Math

  • Most Topular Stories

  • Is Teaching Multiple Children at the Same Time a Good Idea? MATH-U-SEE NEWSLETTER VOL. 30

    Math-U-See
    joellagamon
    4 Oct 2011 | 2:51 pm
    I have been asked this question several times by a parent who has several children and is interested in maximizing her time. As an example, let’s say she has a seven year old student and another who is eight and a half. Perhaps the seven year old, who I will call Seth, is more adept in math than the eight year old, who I will name Jake. She thinks it will be a good idea to move them along together to save teaching time and energy, and she writes and asks my opinion. There are several factors to consider, but generally my experience is that this is not a good idea for the following reasons.

  • 2012 Mathematics Game

    Let's Play Math!
    Denise
    1 Jan 2012 | 7:42 am
    photo by Creativity103 via flickr For our homeschool, January is the time to assess our progress and make a few New Semester’s Resolutions. This year, we resolve to challenge ourselves to more math puzzles. Would you like to join us? Pump up your mental muscles with the 2012 Mathematics Game! Rules of the Game Use the digits in the year 2012 to write mathematical expressions for the counting numbers 1 through 100. You must use all four digits. You may not use any other numbers. You may use +, -, x, ÷, sqrt (square root), ^ (raise to a power), ! (factorial), and parentheses, brackets,…

  • Hitler on Topology

    Ars Mathematica
    Walt
    20 Jan 2012 | 10:56 am
    At this point, I’m sure everyone has seen at least one of the YouTube videos of Hitler ranting (actually actor Bruno Ganz from the movie Downfall) with fake subtitles. Here’s one showing Hitler’s reaction to discovering that in topology a set can be both closed and open. I think we all know how he felt. (This is the clip with accurate subtitles — I’d never seen it before.) Via Cocktail Party Physics.

  • What good is number sense?

    Math-U-See
    joellagamon
    7 Sep 2011 | 1:31 am
    Does your child have number sense? Success in mathematics seems to be linked to a few basic skills that are collectively known as “number sense.” Lack of these skills makes it very difficult to progress to more advanced math. Here are some ways to help your young child become aware of numbers and begin to use them. The first step is to count everyday objects with your child. Count the toys as you pick them up, count the buttons on a coat, and count the spoons as you set the table. Once your child begins to count objects, ask for three blocks or four crayons. When he or she is…

  • Building Lifelong Learners, Math-U-See Newsletter, Vol. 32

    Math-U-See
    joellagamon
    17 Jan 2012 | 1:35 pm
    A Lifelong Learner I was born at a young age and from the moment I entered the world my parents have been involved every step of the way. They raised and educated my three brothers and me at home with a philosophy of building lifelong learners. With four boys who each had a very different learning style, they were able to adapt and creatively develop an approach that produced a good outcome for all of us. More importantly than just having me memorize and repeat facts, my parents taught me how to learn and how to apply that learning. I believe this is what every home educating parent wishes…
  • add this feed to my.Alltop

    MATH - Google News

  • Steve Limbach: Aircraft jobs or rail jobs — do the math - Madison.com

    28 Jan 2012 | 5:06 am
    Steve Limbach: Aircraft jobs or rail jobs — do the mathMadison.comDear Editor: Do the math. We read recently of new aircraft jobs coming to Wisconsin, and jobs are a good thing. However, we also read that the potential 600 jobs come at a price tag of $100 million in loans, incentives and tax credits.and more »

  • Worth Mentioning: You do the math - DesMoinesRegister.com

    28 Jan 2012 | 4:05 am
    Worth Mentioning: You do the mathDesMoinesRegister.comWhen Texas Gov. Rick Perry sat at the conference table with the Register's editorial board in December, I asked him about his comment that the government shouldn't be picking winners and losers. But what about the lower tax rate for capital gains and and more »

  • New Program Prepares High School Graduates For College Level Work at ... - Patch.com

    28 Jan 2012 | 3:16 am
    New Program Prepares High School Graduates For College Level Work at Patch.comParticipants in the new program will earn two college credits and complete the equivalent of Manchester Community College's developmental English and Math sequence. Manchester's Reaching Education Achievement for College Transition (REACT) program is a Community Colleges Consider Math OptionsU.S. News & World ReportNeed for remedial college classes downCarroll County News (blog)all 5 news articles »

  • Nazareth Area educators to learn new hands-on style to teaching math - Lehighvalleylive.com

    28 Jan 2012 | 3:05 am
    Lehighvalleylive.comNazareth Area educators to learn new hands-on style to teaching mathLehighvalleylive.comBy Pamela Sroka-Holzmann | The Express-Times Nazareth Area Intermediate School math teachers this week will learn about a new concept in teaching algebra designed to increase test scores, hold attention spans and help students advance to higher

  • Hononegah hosts math invitational Saturday - Rockford Register Star

    27 Jan 2012 | 9:07 pm
    Hononegah hosts math invitational SaturdayRockford Register StarBy Anonymous ROCKTON — Hononegah High School will host an 11-school Math Invitational tournament, beginning at 9 am Saturday at the school's Performing Arts Center. Four NIC-10 schools — Belvidere, Boylan, Harlem and Hononegah — are in the field.and more »
 
  • add this feed to my.Alltop

    Scientific American - Math

  • How to Make Science and Tech Jobs More Enticing to Undergrads

    25 Jan 2012 | 6:59 am
    The number of U.S. undergraduate degrees being awarded in most STEM disciplines (science, technology, engineering and math) has risen steadily in recent years{link to G Sci page}. Yet some American employers say they are having trouble finding candidates to fill STEM jobs. The mismatch is not occurring because of an actual shortage of graduates; the numbers of job openings and new degree holders align fairly closely. And the shortfall is not because more foreign-born students are returning home after earning U.S. degrees, as has been rumored lately. [More]

  • The Not-So-Hot Hand

    15 Jan 2012 | 7:00 am
    Reggie Miller, Michael Jordan, Kobe Bryant. They’ve all gone on seemingly memorable shooting streaks. But past research has shown that the so-called hot hand is a myth, rooted in our tendency to see patterns where there are none. [More]

  • Are Physical Constants Really Constant?

    14 Jan 2012 | 11:00 pm
    Some things never change. physicists call them the constants of nature. Such quantities as the velocity of light, c , Newton’s constant of gravitation, G , and the mass of the electron, m e , are assumed to be the same at all places and times in the universe. They form the scaffolding around which the theories of physics are erected, and they define the fabric of our universe. Physics has progressed by making ever more accurate measurements of their values. [More]

  • A Brief History of Clocks

    14 Jan 2012 | 11:00 pm
    Humankind’s efforts to tell time have helped drive the evolution of our technology and science throughout history. The need to gauge the divisions of the day and night led the ancient Egyptians, Greeks and Romans to create sundials, water clocks and other early chronometric tools. Western Europeans adopted these tech­nologies, but by the 13th century, demand for a dependable timekeeping instrument led medieval artisans to invent the mechanical clock. Although this new device satisfied the requirements of monastic and urban communities, it was too inaccurate and unreliable for…

  • Stephen Hawking, "Equal to Anything!" [Excerpt]

    6 Jan 2012 | 2:15 pm
    Editor's note: The following is an excerpt from the chapter "Equal to Anything!" from the new book Stephen Hawking: An Unfettered Mind (Palgrave Macmillan, 2012), by Kitty Ferguson . [More]
 
  • add this feed to my.Alltop

    Math-U-See

  • Building Lifelong Learners, Math-U-See Newsletter, Vol. 32

    joellagamon
    17 Jan 2012 | 1:35 pm
    A Lifelong Learner I was born at a young age and from the moment I entered the world my parents have been involved every step of the way. They raised and educated my three brothers and me at home with a philosophy of building lifelong learners. With four boys who each had a very different learning style, they were able to adapt and creatively develop an approach that produced a good outcome for all of us. More importantly than just having me memorize and repeat facts, my parents taught me how to learn and how to apply that learning. I believe this is what every home educating parent wishes…

  • Giving Thanks – Math-U-See Newsletter, Vol. 31

    joellagamon
    23 Nov 2011 | 2:38 pm
    Growing up, our family had a tradition. Every year at Thanksgiving each of us would write a list of what we were thankful for in the past year. This year at Math-U-See we are thankful for many things and we wanted to share them with you. Peter, who teaches our online co-op classes, is thankful for the students that he has the privilege of teaching. Susan from customer service is thankful for many things: Customers with faithful hearts that are dedicated to their family core values and upbringing of their children. A country where we have the freedom to homeschool. Mentors and friends who…

  • Is Teaching Multiple Children at the Same Time a Good Idea? MATH-U-SEE NEWSLETTER VOL. 30

    joellagamon
    4 Oct 2011 | 2:51 pm
    I have been asked this question several times by a parent who has several children and is interested in maximizing her time. As an example, let’s say she has a seven year old student and another who is eight and a half. Perhaps the seven year old, who I will call Seth, is more adept in math than the eight year old, who I will name Jake. She thinks it will be a good idea to move them along together to save teaching time and energy, and she writes and asks my opinion. There are several factors to consider, but generally my experience is that this is not a good idea for the following reasons.

