Online courses that provide better, more focused support to high school students reading below grade level are making it possible for dropout prevention and recovery programs to cost-effectively address reading proficiency challenges in the face of constrained budgets and lack of specialized resources.
Math
-
Topix: Math
-
Online Learning Offers Unique Assistance for Struggling Readers
9 Feb 2010 | 10:44 am -
Thomas Ruff
9 Feb 2010 | 10:43 amDavid Zwirner Gallery Chelsea 525 West 19th Street, 212-727-2070 February 11 - March 13, 2010 Opening: Thursday, February 11, 6 - 8 PM Web Site David Zwirner is pleased to present Thomas Ruff's sixth solo exhibition at the gallery, marking the New York debut of new work in two series: zycles and cassini. -
Dr. Bernard Harris Announces 2010 Summer Science Camps
9 Feb 2010 | 10:40 amDr. Bernard A. Harris, Jr., the first African American to walk in space, and ExxonMobil announced today that more than 1,500 middle school students will participate in free science camps this summer. -
Wonderlic General Assessment of Instructional Needs (GAIN)A ...
9 Feb 2010 | 10:39 amWonderlic, Inc ., the recognized leader in educational and employment assessments and surveys, today announced that its recently developed General Assessment of Instructional Needs assessment has been approved for all Educational Functioning Levels by the U.S. Department of Education. -
Fennimore
9 Feb 2010 | 10:38 amSouthwest Wisconsin Technical College officials recently announced approval by the Wisconsin Technical College System for a facilities lease to expand educational offerings in Richland Center.
-
ScienceDaily: Mathematics News
-
Spherical cows help to dump metabolism law
4 Feb 2010 | 2:00 pmApparently, the mysterious "3/4 law of metabolism" -- proposed by Max Kleiber in 1932, printed in biology textbooks for decades, and described as "extended to all life forms" from bacteria to whales -- is just plain wrong. "Actually, it's two-thirds," says University of Vermont mathematician Peter Dodds. A new paper of his helps overturn almost 80 years of near-mystical belief in a 3/4 exponent used to describe the relationship between the size of animals and their resting metabolism. -
Curing more cervical cancer cases may be in the math
4 Feb 2010 | 5:00 amA third of cervical cancer cases respond poorly to standard therapy or experience recurrence, making cure difficult. A new mathematical model using information gathered by magnetic resonance imaging scans may make it possible to identify patients with non-responding tumors much sooner. These patients could then be offered aggressive or experimental therapy midway through treatment, something not possible now. -
Believing stereotype undermines girls' math performance: Elementary school women teachers transfer their fear of doing math to girls, study finds
26 Jan 2010 | 11:00 amFemale elementary school teachers who are anxious about math pass on to female students the stereotype that boys, not girls, are good at math. Girls who endorse this belief then do worse at math, research shows. The research found that boys' math performance was not related to their teacher's math anxiety while girls' math achievement was affected. -
A computer per student leads to higher performance than traditional classroom settings
22 Jan 2010 | 5:00 pmProviding every student and teacher with a laptop computer can produce improved student performance in some subjects, when compared to traditional classroom settings. -
Nocturnal vision of insects inspires automakers to develop improved night cameras
19 Jan 2010 | 5:00 amThe ability of animals to see in the dark has led to a collaborative project aimed at developing a new type of color camera that could help people drive cars more safely at night.
-
Scientific American - Math
-
CERN Gears Up Its Computers for More Atom Smashing
8 Feb 2010 | 7:00 amA deluge of high-energy physics data is headed toward servers in Geneva, Switzerland, later this month. That's because the European Organization for Nuclear Research (CERN) now says it plans to restart its Large Hadron Collider (LHC) soon for a run that could last as long as two years at a collision energy of seven TeV (tera–electron volts, 3.5 TeV per beam). As CERN ramps up the world's most powerful particle accelerator to operate well beyond its previous best performance , the lab's computer systems must likewise be tuned so they can properly capture and analyze all of this new… -
Street Smarts: The BioBus Brings a Rolling Science Lab to Resource-Strapped Schools
6 Feb 2010 | 7:00 amIt's halfway through first period, and 10th-grade students at Frances Perkins Academy in Brooklyn are in science class--not in school, but on a specially outfitted bus parked outside. [More] -
Thinking Outside the Boxes: Robotic Pallet-Stacking Challenge Aims to Create an Automation Benchmark for Industry
1 Feb 2010 | 10:55 amAnyone who has ever loaded a moving van knows how difficult it is to safely stack boxes of different sizes, weights and levels of fragility, all while minimizing the amount of space those cartons take up. Imagine an endless stream of such boxes and a business that lives and dies by the efficiency of their stacking, and you have an idea of the challenge facing warehouses that process large volumes of cargo onto pallets for shipping. [More] -
Green for Green: U.S. Stimulus Package Offers Businesses $7 Billion in Environmental Incentives
20 Jan 2010 | 10:00 amDear EarthTalk: I've been following reports about President Obama's stimulus package and what it may mean for creating green jobs. Beyond that, are there programs in place to help businesses switch to greener raw materials and/or to green up operations overall? --Diane, via e-mail [More] -
Monkey see, monkey calculate: How are primates' brains wired for math?
18 Jan 2010 | 12:01 pmLike a lot of humans, monkeys might not be able to do calculus. But a new study shows that they can learn and rapidly apply abstract mathematical principles. [More]
-
NYT: Mathematics
-
Doing the Math on Mexican Drug Wars
25 Jan 2010 | 9:00 pmMath protects me from the immediacy of violence. It tells me the conditions that would cause a drug war. -
In a Series, Nickelodeon Will Focus on Math
10 Jan 2010 | 9:00 pm“Team Umizoomi” will try to impart math to young children, squaring off against the didactic “Sesame Street.” -
Packing Tetrahedrons, and Closing In on a Perfect Fit
4 Jan 2010 | 9:00 pmA flurry of academic activity has focused on packing arrangements for a geometric solid that Aristotle wrongly thought would leave no gaps when stacked. -
Ta Da!
2 Jan 2010 | 9:00 pmAmazing feats of mathematics. It’s magic. -
Grigori Perelman’s Beautiful Mind
12 Dec 2009 | 9:00 pmA dogged portrait of an eccentric Russian mathematician who solved a famously unsolved problem, then dropped out.
-
MathNotations
-
Can Your Students Find At Least Three Methods? Odds and Evens Week of 2-1-10
31 Jan 2010 | 5:10 amI've been working on a new website which I will share with you when ready but I haven't forgotten my faithful readers who may have forgotten me! There are so many issues in mathematics education that it would take forever to update you on all of them, however, I know that you are already aware of most of these. Some Significant Current Issues in Math Ed Moving Inexorably Towards Common Standards in Math Teachers Need a Clear Curriculum Map/Content Guide rather than Standards! Rapid Push Toward Including Several Open-Ended Questions on State or Common Assessments is Slowing Down. Can you think… -
If We're 'Packing", Are We Going Somewhere?
5 Jan 2010 | 3:56 amFascinating article from today's New York Times. In 2-dimensions we talk about tessellating objects to fill the plane. Circles of course will always leave gaps. In 3-dimensions, equal spheres will also leave gaps when packed as closely as possible, but the question then becomes, "How do we arrange the spheres which would result in the densest packing. Turns out that the grocer's method of stacking oranges solves that problem! Equal cubes can be packed together without any gaps, so we can say that the densest packing for cubes is 100%, that is, identical cubes can be packed so that they use… -
HAPPY 2 x 3 x 5 x 67! Let The "Problems" Begin!
