# Math

• ## Most Topular Stories

• ### How to Solve a Physics Problem (FUNNY!) plus Mental Math Tips

Maths Tips From Maths Insider
4 Apr 2014 | 8:14 am
I saw the comic strip below last week on Facebook by the funny folks at Saturday Morning Breakfast Cereal (SMBC), and spent a good few minutes cry-laughing (is that a thing?) Even my daughter in the midst of wrangling with Quadratics in preparation for a math test, joined in. You see, even for seasoned math teachers, math lovers and professional scientists and mathematicians, arithmetical errors are all too common when problem solving.   As part of my role as Instructor for International Students at Tabtor Math, I was given 5 math worksheets at Grade 5 and 6 level to test and report…
• ### Graphs of Sine and Cosine Functions

Natural Blogarithms
3 Mar 2014 | 7:52 am
I just posted a new video to the Trigonometry Lecture Series.  This is the 11th in the series. In this video, I cover how to identify properties of sine and cosine graphs, determine the amplitude and period of sinusoidal functions, graph the sinusoidal functions using key points, and find an equation for a sinusoidal graph. View on YouTube
• ### Another Common Core Rant - not a video...

MathNotations
15 Apr 2014 | 5:31 am
While I agree with the concerns of many parents that over-testing is damaging to children and subverts the purpose of education, I don't believe that the Common Core has set the bar too high, at least in math, my area of expertise. I know from direct experience with children that we can expect far more thinking of them than is commonly held. That is the Core Belief of my blog. The problem is that teachers have not received the necessary preparation and the testing has been rushed and lacking in quality control. We're trying to set the bar higher for children without raising the bar…
• ### Easter Egg Hunt

17 Apr 2014 | 11:00 am
Are you read for a quadratic equation word problem that relates to Easter? I can't think of anything more entertaining to do this Easter that links the holiday with Math! Jennifer Ledwith provides us with this entertaining set of questions for a fun filled 'mathy' Easter.  See the exercise questions here. (All questions are supported with answers.)
• ### Do You Blog About Math?

Let's Play Math!
14 Apr 2014 | 1:50 pm
by Mike Licht, NotionsCapital.com It’s carnival time again. Activities, games, lessons, hands-on fun — if you’ve written a blog post about math, we’d love to have you join our Math Teachers at Play (MTaP) math education blog carnival. Posts must be relevant to students or teachers of school-level mathematics (that is, anything from preschool up through first-year calculus). Old posts are welcome, as long as they haven’t been published in past editions of this carnival. Click here to submit your blog post. Browse all the past editions of the Math Teachers at Play blog…
• ## Search for "math OR mathematics"

• ### Hershey Bears 2013-14: A season in four parts, with no playoff chapter

24 Apr 2014 | 11:42 am
The season had four distinct parts that didn't add up to a playoff berth for a team with high aspirations.
• ### Texas releases math, reading STAAR results

24 Apr 2014 | 11:39 am
Almost 80 percent of fifth- and eighth-graders passed the Texas standardized math test on their first try this month while more than 75 percent passed the reading exam.
• ### Why Can't Mortgages Be More Like College Admissions?

24 Apr 2014 | 11:37 am
Learn about this year's finalists and see who won the 2013 MT Award. Charlie Keating, who died on March 31, epitomized an era today's mortgage lenders would do well to remember as low-yielding portfolio assets tempt them to take bigger risks.
• ### Garth GrahamWhy Can't Mortgages Be More Like College Admissions?

24 Apr 2014 | 11:37 am
Learn about this year's finalists and see who won the 2013 MT Award. 2013 MT Awards: 10X Award The 10X Award honors a company, product or technology that's had an exponential impact on mortgage finance.
• ### Teachscape Introduces New Online ELA & Literacy Courses to Help...

24 Apr 2014 | 11:36 am
SAN FRANCISCO, April 23, 2014-Teachscape has expanded its award-winning Teachscape Learn Professional Learning Suite.

• ## Mathematics News -- ScienceDaily

• ### Mapping the road to quantum gravity

23 Apr 2014 | 12:09 pm
The road uniting quantum field theory and general relativity -- the two great theories of modern physics -- has been impassable for 80 years. Could a tool from condensed matter physics finally help map the way?
• ### 'Body hack' app by math researchers shortcuts jet-lag recovery

10 Apr 2014 | 4:46 pm
A different kind of jet-lag mobile app released today by mathematicians reveals previously unknown shortcuts that can help travelers snap their internal clocks to new time zones as efficiently as possible.
• ### Virus structure inspires novel understanding of onion-like carbon nanoparticles

10 Apr 2014 | 9:22 am
Symmetry is ubiquitous in the natural world. It occurs in gemstones and snowflakes and even in biology, an area typically associated with complexity and diversity. There are striking examples: the shapes of virus particles, such as those causing the common cold, are highly symmetrical and look like tiny footballs.
• ### Should you trust your financial advisor? Pseudo-mathematics and financial charlatanism

10 Apr 2014 | 7:30 am
Your financial advisor calls you up to suggest a new investment scheme. Drawing on 20 years of data, he has set his computer to work on this question: If you had invested according to this scheme in the past, which portfolio would have been the best? His computer assembled thousands of such simulated portfolios and calculated for each one an industry-standard measure of return on risk. Out of this gargantuan calculation, your advisor has chosen the optimal portfolio. After briefly reminding you of the oft-repeated slogan that "past performance is not an indicator of future results," the…
• ### Technical tests of biodiversity: When physicists play with genetics of populations

9 Apr 2014 | 6:39 am
The effect of migration on biodiversity (intended as the coexistence of different genetic traits) is an open question: does migration increase or decrease the genetic variability of populations? Or is the relationship more complex than that? A team of physicists has developed and analyzed a model that simulates the effect of migration on the genetic biodiversity of populations, and discovered that the effect is all but trivial.
• ## Scientific American - Math

• ### What’s the Deal with Euclid’s Fourth Postulate?