  • Turning of the Calendar

    joellagamon
    28 Sep 2011 | 2:56 pm
    Prose on changing seasons: In the springtime, Math-U-See employees are busy with fairs in every state. Our reps fly to and fro across the country, while the warehouse crew works overtime to ship fair orders. Trucks roll up to our doors with pallets of books, and other trucks roll out with packages for customers. Finally, the fair schedule lightens as we move into the summer, while parents breathe a sigh of relief and go into vacation mode. Math-U-See HQ In beautiful Lancaster County, the sun shines, the showers fall, and the corn grows. In the Math-U-See warehouse, the shipping of books…

  • What good is number sense?

    joellagamon
    7 Sep 2011 | 1:31 am
    Does your child have number sense? Success in mathematics seems to be linked to a few basic skills that are collectively known as “number sense.” Lack of these skills makes it very difficult to progress to more advanced math. Here are some ways to help your young child become aware of numbers and begin to use them. The first step is to count everyday objects with your child. Count the toys as you pick them up, count the buttons on a coat, and count the spoons as you set the table. Once your child begins to count objects, ask for three blocks or four crayons. When he or she is…
 
  • add this feed to my.Alltop

    Ars Mathematica

  • Mathematics of a Serial Killer

    Walt
    26 Jan 2012 | 8:35 am
    Someone sent me a link to this story about a mathematical model of a particular serial killer’s behavior. Two things struck me about it: How much it sounded like the kind of bizarre model you’d see on Charline on Numb3rs come up with in order to crack the case. That Cosma Shalizi would hate the model, since it’s the kind of a casual use of power laws he regularly criticizes. And here’s his analysis of the paper. He points out that, as in many other cases, a lognormal distribution provides a better fit.

  • Hitler on Topology

    Walt
    20 Jan 2012 | 10:56 am
    At this point, I’m sure everyone has seen at least one of the YouTube videos of Hitler ranting (actually actor Bruno Ganz from the movie Downfall) with fake subtitles. Here’s one showing Hitler’s reaction to discovering that in topology a set can be both closed and open. I think we all know how he felt. (This is the clip with accurate subtitles — I’d never seen it before.) Via Cocktail Party Physics.

  • Best Possible Rejection Letter

    Walt
    16 Jan 2012 | 6:32 am
    Andrew Gelman quotes from the best possible rejection letter from a journal (sent to Charles Babbage): It is no inconsiderable degree of reluctance that I decline the offer of any Paper from you. I think, however, you will upon reconsideration of the subject be of the opinion that I have no other alternative. The subjects you propose for a series of Mathematical and Metaphysical Essays are so profound, that there is perhaps not a single subscriber to our Journal who could follow them. I encourage all journals to adopt this as the standard form letter for rejection.

  • Back, From Outer Space!

    Walt
    9 Jan 2012 | 4:34 pm
    And you just walked in to find me here with that sad look upon my face. The computer that hosted Ars Math (which was at a dedicated web-site hosting company) died a horrible death a couple of months ago. For a while, it looked like several years of posts had been lost. They could be recovered by cutting-and-pasting from the Internet Archive, but I found the idea so depressing that I didn’t do anything about recovering the site. Fortunately, we were able to extract the posts from the database anyway. Someone offered to help out with the WordPress hosting, so we’re back online! At…

  • Shapley-Folkman-Starr Theorem

    Walt
    15 Aug 2011 | 6:57 am
    While economic theory sometimes uses advanced mathematics, such as Brouwer’s fixed point theorem, it’s less common for economic theory to lead to new mathematical developments. The Shapley-Folkman-Starr Theorem is an example of the latter. Roughly, the theorem states that the (Minkowski) sum of a large number of arbitrary sets in a finite-dimensional vector space will be close to convex. Starr was an economics undergraduate who was working on a term paper on approximating non-convex optimization problems with convex ones. This led to collaboration with Shapley (a game theorist),…
  • add this feed to my.Alltop

    Loren on the Art of MATLAB

  • MATLAB Documentation

    Loren Shure
    27 Jan 2012 | 2:12 pm
    For quite a while now, we have made MathWorks product documentation available from the support page on our web site. Though we started with MATLAB documentation initially, we have added documentation for all the rest of our products and have hosted a complete set on the mathworks.com for quite some time now. As you likely know, within the MathWorks family of products, you can often find more than one way, or even more than one product, to accomplish a particular goal. However, it's been difficult to see the whole landscape of possibilities, including functions, examples, information in the…

  • Best Practices for Programming MATLAB

    Loren Shure
    13 Jan 2012 | 6:21 am
    I thought I would share my top goto list of things I try to do when I write MATLAB code. And checking with other MathWorks folks whose code I admire, I found they basically used the same mental list that I use. You can find blog posts on all of these topics by selecting relevant categories from the right side of The Art of MATLAB blog site. Contents My List of Best Practices Missing from Your List? Additions to My List? My List of Best Practices Clearly (at least to me), this is not everything you generally need to do. You still need to comment the code, add good help information and…

  • Liberating Deployed Application Output from the Console Window

    Loren Shure
    2 Jan 2012 | 8:35 am
    Guest blogger Peter Webb returns with another in an occasional series of postings about application deployment. Contents Integrating Output with a Window System Creating a Shared Library Displaying Messages in a Visible Window Integrating Output with a Window System Applications developed with the MATLAB Compiler direct their output to the console window. While this may suffice for batch or background tasks, it is often not suitable for interactive or graphical environments. In an earlier post, I demonstrated how to use message handlers to redirect program output and error messages to a log…

  • Ginger Plot Winner

    Loren Shure
    20 Dec 2011 | 1:00 pm
    If you've been following the comments from my recent post on chaotic maps, you know that there were several entries to the challenge of coming up with an interesting visualization. The entries are each interesting, displaying schemes, including an animation, and extra information placed on the plots in various ways. I have conferred with a few colleagues here and we have chosen the contribution from Rafael Oliveira as the winning entry. Why? Because the code is interesting, he made interesting use interesting of some functions, the and the plot is cute (at least for rng(42). Contents Adorned…

  • Pretty 2-Dimensional Chaotic Maps

    Loren Shure
    7 Dec 2011 | 8:44 am
    Chaos theory has found uses across a broad set of scientific fields to explain some complicated observed behavior. In geophysics, my background, it can help explain the reversals of Earth's magnetic field, for example. Today I thought I'd share a chaotic system, called Gingerbreadman maps, whose equations make the system seem simple. That is, until you do some simulations. Contents Gingerbreadman Map Equations Plot Results Code Listing References Make the Plot Prettier! Gingerbreadman Map Equations The equations for the gingerbreadman map look simple enough. For any given point in space: ,…
  • add this feed to my.Alltop

    Homeschool Math Blog

  • Three-day sale for Math Mammoth

    24 Jan 2012 | 6:37 am
    SORRY I forgot to post it here (I just sent this to my email list).For January 23-25, get 23% off of all Math Mammoth downloads & CDs at Kagi store. Use the coupon code THREEDAYS. Go to http://www.mathmammoth.com first, then find the links to Kagi's order pages. OR, use these direct links:   ~ Light Blue series (complete curriculum)     https://store.kagi.com/cgi-bin/store.cgi?storeID=5KN_LIVE&page=Math_Mammoth_LightBlue_Series   ~ Blue series     https://store.kagi.com/cgi-bin/store.cgi?storeID=5KN_LIVE   ~ Golden and Green Series    …

  • Triangle puzzle - equal areas

    23 Jan 2012 | 10:11 am
    I hope Pat doesn't mind that I copied the image from his blog... He posted this triangle puzzle on his blog and I thought you might enjoy it, too!Basically, we have a triangle DFE inside a rectangle, dividing the rectangle into various triangles.  And, the three areas of fainter color are equal. That is, the area of the triangle DAE = area of the triangle EBF = area of the triangle FCD. (Notice the image is not drawn to scale at all.)And, we're asked to solve the RATIOS AE : EB and BF : FC.I'll post a solution later.