1 Jan 2010 | 3:44 amMay this new year and decade bring happiness and prosperity to each of you now that the2KO's have come to an end! BTW, the italicized symbol in red is my submission for the name we should give to the past 10 years. What do you think of it? Let me know if you came up with one of your own. According to Time Magazine, no one has yet created a name which has caught on (and dozens were listed!). Also, I will avoid debating those who strongly believe that the first decade of the 21st century ends a year from now! As MathNotations begins its 4th year, it has become an annual tradition… -
A Quadratic Trinomial/Factoring Investigation for Algebra I/II
26 Dec 2009 | 5:10 amIn my Christmas post, I raised the issue of how much time should be spent on factoring quadratic trinomials over the integers in light of the new ADP Standards for Algebra I and II. Hopefully, some of you will provide us with the benefit of your knowledge and experience. I may even make this into a poll or survey to be voted on but, in this post, I will appear to contradict myself and propose an investigation of this topic which requires some effort and time on the part of the student. The target audience would be the regular or accelerated Algebra I/II student. We all need to… -
How Much Factoring In 1st Year Algebra?
24 Dec 2009 | 4:14 amSEASON'S GREETINGS Math Notations 3rd Birthday- Thank You! The American Diploma Project is and will be impacting on what is being taught in both Algebra I and II in the 15 states who have joined the ADP Consortium. The classic flow from Standards to Assessments to Course Content is leading to the type of content standardization in our schools which I envisioned decades ago. A natural part of this process is deciding what topics in our traditional courses need to be deemphasized or eliminated to allow more time for the study of linear and non-linear function models, one of the central themes…
-
Wild About Math
-
An information theory puzzle
8 Feb 2010 | 7:59 amMy brother shared this puzzle with me this morning. He heard it on the radio but no solution was offered. Neither of us know what the answer is so I’m looking forward to one of you posting the answer in the comments. Here’s the puzzle: Bob and Alice are both millionaires. They’re both curious to know who is richer but they don’t want to tell the other one how much money they have. Without engaging a trusted third party, how can they both know who is richer? I wonder if the solution has something to do with public and private keys and/or authentication. So, what’s… -
Nonplussed! Review
4 Feb 2010 | 11:47 am“Nonplus” is not a particularly common English word so I looked it up on dictionary.com. –verb (used with object) 1. to render utterly perplexed; puzzle completely. –noun 2. a state of utter perplexity. “Nonplussed” is a book full of perplexing facts, and solid Math to explain the perplexities. In other words, this book is about mathematically provable facts that don’t actually seem to be true. Here is a great example of the state of being nonplussed and my favorite part of the book. Chapter 13 is all about Friday the 13th. Many of know that every year has at… -
How the St. Louis Arch got its shape
18 Jan 2010 | 10:35 amI found this wonderful short video on Science Friday by mathematician Robert Osserman on the Math behind the St. Louis Gateway Arch. This video is a great testament to the beauty of mathematics. Watch it and tell us if you agree. ShareThis -
Intel Partners with President Obama and Commits $200 Million for Math and Science Education
7 Jan 2010 | 11:54 amI received this email from Intel yesterday and thought many of you would be interested: Today, as part of President Obama’s “Educate to Innovate” Campaign, Intel joined with the President to honor America’s best math and science teachers and committed $200 million to help improve math and science achievement in the US. As part of this commitment, Intel will provide math and science training to more than 100,000 U.S. teachers over the next 3 years. At Intel, it is commonly said that computers aren’t magic, teachers are. And that’s why Intel continues to provide teachers with the… -
Mini review: One Wolf HOWLS
6 Jan 2010 | 9:05 pmA while ago I was contacted by Sylvan Dell Publishing, asking me if I’d be willing to review one of their books. The company publishes science and Math books for children. I didn’t think that Wild About Math! wouldn’t be a particularly good match for a review since my audience is older than Sylvan Dell’s audience. I don’t accept books for review that I don’t think are appropriate for this blog. I explained this to the publisher and they were still interested in my proceeding with reviewing one of their books. (more…) ShareThis
-
Ars Mathematica
-
What is a Horn Clause?
6 Feb 2010 | 1:37 pmNow to the actual definition of Horn clause. First, some standard logical terminology. A term is simply an expression built out of variables and function symbols. For example, x y-1 z is a term in the language of groups. An atomic formula is a formula that consists of relation symbols (including equality) applied to terms. So xy = yx is an example of an atomic formula in the language of groups. What makes an atomic formula atomic is that it’s not built out of smaller logical formulas. A Horn clause is built out of atomic formulas in a particular way. Let A_1, … A_n and B be atomic… -
Signatures
28 Jan 2010 | 3:48 pmMy normal tendency is to write long posts that I never finish. I’ll start off this series with small posts to see if I can break the habit. The idea of Horn clauses emerged from model theory, so I will begin there. Model theory considers ideas that can expressed in very limited languages. You begin with a small vocabulary of constants, function symbols and relation symbols, known as the signature. For example, you can express the theory of groups in terms of two function symbols and one constant: the group product, the inverse function, and a constant that represents the unit. The… -
The ubiquitous Horn clause
26 Jan 2010 | 3:05 amI was musing about the foundations of mathematics the other day, when it occurred to me that you could make a pretty good case that the key foundational idea of mathematics is that of Horn clauses (also known as universal Horn sentences). Horn clauses, despite begin obscure outside certain areas, are ubiquitous. Many (perhaps most?) basic mathematical objects can be described by Horn clauses. Fundamental category theoretic notions have Horn clause interpretations. Even first-order logic, which contains Horn clauses as a special case, can be viewed as having inference rules in the form of Horn… -
May on Algebraic Topology
12 Jan 2010 | 3:33 pmJ. P. May’s book, A Concise Course in Algebraic Topology, is available for download on his homepage. The book provides an overview of classical algebraic topology: homology and homotopy groups, K-theory, and cobordism. -
NFL, DNF-style
2 Jan 2010 | 3:19 pmI don’t normally link to sites that require registration, such as the New York Times, but
-
Loren on the Art of MATLAB
-
Constrained Sorting of Arrays
4 Feb 2010 | 1:13 pmIn a variety of applications, customers have requested a way to sort arrays subject to some constraints. One use case is when a row in an array represents a data record. Clearly, to sensibly sort data of this kind, you need to keep each row in tact. The sort function in MATLAB gives you one tool, the permutations, as the second output so you can do secondary array manipulations with it. With character arrays and cell arrays of strings, it made sense to do a lexical sort, which you can do with the function sortrows. Contents Regular Sorting Sort by a Particular Column Sort with Secondary Sort… -
Job Fair for Recent Graduates @ MathWorks
29 Jan 2010 | 4:36 amJob Fair for Recent Graduates @ MathWorks On February 4, 2010, we will be hosting a virtual career fair. Seth supplied the details here in his recent blog post. As you might imagine, Seth, I, and quite few others have found MathWorks to be a great place to work and build a career. If you're interested, please register now. Get the MATLAB code (requires JavaScript) Published with MATLAB® 7.9 -
MATLAB Behavior: for
27 Jan 2010 | 6:59 amConventional wisdom for programming MATLAB used to be that using for loops automatically forced a program to suffer from poor performance. Since MATLAB R13 (version 6.5), MATLAB has taken advantage of some innovations that accelerate many for loops so the code has performance on par with either vectorized code or code written in a lower level language such as C or Fortran. Obviously, details matter here. One thing that most people, even at MathWorks (!) don't appreciate is that the for loop has richer behavior than simply looping over single elements at a time. An informal hallway survey near… -
Mathematical Recreations: Tweetable Game Of Life
19 Jan 2010 | 4:16 amToday I’d like to introduce a guest blogger, Matt, who is consultant over in The MathWorks UK. Some of you may have come across his customer projects and series of demos on using MATLAB in Physics. He’s going to talk about an interesting one line MATLAB program. Contents Introduction Conway's Game Of Life Calculating The Number Of Neighbours Calculating The Next State Reducing The Size Modifications Conclusion Introduction One Saturday afternoon I saw a link on Hacker News to a YouTube video showing Conway's Game of Life in one line of APL. This made me wonder whether MATLAB®… -
The chebfun Project
12 Jan 2010 | 7:03 amNick Trefethen and a team of colleagues have created a MATLAB software package called chebfun. Version 2 is now available on the File Exchange. Version 3 is available on their site. The package is designed to have syntax very much like regular vector notation in MATLAB, though the entities represent functions. They accomplished this using some of the newer features of the MATLAB object system. Basically the project extends familiar notions for numbers to the realm of continuous and piecewise continuous functions. Contents User Guide Recent Additions What Do You Use for Basis Functions and…
-
Homeschool Math Blog
-
Celebrating e-day
6 Feb 2010 | 5:57 amTomorrow 2/7 is e-day.e or Euler's number is a number that is approximately 2.718281828, so that is why someone chose 2/7 as an e-day. But e is an irrational number, so its decimal expansion is never-ending and never-repeating.Why is this number e so important that people have even named a day after it?If you've studied calculus, you already know at least part of the story. But even if you haven't, I'll try to unravel at least the most basic feature of e.Consider the exponential function ex. It is graphed below.It has one remarkable property: when you draw a tangent to it at any particular… -
Multiply and divide decimals by powers of ten (by 10, 100, 1000 etc.)