21 Apr 2014 | 5:30 am
In February, I wrote about Euclid’s parallel postulate, the black sheep of the big, happy family of definitions, postulates, and axioms that make up the foundations of Euclidean geometry. -- Read more on ScientificAmerican.com
• ### A Month of Math, Magic and Mystery

16 Apr 2014 | 8:52 am
Haven't got the Math Awareness Month bug yet? Here are three teasers to get you started: 1. What read the same right side up and upside down, and combine mathematics, art, and language? -- Read more on ScientificAmerican.com
• ### The Secret Spiritual History of Calculus

14 Apr 2014 | 5:00 am
Integral calculus originated in a 17th-century debate that was as religious as it was scientific -- Read more on ScientificAmerican.com
• ### 5 Tips for Faster Mental Division (Part 2)

13 Apr 2014 | 7:00 am
The Math Dude: Quick & Dirty Tips to Make Math Simpler -- Read more on ScientificAmerican.com
• ### 5 Tips for Faster Mental Division (Part 1)

12 Apr 2014 | 7:00 am
The Math Dude: Quick & Dirty Tips to Make Math Simpler -- Read more on ScientificAmerican.com

• ## NYT > Mathematics

• ### If It’s Possible, It Happened

21 Apr 2014 | 10:00 pm
In his new book, Max Tegmark compellingly argues that everything that can happen does happen — in at least one of an infinite number of universes.
• ### The 16th Century’s Line of Fire

7 Apr 2014 | 10:00 pm
Mathematics would seem to be immune to ideology. But not always, as a look back at a controversy from the dawn of the modern era makes clear.
• ### In N.C.A.A. Tournament Bracket, Mathematician Outdoes Matildas

24 Mar 2014 | 10:00 pm
Tim Chartier, a math professor, has picked 33 of 48 men’s games correctly, with help from his son. They have outdistanced a rotating cast of young Broadway stars, as well as coin flips.
• ### Flies That Do Calculus With Their Wings

18 Mar 2014 | 10:00 pm
Scientists glued tiny magnets to fruit flies to learn about the millisecond aerial ballets required to stay aloft when you’re a tiny insect.
• ### Mathematicians Are Hoping Their Calculations Add Up to the Perfect Bracket

15 Mar 2014 | 10:00 pm
The reason behind their motivation? How about 1 billion of them? That is the number of dollars offered by Quicken Loans for an unblemished result in predicting N.C.A.A. tournament games

• ### Visually stunning math concepts which are easy to explain

10 Apr 2014 | 9:01 am
Math StackExchange has a great list of "visually stunning math concepts which are easy to explain."
• ### Tim Chartier – Inspired by Math #34

6 Apr 2014 | 10:35 pm
My favorite kind of Math challenges are those that children can understand and professional mathematicians can't solve easily (or at all.) Math Bytes: Google Bombs, Chocolate-Covered Pi, and Other Cool Bits in Computing is a brand new book from Princeton University Press that has a great collection of fun problems that kids (middle school and above) and their parents can work on together. Author Tim Chartier does a fantastic job of weaving some wonderful stories into his sharing of a number of challenges that are either original or new spins on old problems. And, many (all?) of the puzzles in…
• ### Chuck Adler – Inspired by Math #33

13 Feb 2014 | 6:27 pm
I've admitted before that Physics and I have never gotten along. But, science fiction is something I enjoy. So, when Princeton University Press sent me a copy of Physics Professor Chuck Adler's new book "Wizards, Aliens, and Starships," I was intrigued enough that I wanted to interview the author. This interview rambled, but in a good way. Chuck is a great guest, he's passionate about physics and math as well as fantasy and science fiction. We flowed through a number of subjects and had a grand time. Enjoy! About Chuck Adler Chuck Adler grew up in the DC suburbs, and went to a very good…
• ### Martin Gardner undiluted

22 Nov 2013 | 11:54 am
Princeton University Press recently published "Undiluted Hocus-Pocus: The Autobiography of Martin Gardner." I've not reviewed the book since these days I pretty much only interview authors and living authors at that. So, no review from me, but I highly recommend Shecky's review and Shecky's first impressions at Math Tango. What inspired to blog this afternoon was an email I received from Andrew S. DeSio, Director of Publicity for Princeton University Press. Andrew has asked me to help spread the word that Martin Gardner really did write his own autobiography. Here's an excerpt from Andrew's…
• ### Colm Mulcahy – Inspired by Math #32

21 Sep 2013 | 10:56 am
I had the pleasure of interviewing mathematician and mathematical card magic innovator Colm Mulcahy. Dr. Mulcahy just published a book, Mathematical Card Magic: Fifty-Two New Effects. We spent a delightful hour discussing his book, his love of math and magic, and the inspiration behind writing the book. Plus, Dr. Mulcahy shares a few challenges listeners might enjoy chewing on, sprinkled throughout the interview. And, we discuss Martin Gardner, who Colm Mulcahy knew for the last decade of his life and met with several times. You may also enjoy Shecky's text interview with Colm Mulcahy at Math…

• ## Loren on the Art of MATLAB

• ### Debunking Bad News Analysis with MATLAB

7 Apr 2014 | 8:28 am
With spring comes the tax filing deadline. This post is also about taxes. I'd like to introduce this week's guest blogger, Toshi Takeuchi. Toshi analyzes web data and runs online ad campaigns here at MathWorks.Hi, I am Toshi. I am a big fan of Nate Silver who made analyzing data very cool and mainstream. Because I analyze data a lot, it bugs me when I see questionable analyses passed around in the news media.So when I saw this CNBC post on Google+, my “bogus data analysis” radar started sending high alerts.This map shows you the ranking of states based on average tax amount,…
• ### MATLAB Virtual Conference 2014

17 Mar 2014 | 10:47 am
We are hosting another worldwide conference this month, on-line. Its coming Marcn 26, and has special tracks includingDiscover MATLAB and SimulinkFind Out What's NewSee What Industry Experts Are DoingExplore MATLAB and Simulink in AcademiaContentsRegisterTimezonesKeynoteHope to See You ThereRegisterYou can register on-line here.TimezonesThere are two timezones for the conference, one for the Americas (with four sessions in Spanish), and one for India/Europe.KeynotePlease be sure to attend Roy Lurie's keynote entitled "Embracing Technical Computing Trends with MATLAB: Accelerating the Pace of…
• ### Integer Programming and Hyper Sudoku

