Published on Aug 13, 2015

An exploration of infinite sums, from convergent to divergent, including a brief introduction to the 2-adic metric, all themed on that cycle between discovery and invention in math.

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# Etiqueta: arithmetic

## 2-adic metric

## Common Core Math

## Exponential growth

## Great Internet Mersenne Prime Search

## The 7.11 problem

## Factorization diagrams

## What does it mean to give 100%?

Un lobo perdido en un laberinto

Published on Aug 13, 2015

An exploration of infinite sums, from convergent to divergent, including a brief introduction to the 2-adic metric, all themed on that cycle between discovery and invention in math.

Published on Apr 14, 2013 Presented by Joy Pullmann Managing Editor of School Reform News and an Education Research Fellow at The Heartland Institute Uploaded on Nov 7, 2011 Talk title: Why math instruction is unnecessary John is a teacher … Continue reading →

Published on Apr 14, 2013

Presented by Joy Pullmann

Managing Editor of School Reform News and an Education Research Fellow at The Heartland Institute

Uploaded on Nov 7, 2011

Talk title: Why math instruction is unnecessary

John is a teacher of math and a homeschooling parent who offers a radical-sounding proposal: that we cease to require math instruction in middle and high school. He came to this point of view over a number of years, as he attempted (and failed) to convince students that the math they were learning was beautiful, useful, or an imperative component of their future prosperity. When he stopped trying to connect math with students and simple tried to connect with the students themselves, he made a profound discovery – kids are suffering from “math anxiety.” If the goal of teaching math is to teach us deductive and inductive reasoning, might games and puzzles be equally effective in developing kids’ reasoning skills – and allow them to fulfill their life missions? “We want to reawaken analytical and critical thinking schools that have been anesthetized by the standard curriculum,” says John.

John Bennett is a math teacher in the San Francisco Bay Area and a home-schooling father of four. An outspoken advocate of education reform, he has presented lectures and workshops throughout California. He uses logic puzzles and strategy games in the classroom (and at home) to supplement the traditional mathematics curriculum. John has written three volumes of Pentagrid Puzzles, a new puzzle form he created to challenge deductive logic and visual-spatial reasoning.

Uploaded on Jan 15, 2007

M.J. McDermott is speaking about the current state of math education, as a private citizen .

The main argument for the new way of teaching Mathematics is that this isn’t the 1950’s and nobody does numerical calculations by hand anymore. Scientists, engineers, economists, etc. all use computer programs to do their calculations. If you spend too much time teaching kids how to calculate, you aren’t teaching them mathematics, yAt the core (not pun intended) of this discussion is a basic misunderstand about what it means to understand. Experts at whatever can never explain how they do what they do. Expert knowledge is in the form of pattern recognition procedures regulated by the basal ganglia and not in the form of explicit coding of rational rules. Yet a rich area of research, what is the best way to teach children math in the era of smartphones?

The Tea Party has found another front to attack the Obama administration: elementary arithmetic. The 32-12 problem is making the rounds. I do not know the source and I do not know anything about the core math curricula. There is no context to understand where this example comes from or even if it is really in some workbook. What is the rule? What is the purpose of the exercise? What level? It is not possible to discuss the merit of the method without the context. In any case the video is misleading as “old fashioned” method shown is shorthand for a complicated procedure with the complexity of “borrowing.”

For example 32-17:

17 = 10 + 7

12-7 = 5

32-12 =20

20- 10 = 10

10+5=15

Whereas the new method seems to be

17+3 = 20;

20+10 = 30;

30+2 = 32;

(3+10+2 = 15)

Arkansas is well down in the bottom half of states in educational achievement. The woman doing the presentation doesn’t even realize what she is presenting. What she’s showing is what they teach so kids understand the PRINCIPLES underlying multiplication and division. The kids will eventually do it the “normal” way. A geometric visual explanation of the meaning of addition and multiplication is misconstrued as a procedure to do the calculations.

I am not qualified to discuss how to teach children but I am a parent myself. The fact that a parent gets emotional or pokes fun at the way their children are taught does not make her opinion valid.

Big changes await us. An unrecognizable economy. The main lesson for me is that growth is not a “good quantum number,” as physicists will say: it’s not an invariant of our world. Cling to it at your own peril. Note: This conversation is my contribution to a series at www.growthbusters.org honoring the 40th anniversary of the Limits to Growth study. […]

Big changes await us. An unrecognizable economy. The main lesson for me is that growth is not a “good quantum number,” as physicists will say: it’s not an invariant of our world. Cling to it at your own peril.

