27 Oct 2009 | 9:30 am

  [Photo by *Irish.] In my post Pre-Algebra Problem Solving: The Tools, I introduced word algebra as a way to help students think their way through a story problem. In the next two posts, I showed how the tool worked with simple word problems. Now, before I move on to focus exclusively on bar diagrams, I would like to show how word algebra can help a student solve a typical first-year algebra puzzle. A homeschooling friend who avoided algebra in high school, trying to help her son cope with a subject she never understood, posted: “Help! Our answer is different from the…

• Contest: Write a Number Story

  Denise

  25 Oct 2009 | 12:41 pm

  Math Mama is hosting the next Math Teachers at Play blog carnival (submit your post here) on Friday, and she writes: The Math Teachers at Play blog carnival came out twice as #15. Since then we’ve had #16 and #17. We’d like to iron out the numbering, and so the upcoming issue will be #19. I am personally sponsoring a contest for the best little (ie, very short) story written about how the numbers got mixed up this way… For more details, check out her blog post: Contest: Write a number story by Wednesday Beginning next month, the MTaP carnival will change its schedule, coming…

• 
  Logic Matters

• Gödel Without Tears -- 5

  6 Nov 2009 | 7:16 am

  Here now is the fifth episode on the idea of a primitive recursive function. The preamble explains why this matters and where this is going. [As always, I'll be very glad to hear about typos/thinkos.]The previous episodes are available:Episode 1, Incompleteness -- the very idea (version of Oct. 16)Episode 2. Incompleteness and undecidability (version of Oct. 26)Episode 3. Two weak arithmetics (version of Nov. 1)Episode 4. First-order Peano Arithmetic (version of Nov. 1)

• Ruse gets a beta minus.

  4 Nov 2009 | 3:00 pm

  Philosophers don't get asked often enough to write for the newspapers and weeklies: so it is really annoying when an opportunity is wasted on second-rate maunderings. Michael Ruse writes in today's Guardian on whether there is an "atheist schism". And he immediately kicks off on the wrong foot.As a professional philosopher my first question naturally is: "What or who is an atheist?" If you mean someone who absolutely and utterly does not believe there is any God or meaning then I doubt there are many in this group.Eh? Where on earth has that "or meaning" come from? In what coherent sense of…

• The Autonomy of Mathematical Knowledge -- Chap. 2, §§3-5

  4 Nov 2009 | 3:18 am

  To return for a moment the question we left hanging: what is the shape of Hilbert's "naturalism" according to Franks? Well, Franks in §2.3 thinks that Hilbert's position can be contrasted with a "Wittgensteinian" naturalism that forecloses global questions of the justification of a framework by rejecting them as meaningless. "According to Hilbert … mathematics is justified in application" (p. 44), and for him "the skeptic's path leads to the death of all science". Really? But, to repeat, if that is someone's basic stance, then you'd expect him to very much want to know which mathematics is…

• The Autonomy of Mathematical Knowledge -- Chap. 2, §§1 & 2

  2 Nov 2009 | 7:57 am

  Hilbert in the 1920s seems pretty confident that classical analysis is in good order. "Mathematicians have pursued to the uttermost the modes of inference that rest on the concept of sets of numbers, and not even the shadow of an inconsistency has appeared .... [D]espite the application of the boldest and most manifold combinations of the subtlest techiniques, a complete security of inference and a clear unanimity of results reigns in analysis." (p. 41 -- as before, references are to passages or quotations in Franks' book.) These don't sound like the words of a man who thinks that the…

• Gödel Without Tears -- 4

  2 Nov 2009 | 5:20 am

  Here now is the fourth episode [slightly corrected] which tells you -- for those who don't know -- what first-order Peano Arithmetic is (and also what Sigma_1/Pi_1 wffs are). A thrill a minute, really. Done in a bit of a rush to get it out to students in time, so apologies if the proof-reading is bad!Here are the previous episodes:Episode 1, Incompleteness -- the very idea (version of Oct. 16)Episode 2. Incompleteness and undecidability (version of Oct. 26)Episode 3. Two weak arithmetics (version of Nov. 1)

• 
  The Unapologetic Mathematician

• An Example of a Parallelogram

  John Armstrong

  5 Nov 2009 | 7:46 am

  Today I want to run through an example of how we use our new tools to read geometric information out of a parallelogram. I’ll work within with an orthonormal basis and an identified origin to give us a system of coordinates. That is, given the point , we set up a vector pointing from to (which we can do in a Euclidean space). Then this vector has components in terms of the basis: and we’ll write the point as . So let’s pick four points: , , , and . These four point do, indeed, give the vertices of a parallelogram, since both displacements from to and from to are , and…

• Parallelepipeds and Volumes III

  John Armstrong

  4 Nov 2009 | 9:04 am

  So, why bother with this orientation stuff, anyway? We’ve got an inner product on spaces of antisymmetric tensors, and that should give us a concept of length. Why can’t we just calculate the size of a parallelepiped by sticking it into this bilinear form twice? Well, let’s see what happens. Given a -dimensional parallelepiped with sides through , we represent the parallelepiped by the wedge . Then we might try defining the volume by using the renormalized inner product Let’s expand one copy of the wedge out in terms of our basis of wedges of basis vectors where the…

• Parallelepipeds and Volumes II

  John Armstrong

  3 Nov 2009 | 8:29 am

  Yesterday we established that the -dimensional volume of a parallelepiped with sides should be an alternating multilinear functional of those sides. But now we want to investigate which one. The universal property of spaces of antisymmetric tensors says that any such functional corresponds to a unique linear functional . That is, we take the parallelepiped with sides through and represent it by the antisymmetric tensor . Notice, in particular, that if the parallelepiped is degenerate then this tensor is , as we hoped. Then volume is some linear functional that takes in such an antisymmetric…

• Parallelepipeds and Volumes I

  John Armstrong

  2 Nov 2009 | 4:00 am

  And we’re back with more of what Mr. Martinez of Harvard’s Medical School assures me is onanism of the highest caliber. I’m sure he, too, blames me for not curing cancer. Coming up in our study of calculus in higher dimensions we’ll need to understand parallelepipeds, and in particular their volumes. First of all, what is a parallelepiped? Or, more specifically, what is a -dimensional parallelepiped in -dimensional space? It’s a collection of points in space that we can describe as follows. Take a point and vectors in . The parallelepiped is the collection of…

• Sunday Samples 145

  John Armstrong

  1 Nov 2009 | 8:58 am

  On Tuesday I posted a still from The Coen Brothers’ new film A Serious Man. Firmly rooting the film in mid-1967, and in a sense of existential crisis and alienation, is the repeated use of Jefferson Airplane’s hit, “Somebody To Love”. When the truth is found To be lies And all the joy Within you dies Don’t you want somebody to love? Don’t you need somebody to love? Wouldn’t you love somebody to love? You better find somebody to love When the garden flowers Baby, are dead, yes And your mind, your mind Is so full of red Don’t you want somebody to…

• 
  Basic-Mathematics

• History of fractions

  3 Nov 2009 | 1:28 pm

  This lesson presents a brief history of fractions by outlining its major developmemts over time.