14 Mar 2014 | 9:53 am
I'd like to introduce this week's guest blogger Alan Weiss. Alan writes documentation for mathematical toolboxes here at MathWorks.Hi, folks. While I have not written a blog post for Loren before, if you use Optimization Toolbox™ or Global Optimization Toolbox then you might have read my work.I am excited to describe how to use a new solver. Beginning with Release 2014a, Optimization Toolbox has mixed-integer linear programming. The intlinprog solver attempts to solve problems with linear objective functions, linear constraints, and (this is the new part) the constraint that some…
• ### Arithmetic Associativity – Not So Fast

26 Feb 2014 | 7:07 am
Arithmetic is associative, right? Well, in the world of paper and pencil, where you can often do calculations exactly, that can be true. However, in the computing world, where real numbers can't always be represented exactly because of working with finite precision datatypes, it turns out that you can't depend on the arithmetic to behave the way you were taught in grade school.ContentsLet's Do Some MathLet's Try Another ExampleHave You Rewritten Expressions to Get Better Accuracy?Let's Do Some MathSuppose I want to check the following:$$\sqrt {2} = 2/\sqrt {2}$$I can do this analytically…
• ### Double Integration in MATLAB – Methods and Handling Discontinuities, Singularities, and More

12 Feb 2014 | 7:06 am
In our recent post, Mike Hosea and I talked about adjusting both the absolute and relative tolerances for getting more accurate results when calculating a double integral. Today we'd like to talk about choosing the method of integration as well as which order to choose for the first dimension (direction) of integration.ContentsSet the StageChanging the Order of IntegrationSingularitiesCan You Take Advantage of these New Integration Routines?Set the Stageintegral2 has, at present, two different integration methods, 'tiled' and 'iterated', not counting the 'auto' method that chooses between…
• ## Homeschool Math Blog

• ### A mathematical fib

21 Apr 2014 | 5:12 am
Did you know it's Math Awareness Month (MAM)? The website for MAM features a neat calendar which is filled with tricks, magic, and mystery for each day of April.You'll find knots, Möbius bands, infinity, spirals, tricks, and more :)For example, check out the card trick A Few Little Fibs and how it's based on mathematics:http://www.mathaware.org/mam/2014/calendar/fibs.htmlNow I'm ready to wow my girls. :)
• ### Giveaway - Math Mammoth!

15 Apr 2014 | 7:50 am
It is time for a giveaway for my own products (Math Mammoth)! There will be 17 prizes! The "grand prize":ONE (1) winner will get Math Mammoth All Inclusive bundle - either a download or a CDTWO (2) winners will get Math Mammoth Light Blue Series bundle - either a download or a CDFOUR (4) winners will get Math Mammoth Blue Series bundle - either a download or a CDTEN (10) winners will get one grade level of Math Mammoth Light Blue series - download - the grade level is chosen by each winner.The winners will be chosen by a random number generator. Something SPECIAL This giveaway is COUPLED with…
• ### Fraction lessons updated

2 Apr 2014 | 11:18 am
These fraction lessons on my site have been updated! They are complete lessons with varying exercises and word problems, and give you a great preview to my books Math Mammoth Fractions 1 and Math Mammoth Fractions 2.Understanding fractionsA fractional part of group Mixed numbersFractions to mixed numbers and vv.Adding like fractionsEquivalent fractionsAdding unlike fractions 1Adding unlike fractions 2: Finding the common denominatorAdding mixed numbersSubtracting mixed numbersSubtracting mixed numbers 2Measuring in inchesComparing fractions Simplifying fractionsMultiply fractions by…
• ### Giveaways at Educents

1 Apr 2014 | 1:26 pm
Educents is celebrating their 1-year anniversary... with a SLEW of giveaways! You will want to see this -- dozens on giveaways on the same page (including one for Math Mammoth)! http://www.educents.com/educents-1-year-anniversary/
• ### Grading tests and math homework

31 Mar 2014 | 7:27 am
A few days ago I got a question from Jennifer concerning GRADING a child's math work, and I think it's a good question! How do recommend that parents grade when using Math Mammoth? Should I score every assignment? Or just tests? Before we pulled our children out of public school, only tests were being counted for their grade. What do you recommend? Thanks Jennifer I don't actually give any exact grading recommendations regarding Math Mammoth but leave it up to parents/teachers. I do include a grading rubric for the tests, but that's all.Personally, I feel that grading needs to be such that it…

• ### Memorizing Trig's Functions?

22 Apr 2014 | 11:07 pm
Here's what you need to help you commit Trig's functions to memory. It's called Alison's Triangle and was found in the book 'Twenty Years Before the Blackboard' which was written by who else of course? A math teacher!...Read Full Post
• ### Easter Egg Hunt

17 Apr 2014 | 11:00 am
Are you read for a quadratic equation word problem that relates to Easter? I can't think of anything more entertaining to do this Easter that links the holiday with Math! Jennifer Ledwith provides us with this entertaining set of questions for a fun filled 'mathy' Easter.  See the exercise questions here. (All questions are supported with answers.)
• ### Measures of Central Tendancy

9 Apr 2014 | 8:48 am
This concept is taught as early as the 3rd grade and refers to the law of averages. When the term average is used, most of us mean the 'mean' average. However, there are other averages which are the median and the mode.  If you are looking for a 101 on the Mean, the Median and the Mode, you'll find a quick overview here....Read Full Post
• ### Beginning of Base 10

5 Apr 2014 | 5:52 am
Base 10 concepts begin in Kindergarten. At this early age, base 10 refers to the ability to understand that in a number like 12, the one represents 1 ten or 10 ones, it no longer is the same as 1 when 1 is in isolation. It is also showing the ability to count onward when 10 is recognized, looking at a group of 10 and automatically knowing to count up to determine how many there are when there is a group of 10 and 5 more or 6 more....Read Full Post
• ### Best Graduate Level Math Programs

2 Apr 2014 | 11:43 am
Are you ready to move on to a graduate degree in math? Whether you're looking to pursue graduate level in Algebra, Number Theory, Algebraic Geometry, Analysis, Applied Math, Discrete Math, Topology, Logic or Geometry, you might just find this list of the top schools to pursue graduate level math to be quite helpful. You'll find score levels and useful information to help you guide your decision....Read Full Post

• ## Let's Play Math!