  • Versa Ruler

    23 Jan 2012 | 9:20 am
    Well, this IS something different! A physical ruler that can draw shapes with any angle measure you want.Unfortunately it's not yet in production. In fact, the project is needing funding... but very interesting! Please read more at Rule Like Never Before! NEW Shape-making Versa RulerThis ruler give you accurate measurements for every side and angle. You  can connect sides to form angles, which scale and skew smoothly, and you can lock angles and sides.  Cool!

  • Vi Hart and mathematical doodling

    21 Jan 2012 | 6:59 am
    I just learned about Vi Hart's "doodling in math class" videos (hat tip goes to Fawn Nguyen).Vi calls herself mathemusician - and definitely, she's a talented and smart gal! I'm sure you'll enjoy her videos (as long as you can follow her super fast speeaking). Here are some that I enjoyed:Doodling in Math: Spirals, Fibonacci, and Being a Plant [1 of 3] Here's a link to learn more about Fibonacci numbers in nature, so you can read about it at a slow pace : )Binary Hand Dance was pretty cool too!Her series of "mathematical doodling" videos have become somewhat of a viral success. Here's one…

  • Math teachers are at play again

    20 Jan 2012 | 6:32 pm
    Denise's done a beautiful job with the current Math Teachers at Play carnival number 46, lots to read and explore and see... head on over!
 
  • add this feed to my.Alltop

    About.com Mathematics

  • Taking the March SATs? Register by Feb.10

    25 Jan 2012 | 12:27 pm
    If you are taking the SATs for March, register early, you have until midnight on February 10th. Don't forget to check out the free question of the day, sample questions and free practice test.  Not sure how to study for the SATs, the College Board has what you need. For some additional review, the pre-algebra worksheets...Read Full Post

  • An Opportunity Worth Participating In

    22 Jan 2012 | 3:32 am
    Mathematics and science educators and administrators from around the world will participate in the 24th Annual T3 International Conference.  Participants will learn, and explore the latest TI education technology and learn new ideas for the technology they have in their classroom.  There are hundreds of hands-on sessions and the presenters will offer new and effective ways to engage students and help them learn. Better yet, there will be a focus on project based learning with the Common Core Standards. Don't miss this opportunity, registration…

  • Where Have All the Numerals Gone?

    19 Jan 2012 | 2:38 pm
    Roman Numerals were part of the curriculum when I was in school. However, after looking through a variety of curricula, the concept of Roman numerals is nowhere to be found. No ...Read Full Post

  • We Know What They Say About Assumptions.....

    17 Jan 2012 | 11:07 am
    It has long been thought that there are gender differences in math ability. Boys get it, girls don't. However,  research is beginning to shed new light on some old sets of data. Girls might just have the same ability as boys do for learning mathematical concepts. When women have equity and are well educated, their children (both genders) succeed in math. So then, when a gender gap exists, it may well be that it is due to sociocultural factors that differ among countries. See Science Daily for the study that debunks the myths about gender gaps in math....Read…

  • If You State It, They Will Learn It?

    11 Jan 2012 | 12:53 pm
    I watch with enthusiasm and interest as the Common Core Standards  begin to be implemented in those states who have adopted them.  I am a believer in consistency and although many individuals will argue that a one size approach doesn't fit all, we do know that a research and evidenced based set of age appropriate standards,  implemented consistently is a good thing. Why have every state research what the math curriculum should be?  The nay-sayers will tell you that common core doesn't allow for personalization. Really? Every good teacher…
  • add this feed to my.Alltop

    Let's Play Math!

  • Math Teachers at Play 46

    Denise
    20 Jan 2012 | 5:36 am
    Welcome to the Math Teachers At Play blog carnival — which is not just for math teachers! Here is a smorgasbord of ideas for learning, teaching, and playing around with math from preschool to pre-college. Some articles were submitted by their authors, other were drawn from the immense backlog in my blog reader. If you like to learn new things, you are sure to find something of interest. Living Books for Math A child’s intercourse must always be with good books, the best that we can find… We must put into their hands the sources which we must needs use for ourselves, the best…

  • Send Me Your Mathy Blog Posts

    Denise
    10 Jan 2012 | 1:45 pm
    by thekirbster via flickr Are you a math student or teacher (classroom or homeschool) or an independent learner? Do you blog about teaching or learning mathematics? If you have written anything playful about mathematics, now is the time to share! The Math Teachers at Play blog carnival is seeking articles about learning, teaching, or just playing around with mathematics from preschool to precollege level (through the first year of calculus). Everyone is welcome — you don’t have to be a teacher to join in the fun. You can submit your article online, but the blog carnival website…

  • 2012 Mathematics Game

    Denise
    1 Jan 2012 | 7:42 am
    photo by Creativity103 via flickr For our homeschool, January is the time to assess our progress and make a few New Semester’s Resolutions. This year, we resolve to challenge ourselves to more math puzzles. Would you like to join us? Pump up your mental muscles with the 2012 Mathematics Game! Rules of the Game Use the digits in the year 2012 to write mathematical expressions for the counting numbers 1 through 100. You must use all four digits. You may not use any other numbers. You may use +, -, x, ÷, sqrt (square root), ^ (raise to a power), ! (factorial), and parentheses, brackets,…

  • Build Problem-Solving Skills with Board Games

    Denise
    28 Dec 2011 | 1:00 pm
    Board games are a celebration of problem solving, and problem solving is at the heart of a quality mathematics education… The mathematics might be hidden, but I guarantee you that it will be there. — Gordon Hamilton, MathPickle.com Commercial Games 8 Games for Ages 8+ Games for Ages 12+ Get all our new math tips and games:  Subscribe in a reader, or get updates by Email.

  • MTaP 45 via Virtual Math Tutor

    Denise
    17 Dec 2011 | 12:09 pm
    The Math Teachers at Play Carnival is up at Virtual Math Tutor for your browsing pleasure. Articles range from preschool to high school level in math, and topics include puzzles, worksheets, games, teaching tips, ideas for the math/science lover on your Christmas gift list, and the cutest math monster I’ve seen in ages. Great fun! Get all our new math tips and games:  Subscribe in a reader, or get updates by Email.
  • add this feed to my.Alltop

    The Unapologetic Mathematician

  • Faraday’s Law

    John Armstrong
    14 Jan 2012 | 8:14 am
    Okay, so let’s say we have a closed circuit composed of a simple loop of wire following a closed path . There’s no battery or anything that might normally induce an electromotive force around the circuit by chemical or other means. And, as we saw when discussing Gauss’ law, Coulomb’s law gives rise to an electric field that looks like As we saw when discussing Gauss’ law for magnetism, we can rewrite the fraction in the integrand: So this electric field is conservative, and so its integral around the closed circuit is automatically zero. Thus there is no…

  • Electromotive Force

    John Armstrong
    12 Jan 2012 | 9:03 pm
    When we think of electricity, we don’t usually think of charged particles pushing and pulling on each other, mediated by vector fields. Usually we think of electrons flowing along wires. But what makes them flow? The answer is summed up in something that is named — very confusingly — “electromotive force”. The word “force” is just a word here, so try to keep from thinking of it as a force. In fact, it’s more analogous to work, in the same way the electric field is analogous to force. We calculate the work done by a force in moving a particle…

  • Gauss’ Law for Magnetism

    John Armstrong
    11 Jan 2012 | 8:21 pm
    Let’s repeat what we did to come up with Gauss law, but this time on the magnetic field. As a first step, though, I want to finally get a good definition of “current density”: it’s a vector field that consists of a charge density and a velocity vector , each of which is a function of space. In our example of an infinite line current, this density was concentrated along the -axis, where the velocity was vertical. But it could exist along a surface, or throughout space; a single particle of charge moving with velocity is a current density concentrated at a single point.