• Basic math test

  3 Nov 2009 | 4:29 am

  Take this comprehensive basic math test to find out how well you know your basic math skills.

• Geometry test

  2 Nov 2009 | 6:38 pm

  Take this comprehensive geometry test to find out how well you know your basic skills in geometry.

• Base five numeration system

  26 Oct 2009 | 4:19 pm

  This lesson will give you a deep and solid introduction to base five numeration system

• Converting repeating decimals to fractions

  24 Oct 2009 | 5:24 pm

  A top-notch lesson about converting repeating decimals to fractions. The lesson is crystal clear and right to the point

• 
  The Math Mojo Chronicles

• Goodbye, Soupy

  Brian

  23 Oct 2009 | 4:39 am

  This will not have much to do with math, but a lot to do with mojo. One of my heros, Soupy Sales, died yesterday. Click here to view the embedded video. Soupy was a comedian, who hosted a children’s show in the 50’s and 60’s. He was a master absurdist, with an incredible sense of humor, and a wonderful respect for the minds of his audience. His show was booked as a “children’s show”, but his material was aimed a little higher – over the kid’s shoulders with a nodding wink to their parents. Soupy is among the other master creators, like Lewis…

• Martin Gardner – Happy Birthday!

  Brian

  21 Oct 2009 | 3:43 pm

  How could I have missed it? Or almost have missed it. Today is Martin Gardner’s 95th birthday. Who is Martin Gardner, you ask? I’m glad you asked that question! You can read more about it in today’s New York Times Science Section. I’ll write more about him soon, but for now, do yourself a huge favor and check out that article, then run to a library and check out any math books of his that you can find. Here’s another good article about Martin Gardner in the New York Times.

• What if we are Not Allowed to do it that Way?

  Brian

  15 Oct 2009 | 4:26 pm

  Here’s a dilemma for a lot of parents and other people who are trying to teach their kids math: The methods that many people use are far superior to the standard algorithms taught in elementary school, yet many benighted administrators and school policy-makers do not recognize this, and insist that students do things “the regular way.” Of course they don’t realize that other cultures (besides the U.S.) have a different “regular way” that sometimes beat the poop out of our way – which is proven by our low ranking among most other countries of the world…

• Schools without Principles

  Brian

  12 Oct 2009 | 10:09 am

  I was poking around some old files on my computer this morning, and came across something I’d scanned from our local newspaper back in 2002. It’s just one of the reasons schools need work. Get it? Hotcha, - Professor Homunculus

• How to Present New Math Ideas

  Brian

  26 Sep 2009 | 1:20 pm

  Using magic to present new math Ideas An insightful reader wrote in: Susan Grigor wrote: Good morning, Brian, I want to consult your wife as one who works with little people. I have been looking at the Grade 3 and Grade 4 curricula. There is a lot about looking for alternate strategies such as 26 + 35 = 30 – 4 + 30 + 5 = 61. Note, however, that positive and negative numbers are not taught until Grade 7. Kids even up to Grade 7 are literal/concrete thinkers, not abstract thinkers. How well do they use these abstract ideas? They are mental gymnastics. Susan, I don’t see anything in…

• 
  The Everything Seminar

• The Beam is Back

  Jim Pivarski

  28 Oct 2009 | 10:20 am

  A little over a year after the highly publicized start-up and break-down of the LHC, the damage has been repaired, new protection systems are in place, and all sectors are cold and ready for beam. Yesterday, the first injection test of 2009 was completed— beams of protons and heavy ions were successfully threaded into the LHC beampipe from its predecessor, the Super Proton Synchrotron (SPS). The beams were allowed to flow as far as the first experiments in both directions, ALICE on the clockwise side, LHCb on the other. The publicity of the turn-on events will be somewhat more subdued…

• What killed Madame Curie? (Part 4)

  Jim Pivarski

  7 Sep 2009 | 7:26 am

  New York City, 1956 Leaning on a Chinese restaurant at a busy street corner in Greenwich Village, I crossed my legs, tipped my hat low, and quietly panicked. This case is turning into a nightmare: dozens of suspects, growing daily, and they all seem to swap places when you’re not looking. A pion couldda done it; pions seem to be some kind of front for the nuclear force that Madame Curie was playing with before she died. But leave a pion to itself and it disintegrates into a muon and a neutrino, neither of which claims to have ever heard of nuclear forces. Radiation in the form of muons…

• What killed Madame Curie? (Part 3)

  Jim Pivarski

  27 Jun 2009 | 4:48 pm

  Ithaca, NY, 1948 After a wrong turn in Albuquerque, I caught up with Bugs Bunny, alias Richard Feynman, somewhere near the ends of the earth.  Up to my elbows in snow-drifts, I spied on the little window to his office, in which he seemed to be doing normal professor-things, plus wild gesticulations.  I decided on a particularly frozen morning that I would have to risk visibility if I was to get answers, so I enrolled at Cornell, posing as a G.I. bill student.  In Professor Feynman’s introductory physics lectures, I could see that there was something remarkable happening here. …

• What killed Madame Curie? (Part 2)

  Jim Pivarski

  7 Jun 2009 | 11:55 pm

  Los Alamos, 1946 I should have sought Dr. Fermi right away, back when it was easy.  When Mademoiselle Curie gave me the lead, Enrico was a quiet university professor in Rome.  Since then, he’s got a lot harder to find, and it seems that the professor has government ties— secrets as big as the men who hide them.  I chanced upon a tip leading me to a project in Manhattan, and though I found Fermi on the books as a Columbia professor, I had just missed the man himself.  Asking an associate about where in the New World this Italian Navigator might be, he turned bright red and…

• What killed Madame Curie? (Part 1)

  Jim Pivarski

  21 May 2009 | 1:32 pm

  July, 1934 I was called to investigate the recent death of a famous physicist: Marie Curie, born Manya Skłodowska.  When I arrived on the scene, she was in her death-bed, her face long and grey, a ghostly shadow in the warm light of the mountain sanatorium.  Her daughter Eve was there.  “It’s so quiet,” she said, “so fearfully motionless—” We made our introductions, but she was obviously distracted.  “So motionless, those hands.  No longer nervously shaking, constantly moving, always working…” I took a look at the hands, still and…