• ### Math Teachers at Play #73 via Singapore Maths Tuition

23 Apr 2014 | 10:13 am
woodleywonderworks (CC BY 2.0) The monthly math education blog carnival Math Teachers at Play features games, lessons, puzzles, activities, and teaching tips from classroom teachers, homeschoolers, and self-educated learners around the Internet world. Check out the 15 posts of mathematical fun in April’s edition: Math Teachers at Play (MTaP) Blog Carnival: Top Math Blog Posts! Here’s a peek at a few of the entries: Check out the following awesome blogs! Math Strategies There is such an emphasis on learning math facts that our children do not spend enough time learning strategies…
• ### Reblog: Putting Bill Gates in Proportion

17 Apr 2014 | 4:34 pm
[Feature photo above by Baluart.net.] Here’s a blast from the Let’s Play Math! blog archives: Seven years ago, one of my math club students was preparing for a speech contest. His mother emailed me to check some figures, which led to a couple of blog posts on solving proportion problems. I hope you enjoy… Putting Bill Gates in Proportion and Bill Gates Proportions II Putting Bill Gates in Proportion A friend gave me permission to turn our email discussion into an article… Can you help us figure out how to figure out this problem? I think we have all the information we…
• ### Do You Blog About Math?

14 Apr 2014 | 1:50 pm
by Mike Licht, NotionsCapital.com It’s carnival time again. Activities, games, lessons, hands-on fun — if you’ve written a blog post about math, we’d love to have you join our Math Teachers at Play (MTaP) math education blog carnival. Posts must be relevant to students or teachers of school-level mathematics (that is, anything from preschool up through first-year calculus). Old posts are welcome, as long as they haven’t been published in past editions of this carnival. Click here to submit your blog post. Browse all the past editions of the Math Teachers at Play blog…
• ### Reblog: The Handshake Problem

3 Apr 2014 | 5:49 am
[Feature photo above by Tobias Wolter (CC-BY-SA-3.0) via Wikimedia Commons.] Here’s a blast from the Let’s Play Math! blog archives: Seven years ago, our homeschool co-op held an end-of-semester assembly. Each class was supposed to demonstrate something they had learned. I threatened to hand out a ten question pop quiz on integer arithmetic, but instead my pre-algebra students voted to perform a skit. I hope you enjoy… Skit: The Handshake Problem If seven people meet at a party, and each person shakes the hand of everyone else exactly once, how many handshakes are there in…
• ### Reblog: In Honor of the Standardized Testing Season

24 Mar 2014 | 11:16 am
[Feature photo above by Alberto G. Photo right by Renato Ganoza. Both (CC-BY-SA-2.0) via flickr.] Here’s a blast from the Let’s Play Math! blog archives: Quotations and comments about the perils of standardized testing, now part of my book Let’s Play Math. I hope you enjoy… In Honor of the Standardized Testing Season The school experience makes a tremendous difference in a child’s learning. Which of the following students would you rather be? I continued to do arithmetic with my father, passing proudly through fractions to decimals. I eventually arrived at the…
• ## ChapterZero

• ### Eigenvector two-condition number for a product of PSD matrices

7 Apr 2014 | 9:31 am
I’m pushing to submit a preprint on the Nystrom method that has been knocking around for the longest time. I find myself running into problems centering around expressions of the type $$B^{-1}A$$, where $$A, B$$ are SPSD matrices satisfying $$B \preceq A$$. This expression will be familiar to numerical linear algebraists: there $$B$$ would be a preconditioner for a linear system $$A x = b,$$ and the relevant quantity of interest is the spectral radius of $$B^{-1} A$$. It’s not hard to show that the spectral radius of this product is at most 1… but instead, I’m…
• ### Canonical Correlation Analysis (CCA)

7 Apr 2014 | 9:20 am
I am not completely satisfied with the expositions of CCA that I’ve come across, so I decided to write one that reflects my own intuition. CCA is useful in the case where you observe two random variables that are both noisy linear functions of some underlying latent random variable, and you want to use this fact to help you guess the latent variable. Formally, assume $x = T_X z + n_x, \quad \text{ and } \quad y = T_Y z + n_y,$ where, without loss of generality, we assume that the entries of $$z$$ are uncorrelated and unit variance. Here $$T_X$$ and $$T_Y$$ are matrices whose image…
• ### Decision time: MacPorts vs Homebrew vs Fink

7 Mar 2014 | 8:12 pm
My work macbook pro recently crapped out on me during an update of the OS (apparently something has a tendency to go wrong with the video card or its driver or something similar during this particular update for this particular model … sigh) so I’ve had the joy of reinstalling my personal ecosystem of software again. One of the crucial decisions for me is whether to use MacPorts, HomeBrew, or Fink to allow me to manage the installation of non-trivial Unix packages. This post is really just to remind myself that at this go-round, I chose MacPorts because of these posts.

6 Feb 2014 | 10:16 pm
((Caveat! I am not sure the manipulations done in this post are correct, but the gist is certainly there.)) One of my favorite optimization techniques is Adagrad, a first-order technique that approximates the Hessian by using all the gradients up to that point. It calls for updates of the form: $x_{t+1} = \Pi_{\mathcal{X}}^{G_t^{1/2}} (x_t - \eta G_{t}^{-1/2} g_t),$ or more practically for high-dimensional problems, $x_{t+1} = \Pi_{\mathcal{X}}^{\text{diag}(G_t)^{1/2}} (x_t - \eta \text{diag}(G_{t})^{-1/2} g_t).$ Here, $$g_t$$ denotes the gradient at step $$t$$, $$\eta$$ is a fixed…
• ### Back of the envelope calculations of how fast your computer can do linear algebra operations

23 Jan 2014 | 3:28 pm
Let’s talk about CPU speed, practically. By practically, I mean, how fast can your CPU do linear algebra operations. And by linear algebra operations, I mean matrix-matrix multiplies. First, you need to calculate how many FLOPS your computer can do. The following formula comes in handy: $\text{nFLOPS} = \text{cores} \cdot \frac{\text{clock cycles}}{\text{second}} \cdot \frac{\text{FLOPS}}{\text{cycle}}.$ You probably already know the number of cores in your computer, and the number of clock cyles. The interesting thing here is the number of FLOPS per cycle: this depends on the…
• ## Computational Complexity