  • Gauss’ Law

    John Armstrong
    10 Jan 2012 | 6:18 pm
    Rather than do any more messy integrals for special cases we will move to a more advanced fact about the electric field. We start with Coulomb’s law: and we replace our point charge with a charge distribution over some region of . This may be concentrated on some surfaces, or on curves, or at points, or even some combination of the these; it doesn’t matter. What does matter is that we can write the amount contributed to the electric field at by the charge a point as So to get the whole electric field, we integrate over all of space! Now we want to take the divergence of each side…

  • Charged Rings and Planes

    John Armstrong
    9 Jan 2012 | 7:05 pm
    Let’s work out a couple more examples that may come in handy in the future, if only to get the practice. We’ll start with a “charged ring” which is a charge distribution on a circle. Specifically, we may as well consider the circle of radius in the - plane: . If the charge density is , then the total charge is . First of all, symmetry tells us that we may as well just consider the points of the form for , and we will first specialize to the points . Along this line, the field generated by a little piece of charge on one side of the circle points across to the other…
 
  • add this feed to my.Alltop

    Computational Complexity

  • Guest post on ITCS by Chazelle

    GASARCH
    27 Jan 2012 | 9:18 am
    (Requested announcement: Calling all Women PhD Students (and a few undergrads) We will be having our bi-annual Women in Theory (WIT) Workshop this year in Princeton. The dates are June 23-27, 2012. Applications are due on: Feb 29, 2012. Go here for all the relevant information. Hoping to see you in June. From: Shubhangi Saraf, Lisa Zhang, Moses Charikar and Tal Rabin.) (Guest Post by Bernard Chazelle) Why ITCS? Thanks to Lance and Bill for their kind hospitality. I am delighted to be here. With the third edition of ITCS (formerly ICS) behind us, I thought it would be good to share a few…

  • Ernst Specker (1920-2011)

    Lance Fortnow
    25 Jan 2012 | 8:19 am
    Martin Fürer remembers his former advisor.  While traveling, I received the unexpected sad news that Ernst Specker passed away on December 10, 2011. He was born in Zürich in 1920. After receiving his doctoral degree at ETH Zürich in 1949, he spent a year at the Institute for Advanced Study in Princeton. Then he returned to ETH in 1950 and stayed there with the exception of two visiting appointments at Cornell University. Ernst Specker was teaching Linear Algebra when I started my studies at ETH Zürich in 1967. His teaching style was different from the typical polished and streamlined…

  • What should we do?

    Lance Fortnow
    23 Jan 2012 | 8:31 am
    Time for a post by tweet request. Is a wave of action against big publishers' practices brewing?gowers.wordpress.com/2012/01/21/els…thecostofknowledge.com Should CS do more? @fortnow — Tugkan Batu (@tugkanbatu) January 22, 2012 Quite a lot on the Internets on Tim Gowers' promise not to work with Elsevier anymore. I'm not as anti-Elsevier as Gowers or many of my readers but I understand the frustrations. It's easy to make a promise not to publish, edit or referee papers, especially when you don't need to improve your academic reputation. Still a mathematician of his magnitude really…

  • Teaching an Honors Section of Discrete Mathematics

    GASARCH
    20 Jan 2012 | 10:15 am
    A few years ago I was assigned to teach the HONORS section of Discrete Math (a course for sophomores who have had a year of programming and a year a calculus). They told me it was up to me to figure out what to do to make it an honors course. (My section had 30 students, the non-Honors has about 60.) There were several options: This could be taught separate from the non-honors course. Diff homework, diff exams. PRO: the homework and exams can be more interesting since you do not have to worry about how they are for the non-honors student. CON: If a student would have gotten (say) an A in the…

  • How important are the Fib numbers in math? in Nature? In History of Math books?

    GASARCH
    17 Jan 2012 | 9:00 am
    The following quotes is from In the book Algebra in Ancient and Modern Times by V.S. Varadarajan. Fibonacci numbers thus grow very fast with N, indeed in geometric progression. This is often called exponential growth. They remained as curiosities till in the 1960's they were found to be crucial in certain studies in mathematical logic. I suspected they were refering to its use in Hilbert's tenth problem even though that was really 1970 (a quibble) and I would hardly call it crucial (a more substantial objection). In fact Fib Numbers are not even needed in the end. I asked Chris Lastowksi who…
  • add this feed to my.Alltop

    Mathematics and Computation

  • A puzzle about typing

    Andrej Bauer
    20 Jan 2012 | 7:42 am
    While making a comment on Stackoverflow I noticed something: suppose we have a term in the $\lambda$-calculus in which no abstracted variable is used more than once. For example, $\lambda a b c . (a b) (\lambda d. d c)$ is such a term, but $\lambda f . f (\lambda x . x x)$ is not because $x$ is used twice. If I am not mistaken, all such terms can be typed. For example: # fun a b c -> (a b) (fun d -> d c) ;; - : ('a -> (('b -> 'c) -> 'c) -> 'd) -> 'a -> 'b -> 'd = <fun> # fun a b c d e e' f g h i j k l m n o o' o'' o''' p q r r' s t u u' v w x y z -> q u i…

  • On the Bourbaki-Witt Principle in Toposes

    Andrej Bauer
    4 Jan 2012 | 1:09 am
    With Peter LeFanu Lumsdaine. Abstract: The Bourbaki-Witt principle states that any progressive map on a chain-complete poset has a fixed point above every point. It is provable classically, but not intuitionistically. We study this and related principles in an intuitionistic setting. Among other things, we show that Bourbaki-Witt fails exactly when the trichotomous ordinals form a set, but does not imply that fixed points can always be found by transfinite iteration. Meanwhile, on the side of models, we see that the principle fails in realisability toposes, and does not hold in the free…

  • HoTT Equivalences

    Andrej Bauer
    7 Dec 2011 | 8:57 am
    On December 6th 2011 I gave a talk about homotopy equivalences in the context of homotopy type theory at our seminar for foundations of mathematics and theoretical computer science. I discuss the differences and relations between isomorphism (in the sense of type theory), an adjoint equivalence, and a homotopy equivalence. Even though the talk itself was not super-well prepared, I hope the recording will be interesting to some people. I was going fairly slowly, so it should be possible to follow the talk. I apologize for such a long video, but I really did not see how to chop it up into…

  • How to make the “impossible” functionals run even faster

    Andrej Bauer
    6 Dec 2011 | 8:27 am
    A talk given at “Mathematics, Algorithms and Proofs 2011″ at the Lorentz Center in Leiden, the Netherlands. I explain how to use computational effects to speed up Martin Escardo’s impossible functionals.

  • Embedding the Baire space into natural numbers

    Andrej Bauer
    6 Dec 2011 | 8:22 am
    A talk given at “Computation with Infinite Data: Logical and Topological Foundations” Dagstuhl seminar 11411. I describe a realizability model based on infinite-time Turing machines in which it is possible to embed the Baire space (infinite sequences of numbers) into the space of numbers. Also see the post Constructive gem: an injection from Baire space to natural numbers for written notes on this topic.
 
  • add this feed to my.Alltop

    Precal Blog

  • More Work with Proof by Induction

    Franklin
    26 Jan 2012 | 10:28 pm
    Today in #bienprecal, we did some more solving of proof by induction equations. The first one we did was 2+4+6+8+…+2n=. The steps we used to solve this are as follows: 1. Find what the equation equals. 2+4+6+8+…+2n=n²+n 2. Assume Pk (do this by changing all the n’s to k’s) 2+4+6+8+…+2k=k²+k 3. Prove Pk+1 is true (do this by adding this to the left side and changing all the k’s on the right to k+1) 2+4+6+8+…+2k+2(k+1)=(k+1)²+(k+1) 4 Use the asumption from step 2 to substitute for the “2+4+6+8+…+2k” k²+k+2(k+1)=(k+1)²+(k+1) 5.

  • Proof By Induction (Day 2)

    David
    26 Jan 2012 | 9:08 pm
    We dove right into class today. We review how to do the proof by induction. After we tried a problem we tried something a little more difficult.  Proving 1^2+2^2+3^2+…+2n=n(n+1)(2n+1/6) First: Prove That the First Domino Falls n=1 1^2=1(1+1)(2*1+1/6) simplify 4=4 The first domino falls! Second: Assume another domino falls 1^2+2^2+3^2+…+2k=k(k+1)(2k+1/6)  1^2+2^2+3^2+…+2(k+1)=(k+1)((k+1)+1)(2(k+1)+1/6) Sence  1^2+2^2+3^2+…+2n=k(k+1)(2k+1/6) We can subsitute in the problem above  (k)(k+1)(2k+1/6)+2(k+1)=(k+1)((k+1)+1)(2(k+1)+1/6)…

  • Proof by Induction–Fun with Dominos

    Joanna
    25 Jan 2012 | 9:07 pm
    Well, ladies and gents, we started today with dominos again. We set up our patterns, spelling out “calc” and/or setting up straight lines. Some patterns fell over right away (success!); others, unfortunately, did not. However, it was these so-called “failures” that provided the greatest learning examples. After dominos, we were given our board problem: 1+3+5+7+ … +2n-1 = n^2 Where: n : the number of terms on the left hand side that we use 2n-1 : how we generate the odd numbers … : the infinate amount of odd numbers Our statement to prove: If we add up any…

  • Proof by Induction

    Amber
    25 Jan 2012 | 7:06 pm
    For proof by induction, you  start with an equation where the sum of odd numbers  (2n-1) = n^2   in  1+3+5+…. Then there  are things to proof by induction that must be true in order to prove that this equation works for everything. The first number must work & that every other number must work. To prove this there are 4 steps:  1. the first “domino” has to fall, which means that the first step that you are trying to prove has to be true.                      example:  the first number is 1 so you start with that 2(1) – 1 =1^2  which…