• 
  bodmas blog

• Rodent on steroids

  Keith Burnett

  7 Nov 2009 | 1:49 am

  Orvieto, Italy, November 6, 2009: In partnership with the OpenOffice.org community, WarMouse announced the release of the OpenOfficeMouse, the first multi-button application mouse designed for the world’s leading open-source office productivity suite. With a revolutionary and patented design featuring 18 buttons, an analog joystick, and support for as many as 52 key commands, the OpenOfficeMouse is intended to provide a faster and more efficient user interface for OpenOffice.org applications such as Writer and Calc than the conventional icons, pull-down menus, and hotkeys presently…

• Scientific Poster Links

  Keith Burnett

  5 Nov 2009 | 4:49 am

  Students on science degrees usually learn how to present findings in the form of a ‘poster’. A science poster is a special kind of wall display invented so everyone who attends a conference can present their results even though there is not enough time for them all to speak. MS PowerPoint (and OpenOffice Impress) can be used to make posters easily – just use a single slide resized to A1 or A0 depending on the size of your poster. Then set up columns using text boxes and import (or draw) some images. Must Below are some links to places where you can find out more about…

• Telephone Box Gallery

  Keith Burnett

  31 Oct 2009 | 2:06 pm

  The Gallery on the Green is a postcard gallery in a telephone box in Settle. The Upper Settle green is a small patch of grass in an older and quiet part of Settle, away from the market place. When we visited, there was a range of small images on view, and a comments book. I can remember actually using the phone box when it had a working pay phone in the days when mobile phones needed separate battery packs. The red box looks reassuringly familiar. The crows seem to have decamped from the large plane tree, judging by the quiet and absence of ‘crow marks’ on the seat under the tree.

• Lowest terms

  Keith Burnett

  22 Oct 2009 | 2:11 am

  6 minutes and 43 seconds on how to cancel down a fraction to its lowest terms. I’d rather describe that as ‘remove all the common factors from a fraction’. Produced using the NCH Debut video capture software, and edited in Windows Movie Maker. Notes on how to do all this coming soon.

• Multiplying fractions

  Keith Burnett

  19 Oct 2009 | 2:02 pm

  2 minutes and 28 seconds on multiplying fractions. Recorded as a quick reminder for students on a return to study course. Produced on my College issue laptop using the free version of the NCH Debut screen and Webcam capture software, and using the cheapo USB microphone (Logitech and Belkin sell the same oem device). Attempts to use the built in microphone on the laptop failed despite the placement of the microphone high up on the screen near the Web cam.

• 
  ChapterZero

• Graph layout by Stress Majorization by Optimization of A Complicated Function

  Alex

  6 Nov 2009 | 6:30 pm

  I haven’t had much to talk about lately– the Probabilistic Graphical Models course is eating up my time like crazy: I haven’t had time to do anything but that and prepare my lectures and homeworks for the Matlab/Mathematica course– but I have been doing a lot of coding for the course I’m teaching and the course I’m taking. Most of it isn’t fit for public consumption, but some of it is worth sharing/archiving here. The code below takes the weighted adjacency matrix of a graph and returns a planar embedding using stress majorization by optimization of a…

• OS Choices

  Alex

  25 Oct 2009 | 3:10 pm

  Ubuntu 9.10, or Windows 7? I like the idea of Ubuntu, and I can do almost everything I want with it, with the important exception of easily accessing the campus wireless network. I also don’t know if it interfaces with projectors as easily as Windows does. Those are my two main issues. Other than that, there’s the eye candy factor: Windows probably will have a slicker interface. The change from Hardy to Jaunty was striking to me, visually, but what I’ve read of Karmic Koala doesn’t indicate that I can expect a similar jump. I could always do a dual boot again, but…

• Good news for people who like bad news

  Alex

  20 Oct 2009 | 6:56 pm

  I’ve discovered, once again, the problem with using random test cases. I thought I’d come up with some nice manipulations that reduced the nonnegative least squares problem to a problem on a polytope (more relevantly, a bounded convex set), so I could apply any number of methods that have been developed for constrained minimization over bounded convex sets. When I tested one such algorithm in combination with my reduction, it gave wonderful results. But now, I’ve realized that my reduction was completely wrong (at some point I implicitly assumed that the matrix I’m…

• example MATLAB animation -> animated gif

  Alex

  15 Oct 2009 | 7:23 pm

  I always forget how to make animations in MATLAB, and I never knew how to make animated gifs before. I figured this out for the MATLAB course, but I don’t think I’ll go over it in class, since I don’t want to get into handle graphics nastiness. But for my own reference, and anyone who may be looking for ways to do this, this code gives the gist of it: clf theta = linspace(0, 2*pi, 200); x = cos(theta); y = sin(theta); hbead = line(x(1), y(1), 'marker', 'o', 'markersize', 8); htrail = line(x(1), y(1), 'marker', '.', 'color', 'r'); axis([-1 1 -1 1]); axis('square'); im = {};…

• Any mathematicians want to give Sex Advice?

  Alex

  30 Sep 2009 | 11:14 pm

  I know several mathematicians read this blog. Hahahahahaha. Seriously, if you are an element in this set and are interested in participating in the Nerve.com “Sex Advice From” column, let me know. They’re looking for mathematicians to go through an interview, by email or over the phone. (Apparently graduate students count, or they wouldn’t have contacted me?) They’ll publish some of your answers along with a picture. Here are three sets of past interviews from the column, so you’ll know what you’re signing up for:…

• 
  Computational Complexity

• Button Button

  Lance

  6 Nov 2009 | 5:29 am

  Here is the offer: If you press the button you will receive $200,000. The caveat: Someone you don't know will die. I was born during run of the original Twilight Zone but growing up watched them over and over again in reruns. People dealing with some small change in reality often with a clever twist in the ending. But they made you think. CBS had a remake of the Twilight Zone series in the mid-80's. But nearly all the episodes were quite bland and highly predictable stories. But one episode in that new series, "Button Button", which made that offer above, caught be by surprise and worthy of…

• Innovation

  Lance

  5 Nov 2009 | 4:21 am

  The new Innovations in Computer Science conference announced their accepted papers earlier this week including my paper with Rahul Santhanam "Bounding Rationality by Discounting Time". Shiva is collecting PDF pointers (hope to get ours posted and on that list soon). According to Noam, "this is the most interesting list of accepted papers that I’ve seen in years". Suresh seems happy too but some of his commenter's were less impressed. I view ICS as playing an orthogonal to STOC/FOCS, trying to present papers with potentially interesting ideas that wouldn't normally be accepted into STOC or…

• Amir Pnueli (1941-2009)

  Lance

  4 Nov 2009 | 3:26 am

  Amir Pnueli passed away Monday from a brain hemorrhage. Amir was an expert in program verification who won the 1996 Turing Award primarily for his 1977 FOCS paper The Temporal Logic of Programs. Lenore Zuck shares her thoughts.I'm reading through what people wrote about Amir in the past 30 or so hours since we received the sad news of his passing. I'm leafing through the citations of his numerous awards and honorary degrees, the list of academies of which he was a member, and the lists of his unique accomplishments. Throughout today I was helping with NYU's press release about him. Everybody…