• ### Libraries Without Books

24 Apr 2014 | 8:01 am
Georgia Tech in its library renovation will move the vast majority of its books into a combined Emory/Tech Library Service Center off-campus. Very few people use the stacks anymore, particularly at this institute dominated by engineering and computer science. As a young assistant professor at the University of Chicago in the 90's, I averaged about one trip a day to the joint Math/CS library to track down research papers or old books to find various mathematical definitions and theorems. These days I can access all these papers online and get access to mathematical definitions…
• ### Changing the ORDER you teach things in might help A LOT

21 Apr 2014 | 4:57 pm
I am teaching the undergrad jr/sr course Elementary Theory of Computation which is Reg Langs, Context free Langs, Computability theory, P and NP. Over the last few years I've changed some of the content (I dumped CFLs-- don't worry, they cover them some in the Prog Langs course) but more to my point today changed the ORDER I do things in Change  1: Do P and NP first and Computability later. While this is not historically accurate (which may be why the order was what it was) this is better pedagogically. Why?  Consider the following reductions: 1) Given a FORMULA phi produce a graph…
• ### Announcements

18 Apr 2014 | 8:25 am
Time for a short rundown of announcements. STOC will be held May 31-June 3 in New York City. Early registration and hotel deadline is April 30. Student travel support requests due by this Monday. The newly renamed ACM Conference on Economics and Computation (EC '14) will be held in Palo Alto June 8-12. Early registration deadline is May 15. Hotel deadline is May 19th but the organizers suggest booking early because Stanford graduation is June 13. The Conference on Computational Complexity will be held June 11-13 in Vancouver. Local arrangements information will be posted when available.
• ### Should you reveal a P = NP algorithm?

17 Apr 2014 | 5:13 am
A reader asks What would you do if you could prove that P=NP with a time-complexity of n2 or better... moreover, would you publish it?   There are all these statements of the good that could come of it. But how would the government react in its present state? Would it ever see the light of day? How would a person be treated if they just gave it away on the internet? Could a person be labeled a threat to national security for giving it away?  I consider this a completely hypothetical and unlikely scenario. If you think this applies to you, make sure you truly have a working…
• ### Factorization in coNP- in other domains?

13 Apr 2014 | 7:40 pm
I had on an exam in my grad complexity course to show that the following set is in coNP FACT = { (n,m) : there is a factor y of n with 2 \le y \le m } The answer I was looking for was to write FACTbar (the complement) as FACTbar = { (n,m) | (\exists p_1,...,p_L) where L \le log n for all i \le L we have m < p_i \le n and p_i is prime (the p_i are not necc distinct) n =p_1 p_2 ... p_L } INTUITION: Find the unique factorization and note that the none of the primes are < m To prove this work you seem to need to use the Unique Factorization theorem and you need that PRIMES is in NP (the…

• ## Natural Blogarithms

• ### Review Activity Ideas

29 Mar 2014 | 12:11 pm
During the Teacher Quality Grant class today, we began preparing for the Post-Test that will take place in two weeks. Class participants shared a variety of ways that they conduct reviews in their junior high and high school classrooms. This group of teachers shares some very interesting games that they have used to engage students and get them more excited about math. Here are the ideas they shared: Jeopardy®: This is a classic game where students compete for points by selecting a category and point value. The question (or answer) is revealed and they are given the opportunity to buzz in…
• ### How to Insert Equation Numbers in Word 2010

3 Mar 2014 | 10:46 am
How to Insert Equation Numbers in Word 2010.  In most cases, I’m using LaTEX to typeset my math docs but when I am in a hurry or I’m having my students write up reports, I need to use Word.  Here’s a quick demo for adding equation numbers in word that auto-number and can be referenced in the text.
• ### Graphs of Sine and Cosine Functions

3 Mar 2014 | 7:52 am
I just posted a new video to the Trigonometry Lecture Series.  This is the 11th in the series. In this video, I cover how to identify properties of sine and cosine graphs, determine the amplitude and period of sinusoidal functions, graph the sinusoidal functions using key points, and find an equation for a sinusoidal graph. View on YouTube
• ### How to Insert an Excel Chart into a Blackboard Discussion Board

2 Mar 2014 | 8:44 pm
• ### New Videos in the Trigonometry Video Series

10 Feb 2014 | 5:46 pm
Just finished uploading five new videos to my online video lecture series in Trigonometry.  Here’s the first and a link to the playlist on YouTube: Link to Full Playlist Newly added: Lecture 6: Measuring Angles in Radians Lecture 7: Definition of Trigonometric Functions Lecture 8: Trig Values of Special Families of Angles Lecture 9: Properties of Trig Functions Lecture 10: Basic Identities of Trig Functions
• ## eon

• ### “Gods” make Comeback at Toyota

10 Apr 2014 | 8:30 pm
is the headline of this bloomberg piece that reports the strange phenomena that human beings are replacing robots in the manufacturing lines. The point is that by automating some of these production process, much of the skill learnt by the human worker is lost. Without these knowledge, the humans cannot innovate and improve on the current process. I see a close parallel between this and how students are losing their mathematical/computational ability because they are doing all their calculations on a calculator. Sure, if all the mathematics that you will do in future is to add some numbers on…
• ### Come Together

8 Apr 2014 | 6:22 pm
is not the beatles song but the title of episode 16 of a tv program called discover science. I happened to catch it on local tv and the combination of quirky Japanese humour and the clever introduction to mathematics and science caught my attention. A preview of the episode is available at the above link but you need to watch the whole episode to find the link to parabolas.
• ### Mathematics and poetry

4 Apr 2014 | 2:59 pm
A nice article by Ornes on slate and a paper by Glaz. My favourites has to be the Fermat Last Theorem Poetry Challenge which I have read about previously elsewhere. Here’s one entry by E. Howe, H. Lenstra, D. Moulton: “My butter, garcon, is writ large in!” a diner was heard to be chargin’. “I HAD to write there,” exclaimed waiter Pierre, “I couldn’t find room in the margarine.”
• ### Maths & Fashion