  • Creating Blog Posts and Dominoes

    Tyler
    24 Jan 2012 | 8:56 pm
    With the dawn of a new semester, the class was introduced to the blog today. We were told the basic rules, such as posting an important title and filling the post with information learned in class. Besides the website we also started a project involving dominoes. First we watched a few really cool videos of domino chains and even a chain of pound coins from the UK. These videos remind me of a music video in which the band set everything up perfectly to make a huge chain of events all shot in one clip: In our project, each group of four was assigned to create a chain of dominoes using the…
  • add this feed to my.Alltop

    The Math Less Traveled

  • u-tube

    Brent
    10 Jan 2012 | 12:15 am
    [This is the eighth in a series of posts on the decadic numbers (previous posts: A curiosity, An invitation to a funny number system, What does "close to" mean?, The decadic metric, Infinite decadic numbers, More fun with infinite decadic numbers, A self-square number).] In my previous post, we found a decadic number with the curious property that it is its own square. We also discovered an algorithm for computing : starting with , we square each and take the remainder (that is, we keep only the last digits) to give us . Then is defined as the limit of the as . (As an aside, notice…

  • Herbert Wilf: 13 June 1931 – 7 January 2012

    Brent
    8 Jan 2012 | 10:34 pm
    I was sad to learn that Herbert Wilf died yesterday. Long-time readers of this blog may remember him as one of the discoverers of the Calkin-Wilf tree, which I wrote about in a ten-part series of posts (1, 2, 3, 4, 5, 6, 7, 8, 9, 10). The Calkin-Wilf Tree He also wrote generatingfunctionology, a textbook about generating functions, a topic near and dear to my heart (which I hope to write about here someday). Although he was an emeritus professor at the University of Pennsylvania (where I am currently doing my PhD) I sadly never got a chance to meet him.

  • A self-square number

    Brent
    4 Jan 2012 | 1:45 pm
    [This is the seventh in a series of posts on the decadic numbers (previous posts: A curiosity, An invitation to a funny number system, What does "close to" mean?, The decadic metric, Infinite decadic numbers, More fun with infinite decadic numbers). I know it's been a while since I've written on this topic, so if you've been following along, you might want to go back and refresh your memory.] Finally, as promised, I can show you the strange number u which is its own square (but which isn’t zero or one!). Up until now all the decadic numbers we’ve considered have been equivalent to…

  • Four-figure offer

    Brent
    1 Dec 2011 | 10:56 am
    This just arrived in my inbox: My name is Becky Raymond, I’m a Domain Brokerage Consultant working on behalf of the owner of traveled.com to sell this premium asset. While searching online I came across your domain mathlesstraveled.com; since both domains have listings under a related keyword I thought perhaps your company may be interested in acquiring traveled.com? If this domain is of interest to you, please submit an offer in the four figure range and above to qualify as a potential buyer. Sure thing, Becky! Here is my four-figure offer: Fig. 1. A graph of the first 1000 hyperbinary…

  • Sigmas and sums of squares

    Brent
    29 Nov 2011 | 12:07 am
    Commenter Rachel recently asked, How would you find the sum of ? See here for an explanation of sigma notation—in this case it denotes the sum Of course, for any particular value of we can just plug in values and do a bunch of adding. But I interpret Rachel’s question to mean “can we find an algebraic expression in terms of which lets us compute the sum more quickly than actually adding the individual terms?” Let’s try! First, we observe that Why? If you think about it a bit, you can see that the same terms show up on the left and the right, just in a different…
  • add this feed to my.Alltop

    The Math Factor Podcast

  • HJ. Strange Suitor

    strauss
    27 Jan 2012 | 7:54 am
    We’ll have some pursuit puzzles over the next couple of weeks; this segment’s puzzle has a simple and elegant solution, but it might take a while to work it out! In the meanwhile, here’s a little discussion about the glass of water problem. Each time we add or subtract 50%, we are multiplying the quantity of water by 1/2 or 3/2. If we began with 1 glass’ worth, at each stage, we’ll have a quantity of the form 3m/2n with m,n>0  Of course that can never equal 1, but we can get very close if m/n is very close to log3 2 = 0.63092975357145743710……

  • Hi! Getting Closer

    strauss
    16 Jan 2012 | 2:31 pm
    So how close, and how quickly, can we get back to exactly one glass of water, adding and subtracting 50% of the total at each step. And what is happening with the “reverse of the square is the square of the reverse” property of 2012, 2011 and 2010?

  • HH. Corpuscle Candies

    strauss
    11 Jan 2012 | 2:37 pm
    In which we continue our contest for SOME interesting fact about the number 2012, describe Newton’s Law of Cooling, and ask another puzzle on the mixing liquids. We HAVEN’T yet fully answered the coffee and cream question: a follow up post will be coming soon!

  • HG. Two Love

    strauss
    1 Jan 2012 | 12:12 pm
    In which we confess further delight in arithmetic… 1) Send us your candidates for an interesting fact about the number 2012; the winner will receive a handsome Math Prize! As mentioned on the podcast, already its larger prime factor, 503, has a neat connection to the primes 2,3,5, and 7. 2) So what is it about the tetrahedral numbers, and choosing things? In particular, why is the Nth tetrahedral number (aka the total number of gifts on the Nth day of Christmas) is exactly the same as the number of ways of choosing 3 objects out of (N+2)? Not hard, really, to prove, but can you find a…

  • HF. True Love

    strauss
    23 Dec 2011 | 3:34 pm
    How much does my True Love love me truly? Kyle and Chaim ponder the question… Show Spoiler ▼ This is, of course, the on air version of last year’s post, The Nth Day of Christmas, when the podcast was quiet. But don’t peek! Quick answer soon, and in the New Year, a longer discussion on the merits of mixing cream with your coffee. In the meantime, Peace on Earth, for all living things, Chaim and Kyle
 
  • add this feed to my.Alltop

    mathematics « WordPress.com Tag Feed

  • 400

    thomasinterestingblog
    28 Jan 2012 | 3:14 am
    WordPress has kindly decided to remind me that this is my 400th post on my blog. I had previously done posts once every hundred posts (100 and 200) however I don’t really see the need seen as there is a search box on the right of this post. Instead I thought that it would be interesting to look at the number 400. I don’t normally spend much time thinking about numbers and most of these facts about the number 400 have been obtained from the web however if you do want an interesting book about numbers I recommend Number Freak by Derrick Niederman which I got for my birthday last…

  • Learning Without Frontiers 2012 Day Two

    lynettebarr
    28 Jan 2012 | 2:01 am
    9.40am Here we are again, we’ve packed our suitcases (I had to sit on mine to close it, and while I am sure it now weighs more than I do, I am assured that it doesn’t) so that we can go to the airport after the last presentation of the day. Morning Session – 21st Century Learning 9.40am 21st century learning is the theme, and Lord David Puttnam is kicking off the day by chairing a panel. Lord Putnam presented at last year’s LWF, and was one of my favourite presenters. Many of those in ps are likely to spend their working lives predominantly dominated by voice…

  • Vi Hart and More Fun with Fibonacci, Plants, and "Spiraly Things"

    Gareth Branwyn
    28 Jan 2012 | 1:30 am
    Here are parts two and three of Vi Hart’s brilliant and dizzying exploration of the Fibonacci number, plant growth patterns, and the mathematics behind other cool, spiraly things. More: Spirals, Fibonacci, and Being a Plant

  • Fridays With Elliot

    dangillis
    27 Jan 2012 | 10:12 pm
    Well it’s Friday. Again. It seems that the weeks are just flying by. I put the blame squarely on the two courses that I’m teaching. But this isn’t a bad thing. Not even slightly. In fact, I think time is flying because I’m having so much fun. Don’t get me wrong, I’m also exhausted. But it’s the good kind of exhaustion. The kind where you know you’ve just finished something really rewarding and now deserve the sleep of kings. Or perhaps some chocolate (thanks – don’t mind if I do). Sadly, my reward is going to be short-lived. I have a…

  • Expansion of Terms

    Josh Young
    27 Jan 2012 | 9:49 pm
    Good morning, everyone! Sorry about a lack of a post yesterday, work called, so I ran. It happens, but in future, I think I’ll leave a few posts on standby just in case I don’t have the time to write one up. Today’s post is about expansion of terms. I’ve included an info sheet, a summary sheet and a tutorial, similar to what I made for the Introduction to Sets tutorial and Quadratic Formula/Equation sheet. I’ll add them to the Resources page later when I get a chance, but for the moment, I hope that this will help out. Expansion of Terms – A Mathematical…
  • add this feed to my.Alltop