29 Jan 2010 | 4:17 amIn this video I show, first of all, the common shortcut: you move the decimal point in the number as many steps as there are zeros in the number 10, 100, 1000 etc. For example:2.16 × 10,000 = 21,600.0It is as if the point moved four steps from between 2 and 1 to between zeros. You can see better examples of this in my lesson Multiply and Divide Decimals by 10, 100, and 100 at HomeschoolMath.net.Then, I also show where this shortcut originates, using PLACE VALUE charts. In reality, it's not the decimal point moving (it's sort of an illusion), but the digits of the number move within the… -
Female teachers pass math anxiety to girls
26 Jan 2010 | 9:02 amThis is a very interesting piece of research, and I personally believe in this "effect": that a teacher's attitude towards math can easily be passed on to his/her students.In this case, all the teachers studied were elementary and female. I figure the same could happen with male teachers too, affecting boys, if the teacher feared and/or disliked math. It's just a lot less likely because most elementary teachers are female, and also because math anxiety is more common among females.Girls may learn math anxiety from female teachersThe article also points to the best solution: the elementary… -
Language Arts resources
23 Jan 2010 | 8:41 amYou might wonder what is that kind of title all about? Well, while this is definitely a math blog, and I do not claim to be an expert on language arts, I just keep having people ask me about language arts resources, if I have any, or if I can recommend any. So, I want to answer this question here once and for all, and then I can just reference this blogpost whenever someone else asks the same.I have been doing an "eclectic" mix of various language arts resources with my kids.1. Learning to read.Photo courtesy by YvesI definitely am an advocate of teaching children to read as early as they are… -
Math Teachers at Play carnival
20 Jan 2010 | 6:25 am...is posted at Math hombre. Again lots of interesting things to explore and digest. Go check it out!
-
About.com: Math
-
Why Take Math?
8 Feb 2010 | 10:26 amThis question is one that pops up over and over again. I decided to surf around to see what others respond to as I'm somewhat biased. Well, I did discover that the reasons and responses tend to be quite similar to my own. Her's what I discovered: From a Norwegian professor. From the Drexel Math Forum From the University of Kentucky: Where Can Math Take Me? Have a comment to add? We'd love to hear from you.Why Take Math? originally appeared on About.com Mathematics on Monday, February 8th, 2010 at 18:26:38.Permalink | Comment | Email this -
100th Day of School
6 Feb 2010 | 5:14 amFor some educational jurisdictions, February marks the month that students will have been in school for 100 days. The 100th day provides a great opportunity to do some fun math activities! If you're a teacher and want to have a little math fun on the 100th day with your classroom, try some of the following: Have each child make and decorate a few paper rings, make the paper chain of 100 and ask the principal to wear it for the day! Brainstorm all the things you can count a 100 of in the school. (chairs, crayons, erasers etc.) Have students list all the things they would want 100 of and all… -
Be a Problem Solver
2 Feb 2010 | 12:18 pmMath involves problem solving and so does life! So why not embrace it and get good at it?! Jennifer Ledwith offers some great advice about becoming a problem solver in Algebra. She also provides you with a great 5 step plan that is sure to provide you with a life long skill for attacking algebraic problems. AND, when I really think about it, those same 5 steps will equip you well to solve life's problems too!See also, a more in depth look at the problem solving plan.Be a Problem Solver originally appeared on About.com Mathematics on Tuesday, February 2nd, 2010 at 20:18:13.Permalink | Comment… -
Majoring in Math?
31 Jan 2010 | 9:50 amWhat can you do with a major in math? Well, if you're majoring in math to begin with, I'm sure you've already given the question a bit of thought. You enjoy math, you know it's an opportunity gateway and now you're trying to decide on a career path? Not a bad idea! Perhaps you're interested in stats? Actuarial Science? Research? Teaching? Regardless, if you're taking math, you're on the right path. Read more about the careers requiring math. Majoring in Math? originally appeared on About.com Mathematics on Sunday, January 31st, 2010 at 17:50:50.Permalink | Comment | Email this -
Female Math Teachers Beware
28 Jan 2010 | 12:09 pmIf you are female and teach math, let's hope you aren't anxious about it. Why? Well, according to a research study at the Univesrity of Chicago, female elementary school teachers who are anxious about math may undermine girls' confidence and unwittingly encourage them to believe that boys are better at math than girls. Being female myself, I've always sort of made it my mission in life to be an advocate of helping female students to see that they CAN do math successfully. So, what does it all mean? Well, we just need to work that much more diligently to hook our girls on math and help them…
-
Let's Play Math
-
Head’s Up for e-Day
5 Feb 2010 | 2:15 pmIt’s beyond Kitten’s level and beyond my math club (what’s left of it), but for those of you who are interested, this Sunday is e Day. The only place I can remember seeing the announcement is on the blog 360: Things that equal e e-day, or why cooking and math don’t mix [Do you have an e-Day post? I'd be glad add your link!] If you’ve never heard of e before, then perhaps you are young enough (or young at heart? ) to enjoy celebrating his more famous cousin. Pi Day is coming next month. . . Updates Maria posted a good introduction to e: Celebrating e-day And Zac… -
What is a Math Carnival?
1 Feb 2010 | 4:14 amOver at Walking Randomly, Mike has posted a great explanation with FAQs: What is a Maths Carnival? You can send in articles now for either carnival: the Carnival of Mathematics, coming to The Endeavour this Friday, the latest edition is now posted here, or the Math Teachers at Play carnival, which will appear at mathrecreation on February 19th. -
Battlestations!!!
30 Jan 2010 | 9:01 amNerds battle hungry football players who want to eat their giant fractal Dorito creation: For more details on this video (and photos of the fractal’s construction), check out the Blown Apart Studios page. I’m looking forward to their next project, Nerd High, a musical comedy set in an alternate reality where nerds rule the school and jocks are the outcasts. -
Free Books? What’s the Catch?