20 Mar 2014 | 3:21 pm
That headline caught my eye and earned the newspaper article a more detailed look. It’s about a sub brand from Issey Miyake called 132.5, which apparently stands for 1 piece of material which forms a 3d dress but yet can be folded flat into 2d. The meaning of the .5 wasn’t that clear to me. Fashion’s not my thing but this is certainly cool enough to merit a link. http://www.isseymiyake.com/en/brands/132_5.html
• ### Advice to Young Mathematicians

27 Jan 2014 | 8:25 pm
The Princeton Companion to Mathematics contains a short section of sound advice to young mathematicans by Sir Micheal Atiyah and others. It is certainly worth reading. The section can be downloaded from here.
• ## mathematics « WordPress.com Tag Feed

• ### Scholarship For Turkey

21 Apr 2014 | 10:05 am
Subanci University Turkey Graduate admissions (scholarships) upportunity for those without IELTS and
• ### Tegmark's Mathematical Universe Hypothesis

21 Apr 2014 | 10:01 am
Mandelbrot set (Source: Wikipedia) I recently read Max Tegmark’s latest book, ‘Our Mathematical Universe‘, about his views on multiverses and the ultimate nature of reality.  This is the fourth and final post in a series on the concepts and views he covers in the book. The previous entries were: Tegmark’s Level I Multiverse: infinite space Tegmark’s Level II Multiverse: bubble universes Tegmark’s Level III Multiverse: The many worlds interpretation of quantum mechanics This final post in the series is a commentary on the overall book.  Tegmark spends the early parts reviewing…
• ### An Un-PAC-learnable Problem

21 Apr 2014 | 8:00 am
In a previous post we introduced a learning model called Probably Approximately Correct (PAC). We sa
• ### Mathematics: Natural or Supernatural?

21 Apr 2014 | 7:42 am
Yet again, Dr. William Lane Craig’s weekly Reasonable Faith podcast discusses a topic with which I am keenly interested. Unfortunately (and unlike last week), I once again find myself in a state of disagreement with the famous apologist. Dr. Craig’s discussion, this week, is entitled “God and Math,” and centers around a claim that mathematics is “unreasonably” effective. WLC builds his argument off of an article published in 1960 by a physicist named Eugene Wigner, “The Unreasonable Effectiveness of Mathematics in the Natural Sciences.” Having…
• ### Area and Perimeter Quiz

21 Apr 2014 | 6:55 am
Try a Small Quiz http://www.bgfl.org/bgfl/custom/resources_ftp/client_ftp/ks2/maths/perimeter_and_area/index.html

• ## MathNotations

• ### A Common Core Alg Activity Using Desmos - Piecewise Linear Functions and Squares

20 Apr 2014 | 4:29 am
This is my first attempt to use Desmos, the outstanding free online graphing calculator (and a free iPad app). I'm sure many of you have been utilizing this powerful resource. There are already many available teacher samples you can use.CLICK ON THE GRAPH TO LOAD THE APP. Let me know if you can view the graph (you may have to adjust the window slightly). More importantly, what do you think of the activity and do you see its potential for deepening understanding of algebra? If interested in purchasing my NEW 2012 Math Challenge Problem/Quiz book, click on BUY NOW at top of…
• ### Another Common Core Rant - not a video...

15 Apr 2014 | 5:31 am
While I agree with the concerns of many parents that over-testing is damaging to children and subverts the purpose of education, I don't believe that the Common Core has set the bar too high, at least in math, my area of expertise. I know from direct experience with children that we can expect far more thinking of them than is commonly held. That is the Core Belief of my blog. The problem is that teachers have not received the necessary preparation and the testing has been rushed and lacking in quality control. We're trying to set the bar higher for children without raising the bar…
• ### Developing Fraction Sense Using Egyptian Fractions

5 Apr 2014 | 12:01 pm
This MathCast describes a procedure for writing proper fractions as a sum of unit fractions, e.g., 5/6=1/2+1/3. This exploration is appropriate for Gr5 on up.A simplified form of the Greedy Algorithm.Watch "Developing Fraction Sense Using Egyptian Fractions" on YouTube: http://youtu.be/ulb6E4OcQ8g I'm experimenting with embedding these MathCasts directly into my blog post, however, the audio may not come out right. May work on your computer but not your tablets or smartphones. Please let me know. If there is a problem you can just click on the link to YouTube. VISIT ME DAILY ON TWITTER AT…
• ### A Data-Based Percent Problem for the New SAT and Common Core

30 Mar 2014 | 3:07 pm
The MathCast below is a more sophisticated % problem which requires processing several pieces of data expressed in percent form. Students have to make sense of the information and  develop a model to represent the data. Both a tree model and a table/spreadsheet approach are demonstrated. These are the kinds of data-based applications which will become a central theme of the newer assessments from PARCC, SBAC and the College Board. Sorry, you'll have to watch the video to see the problem but I'll give you a glimpse: 70% of the left-handed students surveyed were boys... Watch…
• ### 40% of 9th graders play sports...Math Challenges for the Old/New SAT and the Common Core

24 Mar 2014 | 5:07 am
David Coleman of the College Board has stated that ratios, percents, etc., will be an important focus of the new SAT, particularly in an applied setting.The MathCast below demonstrates a classic medium-hard percent word problem which should continue on all of our "new" assessments. Watch "40% of the 9th grade... Percents,New SAT and…" on YouTube-40% of the 9th grade... Percents, the New SAT and…: http://youtu.be/WjNQ8VHhD4U I encourage all my readers to offer constructive criticism re both the content and the technology of these videos and suggest…
• ## Neoformix

• ### Markham Winter of 2014

1 Apr 2014 | 4:30 am
Winter has finally ended in Markham where I live and it has seemed a very long and cold season this year. I decided to take a look at the weather data from Environment Canada and see whether my impression is supported by the data. The result is the graphic below. Click on it to see a larger version. Yes, 2014 was the coldest winter in Markham since 1994. We had an average temperature during the winter of -8.2 C this year and in 1994 it was -9.2 C. Both last year and especially 2012 were warmer than usual so it likely felt that much worse in comparison. We also had the 4th most snow in the…
• ### Toronto Visible Minorities