    Neoformix

  • Spot

    12 Jan 2012 | 4:15 am
    Spot is an interactive real-time Twitter visualization that uses a particle metaphor to represent tweets. The tweet particles are called spots and get organized in various configurations to illustrate information about the topic of interest. Spot has an entry field at the lower-left corner where you can type any valid Twitter search query. The latest 200 tweets will be gathered and used for the visualization. Note that Twitter search results only go back about a week so a search for a rare topic may only return a few. When you enter a query the URL is changed so you can easily bookmark it or…

  • Obama Mosaic Portrait

    30 Nov 2011 | 4:25 am
    Here is a Multiscale Mosaic of Obama created from hundreds of pictures taken during his time in office. The Van Gogh Portrait Mosaics were fun but I wanted to try an example that uses photographs as opposed to paintings. I settled on a portrait of Obama because of the widespread availability of photographs of him that are free of copyright restrictions. The subimages for this design are taken from the White House's Flickr photostream and seem to have been primarily taken by Pete Souza. I downloaded the 1000 most 'interesting' photos from the stream and used those as input to my process. I…

  • Van Gogh Mosaic Portraits

    23 Nov 2011 | 5:10 am
    Here are four mosaic portraits of Vincent Van Gogh. The primary images and all the various component tiles are regions of paintings by Van Gogh. A few more details on the multiscale mosaic process can be found in the post Multiscale Mosaics. The portrait images are all from WikiMedia Commons. The other Van Gogh paintings came from here. I created these by writing custom code in Processing.

  • Multiscale Mosaics

    22 Nov 2011 | 4:20 am
    I have been further refining my multiscale mosaic technique in search of the overriding goal of reconstructing an image from sub-images in such a way that balances the clarity of the large target image and the sub-images. I have tried out lots of ideas and the ones that seem to have the most potential for creating interesting multiscale mosaics are: Allow use of lightened and darkened versions of the sub-images Allow manual adjustment of the detail level (size of sub-images used) in different regions of the image When matching sub-images to regions consider how often each sub-image has…

  • Phyllotaxy Spiral Mosaics

    15 Nov 2011 | 10:10 am
    The post Mona Mosaics showed a number of ways to segment a flat surface and build mosaics by filling regions with the average colour for that region in some underlying image. Here is another example of the same technique but this time using a Phyllotaxy spiral, sometimes called a Fibonacci spiral. It's an arrangement commonly found in plant growth - for example in the Sunflower. Jim Bumgardner has an excellent tutorial where he develops the idea and gives code for producing the pattern and several variations. I'm using something based on his Example 10 code to produce the mosaic below from a…
  • add this feed to my.Alltop

    Math Bootcamps - Online Bootcamps, Math Tips, and How-to Articles

  • The Four Stages of Learning Math

    Jerimi
    25 Jan 2012 | 2:18 pm
    Everyone (yes, EVERYONE) who learns new math struggles at first and then slowly puts the pieces together. The only difference is that the people with more experience learning math know what to expect and how to push through it. This is the key to not only understanding math but really to doing anything tough in life. Think about how it feels when you start a new topic in math. Can you identify these stages in your process? Do you let yourself get caught up in frustration before you push through? Stage 1: Bewilderment – I’m sorry. The fact that no one uses this word anymore made it…

  • Sketching Quick and Accurate Graphs of Linear Equations

    Jerimi
    16 Jan 2012 | 1:08 pm
    While there are plenty of methods to get a good hand drawn graph of a linear equation, many plot more points than necessary and (if you aren’t careful) misrepresent the location of two important points: the x and y intercepts. Using the intercepts to plot your line takes care of both of these problems and more importantly: its fast! In this video, I will use two examples to show you exactly how it’s done. Click here to view the embedded video.

  • Here it is: The Math BootCamps Spring Schedule!

    Jerimi
    15 Jan 2012 | 7:51 am
    Its time to get the bootcamps rolling for 2012! You’ve been waiting much too long to see when the next pre-algebra, algebra, and stats bootcamps will be held. Well, here they are for your math reviewing needs! Pre-Algebra Bootcamp This bootcamp is designed for anyone who needs to review the basics like working with fractions, negative numbers, and variables before starting algebra. Feb 6 – 12 Mar 5 – 11 Algebra Bootcamp A little rusty on algebra? This bootcamp reviews important algebra skills that come up in courses like algebra 1 (or beginning algebra) and a few of the…

  • Want to ACE your Online Math Classes this Spring?

    Jerimi
    10 Jan 2012 | 9:03 pm
    Are you taking an online math class this spring? I could give you tons of advice but my #1 tip is: Treat it like a real math class. People feel silly writing notes from something they are reading online. That’s silly. You take notes in a face to face class right? Don’t let yourself become more passive simply because there isn’t the pressure of the professor looking at you funny while you just sit there doing nothing. Write. If there are online videos, take notes. If there are online notes, write your own notes from them and try to work the examples as you go. You should…

  • Deadline Extended for January 9 Statistics Bootcamp

    Jerimi
    6 Jan 2012 | 12:53 pm
    If you thought you missed out on taking this round of the statistics bootcamp, you are in luck! The deadline has been extended and you can now sign up anytime before THIS MONDAY. If you are enrolled in a stats class for the spring semester, this would be a great way to get ahead of your classmates and make the semester that much easier on yourself! Here are the details: Start date: Monday Jan 9, 2012 Duration: 7 days – all online More info: http://www.mathbootcamps.com/statistics_bootcamp.php Hope to see you there!
 
  • add this feed to my.Alltop

    Institute for Mathematics and Computer Science

  • More Modular Arithmetic with the Clock Game

    admin
    19 Jan 2012 | 6:00 am
    Editor’s note: The material below is adapted from ‘Book 0 Chapter 1: Operational Systems’ of the Elements of Mathematics series. The EM series of secondary school mathematics textbooks is a 27-volume collection written and published by the IMACS Curriculum Development Group and serves as a basis for the high-level online math courses available through eIMACS, the distance-learning division of IMACS. In our previous IMACS blog post on modular arithmetic, we introduced the Clock Game as a fun way to teach children about modular addition. Now, we’ll introduce a few…

  • Georges Papy: A Mathematics Educator for the Ages

    IMACS Staff Writer
    5 Jan 2012 | 6:00 am
    Mathematics educator, Georges Papy, in 2009. IMACS pays tribute to Belgian mathematician and mathematics educator, Georges Papy, who died in Brussels this past November at the age of 91. Georges and his wife, Frédérique, also a noted mathematics educator, were two of the seminal figures in the development of what eventually became the IMACS Mathematics Enrichment curriculum. We are deeply grateful to the Papys for their life’s work on behalf of mathematics students and their teachers. The Early Years Georges Papy was born in Anderlecht, a municipality in Brussels, Belgium of not quite…

  • High School Computing: The Inside Story

    IMACS Staff Writer
    22 Dec 2011 | 6:00 am
    IMACS alumna Natasha Chen on her way to visit the Institute for Advanced Study in Princeton, NJ. Originally published in the May 1992 issue of The Computing Teacher, this essay by IMACS alumna Natasha Chen brought much needed attention within computer science education circles to the debate over teaching computer programming for beginners. Amazingly, almost 20 years later, the key issue raised by the article – how to teach fundamental computing concepts in a way that is effective, engaging and empowering – remain unresolved. Many students still find themselves in syntax-driven classes…

  • Winter 2011 Staff Picks

    IMACS Staff Writer
    8 Dec 2011 | 6:00 am
    It’s winter at IMACS headquarters in South Florida. What does that mean? Sunshine. Temperature in the 70s and 80s. New Yorkers at the mall. Gotta love it! With the holidays around the corner, you might be wondering what to get for the math or science lover in your family. So we asked members of our IMACS family to share some of their favorite books or movies for our Winter 2011 Staff Picks list. Instructors Guy Barmoha, Frances Keiper and Jeff Piskun offered some terrific recommendations. If you’re still in need of ideas, check out more favorites from our Summer 2011 Staff Picks…

  • An Interview with Milo Gardner, Cryptanalyst

    IMACS Staff Writer
    24 Nov 2011 | 6:00 am
    Milo Gardner at US Army code breaking school, Fort Devens, 1957. Milo Gardner may be retired, but he’s not letting his mind rest idle. This amateur code breaker chatted with IMACS about his mathematics background and how it influenced his life. After serving in the United States Army as a cryptanalyst, Milo went on to earn his B.A. in Mathematics with a minor in History of Economic Thought at California State University – Chico. What followed was a career in aerospace engineering and an M.B.A. from CSU – Fullerton. Years later in retirement, Milo’s curious mind, a letter to the…
  • add this feed to my.Alltop

    Math Concepts Explained

  • Convert Polar to Rectangular

    SK19
    14 Jan 2012 | 7:33 pm
    In this post, I am going to describe the theory that allows you to convert polar to rectangular coordinates.  This follows up my previous post that describes graphing polar coordinates, where I introduced the concept of this new method of graphing.  However, the relationships that I will show you here will hopefully allow you to see the connection between polar and Cartesian coordinate systems, which will make them easier for you to work with! To quickly refresh what I explained last time, start at the origin (or pole) of your graph and extend the polar axis line out to the right.