23 Jan 2010 | 9:53 am[Photo by Jayel Aheram.] When I first read about Swagbucks, I figured there had to be a catch. How could they give away $5 Amazon.com gift certificates just for using their search engine? But over the past 12 months, I’ve collected $45 worth of free books, just for doing searches I would have done anyway. I bought a couple of Christmas gifts and an Ed Zaccaro book to supplement Kitten’s schoolwork. If you’d like to try it out for yourself: Swagbucks Search & Win A Few Observations The SB search engine doesn’t go as deep as Google does. When I want something beyond… -
New Edition of Must-Read Math Book
20 Jan 2010 | 11:21 amI thought I knew math fairly well. I thought arithmetic was boring. I thought the reason other nations beat America in international math tests was that their students worked harder than ours. I thought all sorts of silly things before I read Liping Ma’s Knowing and Teaching Elementary Mathematics. Now this must-read book is coming out in a new edition, due in bookstores next week. I can hardly wait! In American elementary mathematics education, arithmetic is viewed as negligible, sometimes even with pity and disdain—like Cinderella in her stepmother’s house. Many people seem to…
-
The Unapologetic Mathematician
-
The Fundamental Weyl Chamber
9 Feb 2010 | 8:42 amWhen we first discussed Weyl chambers, we defined the fundamental Weyl chamber associated to a base as the collection of all the vectors satisfying for all simple roots . Today, I want to discuss the closure of this set — allowing — and show that it’s a fundamental domain for the action of the Weyl group . To be more explicit, saying that the fundamental Weyl chamber is a fundamental domain means that each vector is in the orbit of exactly one vector in . That is, there is a unique so that for some . First, to existence. Given a vector , we consider its orbit — the… -
Lengths of Weyl Group Elements
8 Feb 2010 | 8:34 amWith our theorem from last time about the Weyl group action, and the lemmas from earlier about simple roots and reflections, we can define a few notions that make discussing Weyl groups easier. Any Weyl group element can be written as a composition of simple reflections where all are simple roots for some choice of a base . In general we can do this in many ways, and some will have larger values for than others. But there must be some minimal number of simple reflections it takes to make — some smallest possible value of . This number we call the “length” of the root… -
Sunday Samples 159
7 Feb 2010 | 8:50 amAs I write, Maryland is snowed in. There’s over two level feet of snow in the still-unplowed street, though luckily my car is already out of the way for when the plow does make it through. This evening, of course, is the Super Bowl, including the first appearance of the New Orleans Saints. You might remember that I spent a year at Tulane, and it really was one of the best cities I lived in while trying to keep up an ultimately doomed academic career. So here’s Tom Waits, with “I Wish I Was in New Orleans”. I wish I was in New Orleans I can see it in my dreams Arm in… -
The Action of the Weyl Group on Weyl Chambers
5 Feb 2010 | 8:56 amWith our latest lemmas in hand, we’re ready to describe the action of the Weyl group of a root system on the set of its Weyl chambers. Specifically, the action is “simply transitive”, and the group itself is generated by the reflections corresponding to the simple roots in any given base . To be a bit more explicit, let be any fixed base of . Then a number of things happen: If is any regular vector, then there is some so that for all . That is, sends the Weyl chamber to the fundamental Weyl chamber . If is another base, then there is some so that . That is, sends to . We say… -
Some Lemmas on Simple Roots
4 Feb 2010 | 8:58 amIf is some fixed base of a root system , we call the roots “simple”. Simple roots have a number of nice properties, some of which we’ll run through now. First off, if is positive but not simple, then is a (positive) root for some simple . If for all , then the same argument we used when we showed is linearly independent would show that is linearly independent. But this is impossible because is already a basis. So for some , and thus . It must be positive, since the height of must be at least . That is, at least one coefficient of with respect to must be positive, and so they…
-
Basic-Mathematics
-
Heron's formula
8 Feb 2010 | 11:52 amThis lesson will show you how to use Heron's formula to calculate the area of a triangle with sides a, b, c. -
Difference of sets
5 Feb 2010 | 12:45 pmA thorough coverage of how to find the difference of sets with crystal clear explanations. -
Complement of a set
5 Feb 2010 | 7:22 amA thorough coverage of how to find the complement of a set with crystal clear explanations. -
Heron's formula calculator
3 Feb 2010 | 7:13 pmUse Heron's formula calculator to calculate the area of a triangle with sides a, b, c. No need to know the height -
Celcius to Fahrenheit converter
3 Feb 2010 | 6:02 pmUse this Celcius to Fahrenheit converter to convert temperature from Celcius to Fahrenheit and from Fahrenheit to Celcius.
-
The Math Mojo Chronicles
-
Math Mojo and Financial Insights
5 Feb 2010 | 4:50 amUnfortunately for me, they are not my financial insights. If I had any financial savvy I wouldn’t be a math blogger. But recently I was googling “math mojo” and I came upon the Reading the Markets blog. In this post, the author says, “I think we profit enormously from looking at alternative approaches to a problem.” She mentions this MathMojo blog as an example thereof. I was impressed, not just for the ego stroke, but by the fact that the author “gets it.” It turns out that she is a Yale-trained philosopher, so I imagine that she gets it more than… -
Homunculus Nebula
27 Nov 2009 | 2:33 amSky and Telescope.com has an interesting article this month. In “A Rogue Star Going Wild?” (no, it’s not about her) it discusses the Homunculus Nebula. It’s not exactly a math article, but Professor Homunculus likes it anyway. Check it out. -
Speed Addition Demonstration and Tips
15 Nov 2009 | 3:13 pmI’m almost finished putting up the first week of the new “Quick and Dirty Multiplication” Math Mojo course. In the meantime, a few people have asked me to get to work on a “Quick and Dirty Addition” Math Mojo course. I won’t be able to get to that for a few weeks, but if you need immediate help, I’ve put together a few resources that I’ve created over the last year or so. The goal would be to take anyone who can already say, 3+ 6, and knows the difference between the ones column and the tens column, and be able to add huge columns and rows of… -
Mathematics in the Soviet Union
8 Nov 2009 | 7:47 pmThere was a wonderful article in the Wall Street Journal today about mathematics in the former Soviet Union. It is worth reading for anyone interested in finding out a little about the inner beauty of math. Here’s a short except: what mathematics really is: “It was a wonderful education… Gelfand amazed me by talking of mathematics as though it were poetry.” In the mathematical counterculture, math “was almost a hobby,” recalls Sergei Gelfand. “So you could spend your time doing things that would not be useful to anyone for the nearest decade.”… -
Goodbye, Soupy
23 Oct 2009 | 4:39 amThis 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…
-
bodmas blog
-
Ten Data Sets
7 Feb 2010 | 2:54 amDownload a PDF file with 10 data sets that can be used to illustrate a variety of statistical techniques Useful pages: Selected Data-sets from Publications by Martin BlandA stroop effect lap report with actual dataOne for the tree huggers – I always loved that picture of a road tunnel in the trunk of a Giant Redwood as a childFavourite Data sets from drugs research (Bradstreet) A spreadsheet with all the data sets is on its way so I can demonstrate how to analyse the data once we have decided what methods are appropriate. I like having a dialogue and a spreadsheet instead of Yet Another… -
February 2010 desktop
6 Feb 2010 | 4:36 amClick on the thumbnail above for a 1280 by 1024 pixel desktop image with a February 2010 calendar. Its on my desktop computer for what is left of this month. James Watt (with slide rule and plan) on the left, so a tenuous link to Maths. -
Five number summary
5 Feb 2010 | 1:05 pmJust 10 minutes on the five number summary. I’ve not produced a screencast for some time, and this topic presented itself as potentially useful to a range of students but not ‘mainstream’ on any of their courses. I used the NCH screencam software. This YouTube is a ‘single take’ without script walking through the PowerPoint I usually use for this topic. You may notice that I ‘loose’ it in the middle slightly. -
Chocolate mushroom package