27 Sep 2013 | 4:30 am
Toronto is the most multicultural city in the world. According to the 2011 National Household Survey, 46% of the population were foreign-born immigrants and 47% are members of a visible minority. (ref) These immigrants come from a wide variety of places across the globe and their diversity makes the city a truly remarkable place. I have created a Dot Map that shows a single point for every person in the Toronto area, coloured by visible minority status. There are 5,700,628 in all and they are positioned at their place of residence and coloured based on the information from the 2011 census and…
• ### Toronto 311 Visualization

6 Sep 2013 | 4:20 am
The calls people make into the 311 service line in Toronto give an interesting glimpse into the pulse of the city. The City of Toronto makes this data available through their Open Data initiative. I did some analysis and design work with it to produce a visualization for illuminating time-based patterns during 2012. The visualization is a set of small multiple calendar heatmaps, one for each data series. The one shown above is for reports about 'long grass and weeds'. I was inspired to use this visual form by this example: Vehicles involved in fatal crashes by Nathan Yau. I experimented with…
• ### Visual Book Selector

8 May 2013 | 5:00 am
One common pattern I see in many interactive applications is to support a person who is selecting a few items from some larger set. Often these items have various characteristics that the person wants to use in some way to guide their selection process. The characteristics can be numeric quantities, dates, categories, or names of things. Showing all the items in a list and allowing the person to sort by one of the attributes is often a decent default solution. In other cases it's more useful to consider multiple attributes at a time during the selection process. Maybe you want items that are…
• ### Star Wars Movie Fingerprints

27 Mar 2013 | 4:35 am
Recently YouTube had a video that showed all six Star Wars movies at once. They were placed in a 2 by 3 matrix and had an audio track of all the movies superimposed. It was an interesting experiment that has since been removed based on copyright grounds. Before it was removed I was able to do some simple analysis on the video and extract some details of the individual episodes of the Star Wars series. Basically, I produced something very similar to a classic work called Cinema Redux™ by Brendan Dawes, done in 2004. Each individual movie in the series was reduced to a collection of small…
• ## Institute for Mathematics and Computer Science

• ### What Does It Mean to be Genuinely Good at Math?

17 Apr 2014 | 5:35 am
Have you seen the latest video of a young child reciting multiplication tables or the digits of pi? Or maybe you know a kid who has always gotten straight A’s. Pretty neat, but does it equate to being genuinely good at math? No. Bright students often do well in school with little or no effort. And an airtight memory facilitates excellent grades, especially when those grades depend on regurgitating information that’s already been provided. Being genuinely good at math is more about having a deep understanding of how and why things work. It also means being able to take that…
• ### From Public School to the Ivy League

19 Mar 2014 | 10:00 pm
The following excerpt is from the new book by Mandee Heller Adler, From Public School to the Ivy League: How to get into a top school without top dollar resources, which is available at Amazon.com. Ms. Adler is the founder and principal of International College Counselors, a Florida-based firm that provides expert strategies for admission to undergraduate colleges, graduate programs, business schools, law schools, medical schools, dental schools and other postgraduate schools. From Chapter 4: Writing Essays … ANSWERING THE QUIRKY QUESTIONS In recent years, a number of colleges have…
• ### IMACS Math Academy for Broward County Middle School Students

19 Feb 2014 | 10:00 pm
The IMACS Math Academy is an intensive one-week program for exceptional students currently attending middle school in Broward County, Florida. Broward County, Florida students currently attending grades 6-8 are invited to apply to the IMACS Math Academy, an intensive one-week program designed to stimulate talented students’ interest in mathematics beyond the traditional classroom. There is no cost to attend the IMACS Math Academy! There are two scheduled sessions. The first will be held March 24 – 28 during Spring Break. The second will be held June 23 – June 27 during…
• ### AP Computer Science … Updating

29 Jan 2014 | 10:00 pm
Following a recent review of the AP Computer Science A course and exam, the College Board has decided to replace its case study requirement with a requirement to complete a minimum of 20 hours of hands-on lab experiences. This change, which will take effect for the 2014-2015 school year, is being implemented to more effectively support student learning of core concepts in computer science. IMACS continues to follow closely all communications from the College Board, as well as discussions within the APCS community, on the forthcoming changes and will act accordingly. From the beginning,…
• ### Letters to a Young Math Teacher

1 Jan 2014 | 10:00 pm
The following letter is extracted from the new book, Letters to a Young Math Teacher, by Gerald Rising and Ray Patenaude, which is available from Amazon.com and other sources. Gerry Rising is Distinguished Teaching Professor Emeritus at State University of New York at Buffalo where he co-founded the university’s Gifted Math Program for highly-qualified regional students in grades seven through twelve. Gerry Rising was for many years associated with IMACS activities and is a strong supporter of our work. Letter Seventeen: A Bag of Tricks Paul Rosenbloom enjoyed an international…

• ## Maths Tips From Maths Insider

• ### How to Solve a Physics Problem (FUNNY!) plus Mental Math Tips

4 Apr 2014 | 8:14 am
I saw the comic strip below last week on Facebook by the funny folks at Saturday Morning Breakfast Cereal (SMBC), and spent a good few minutes cry-laughing (is that a thing?) Even my daughter in the midst of wrangling with Quadratics in preparation for a math test, joined in. You see, even for seasoned math teachers, math lovers and professional scientists and mathematicians, arithmetical errors are all too common when problem solving.   As part of my role as Instructor for International Students at Tabtor Math, I was given 5 math worksheets at Grade 5 and 6 level to test and report…
• ### Check out These Challenging Online Math Tools for Gifted Kids

3 Dec 2013 | 1:28 am
This is a guest post by Joseph Rodriguez While many educators agree that it is essential to improve the quality of math education in our public schools, a debate persists about how it should be done. Do we work with the students who are struggling, so that they can do better? Or do we push the students who are excelling, so they can move on to even greater things? Budgets are tight and many schools are pushed to decide one path or the other. Fortunately, many online resources can challenge gifted math students with new coursework and an outlet for their ingenuity. Here’s what you…
• ### Holiday Math and More

28 Nov 2013 | 1:12 am
If you’ve read my Tabtor vs Kumon blog post a few months back, you’ll know that I’ve been working with Tabtor Math, the personalized iPad based math program. I’m Tabtor’s instructor for many of their international students, and I’m also recording instructional videos which accompany each of the Tabtor worksheets as well as writing articles for their blog. As a result, It’s been a bit quiet here at Maths Insider but after the holiday I’ll hopefully be back here with a vengeance. I’ve still got plenty of ideas to share with you on Maths…
• ### Educator.com – A Great Math Program for Self Motivated Teens