  • Graphing - Polar Coordinates

    SK19
    16 Dec 2011 | 10:55 pm
    Polar coordinates are a system of describing points on a plane, in a way that is similar yet still quite different from what you have previously used.  I am going to explain what polar coordinates are here, and then in a subsequent post, I am going to explain their relationship to the graphing system that you already know about.  Hopefully you will find that graphing polar coordinates are not really any harder than what you already know how to do! Up until now, you have likely only ever worked with rectangular coordinates, otherwise known as the Cartesian coordinate system.

  • Now on Google+! Add me to your circles!

    SK19
    6 Dec 2011 | 12:19 am
    I've finally gotten around to connecting my site to Google+! I've set up a page specifically for this Math Concepts Explained blog.  Visit my Google+ page at https://plus.google.com/114879190180011260820 and add me to your circles!  I'm planning on posting brief bits of my blog posts there as I generate new ones, but you're going to have to visit this blog for the full deal!  You can also send me emails to ask questions or leave comments, if you don't want to do so on the blog's comment section.  Please send your math questions or comments to my new email address at…

  • Degree of a Polynomial

    SK19
    28 Nov 2011 | 9:40 pm
    One of the most common questions you will find when first learning about polynomials, "How do you find the degree of a polynomial," sounds incredibly complicated and difficult, but really couldn't be simpler.  Sometimes, you don't need to use a bunch of math concepts to find the answer, or to do several mathematical manipulations to arrive at the solution.  Often, you don't have to do anything but just LOOK at the equation, and you can figure out the degree of a polynomial.  And that is because finding the degree of a polynomial is simple. The degree of a polynomial is simply…

  • Using the Quadratic Formula

    SK19
    12 Nov 2011 | 5:05 pm
    So, now that you know the answer to 'What is the Quadratic Formula,' next I will show you examples of Using the Quadratic Formula.  Refer back to my last post to familiarize yourself with what the quadratic formula looks like.  I've also explained there the nature of the roots of a quadratic equation.  If you haven't read it, I recommend taking a look as it might help you to visualize and to find the solution to a quadratic equation easier. For my first example of using the quadratic formula to find the roots of a quadratic equation, let's keep it simple. x2 - 2x -3 = 0…
  • add this feed to my.Alltop

    mathrecreation

  • primes on a log spiral

    Dan MacKinnon
    11 Jan 2012 | 1:29 pm
    Since looking again at Theodore Andrea Cook's The Curves of Life a few posts back I've been planning on playing with logarithmic spirals, which are identified in that book as the type of spiral that you often encounter in nature and in architecture. I was inspired to finally spend some time with them after reading a recent post on Math Hombre. For fun I treated the curve like a number line and plotted prime numbers on it  using Processing. It seems to me that a nice thing about curling up the number line is that it allows you to take in more of the line at a glance. You can…

  • the best of 2011

    Dan MacKinnon
    10 Jan 2012 | 4:45 pm
    Once in a while I get sent books to review and recommend - this is very nice, but unfortunately I haven't had the chance to post many reviews. It is not only in the book review department that I'm failing - I seem to be having a more general problem finding time to do any recreational mathematics (and then to post about it here). So it was a treat to receive a copy of The Best Writing on Mathematics, 2011 (Mircea Pitici, ed.), a book that solves both problems: it is a book that I really have to recommend, and it is also certain to inspire me in more mathematical recreations.  …

  • more window patterns in gsp

    Dan MacKinnon
    20 Nov 2011 | 8:40 pm
    You'd be right in saying 'hey, these are just a bunch of overlapping squares.' Yes. The only redeeming thing that I can point to is that they are made by following a rule, and the rule is one that is easy to reproduce without using any external measuring device (like a ruler or protractor), only the squares themselves. Think origami: you find midpoints by folding, etc. In this case, GSP is used, but only simple constructions like mid-point finding and segment creating. The trick is to find a rule that allows you to start with a square and then construct two points that you can base another…

  • A4 window patterns and special triangles

    Dan MacKinnon
    11 Nov 2011 | 10:30 pm
    A short while ago I mentioned that A4 paper has nice proportions - it's a silver rectangle, which means that the ratio of its long side to its short side is sqrt(2). Because of their nice proportions, silver rectangles can be used to construct special triangles that we know and love from trigonometry. One nice way to note the angles in these triangles is to form window patterns based on them - these are shapes made from overlapping pieces of paper that have been rotated according to a rule. The term window pattern comes from William Gibbs - so named because if you put them up…

  • animated iterations - too much fun

    Dan MacKinnon
    11 Nov 2011 | 12:38 pm
    Not much to this post - just playing with the GSP sketch that I pointed to earlier. These are just iterations, plus animation, plus tracing, with what I think are some nice results. The 'colored Pythagoras tree' fractal below is a classic that I learned in a GSP workshop years ago, and it's based on one of the projects in the free booklet 101 Project Ideas for GSP. I'm sure there are some instructions for the whole thing floating around somewhere. [Update: See the Nov 15th blog post at sine of the times for some instructions on the basic tree.] The image below is a later stage of the one…
 
  • add this feed to my.Alltop

    Maths Insider

  • Maths Meets Psychology: How Shad Moarif Mixes the Two at Karismath

    Caroline Mukisa
    24 Jan 2012 | 5:13 am
    Shad Moarif runs the Karismath website where he offers lessons that explains Mathematics visually, using the principle of Visual Mediation and UDL (Universal Design in Learning). Check out the free Karismath You Tube videos which are perfect for breaking down concepts for visual learners. Find out how Karismath uses maths mixed with psychology to “turn minds.”Tell us about yourself.  Why did you develop Karismath?I have background in Psychology, Reading and Mathematics. It’s a unique combination which makes it possible for me to come at Mathematics teaching from 3…

  • Does Your Teen Know Their Times Tables?

    Caroline Mukisa
    17 Jan 2012 | 5:30 am
    I’m taking a 1 month break from posting new posts here on Maths Insider while I work on other projects. In the next few weeks I’ll be highlighting some posts I’ve written here and on other websites that you may have missed. Enjoy!I wrote the following guest post for the cool maths blogger Bon Crowder over at Math is Not a Four Letter Word. When I ran a Kumon centre I would often enrol teens who had weak mental maths skills, which were causing them to struggle with maths. Fixing this problem enough to give them the confidence and skills to improve their maths took around 6…

  • Guinness Book of World Records Maths

    Caroline Mukisa
    10 Jan 2012 | 1:00 am
    I’m taking a 1 month break from posting new posts here on Maths Insider while I work on other projects. In the next few weeks I’ll be highlighting some posts I’ve written here and on other websites that you may have missed. Enjoy!One of my first guest posts was for the Wild About Math website: Sneaking Math into Children’s Diets, where I found some fascinating facts from the 2010 edition of the Guinness Book of World Records and made up some cool maths questions to accompany them. Here’s a sneak peak at the post:This blog post is the culmination of a fight; a…

  • Defrost Your Child’s Maths-Brain Freeze: Back to School Maths

    Caroline Mukisa
    3 Jan 2012 | 5:30 am
    I’m taking a 1 month break from posting new posts here on Maths Insider while I work on other projects. In the next few weeks I’ll be highlighting some posts I’ve written here and on other websites that you may have missed. Enjoy! One of the best things about school holidays is not having to worry about piles of school homework. Of course, being Maths Insider parents, I’m sure you’re always on the lookout for ways to highlight every-day maths in interesting ways. During the summer, I got together with Bon Crowder from the Math is Not a Four Letter Word website…

  • Inside the Head of a Maths Parent: Math Four Interviews Maths Insider

    Caroline Mukisa
    27 Dec 2011 | 1:00 am
    I’m taking a 1 month break from posting new posts here on Maths Insider while I work on other projects. In the next few weeks I’ll be highlighting some posts I’ve written here and on other websites that you may have missed. Enjoy!I’m a big fan of the Math Four blog run by Bon Crowder. She’s an expert at talking straight when it comes to helping kids with maths. I love the idea of her Mathematician Parent series where she interviews real life maths educators and asks them how they use maths with their own kids. I was excited to share my own family maths…
  • add this feed to my.Alltop