• Really Liked Bertinoro- Ramsey Thing

  GASARCH

  3 Nov 2009 | 10:56 am

  (Reminder: STOC Deadline Thursday Nov 5, 7:00PM, Eastern: link.) After yesterday's post about RaTLoCC 2009 (Ramsey Theory in Logic, Combinatorics, and Complexity) at Bertinoro some people emailed me and others commented asking Did you like it?. AH- my post was about what I learned there but not whether I liked it. IT WAS GREAT! I was at Dagstuhl Complexity a few weeks earlier and that was also GREAT! Some comparisons: Both meetings had the same format. Guests are invited, the area is specialized, there are talks in the morning, then a long lunch break (12:00-3:00 or so) then more talks. Also…

• Report From Ramsey-Logic-Complexity Workshop

  GASARCH

  2 Nov 2009 | 10:47 am

  Back from RaTLoCC 2009 which is Ramsey Theory in Logic, Combinatorics, and Complexity. Here are the list of talks: here. Reverse Mathematics tries to classify theorems by what is the strength of the axioms needed to prove them. There are five levels that almost all theorems in mathematics fit into. One curious outlier: the infinite Ramsey Theorem for pairs (for all c, for all c-colorings of the unordered pairs of naturals, there exists an infinite homogeneous set--- that is, a set of naturals where every pair has the same color). It does not fit in nicely. Ramsey for triples, etc, does. One…

• 
  Mathematics and Computation

• Constructive gem: double exponentials

  Andrej Bauer

  11 Oct 2009 | 3:58 pm

  In the last constructive gem we studied the exponential `2^NN` and its isomorphic copies. This time we shall compute the double exponential `2^(2^NN)` and even write some Haskell code. By `2` we mean the set `{0,1}` of the Boolean values. First note that there is a difference between `(2^2)^NN` and `2^(2^NN)`. The former is isomorphic to the Cantor space `2^NN` because `(2^2)^NN = 2^(2 \times NN) = 2^NN`, while the latter is the space of functionals, which are maps from infinite binary sequences to bits. In Haskell we would define these as type Nat = Int -- notational convenience type Natural…

• Constructive gem: juggling exponentials

  Andrej Bauer

  9 Sep 2009 | 10:58 am

  Constructive gems are usually not about particular results, because all constructive results can be proved classically as well, but rather about the method and the way of thinking. I demonstrate a constructive proof which can be reused in three different settings (set theory, topology, computability) because constructive mathematics has many different interpretations. Let me first introduce some notation: `1 = {0}` is the singleton set, or the unit. `2 = 1 + 1 = {0,1}` is the booleans. In general, `[n]= {0, 1, …, n-1}` is the `n`-fold coproduct of singletons. For brevity we will write…

• Constructive stone: minima of sets of natural numbers

  Andrej Bauer

  8 Sep 2009 | 1:58 pm

  I promise I will post a constructive gem soon. This constructive stone came up as a reaction to the cardinality of finite sets stone. I show that inhabited sets of natural numbers need not have minima, constructively. Here is a seemingly reasonable attempt at defining the cardinality of a finite set `S`: it is the least `n` such that there is a listing `(x_1, …, x_n)` of `S`. Unfortunately, constructively we cannot show that such a minimal `n` exist! Proposition: If every inhabited subset of `NN` has an infimum then the law of excluded middle holds. Proof. I hope you’re getting…

• Constructive stone: cardinality of sets

  Andrej Bauer

  8 Sep 2009 | 8:06 am

  Cardinality of sets in constructive mathematics is not as well behaved as in classical mathematics. Cardinalities of finite sets are not natural numbers, and cardinalities are not linearly ordered. First of all, constructively we cannot measure the size of finite sets with natural numbers. As soon as we require that the cardinality of singletons be 1, we’re in trouble (recall that a set `S` is a singleton when there exists an element of `S` and, for all `x, y`, if `x in S and y in S` then `x = y`): Proposition: Suppose `c` is a map which assigns to each finite set a natural number, such…

• Constructive stone: finite sets

  Andrej Bauer

  7 Sep 2009 | 2:15 pm

  Just like in real life, constructive stones are easier to find than constructive gems, so let me start the series with a stone about constructive finite sets. There are several possible definitions of finite sets. The one that works best classically and constructively is the following. Definition: A set `S` is finite when there exists a natural number `n` and a surjective map `e : {1, 2, …, n} -> S`. We call such an `e` a listing of the elements of `S`. A listing `e : {1, 2, …, n} -> S` is conveniently displayed as a list `(e(1), e(2), …, e(n))`. Given objects `x_1,…

• 
  Natural Blogarithms

• How the Psalms Motivate Us to Marvel at Creation

  SplineGuy

  30 Oct 2009 | 6:45 am

  This week I was given the privilege of leading our campus Environmental Stewardship Bible Study.  Currently the study is walking through various sections of the Bible in order to provide a scriptural foundation for concepts in environmental stewardship.  It was my good pleasure to lead a study on Psalms.  While the actual Bible Study was driven by some excellent discussion, much of the material in the study below I was unable to get to.  This outline has been posted in our Blackboard classroom for the Bible study but I also post it here for those folks that have been…

• Where the Study of Environmental Stewardship Begins

  SplineGuy

  20 Oct 2009 | 10:17 pm

  In several lengthy discussions that I’ve had with friends and colleagues over my new interest in environmental stewardship, inevitably we begin discussing the stereotypes of environmental activists.  Being raised in West Texas my whole life, I haven’t really encountered very many individuals that would be classified as environmental activists, but I’ve certainly heard my fair share of disparaging political epithets: hippy, environmentalist wacko, tree hugger, ecoterrorist, econazi, etc. If you have a personal conviction to care for God’s creation and feel that abuse to the…

• Euler’s Method in Excel – Very Simple

  SplineGuy

  19 Oct 2009 | 2:56 pm

  During Calculus last week, we covered slope fields and Euler’s method of first order initial-value problems of the form During class we demonstrated the use of slope field to perform a basic qualitative analysis. We utilized a couple of different online applets as well as Maple 13. Visualizing Slope Fields and solutions Another similar page, with zoom Direction Fields – A Maple 13 Worksheet Below is a short demonstration of how we set up a simple application of Euler’s Method in Excel 2007. Consider the simple initial value problem: Recall that Euler’s Method is given by…