17 Oct 2013 | 6:11 am
This is a guest post by Stephanie from houstonnanny.com. For those who need a math education program that can allow high school students to work at their own pace, Educator.com may be what you’re looking for. Subject material from basic math skills to more advanced forms of linear algebra are present and ready for you to explore, as well as science and computing courses. While there are some materials that can be tested for free, a subscription is needed in order to take advantage of the courses at this website. How Detailed are the Courses? Each course is divided among several…
• ### Pretend Mind Reading – A Way Of Learning Algebra by Lawrence Ball

30 Sep 2013 | 11:49 pm
This is a guest post by Lawrence Ball Here’s a way to pretend you read someone’s mind. It’s also a way to get familiar with algebra. I want you to do some calculations for me, are you ready?   Think of a number between 1 and 5, don’t tell me what it is, but remember it for later. OK? Got one? Now double it. OK? Now add 10. Now halve it (or divide it by 2 – same thing) Now take away the number you started with. Your answer is 5. Well it should be, if it isn’t you made a mistake! Lets try another one. Think of a number between 1 and 5 The reason I keep…
• ## CSE Blog - quant, math, computer science puzzles

• ### Value of Pi - Estimation using Dice

30 Mar 2014 | 5:21 am
Source: Asked to a friend at Goldman Sachs Quant Interview Problem: Estimate the value of pi using a dice
• ### (2n choose n) is never a perfect power

15 Feb 2014 | 11:22 pm
Source: Cute problem sent by Sudeep Kanath Problem: Prove that (2n choose n) is never a perfect power
• ### Coin Problem - Wolfram Mathematica Puzzle

10 Feb 2014 | 3:29 am
Source: The super awesome puzzle blog by Gowtham Kumar - Puzzle Tweeter - Coin Problem who got it from Wolfram Mathematica Problem: Suppose you have an infinite stock of $a bills and$b bills such that g.c.d(a,b)=1. Find the largest amount of money (integer) that cannot be represented using $a and$b denominations. Shameless plug: If you have not done it already, please like / +1 / follow on: Quora, Twitter, Facebook, G+
• ### Determinant of Matrix (17-11)

24 Dec 2013 | 12:53 am
Source: Mailed by Sudeep Kamath (EECS PhD Student, UC Berkeley, EE IITB 2008 Alumnus) Problem:A is a 300 x 300 matrix with 17 on the diagonal, and the rest of the entries being 11. What is det (A) ?
• ### Open Ended Search Problem

20 Dec 2013 | 8:50 pm
Disclaimer: It is a made up problem. Not to be attempted by light hearted. Problem: I have a 300 word text. I have a large list of indexed strings (Length of string ~ 20, Number of strings ~ 1M). I need to figure out phrases in the 300 word text that match exactly to one of the strings in the large list of strings I have. A naive approach: Taking all 45000 (300 C 2) phrases, search in the large list of strings. Can we do better than this? We need to minimize calls to list of indexed strings!
• ## PlainMath.net

• ### SBI-PO Study Plan: Reasoning section

20 Apr 2014 | 12:41 am
SBI-PO MCQ exam is divided into four sections:General Awareness - 50 quesData Interpretation - 50 quesReasoning - 50 quesEnglish - 50 quesToday I will cover only Reasoning section thoroughly and soon I will cover other sections too. For SBI-PO and SSC too, reasoning is a scoring subject. So you should leave this section and try to cover its topics first and then proceed to other sections. ReasoningIn reasoning section, the major part is of verbal topics like inference conclusion, sullogism, data sufficiency etc. From last few years the weightage of section is almost same. Just little changes.
• ### Important Questions of Mensuration: Quantitative Aptitude

9 Apr 2014 | 4:46 am
Mensuration is one the toughest topic of quantitative aptitude section. The only thing is it takes time to analyze the question. Rest is just clarification and formula learning ability of candidate. This chapter is a part of quantitative aptitude section of SSC CGL and SBI PO. Today I will discuss some questions related to basic terms of mensuration.Examples with Solution Example1: What will be the area and perimeter of triangular plot whose sides are 17 m, 8m and 15m long?Solution: Firstly, we will check which kind of triangle it is.Since, 8^2 + 15^2 = 17^2.......  (`H^2 = P^2 +…
• ### Syllabus of SBI-PO Recruitment 2014

4 Apr 2014 | 7:29 am
SBI-PO exam includes both multiple type questions and descriptive paper. Total marks including descriptive exam is 250.Objective type Paper : 200 MarksDescriptive Paper: 50 MarksObjective type exam consists of four sections:English LanguageData Analysis and InterpretationReasoningGeneral Awareness, Computers and Marketing. Descriptive ExamDescriptive exam is of half an hour and it can be about anything discussed Essay writingLetter writingParagraph writingPrecise writing English sectionThis section basically covers comprehensions, faulty sentences, jumbled sentences, closed passages etc.
• ### SBI-PO Recruitment 2014 notification out

4 Apr 2014 | 4:23 am
SBI-PO Recruitment 2014 notification out. All the best to all the candidates.Important datesOnline registration : 07.04.2014Payment of fees- Online : 07.04.2014 to 25.04.2014  Payment of fees- Offline : 07.04.2014 to 25.04.2014  Eligibility criteriaAll graduates and third year students from recognized university are eligible.Age range: 21- 30 yearsDetails official notification: hereSoon, I will post syllabus, study plan and strategies to crack this exam.
• ### How to prepare for Quantitative Aptitude section

27 Mar 2014 | 1:59 am
Quantitative aptitude section is one of the four sections of bank exams, SSC and others. Some candidates think that it is not possible to crack Quant section. But, I want to tell you that a perfect study plan and regularity can easily help you to score good in this section because in numerical ability questions level is moderate. Tough questions have never been asked earlier. So you just need to clear all the basics of quantitative aptitude section. Rest will depend on you time mangement.Tricks to crack Quantitative aptitude section  Attempt chapters of your interestWhen you start…