    Math-Blog

  • Recent Data For Planning Mathematical Software Projects

    John F. McGowan, Ph.D.
    19 Jan 2012 | 7:35 am
    This article is a follow up to the previous article Estimating the Cost and Schedule of Mathematical Software. In the previous article, the author advocated using software engineering expert Barry Boehm’s Basic COCOMO Embedded Mode cost model to estimate the cost and schedule of mathematical software projects, with the important qualification that there are substantial variations between actual effort and estimated effort using this model. By Boehm’s own account, Basic COCOMO estimates are within a factor of two of actual effort only 60 percent of the time. The formula for Basic…

  • Estimating the Cost and Schedule of Mathematical Software

    John F. McGowan, Ph.D.
    10 Jan 2012 | 1:50 pm
    Mathematics and mathematical software combined with today’s powerful computers can deliver large improvements in speed and efficiency as well as new useful features. Mathematical software is in widespread use: digital video such as YouTube and Skype, digital audio such as MP3 files, JPEG images, speech recognition such as Apple’s Siri, computer generated images in movies and video games, and the Global Positioning System or GPS that tells people where they are, all multi-billion dollar markets today. Mathematical software may offer solutions to many pressing problems such as…

  • A Big List of Interesting Mathematics Books Released in 2011

    Antonio Cangiano
    16 Dec 2011 | 1:11 pm
    The following is a list of 46 interesting math books that were released in 2011. As some of you know, I run a service called Any New Books?, which emails you a list of new books that are related to the categories of your choice each week. For the most part I pulled this list from the weekly staff picks there throughout this past year, just in time for your Christmas shopping. The books are ordered by their current sale rank on Amazon (from the most popular to the least popular at the moment, with hardcovers first). I hope this page will help you discover a few titles you may have not have…

  • Animations of a Possible Cure for Cancer

    John F. McGowan, Ph.D.
    31 Oct 2011 | 5:00 am
    This article is the third in a series on possible ways to use mathematics to cure or treat cancer, that began with Can Mathematics Cure Cancer?. It presents the Bathtub Mechanism, a possible way to kill cells with abnormal numbers of chromosomes, a common characteristic of many cancer cells, in greater detail and presents several animations of the mechanism. Cancer is the second leading cause of death in the United States. Over five-hundred thousand people died from cancer in 2007. If current trends continue, about one in three of readers will die from cancer. Since 1971 the United States has…

  • Tackling Cancer with Math

    John F. McGowan, Ph.D.
    7 Oct 2011 | 3:28 am
    The recent death of Apple founder Steve Jobs from pancreatic cancer at the young age of fifty-six highlights the dismal progress in the War on Cancer, despite over $200 billion, over one million published research papers, and the efforts of hundreds of thousands of highly qualified, hard working, committed researchers since 1971. Steve Jobs inspiring commencement address to Stanford University is also a poignant reminder of the ephemeral nature of words like “cured” and “curable” in cancer research and treatment. Steve Jobs may well have believed his rare form of…
  • add this feed to my.Alltop

    MathFour

  • Break the Rules and Get Fired!

    Bon
    16 Jan 2012 | 2:27 pm
    I was reading a research paper about math teacher shortages by D.R. Sterling. Turns out that less than 12% of math teachers leave the profession through retirement.So 88% of the time math teachers quit, get fired or die!by ewen and donabel | Flickr.com | CC BYSo why not be a math teacher?Are you good at teaching math?Have you avoided the profession because it doesn’t pay anything near what you make now?Could you use a 9 month vacation to do something totally different, worthwhile and exciting?Can you afford a 70% cut in pay for 9 months to really make a difference?If you want to change…

  • Performance vs. Understanding

    Wil
    15 Jan 2012 | 5:56 am
    This is a feature article by William Devine, MS, LPC, CART. Wil is the Director of Research at MathFour.com.The “old guard” of academics focused on rote memorization, correct answers, and academic performance – performance based, measurable objectives. To a large degree some of these focuses continue to prevail.But a different way of teaching is emerging. Based on the research, this new way is more helpful, sustainable, and effective.Research was done in the everyday math classroom.Teachers were profiled in a research paper titled  The classroom environment and…

  • Links for Learning January 14, 2012

    Bon
    14 Jan 2012 | 7:56 am
    by Martin Pettitt | Flickr.com | CC BYAnother wad of links have collected in my Evernote account. Gotta share…Competition – looks cool! (deadline April 25, 2012)Math images - beautiful!Math education linksMath site done by teenagers - done long ago through that competition above!Math teacher responds to goofy economistsTarsia puzzlesAnother Competition – “Math of Planet Earth” (deadline September 15, 2012)Poster of a Zookeeper doing mathEnjoy!And share any you’ve found in the comments!Related articles2012 MathFour ManifestoLinks for Learning November 7,…

  • Preschool Math Success

    Bon
    12 Jan 2012 | 10:44 am
    Through the Living Math Yahoo Group, I got this list for the typical courses of study for various grade levels. In each grade level link, there’s a list of math concepts.Since daughter is two, I immediately clicked on the preschool link. I was a little offended to find such a long reading list and no list titled, “Math.”And then I read the list. In almost every line I found math concepts!If you teach your little one these things on this list, check out the advanced math they will also be getting!(Note: my comments are italicized.)SizeUnderstands big and little.This preschool math…

  • Area of a Triangle & Area of a Hexagon

    Bon
    11 Jan 2012 | 12:00 pm
    Part of Wordless Wednesday…Related articlesWhat is a Ruler and Compass Construction?Wordless Wednesday: Fibonacci BasketsPrime Numbers Are Fun to Learn!3 Words to Improve Your Child’s Success in MathThis post - Area of a Triangle & Area of a Hexagon - first appeared on MathFour, a blog dedicated to helping teachers, tutors, parents and homeschoolers teach math. Visit that website for more information!
 
  • add this feed to my.Alltop

    CSE Blog - quant, math, cse puzzles

  • Number Board Puzzle: Sum of Colours

    Pratik Poddar
    19 Jan 2012 | 2:53 am
    Source: Asked to me by Anuj Jain (EE IITB 2010 Graduate, MFE Student at Baruch College NY) Problem: You have a 8x8 square board with numbers in each cell. 12345678 910111213141516 1718192021222324 2526272829303132 3334353637383940 4142434445464748 4950515253545556 5758596061626364 Each number is given a colour (red or white) such that each row and each column has exactly the same number of red number and white numbers (i.e. four). Prove that the sum of 32 red numbers on the board is equal to the sum of the other 32 white numbers on the board. Cheers! Update (21 Jan 2012): Solution: Posted…

  • Pile Puzzle

    Pratik Poddar
    11 Jan 2012 | 7:28 am
    You have 55 matches arranged in some number of piles of different sizes. You now do the following operation: pick one match from each pile, and form a new pile. You repeat this ad infinitum. What is the steady state? Is it unique? Answer is intuitive :) Cheers!

  • Digit Permutation Puzzle

    Pratik Poddar
    4 Jan 2012 | 8:10 am
    Source: Taken from Thomer's Puzzle Website (http://thomer.com/riddles/) Problem: You have a number that consists of 6 different digits. This number multiplied by 2, 3, 4, 5, and 6 yields, in all cases, a new 6-digit number, which, in all cases, is a permutation of the original 6 different digits. What's the number?

  • Number of digits in 125^100

    Pratik Poddar
    23 Dec 2011 | 5:24 am
    Source: Asked to me by Suman Kalyan Bera (M.Tech  Student IIT Delhi) on contact page Problem: How many digits does the number 125^100 have? Very interesting problem and equally interesting solution :) Update (25 December 2011): You are not allowed to use your high school notes on values of log_10(2) or log_10(5) Solution: Posted by me in comments!

  • Array Problems - Contiguous Sum and Distinct Elements

    Pratik Poddar
    23 Dec 2011 | 5:12 am
    Source: Posted by Algo Muse on contact page. Also posted on Algo Muse (December 2011) http://www.algomuse.appspot.com Problem: Two definitions: 1) Contiguous t-sum problem Given an array A[1..n] and a number t as input, we want to find out if there exists a sub-array whose sum is t. For example, if the following array and t=8 is the input, the answer is YES since it contains the sub-array A[2..4] whose sum is t.  1 4 -1 5 -8 5 -6 3 10 3  2) Distinct-elements problem Given an array A[1..n], find out if all the elements in the array are distinct. Return YES if all the numbers are…
Log in