• Christian Stewardship of the Environment

  SplineGuy

  16 Oct 2009 | 5:45 pm

  At Wayland, there has been an increased emphasis on the need to "go green".  I’ll admit to having inherited a very West Texas conservative viewpoint on the environment.  I’ll even go so far as to admit not giving it much thought at all and just taking for granted the natural resources that are available to me. So, what is a West Texas conservative viewpoint on the environment?  Allow me to attempt to describe what I think it is and please don’t necessarily take the following as truth or even a fair representation of what I currently believe. And…

• List Your Self: Turning Points

  SplineGuy

  15 Jun 2009 | 12:14 pm

  I have a book on my shelf that I’ve probably had for close 15 years.  Every once in a while I pull it off the shelf and tell myself that I should read it and try it out.  The book is called “List  Your Self: Listmaking as the way to Self-Discovery”.  The subtitle says that it is “A provocative, Probing and Personal Expedition Into Your Mind, Heart, and Soul” Seems to me that this is not only great fodder for a blog but also for a social network like facebook.  While many meme’s that go around annoy me to no end, there have been a few that have allowed me…

• 
  Precal Blog

• Vertically Dilating and Translating the Graph of Cosine

  Stephenie

  6 Nov 2009 | 12:40 pm

  Before we get started, here’s a quick review.  We all know that a graph can be transformed.  It can either be dilated or translated.  Algebraically it would look something like this:  f(x)=a+b(cx-d).  We know that a is a vertical translation, b is a vertical dilation, c is a horizontal dilation, and d is a horizontal translation.  Knowing this, we can transform the graph of Cosine.  The graph of cosine algebraically would look like y=A+Bcos[C(?-D)], where A is a vertical translation, B is a vertical dilation, C is a horizontal dilation, and D is a horizontal translation. The…

• Cover It Live! Session

  Reversearp

  3 Nov 2009 | 5:43 pm

  Quarter 1 Exam Study

• Inverse, Reciporical and Applying Algebra Trig

  Eric

  1 Nov 2009 | 8:03 pm

  Eric here to summarize our third hour class period from wednesday. For the first portion of class, we reviewed the difference between the reciporical and the inverse of cosine. Reciporical: 1/cos? = sc? = cos?^-1 Inverse: cos^-1 = cos^-1(u/r) =? The second part of class included applying what we have learned in the past years to what we have learned in the past days.  Last year we learned how to solve algebra trigonometrey problems.  What we have learned so far in the last few class periods have helped us better understand the main concepts of these problems. We did two problems of this…

• Inverse vs. Reciprocal

  Dushan

  27 Oct 2009 | 8:52 pm

  Today in class, we began by going over the claims for sections 2-2 and 2-3. Ali presented the first problem and it asked for the refence angle if theta=-2746 degrees. What he did was divide -2746 by 360, and the answer ends up being -7.62777778.  THis number means that theta makes 7 full rotations in the negative direction and a partial rotation of .62777778.  Net he multiplied -.62777778 by 360, and that answer would give him the measure of theta so he could plot it on a uv axis without spiraling seven times around the origin.  The value for theta is -226 degrees, making it in the 3rd…

• Reciprocal Trig. Functions

  Jack

  26 Oct 2009 | 6:17 pm

  Today in class we learned about Reciprocal Trig. Functions and how they are related to their Reciprocals. To start out, our original functions are Sin of Theta = V/R, Cos of Theta = U/R, and Tan of theta = V/U. Sin’s reciprocal is CSC theta = 1/sin of Theta = R/V. Cos’s reciprocal is SEC theta = 1/Cos theta = R/U. Last, Tan’s reciprocal is COT theta = 1/Tan theta = U/R. It is very important that everyone is clear that the Reciprocals and Inverse are two DIFFERENT things. Also, remember that 1/csc = Sin theta, 1/sec = Sin theta, and 1/cot = Tan theta. Next we moved onto an…

• 
  The Calculist

• Ezra: Function calls are not stack frames

  4 Nov 2009 | 1:30 pm

  I don't have much to add to this but Ezra's saying things that are true:Tim Bray is spreading more misinformation about tail recursion. He describes it this way: It looks like a subroutine call, but in the case where it occurs as the last thing in the routine, it magically, silently, and automatically gets turned into, now how did I put it? “A highly controlled and structured GOTO.” A tail-call is a subroutine call. The efficient implementation does not magically transformed into something else; if it doesn't create a stack frame on such a call, it's because one simply isn't relevant.It's…

• Proposed json.plt change

  8 Sep 2009 | 7:49 am

  I'm not sure how many users I have of my json.plt PLaneT package, nor how many of them read my blog. But I thought I'd see if I could take a straw poll here. I'm thinking about changing the data definition in a backwards-incompatible way. What if I said:A jsexpr is one of:'nullbooleanstringintegerinexact-real(vectorof jsexpr)(listof (cons symbol jsexpr))The nice thing about this representation is that it's easier to quote and quasiquote. The down-sides are that array manipulation is a little less convenient, and table lookup is slower.Another alternative is:A jsexpr is one of:#:null boolean…

• Mitchfest blog

  3 Sep 2009 | 2:07 pm

  We've created a Mitchfest blog where we'll be posting updates on new material as it becomes available, including presentation slides, videos, and publication of issues of the Festschrift.

• Quote of the day

  17 Aug 2009 | 9:52 am

  "What's surprising to me is that this language ever managed to achieve widespread use - but I guess it's just another example of how you can break a whole bunch of precious rules and the sky doesn't necessarily fall in. Software is full of people declaiming their 'thou shalt not' lists, and right across the street there's another bunch of people breaking those very rules quite profitably." -- Daniel Earwicker

• Mitchfest program

  11 Aug 2009 | 1:28 pm

  We've posted the Mitchfest schedule and program!

• 
  The Math Less Traveled

• minim

  Brent

  4 Nov 2009 | 9:00 am

  A fun game I discovered recently, minim. In each level you start out with a network of numbered nodes, and the object is to successively combine the nodes according to certain mathematical rules in order to end up with only a single node. The levels start out easy but get fiendishly difficult by the end. My only complaint is that it isn’t possible to make up your own custom levels.