30 Jan 2010 | 12:03 pmRuth gets chocolate from an international sweet shop in Birmingham. This Japanese pack seems to contain mock mushrooms with chocolate caps and biscuit stalks. I love the typography on the back of the package… Some of the details appear to be telling a story (aimed at children?) And the teacher figure appears in red on the back – I wonder if this is some kind of food labelling thing? I rather like the teacher-cat, so I used the levels tool in GIMP to remove the colours and exported him (her?) as a GIF cartoon. I might add this as a logo to some of my worksheets to keep the… -
Five number summary
28 Jan 2010 | 1:38 pmDownload a two sided handout on finding the five number summary for a set of data The five numbers are the maximum, the minimum, the median and the upper and lower quartiles. This set of numbers can tell you about the central tendency of your data, the spread, the extreme values, and provide low order information about the shape of the distribution. The blood pressure data sets came from Dr Bradstreet’s Favorite Datasets in Early and Late phases in Drug Research. Box and whisker plot next, so I can explain how to interpret the five number summary. This series is part of a few sessions…
-
ChapterZero
-
In a Graveyard
29 Jan 2010 | 10:57 amI’ve often been asked how I feel about death. (Because, as you know, if you don’t believe in an afterlife, then you must be terrified to die). A couple days ago, I was listening to Poses and reencountered this gem, “In a Graveyard”. I love the piano, but this is one of his songs that I fell in love with just for the lyrics. It pretty much captures my attitude towards death. Death can be good, something to be desired even: can you imagine what it’d be like to be doomed to live forever? To put up with all the foibles of humanity forever? Much better to live a full… -
Convex set questions
28 Jan 2010 | 5:44 pmIn some Hilbert space, let be a unit ball polytope of some norm and be the unit ball of its dual norm. Is it the case that for every face in there is a vertex of which defines a normal on that face, and vice versa? I just looked up this stuff, so I barely know what a face is, much less how to tackle this problem right now. My intuition comes only from the knowledge that the dual of the ball is the ball, in which case it’s easy to see that this is the case. Another question: what are the vertices of the and norm balls? (Are these balls even polyhedral? I think so.) Possibly relevant… -
Estimation of the norm using an SDP
27 Jan 2010 | 7:57 pmUpdate: This is utter bollocks, but I’ve yet to get around to correcting it. Continuing in the vein of the previous post, we have that , so if we’re interested in approximating (which looks like it’s hard to compute exactly), then we’d find it useful to be able to compute . It turns out this is easily done with an SDP when is strictly positive: Then . I’m not sure what happens if isn’t full rank, and this definitely won’t work if is not positive semi-definite.Possibly relevant posts: Trace dual of the norm (1/19/2010) A failed attempt to use an SDP to… -
Equivalence of the norm and the norm
27 Jan 2010 | 7:08 pmIt turns out that the norm ( the trace dual of the norm, explicitly given as ) is equivalent to the factorization norm, which is defined as Note that constraining the norm constrains the Euclidean norms of the rows of and A quick proof relies on Grothendieck’s inequality, which more or less states that If is a real matrix, then for every choice of unit vectors in a real Hilbert space, where is an absolute constant. Note that the trace dual norm of is where the supremum is over all choices of lengths for . Therefore so (it’s easy to check that if then and that ) To show the other… -
A dictionary, or not?
27 Jan 2010 | 3:52 pmI realized that I’ve been attempting to do greedy approximation in the set of symmetric matrices using the “dictionary” without checking that this is indeed a dictionary: is the closure of the span of this set the set of all symmetric matrices? As someone just pointed out, this is obviously not the case, since the diagonals of symmetric rank one sign matrices are constant. Darn (and don’t I feel stupid). Ok, I guess I’ll have to settle for greedy approximation with the dictionary Maybe that original dictionary of symmetric rank one sign matrices is a dictionary…
-
Computational Complexity
-
The more things change the more things change
4 Feb 2010 | 7:00 amThere have been some articles on how much things have changed because of technology. One from the Washington Post Magazine, titled Going, Going, ..., Gone lists out items that are fading out of our lives Here are a few: Cash: When is the last time you used cash in a transaction that was over 20 dollars? Over 10? Slide rules: I thought they were already gone gone gone. You can buy them off the web here. The site does not seem to think of them as antiques. Truly blind dates: In my day we couldn't Google our dates ahead of time. FAX machines: Not sure they are really going going gone. If they… -
Time Space Tradeoffs for SAT- good resuls but...
3 Feb 2010 | 8:13 amThis is a real conversation between BILL and STUDENT (a Software Engineering Masters Student who knows some theory). As such there are likely BETTER arguments BILL or STUDENT could give for there point of view. I invite you to post such as comments. (ADDED LATER: Some of the comments below DO give VERY GOOD arguments for why the results are interesting. I URGE anyone reading this now to read the comments. They are an integral part of this post, more than usual.) BILL: In 2007 the best student paper award at COMPLEXITY went to Ryan Williams for proving that SAT cannot be done in time… -
Naming and Ranking
2 Feb 2010 | 7:10 amMartin Kruskal invented Soliton Waves which were a very important concept in Physics. (NOTE- one of the comments clarifies this statement.) Rebecca Kruskal (Martin's Granddaughter): Daddy, how come they are not called Kruskal Waves? Clyde Kruskal (Martin's Son, Rebecca's Father): You can't name things after yourself. Rebecca Kruskal: Why not? Rebecca raises a good question. In academia the etiquette has evolved that you simply do not name things after yourself. Why is this? Is it a good thing? How did this tradition get started? Have people tried to name things after themselves? What happens… -
Travel Support for Grad Students who GOTO STOC 2010
1 Feb 2010 | 8:33 amIf you are a grad student and want to goto STOC 2010 there is travel support money that you can apply for. See here for details. What is the best way to get this information out? What is the best wayy to get any kind of information out? Websites. For STOC there is an obvious website, and indeed it is there under Travel Support. This works for conferences. It does not work if the info is hidden deep in a non-obvious place OR if its not there and should be. This happens more than it should. Big Plus: Posting on a website is NOT intrusive like email. Blogs: There are so many blogs and its not… -
Referees'''' reports
28 Jan 2010 | 7:09 amA commenter a LOOOOONG time ago left the following: Tell me, Gasarch, how in the world do you get your papers published when you consistently skip the apostrophe in it's and that's? Do referees notice these things anymore, or are you simply careless in blogs. This commenter unintentionally raised some good questions: Do referees notice these things anymore... This indicates that there was a time when referees were real referees, and men were real men, and women were real women, and little blue fuzzballs from alpha-8 were real little blue fuzzballs from alpha-8. Was there such a time? Or is…
-
Natural Blogarithms
-
A Kindle for all Seasons
21 Jan 2010 | 8:46 pmAbout three weeks ago, I splurged and ordered myself a Kindle 2. I had bounced back and forth between wanting one and not but finally convinced myself that it was time to add another gadget to my repertoire. And let me say, I love it!! To alleviate any guilt over spending that kind of cash on another gadget, I replaced my personal laptop with it and I haven’t regretted that decision for even a minute. Here’s a short summary of what I’m using it for these days. Reading Books. Duh! I know. Who would’ve of thought that an ebook reader would work so well for… -
How to lie with your graphs
23 Nov 2009 | 6:25 amStumbled across an interesting little post about 5 ways that you can lie with your graphs. Actually, a better lesson to take from the post is “5 ways other people lie with their graphs and now you can call them on it.” The post was on Talking Squid, entitled “Five Easy Lies”: Two of the most common ones I’ve seen in talks are below: Choose your cutoffs “The trend shows no increase for the last [n] days/months/years.” Don’t mention the previous [20 n] data points. Talk about the trend of the trend “Sure the graph is going up for now, but the rate of increase is… -
How do you measure two-thirds?