• Logicomix: An Epic Search for Truth

  Brent

  2 Nov 2009 | 4:58 am

  I recently acquired a copy of Logicomix: An Epic Search for Truth, by Apostolos Doxiadis and Christos Papadimitriou, with art by Alecos Papadatos and Annie Di Donna. It defies categorization: is it a comic book? A biography? A book of philosophy? Of history? Of mathematics? Well, it’s all of these things, and manages to pull it off with grace and style. Logicomix is a graphic novel focusing on the story of Bertrand Russell, the English mathematician and philosopher, and the quest at the beginning of the twentieth century to discover a logically rigorous foundation for mathematics. This…

• The hyperbinary sequence and the Calkin-Wilf tree

  Brent

  18 Oct 2009 | 11:45 am

  Recounting the RationalsRecounting the Rationals, part IRecounting the Rationals, part II (fractions grow on trees!)Recounting the Rationals, part IIIRecounting the Rationals, part IVRecounting the Rationals, part IVb: the Euclidean AlgorithmChallenge #12: sums of powers of twoChallenge #12 solution, part IIMore hyperbinary funHyperbinary conjecture seeking proof for a good time, long walks on the beachThe hyperbinary sequence and the Calkin-Wilf tree And now, the amazing conclusion to this series of posts on Neil Calkin and Herbert Wilf’s paper, Recounting the Rationals, and the…

• Hyperbinary conjecture seeking proof for a good time, long walks on the beach

  Brent

  12 Oct 2009 | 6:31 am

  Recounting the RationalsRecounting the Rationals, part IRecounting the Rationals, part II (fractions grow on trees!)Recounting the Rationals, part IIIRecounting the Rationals, part IVRecounting the Rationals, part IVb: the Euclidean AlgorithmChallenge #12: sums of powers of twoChallenge #12 solution, part IIMore hyperbinary funHyperbinary conjecture seeking proof for a good time, long walks on the beachThe hyperbinary sequence and the Calkin-Wilf tree Here’s the latest progress on the hyperbinary sequence. We’re trying to figure out the inverse relation of the function : given a…

• New and improved: bookshelf and Carnival of Mathematics

  Brent

  10 Oct 2009 | 12:01 pm

  Two things today: first, I’ve updated my “bookshelf” (go to http://www.mathlesstraveled.com/, scroll down a bit and look in the right margin). The books come from my LibraryThing library, and I’ve now figured out how to write reviews of the books and have them show up directly in my bookshelf! I’ve added one or two reviews but plan to add more over the coming weeks. I also plan to write blog posts reviewing a few particular books I’ve acquired recently. If you’re looking for a fun math book, I hope you’ll find this a good place to start!

• 
  Rational Mathematics Education

• Good Tests, Bad Tests: Can The Testing Fanatics Tell The Difference?

  29 Oct 2009 | 1:09 pm

  And do they really care?Consider the following problem:=====================================3, 4, 6, 7, 10, 12The number n is to be added to the list above. If n is an integer, which of the following could be the median of the new list of seven numbers?I. 6II. 6 1/2III. 7(A) I only (B) II only (C) III only (D) I and III only (E) I, II, and III==============================================In considering your evaluation of the question, you may wish to know the following facts: this is the 13th of 16 questions for which the total time allotted is 20 minutes. The question appeared on the last of…

• You Want Proof? I'll GIVE You Proof!

  13 Jun 2009 | 10:17 am

  Once again, the fires of discord are raging on math-teach@mathforum.org. One of the threads I've been embroiled in revolves on several axes: one is about teaching pure mathematics in K-12. Another is about visual proofs. The one I wish to specifically deal with here is the one that links the two: what comprises the nature of proof in elementary school mathematics classrooms and how do we get students in those grades to develop their notions of what a mathematical proof actually is?The problems in having this sort of conversation in a hostile forum like math-teach are legion. One problem is…

• Math Test - a poem.

  3 Jun 2009 | 2:07 pm

  I occasionally get requests to post guest pieces at RME, but invariably they prove to be from people looking to promote some sort of commercial web site or service. As those so requesting fail to offer to adequately grease my palm, I always refuse, sometimes in less than friendly fashion.However, I received a work today of such outstanding literary merit, so fraught with relevance to many of the concerns of this blog, that I could not refuse despite the lack of financial incentives from the author. For now, I am going to publish this without attribution to the author, though in due course his…

• Professor Frank Quinn Says: "Calculators? Whoa!"

  25 May 2009 | 10:15 am

  Frank Quinn doesn't like calculators:(what about his dog?)The current (May 2008) NOTICES OF THE AMS contains the following opinion piece from Virginia Tech mathematician, Frank Quinn. It bears noting that the mathematics education folks at his university are members of the math department, which must make for some fun faculty meetings.K–12 Calculator WoesIn the third grade my daughter complained that she wasn’tlearning to read. She switched schools, was classified asLearning Disabled, and with special instruction quicklycaught up. The problem was that her first teacher useda visual word…

• Do I Repeat Myself? - Getting Rote Right

  22 May 2009 | 8:15 pm

  Joseph Mazur, dangerous guyIf you want to get educational traditionalists all aflutter, say something the implies that rote learning may not be all it's cracked up to be. It's about as effective in stirring up ire as burning a US flag in front of the local branch of the American Legion (though I think impugning rote learning isn't likely to get one arrested, jailed, or fined. Yet.)Because I'm basically a bad person, I like to post without comment quotations I consider interesting and potentially provocative on lists inhabited by knee-jerk anti-progressives and educational conservatives. The…

• 
  The Math Factor Podcast

• GJ. Mathletics!

  strauss

  3 Nov 2009 | 11:01 am

  Wayne Winston tells us about his new sports-math book, Mathletics!    

• Yoak: Average Salary

  jyoak

  28 Oct 2009 | 12:47 pm

  Finding yourself chatting around the water cooler one afternoon, you and two co-workers agree that you would all like to know the average of your three salaries but none of you want your individual salary to be known to either of the other two.  Without need of involving any external person or machine as some sort of secret keeper, how can you achieve this end?  

• Morris: Living with Crazy Buttocks

  Stephen Morris

  23 Oct 2009 | 6:59 pm

  Janine is one of twenty guests at a Christmas party.  Each guest is given a book as a present.  Janines’s book is called ‘Living with Crazy Buttocks’.  She isn’t sure what to make of that. The guests are invited to play a game.  Each book is put into an identical cardboard box.  The boxes can be opened and closed without leaving a mark.  The twenty boxes are piled up around the Christmas Tree. The guests are told that they will each have the opportunity to open half of the boxes.  Their objective is to find their own book.  If…

• GI. Mrs Perkins’ Electric Quilt

  strauss

  21 Oct 2009 | 1:49 pm

  Paul Nahin discusses his fabulous new book “Mrs Perkins Electric Quilt“, mosquitos, falling through the Earth, whether mathematics is “real” and much more!  

• Yoak: Foxy!

  jyoak

  14 Oct 2009 | 1:41 pm

  There are five holes in a row in my yard.  A fox lives in them moving around as follows:  Each night, it abandons it current residence and moves to an immediately neighboring hole.  If I’m allowed to check one hole each morning, identify a sequence of holes that I can check in order to be sure to catch the fox.