18 Nov 2009 | 6:53 amFrom an article by Mary Ann Bragg which appeared on CapeCodeOnline and was also printed in this month’s College Mathematics Journal: TRURO — Voters narrowly approved one of four zoning amendments late Tuesday night at the annual town meeting. But town officials were still looking at the exact vote count on that article yesterday. In a vote of 136 to 70, voters passed a new time limit on how quickly a cottage colony, cabin colony, motel or hotel can be converted to condominiums. The new limit requires that those properties be in operation for three years before being converted to… -
Interesting facts about Euler
17 Nov 2009 | 8:30 amI’ve not studied much of the history of mathematics but occasionally I read from a few books I have on my shelf on the subject. When my mind is bogged down and I am unmotivated on my current projects, I pick up, say, Makers of Mathematics, by Stuart Hollingdale. Today, I flipped open to the chapter on Leonhard Euler (one of my mathematical heroes) and learned (or re-learned) a few interesting facts about the man. Entered the University to study theology and Hebrew but his mathematical abilities attracted the attention of Johann Bernoulli who gave him a private lesson once a… -
How the Psalms Motivate Us to Marvel at Creation
30 Oct 2009 | 6:45 amThis 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…
-
Precal Blog
-
Activity 2.4: Logarithms!
9 Feb 2010 | 8:58 amThe past two days in class, we have been working on Activity 2.4 in our packets. Activity 2.4 discusses the power scale versus the the exponent scale. By adding one on the exponent scale, we see that it is equivalent to multiplying by ten on the power scale. So, on the exponent scale, the difference [0,1] makes the difference on the power scale: [1, 10]. This is because 10^0 is 1, and 10^1 is 10. By realizing this, we can also prove that adding 2 on the exponent scale is equivalent to multiplying by 100 on the power scale. Therefore, we can say that 10^0 is 1, and 10^2 is 100. The difference… -
Logarithms
8 Feb 2010 | 3:43 pmNow that my computer is virus free, i can post my blog on logarithms. So the past few days we’ve spent time using logarithms to find things like magnitudes and decibels. We’ve come to defining the logarithm as the exponent raised to a power of 10. For example: log(100)=2 because 10^2=100 We’ve learned to find Magnitude of an earthquake as log(I/Io). (I/Io) is the relative intensity. That means you take the value for which you want to find the magnitude of over the smallest detectable earthquake which is given. Io= 2.00 x 10^11 in any case that deals with magnitude. -
Analyzing Logarithmic Functions
7 Feb 2010 | 8:03 pmOn Friday in class, Mr. B gave us a problem to start with. It was as follows: How many times more powerful is the sound of a chainsaw (110 db) than the noise generated by a vacuum cleaner (sound intensity 10^-1)? Using the equation we know for finding the intensity of a sound, we can set up the equation: 110 = 10 * log (I/Io) Since we know that the relative intensity (the sound of a whisper) is 10^-12, we can fill that in for Io, giving us this: 110 = 10* log (I/10^-12) Next, we can divide by 10 on both sides to simplify: 11 = log(I/10^-12) Here is the important part….Since the… -
Logarithmic Scale
3 Feb 2010 | 8:19 pmToday in class we recieved a new packet. This packet introduces the concept of a logarithm function. The logarithm converts any positive number into its “power-of-ten exponent”. Today we did activity 2.3 in the packet through number 3. These problems used two new concepts: magnitude: M=log(l/l0) relative intensity: RI=l/l0 Tomarrow we will be going over these problems so everyone should have problems 1-3 completed. The next scribe will be stefan. -
The Constant e and Similar Application Problems
2 Feb 2010 | 3:15 pmToday in class we presented the claims for exercise 2.1. So I’m going to explain the problems that were presented and later I’ll try to clarify the concept of e in mathematics and how to use it. Exercise 2.1 Practice Problems 3. A bank account paying 8% annual interest compounded quarterly actually pays 2% interest each quarter. The annual yield is slightly higher than 8% due to the compounding. a) If $1500 is deposited when the account is opened, how much interest is earned during the first year? If you took notes on Thursday, this problem is very similar to the first problem in…
-
IMA Journal of Applied Mathematics
-
Solutions and symmetry reductions of the n-dimensional non-linear convection-diffusion equations
25 Jan 2010 | 9:44 amThis paper discusses a wide class of n-dimensional non-linear convection–diffusion equations with source term. It is shown that the radially symmetric equations admit certain types of conditional Lie–Bäcklund symmetries. As a result, exact solutions and symmetry reductions to 2D dynamical systems of the resulting equations are obtained. Those solutions extend the known ones such as self-similar solutions and instantaneous source-type solutions of the porous medium equation with absorption term. The behaviour of extinction and blow-up to many of the solutions are described. -
Energy and helicity dissipation rates of the NS-alpha and NS-alpha-deconvolution models
25 Jan 2010 | 9:44 amWe consider the Navier-Stokes (NS)-alpha and the family of high-accuracy NS-alpha-deconvolution models of turbulence on = [0, L]3 subject to periodic boundary conditions. For body-force-driven turbulence, we prove directly from the model equations of motion the following bounds on the time-averaged modified energy dissipation rate, <, N(w, N)>, and unmodified helicity dissipation rate, <(w, N)>, for the Nth model (N = 0, 1, 2, ...): Here, N is the degree of the approximate deconvolution operator, UN and LN are global velocity and length scales and C1 and C2 are constants that do… -
Qualitative dynamics of a vaccination model for HSV-2
25 Jan 2010 | 9:44 amA new mathematical model for the transmission dynamics of herpes simplex virus type 2 (HSV-2), which takes into account disease transmission by infected individuals in the quiescent state and an imperfect HSV-2 vaccine, is designed and qualitatively analysed. In the absence of vaccination, it is shown that the model has a globally asymptotically stable (GAS) disease-free equilibrium (DFE) point whenever an epidemiological threshold, known as the ‘basic reproduction number’, is less than unity. Further, this model has a unique endemic equilibrium whenever the reproduction number… -
Linear wave forcing of an array of axisymmetric ice floes
25 Jan 2010 | 9:44 amUnder linear and time-harmonic conditions, a set of periodic Green's functions is derived to combine the interactions of an infinite number of identical equispaced floating bodies. The bodies themselves are compliant thin elastic plates that can represent ice floes, and unlike previous studies, they are permitted to vary axisymmetrically in thickness through both their upper and their lower surfaces, with a realistic draught also admitted. Initially, the governing equations are simplified by means of an expansion of the vertical dependence of the unknown velocity potential combined with a… -
Asymptotic behaviour of thin linearly elastic layers of oscillating thickness
25 Jan 2010 | 9:44 amWe consider a 3D linearly elastic material whose thickness is a positive Lipschitz continuous function r(x1, x2) ≤ . We study the asymptotic behaviour, when tends to 0, of the associated sequence of rescaled energy functionals using -convergence methods. According to the bounds of the function r, we obtain two possible asymptotic behaviours: a membrane and a flexure one.
-
The Calculist
-
Wading into the C
25 Jan 2010 | 7:29 pmNo time for deep thoughts these days; too much hacking, dissertating, designing, and committeefying going on. Just a couple notes based on recent experiences hacking in C/C++:1. Not being able to rely on recursion makes me sad.2. "Downwards macro-args" in C:#define MY_ENUM_LIST(m) \ m(RED, 0), \ m(GREEN, 1), \ m(BLUE, 2)#define DEF_ENUM_ENTRY(c, v) c = v#define QUOTE_ENUM_ENTRY(c, v) #ctypedef enum rgb { MY_ENUM_LIST(DEF_ENUM_ENTRY)} rgb;const char *rgb_names[] = { MY_ENUM_LIST(QUOTE_ENUM_ENTRY)};3. I am fast becoming acquainted with gdb.4. And a few choice command-line shortcuts really save… -
Computer Science Education Week
11 Dec 2009 | 11:26 amIn honor of Computer Science Education Week, I'll just cite a passage I find inspirational about the role of computer science education:Yet programming is more than just a vocational skill. Indeed, good programming is a fun activity, a creative outlet, and a way to express abstract ideas in a tangible form. And designing programs teaches a variety of skills that are important in all kinds of professions: critical reading, analytical thinking, creative synthesis, and attention to detail. We therefore believe that the study of program design deserves the same central role in general education… -
Ezra: Function calls are not stack frames
4 Nov 2009 | 1:30 pmI 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 amI'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 pmWe'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.
-
The Math Less Traveled
-
Irrationality of pi: the impossible integral
6 Feb 2010 | 9:30 amIrrationality of piIrrationality of piIrrationality of pi: the unpossible functionIrrationality of pi: derivatives of fIrrationality of pi: curiouser and curiouserIrrationality of pi: the impossible integral We’re getting close! Last time, we defined a new function and showed that and are both integers, and that . So, consider the following: The first step uses the product rule for differentiation (recalling that and ); the last step is what we showed last time. Now we see the point of defining : it’s just so that we have a convenient way to talk about the antiderivative of . We… -
Dimensions
3 Feb 2010 | 8:38 pmI’ve only watched the trailer so far, but this looks extremely cool! Some beautiful, fascinating videos about math, with lots of extra accompanying material and explanations on the website. Hat tip to Phil Wadler. -
Divisor nim
3 Feb 2010 | 3:12 pmYesterday in math club I had the students play a game which I dimly remember seeing somewhere but forget where. Since I don’t know what it is really called, I’m calling it “divisor nim”. Here’s how it works: The players pick a positive integer. The two players work together to write down all the divisors of the chosen integer (being sure to include 1 and the integer itself). The players now alternate moves as follows: on a player’s turn, she must choose one of the divisors , and then cross out that divisor as well as all of the other listed numbers which… -
Battlestations!
1 Feb 2010 | 7:40 amThe world’s LARGEST FRACTAL DORITO! -
Irrationality of pi: curiouser and curiouser
30 Jan 2010 | 1:49 pmIrrationality of piIrrationality of piIrrationality of pi: the unpossible functionIrrationality of pi: derivatives of fIrrationality of pi: curiouser and curiouserIrrationality of pi: the impossible integral I’ve been remiss in posting here lately, which I will attribute to Christmas and New Year travelling and general craziness, and then starting a new semester craziness… but things have settled down a bit, so here we go again! Since it’s been a while since my last post in this series, here’s a quick recap: I’m presenting a proof by Ivan Niven that is…
-
The Math Factor Podcast
-
Yoak: Pirate Treasure Map
25 Jan 2010 | 11:00 amOur band of intrepid pirates, having resolved previous squabbles over distributing booty amongst themselves and other issues have come across a treasure map fragment. The picture has been destroyed, but the following text can be read: Stand upon the gravesite and you’ll see two great palms towering above all others on the island. Count paces to the tallest of them and turn 90 degrees clockwise and count the same number of paces and mark the spot with a flag. Return to the gravesite and count paces to the second-tallest of the trees, turn 90 degrees counter-clockwise… -
GO. More Coin Fraud
19 Dec 2009 | 7:30 amIn this segment, we give some explanation of how Benford’s Law actually arises in so many settings: why are so many kinds of data logarithmically distributed? And we give a surprising fact about runs of coin tosses, and a new puzzle. -
GN. Benford’s Law
8 Dec 2009 | 6:38 amBenford’s Law is really quite amazing, at least at first glance: for a wide variety of kinds of data, about 30% of the numbers will begin with a 1, 17% with a 2, on down to just 5% beginning with a 9. Can you spot the fake list of populations of European countries? List #1 List #2 Russia 142,008,838 148,368,653 Germany 82,217,800 83,265,593 Turkey 71,517,100 72,032,581 France 60,765,983 61,821,960 United Kingdom 60,587,000 60,118,298 Italy 59,715,625 59,727,785 Ukraine 46,396,470 48,207,555 Spain 45,061,270 45,425,798 Poland 38,625,478 41,209,072 Romania 22,303,552 25,621,748… -
Morris: Follow Up: Triel/Truel/Whatever
5 Dec 2009 | 9:34 amThis is the solution to Morris: Trial/Trual/Whatever. Please look there before reading the solution. It turns out the right word is truel, first coined in 1954 by Martin Shubik. Jeff suggested that they might all choose not to shoot at each other and it would go on forever. This made me think about the logic. I’m going to say that someone shoots at someone at some point and everyone knows this. So everyone knows that if they shoot to miss then one of the others will shoot to hit at some point. If anyone shoots to hit then they will shoot at the best shot. -
Yoak: Miles, Kilometers and Fibonacci Numbers
2 Dec 2009 | 8:43 pmI’m overdue to post a puzzle, but I’m momentarily tapped out. Here’s a curiosity in the meantime: You can provide a very good estimate of a conversion from miles to kilometers by choosing sequential Fibonacci numbers. The conversion rate is 1.609344 kilometers to a mile. So this gives us: 1 2 1.609 2 3 3.219 3 5 4.828 5 8 8.047 8 13 12.875 13 21 20.921 21 34 33.796 34 55 54.718 55 89 88.514 89 144 143.232 144 233 231.746 233 377 374.977 377 610 606.723 610 987 981.700 987 1597 1588.423 This leaves you in pretty good shape if you need to get from Cincinnati, OH to…
-
WordPress Tag: Mathematics
-
How to memorize the value of e to 15 decimal places
9 Feb 2010 | 10:34 amI learned the following trick for memorizing the value of e from my colleague, Gene White. It never fails to impress calculus students (given a wide enough definition of “impress”). Start by carefully looking at this picture: That’s a 20 dollar bill, so memorize “2″ and put down the decimal point. The picture on the bill is of Andrew Jackson. He was our seventh President, so put a “7″ after the decimal point to get 2.7. Jackson was elected in 1828, so put down “1828″ next. Since there’s a 2 in front of the decimal place, put… -
Notation
9 Feb 2010 | 10:32 amThis page will be updated from time to time, whenever we introduce new notation. (more to come) -
Too Bad It Doesn't Bring Home the Bacon
9 Feb 2010 | 10:32 amI spent the last two days reviewing and delving deeper into some details on the construction of Galois representation from modular forms. It was a refreshing getaway from the occasional frustrations and disappointments one experiences while conducting new research. Learning new things in mathematics is not as much a challenge nowadays as it was when I began. I suppose I can take pride and comfort in the knowledge that I have grown in mathematical maturity. Everyone needs to return to his or her comfort zone once in awhile to refuel and rekindle the desire and aspiration for improvement, and… -
Five intuitive approaches to teaching the infinitely small
9 Feb 2010 | 9:17 amThe truth of infinity being central to the process is singular and univocal. I can’t imagine anyone being able to invent 5 let alone 20 ways to uniquely and intuitively approach this in their teaching. — Will Faris Twenty might require help from my esteemed commenters, but here’s five: 1. Zeno’s first paradox Suppose a runner is trying to get from point A to point B. To make the traversal, at some point the runner must reach halfway: To get from the 1/2 point to B, the runner must pass through the 3/4 point. To get from the 3/4 point to B, the runner must pass through the… -
Fractions And Decimals Flower Power Game
9 Feb 2010 | 9:09 amHere is another fun game involving fractions and decimals! Flower Power
-
MathNotations
-
Can Your Students Find At Least Three Methods? Odds and Evens Week of 2-1-10
31 Jan 2010 | 5:10 amI've been working on a new website which I will share with you when ready but I haven't forgotten my faithful readers who may have forgotten me! There are so many issues in mathematics education that it would take forever to update you on all of them, however, I know that you are already aware of most of these. Some Significant Current Issues in Math Ed Moving Inexorably Towards Common Standards in Math Teachers Need a Clear Curriculum Map/Content Guide rather than Standards! Rapid Push Toward Including Several Open-Ended Questions on State or Common Assessments is Slowing Down. Can you think… -
If We're 'Packing", Are We Going Somewhere?