• 
  WordPress Tag: Mathematics

• Google Treasure Hunt 1 Solution

  orangeverest

  7 Nov 2009 | 12:12 am

  I read in a website regarding a Treasure Hunt Event sponsored by Google dated almost one year ago. The Event is actually a challenge wherein contestants must solve 4 programming problems in order to find the ‘treasure’. I found the first problem easily solved in O(1) runtime via a permutation solution. The event is over so maybe there is nothing wrong if I share my solution. haha. The Problem: A robot is located at the top-left corner of a 44 x 66 grid (marked ‘Start’ in the diagram below). The robot can only move either down or right at any point in time. The robot is trying…

• New study reveals how school choice benefits the poorest students

  Wintery Knight

  7 Nov 2009 | 12:00 am

  Article in the Wall Street Journal. (H/T Jay P. Greene) Excerpt: Opponents of school choice are running out of excuses as evidence continues to roll in about the positive impact of charter schools. Stanford economist Caroline Hoxby recently found that poor urban children who attend a charter school from kindergarten through 8th grade can close the learning gap with affluent suburban kids by 86% in reading and 66% in math. And now Marcus Winters, who follows education for the Manhattan Institute, has released a paper showing that even students who don’t attend a charter school benefit…

• Ladder...

  ironicrantings

  6 Nov 2009 | 10:00 pm

  How about a puzzle to bring the week to a great ending…   Ladder If a ladder is leaning against a building and it touches a bow which is flush against the wall of the building. If the box has a height of  64 units and a width of 27 units then calculate the length of the ladder so that it touches the wall, the floor and the box at the same time…  

• LaTex Example

  vieplivee

  6 Nov 2009 | 9:27 pm

  Copyright by LaTex to WordPress Look at the document source to see how to strike out text, how to use different colors, and how to link to URLs with snapshot preview and how to link to URLs without snapshot preview. There is a command which is ignored by pdflatex and which defines where to cut the post in the version displayed on the main page Anything between the conditional declarations ifblog . . . fi is ignored by LaTeX and processed by latex2wp. Anything between iftex . . . fi is processed by LaTex and ignored by latex2wp. This green sentence appears only in WordPress   This is…

• links for 2009-11-06

  Colleen Young

  6 Nov 2009 | 8:36 pm

  The Google Wave Will Change Education Forever | ISTE Connects – Educational Technology (tags:

• 
  Mr. L's Math

• Algebra Activities that Reach the Kids and Teach the Standards

  Bill Lombard

  5 Nov 2009 | 11:34 am

  I will be presenting a session at the California Math Council’s conference in southern California on 7 November, 2009 with the title of this blog article. I’ve included a link below to the conference presentation. This session will cover several pedagogical topics that have made my students successful learners, including Conceptual Layering, as well as snippets of three popular Teacher to Teacher Press activities that illustrate these topics. I’ll also be presenting another session about GeoGebra, the free open-source software program that is gaining wide acceptance across…

• George Polya, Master Problem Solver – a Model for All Math Teachers

  Bill Lombard

  27 Oct 2009 | 1:20 am

  George Polya George Polya was a master of problem solving, and his effect on other teachers has been extraordinary. His most popular book, How to Solve It, has sold over a million copies. As is the case with many great books, Polya had been turned down by three publishers before finding one to publish the English version in the United States. It has also been translated into 17 languages. I remember reading this book as a high school student and thinking “What a great writer Mr. Polya is, how clearly he presents his topic: Problem Solving.” His approach has had a lasting…

• Martin Gardner – For Decades, Puzzling People With Mathematics

  Bill Lombard

  25 Oct 2009 | 10:54 am

  Martin-Gardner Martin Gardner has published over 70 books and is the chief person responsible for the widespread interest in recreational mathematics. He turned 95 on 21 October, 2009 and celebrated by publishing another book. He authored the Mathematical Games column in Scientific American for 25 years. He quite possibly has introduced more people to the fun inherent in mathematics than any other person. I currently have twelve of his books, and occasionally reread one and get enthused about his topics anew. The New York Times ran a special article on this special person recently. For more…

• First North American GeoGebra Conference – Ithaca, New York

  Bill Lombard

  4 Oct 2009 | 8:08 pm

  The First North American GeoGebra Conference will be held 27-28 July, 2010 at Ithaca College in Ithaca, New York. I’ve been honored to be a part of the Scientific Committee for this conference. This committee has the responsibility of reviewing conference proposals. I’m looking forward to an interesting experience seeing how others use the powerful program, and also what’s in the future for this creative software. The website above has just been created and will be updated as information becomes available. Mark you calendar for an exciting two days with fellow GeoGebra…

• 20 Free Online Math Games for Students

  Bill Lombard

  26 Aug 2009 | 6:24 pm

  Karen Schweitzer The following is a Guest Post from education writer Karen Schweitzer. Karen is the About.com Guide to Business School. She also writes about online colleges for OnlineColleges.net. ++++++++++++++++++++++++++++++++++++++ Interactive math games can make it easier for students to grasp some of the more difficult or tedious concepts in math. The Internet is a good source of free interactive math games for students of all grade and skill levels. Here is a list of 20 math games and sites for K-12 students to explore: APlusMath – APlusMath offers a wide range of mathematics…

• 
  MathNotations

• THE OPEN-ENDED CONTEST PROBLEM AND SOLUTIONS

  Dave Marain

  4 Nov 2009 | 3:04 am

  As promised, here is the open-ended, rubric-based, holistically scored, performance-assessed, student-constructed first problem from MathNotation's Third Contest:1. A primitive Pythagorean triple is defined as an ordered triple of positive integers (a,b,c) in which a2 + b2 = c2 and the greatest common factor (divisor) of a, b and c is 1. If (a,b,c) form such a triple, explain why c cannot be an even integer.Comments(a) The content here is number theory. Is some of this covered in your district's middle school curriculum or beyond? More importantly, at what point do students begin to formulate…

• RESULTS OF THIRD MATHNOTATIONS CONTEST and OTHER NEWS...

  Dave Marain

  3 Nov 2009 | 6:00 am

  FINALLY -- THE RESULTS ARE IN!!I apologize for the delay in getting these results out. The participating schools have all been notified.NOTE: If any participating school did not receive an email from me, the advisor should email me. Also, if I misspelled anyone's name pls let me know and I'll correct it immediately!INITIAL COMMENTS ON CONTEST, ETC...MEAN SCORE: 5.6 PTS OUT OF 12TOPICS INCLUDED Number Theory, Geometric Sequences, Function Notation, Geometry, Discrete Math, Quadratic Functions, and Absolute Value Inequalities (advanced level)Twenty schools registered from around the world, but…

• A Rant, An Update and Model Problems for You

  Dave Marain

  12 Oct 2009 | 3:42 am

  And the seasons they go round and round And the painted ponies go up and down We're captive on the carousel of time We can't return we can only look behind From where we came And go round and round and round In the circle game...Oh, how I love Joni Mitchell's lyrics made famous by the inimitable Buffy Sainte-marie. Oh, how The Circle Game lyrics above describe my feelings about the state of U.S. math education. I feel I've been on this carousel forever. But I do believe that all is not hopeless. I do see promise out there despite all the forces resisting the changes needed to improve our…

• Another Sample Contest Problem - Counting...

  Dave Marain

  5 Oct 2009 | 3:29 am

  There is still time to register for the upcoming MathNotations Third Online Math Team Contest, which should be administered on one of the days from Mon October 12th through Fri October 16th in a 45-minute time period.Registration could not be easier this time around. Just email me at dmarain "at" "gamil dot com" and include your full name, title, name and full address of your school (indicate if Middle or Secondary School).Be sure to include THIRD MATHNOTATIONS ONLINE CONTEST in the subject/title of the email. I will accept registrations up to Fri October 9th (exceptions can always be…

• MathNotations Third Online Free Math Contest Update and Sample "Proof"

  Dave Marain

  4 Oct 2009 | 5:44 am

  There is still time to register for the upcoming MathNotations Third Online Math Team Contest, which should be administered on one of the days from Mon October 12th through Fri October 16th in a 45-minute time period. Registration could not be easier this time around. Just email me at dmarain "at" "gamil dot com" and include your full name, title, name and full address of your school (indicate if Middle or Secondary School). Be sure to include THIRD MATHNOTATIONS ONLINE CONTEST in the subject/title of the email. I will accept registrations up to Fri October 9th (exceptions can always be…

• 
  Neoformix

• More Abstract Images

  6 Nov 2009 | 11:18 pm

  Here is another Delaunay Image, this one created from a well known photograph by Steve McCurry for the National Geographic. The subject was Sharbat Gula and a retrospective on her life done by National Geographic can be found here. Here are a couple of more Voronoi designs based on the same image. I created these images with custom software written in Processing that relies heavily on the Mesh library by Lee Byron. I also used the Mesh demo created by Marius Watz as a starting point for my code. Thanks!

• Delaunay and Voronoi Mona Lisa

  31 Oct 2009 | 10:00 am

  One reason the images I referenced in my previous post caught my eye was that I've been playing around with a similar technique for a couple of months now. I dusted off the code and improved it to support Delaunay images as well as to do shading of the triangles or polygons. Image 1 below shows a Delaunay image constructed from the Mona Lisa. The triangles in the first image are coloured evenly and the shade is the average colour of the three vertices. Image 2 is the same except I'm colouring the triangle pixels based on a function of how far they are from the various vertices and the colours…

• Delaunay Images

  30 Oct 2009 | 1:00 am

  I really like these Delaunay Images created by Jonathan Puckey. The expressiveness derived from a few well chosen triangles is quite impressive. The link above shows a few more as well as a video showing one being created.

• Random Tiles

  25 Oct 2009 | 2:05 pm

  I stumbled across this image by Hugo Dechesne and liked the sense of depth suggested by the stacked tiles. Click on his image to see a higher resolution version. I've tried to recreate the technique and applied it to a more famous image. The second version below just uses smaller tiles. I'm pretty happy with how it came out for such a simple technique but I still prefer the shading in Hugo's images. I think he's using a more diffuse and rounded shadow.    

• Alphabeasties

  25 Oct 2009 | 3:10 am

  I love typographic designs. When I was doing my first work with Word Portraits a year ago it occurred to me that I could probably make a really cool childrens ABC book where the representative images were constructed with words or letterforms. I thought it might be visually interesting and that potentially there might even be an educational benefit for the kids learning to read if the images helped them remember the beginning letter for the word. I haven't pursued the idea yet but I just stumbled across a beautiful example of the same idea. It's called alphabeasties: and other Amazing Types…

• 
  Math & Engineering

• J&B at COMSOL Conference: A Hit with Engineering Enthusiasts

  Molly Whitman

  19 Oct 2009 | 8:23 am

  October 8-10, 2009 marked the annual COMSOL Conference, held in Boston, MA. Engineers, professorEditorial Assistant, Molly Whitman, proudly displays J&B Engineering titles at COMSOL Boston 2009.s, students, and software specialists gathered at the event to share ideas, view new functionality, hear keynote speakers and user presentations – including one by J&B author Roger Pryor, PhD – and view poster sessions created by their colleagues and peers. Dr. Pryor’s presentation, titled “Expanding Your Materials Horizon,” touched upon the use of COMSOL…

• US Enrollments on the Rise - International Enrollments Higher

  Lindsay Ruggiero

  5 Oct 2009 | 8:55 am

  A recent study for the National Bureau of Economic Research shows that student enrollment in US higher education programs has increased from 1970 to 2006, as reported by Inside Higher Ed.  As of 2006 the US held 12% of world enrollment as opposed to the 20% in 1990. Using this data it has been reported that American students are much less likely to enter science and engineering programs than those in other developed countries, such as China. In 2004, for example, 12.9 percent of the first degrees awarded to students went to those in the United States. But only 8.5 percent of the…

• J&B Author to Present at COMSOL Conference in Boston

  Lindsay Ruggiero

  2 Oct 2009 | 10:31 am

  Roger W. Pryor, PhD, author of Multiphysics Modeling Using COMSOL®: A First Principles Approach, will be taking part in the User Presentation on October 8th at the COMSOL Conference 2009 in Boston. In his presentation, titled "Expanding Your Materials Horizon," Dr. Pryor will discuss the many opportunities for computerized modeling of physical systems and devices with the use of the COMSOL Mulitphysics software. Materials and their related properties are intrinsically fundamental to the creation, development and solution of viable exploratory models when using numerical analysis…

• Top Ten Engineering Schools

  Lindsay Ruggiero

  3 Sep 2009 | 9:57 am

  The go-to website for everything engineering related, Engineering.com, posted its list of the top ten US schools with engineering programs.  It may come as no surprise that the Massachussetts Institute of Technology (MIT) is leading the list as the frontrunner of Engineering Education, offering degrees in aerospace, biomedical, chemical, civil, materials, mechanical, metallurgical, and nuclear engineering. Top Ten U.S. Engineering Schools Massachussetts Institute of Technology Stanford University University of California - Berkeley Georgia Institute of Technology University of…

• Students Use Mathematics to Save Humankind from Zombies

  Lindsay Ruggiero

  21 Aug 2009 | 5:53 am

  We've all seen the plethora of zombie films where humans outrun and outlive the slow moving, flesh eating undead. Of course in the films, humans survive the zombie attack and live happily ever after, but how accurate is this optimistic outcome if a zombie epidemic really were to occurr? Graduate students in Canada used advanced mathematical modeling to explore this potentially world-ending outbreak. With all possible variables taken under consideration (e.g. births and deaths of human population at time of attacks), the students simply concluded that humankind is ill-prepared to survive a…