5 Jan 2010 | 3:56 amFascinating article from today's New York Times. In 2-dimensions we talk about tessellating objects to fill the plane. Circles of course will always leave gaps. In 3-dimensions, equal spheres will also leave gaps when packed as closely as possible, but the question then becomes, "How do we arrange the spheres which would result in the densest packing. Turns out that the grocer's method of stacking oranges solves that problem! Equal cubes can be packed together without any gaps, so we can say that the densest packing for cubes is 100%, that is, identical cubes can be packed so that they use… -
HAPPY 2 x 3 x 5 x 67! Let The "Problems" Begin!
1 Jan 2010 | 3:44 amMay this new year and decade bring happiness and prosperity to each of you now that the2KO's have come to an end! BTW, the italicized symbol in red is my submission for the name we should give to the past 10 years. What do you think of it? Let me know if you came up with one of your own. According to Time Magazine, no one has yet created a name which has caught on (and dozens were listed!). Also, I will avoid debating those who strongly believe that the first decade of the 21st century ends a year from now! As MathNotations begins its 4th year, it has become an annual tradition… -
A Quadratic Trinomial/Factoring Investigation for Algebra I/II
26 Dec 2009 | 5:10 amIn my Christmas post, I raised the issue of how much time should be spent on factoring quadratic trinomials over the integers in light of the new ADP Standards for Algebra I and II. Hopefully, some of you will provide us with the benefit of your knowledge and experience. I may even make this into a poll or survey to be voted on but, in this post, I will appear to contradict myself and propose an investigation of this topic which requires some effort and time on the part of the student. The target audience would be the regular or accelerated Algebra I/II student. We all need to… -
How Much Factoring In 1st Year Algebra?
24 Dec 2009 | 4:14 amSEASON'S GREETINGS Math Notations 3rd Birthday- Thank You! The American Diploma Project is and will be impacting on what is being taught in both Algebra I and II in the 15 states who have joined the ADP Consortium. The classic flow from Standards to Assessments to Course Content is leading to the type of content standardization in our schools which I envisioned decades ago. A natural part of this process is deciding what topics in our traditional courses need to be deemphasized or eliminated to allow more time for the study of linear and non-linear function models, one of the central themes…
-
Neoformix
-
Apple Logo from Products
1 Feb 2010 | 11:10 pmI was looking for pictures of the new Apple iPad and stumbled across this image of Apple form Factor Evolution. It's got lots of images of Apple products on a nice simple white background and was perfect fodder to use with the Image Foam Technique so I made this version of the Apple logo from the product sub-images. -
SOTU 2010 Word Cloud Map
28 Jan 2010 | 1:15 amLast night President Obama delivered the State of the Union Address. The Shaped Word Cloud below was created from the text. -
More Visualization Links on Twitter
23 Jan 2010 | 1:55 amIn a recent post I showed the Top 20 Individual Data Visualizations Mentioned on Twitter and remarked that many of the most frequently mentioned twitter links were to collections of visualizations. Shown below is a meta list of the top collection-type data visualization or infographic links. Top Collections of Data Visualization Links 50 Great Examples of Data Visualization - Webdesigner Depot Data Visualization and Infographics Resources - Smashing Magazine 15 Stunning Examples of Data Visualization - Web Design Ledger 20 Essential Infographics & Data Visualization Blogs - Inspired… -
Charting the Beatles
18 Jan 2010 | 10:30 amMichael Deal has published an interesting collection of graphics in his Charting the Beatles project. This first snippet below shows the beginnings of a graph illustrating authorship and collaboration in songwriting throughout their song collection. The full graphic clearly shows the trend towards less collaboration over time in songwriting, the increasing contribution from George, and increasing contribution by outside contributors. This second image is from a chart showing references in Beatles songs to earlier songs. There are full images and several other interesting graphics on his site. -
Top 20 Data Visualizations Mentioned on Twitter
17 Jan 2010 | 11:15 pmFor many people Twitter has become the best place for discovering the latest and most interesting work in a variety of fields. In my twitter client I keep a search column open that gets constantly updated with the latest tweets pertaining to data visualization or infographics and I see lots of beautiful content flow by. I've been collecting these tweets for quite a while and thought it would be interesting to analyze them and see which visualizations were shared through twitter the most often. Many of the top links in the domain were articles containing collections of visualizations chosen to…
-
Math & Engineering
-
3D CFD Aids in Green Movement
27 Jan 2010 | 6:18 am3D modeling has become the desired means of analysis in various industries (including mainstream entertainment - think Avatar). Specifically, the AEC industry (architecture, engineering, construction) is responding to the demand of their clients by providing 3D models and simulation. Since the recent shift to 'go green,' employing 3D software to analize computational fluid dynamics (CFD) is now essential in todays building trends. I read an interesting article by ConnectPress Editor Lauren Brown, in which she discussed how 3D modeling of CFD assisted in… -
CATIA V6 2010 Recently Launched - CATIA V6 Essentials Just Published
15 Dec 2009 | 6:06 amLast month Dassault Systèmes announced the launch of their latest version of the world's leading multi-platform CAD/CAM/CAE software suite, CATIA V6R2010x (read the full press release). Dominique Florack, Senior Executive Vice President, Products-Research and Development, Dassault Systèmes had this to say about the release: “The V6R2010x platform delivers new and unique capabilities that connect users within their companies or with external online communities. It enables them to create and share their IP and 3D experiences with the ease of use of common… -
A 19th-Century Mathematician Finally Proves Himself
10 Dec 2009 | 6:18 amCharles Babbage, the man whom many consider to be the father of modern computing, never got to complete any of his life's work. Now engineers have successfully built his Difference Engine using only materials that would have been available to Babbage himself in 1840. The Difference Engine fills half a gallery and stands taller than most men. It's 5 tons of cast iron, steel and bronze woven together from 8,000 distinct parts. Though it looks like it could be a sculpture, the machine is essentially a giant calculator. Tim Robinson, a docent at the museum, says it's "the first… -
Engineers Design iPhone Application to Drive a Car
24 Nov 2009 | 12:36 pmEngineers from Austin-based National Instruments have invented a technology to actually drive a vehicle with the popular handheld communication device. As if that were not impressive enough, it took them a mere four weeks to write the program. "The iPhone has an accelerometer on it, which means it can detect rotational motion," said Will Schoettler, an applications engineer with National Instruments. "And so whenever you turn the iPhone, it sends a different signal. And then, we can use the sliders on the iPhone app to control the gas or the brake." Their video on YouTube explaining the… -
J&B at COMSOL Conference: A Hit with Engineering Enthusiasts
19 Oct 2009 | 8:23 amOctober 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…