*Note: This conversation is my contribution to a series at www.growthbusters.org honoring the 40th anniversary of the Limits to Growth study. You can explore the series here. Also see my previous reflection on the Limits to Growth work. You may also be interested in checking out and signing the Pledge to Think Small and consider organizing an Earth Day weekend house party screening of the GrowthBusters movie.*

Published on Sep 19, 2012

This video quickly covers the key points that you will find in the long version. Everyone needs to see the long version but many won’t because they don’t have the time. My hope is that people will watch this short version and then be motivated to watch the long version.

I came across “The Most Important Video You’ll Ever See” on YouTube and clicked on it. I didn’t realize that it was an eight part video that lasted over an hour but after finishing part one I had no choice but to watch the whole thing. It truly could be called the most important video you’ll ever see.

The Great Internet Mersenne Prime Search (GIMPS) is a collaborative project of volunteers who use freely available software to search for Mersenne prime numbers. The project was founded by George Woltman, who also wrote the software Prime95 and MPrime for the project. Scott Kurowski wrote the Internet PrimeNet Server that supports the research to demonstrate […]

The **Great Internet Mersenne Prime Search** (**GIMPS**) is a collaborative project of volunteers who use freely available software to search for Mersenne prime numbers. The project was founded by George Woltman, who also wrote the software Prime95 and MPrime for the project. Scott Kurowski wrote the Internet PrimeNet Server that supports the research to demonstrate Entropia-distributed computing software, a company he founded in 1997. GIMPS is registered as **Mersenne Research, Inc.** Kurowski is Executive Vice President and board director of Mersenne Research Inc. GIMPS is said to be one of the first large scale distributed computing projects over the Internet for research purposes.^{[1]}

The project has found a total of fourteen Mersenne primes as of 5 February 2013, eleven of which were the largest known prime number at their respective times of discovery. The largest known prime as of January 2013 is 2^{57,885,161} ? 1 (or M_{57,885,161} in short). This prime was discovered on January 25, 2013 by Curtis Cooper at the University of Central Missouri.^{[2]}

To perform its testing, the project relies primarily on Édouard Lucas and Derrick Henry Lehmer‘s primality test,^{[3]} an algorithm that is both specialized to testing Mersenne primes and particularly efficient on binary computer architectures. They also have a less expensive trial division phase, taking hours instead of weeks, used to rapidly eliminate Mersenne numbers with small factors, which make up a large proportion of candidates. John Pollard’s p ? 1 algorithm is also used to search for larger factors.

On January 25th, prolific GIMPS contributor Dr. Curtis Cooper discovered the 48th known Mersenne prime, 2^{57,885,161}-1, a 17,425,170 digit number. This find shatters the previous record prime number of 12,978,189 digits, also a GIMPS prime, discovered over 4 years ago. The discovery is eligible for a $3,000 GIMPS research discovery award.

Dr. Cooper is a professor at the University of Central Missouri. This is the third record prime for Dr. Cooper and his University. Their first record prime was discovered in 2005, eclipsed by their second record in 2006. Computers at UCLA broke that record in 2008. UCLA held the record until Dr. Cooper and the University of Central Missouri reclaimed the world record with this discovery.

While Dr. Cooper’s computer found the record prime, the discovery would not have been possible without all the GIMPS volunteers that sifted through numerous non-prime candidates. GIMPS founder George Woltman and PrimeNet creator Scott Kurowski thank and congratulate all the GIMPS members that made this discovery possible.

Mersenne primes are extremely rare, only 48 are known. GIMPS, founded in 1996, has discovered the last 14 Mersenne primes. Mersenne primes were named for the French monk Marin Mersenne, who studied these numbers more than 350 years ago. Chris Caldwell maintains an authoritative web site on the history of Mersenne primes as well as the largest known primes.

The primality proof took 39 days of non-stop computing on one of the University of Central Missouri’s PCs. To establish there were no errors during the proof, the new prime was independently verified using different programs running on different hardware. Jerry Hallett verified the prime using CUDALucas running on a NVidia GPU in 3.6 days. Dr. Jeff Gilchrist verified the find using the standard GIMPS software on an Intel i7 CPU in 4.5 days. Finally, Serge Batalov ran Ernst Mayer’s MLucas software on a 32-core server in 6 days (resource donated by Novartis IT group) to verify the new prime.

You can read a little more in the short press release.

Start the program! (Linux and FreeBSD users should run the program from the command line with a -m switch, i.e. “./mprime -m”). Enter your optional userID created on the website in Step 1, and optionally name your computer. We recommend Windows users select Options, Start at Bootup or Start at Logon. | ||

That’s all you need to do! The program contacts a central server called PrimeNet to get some work to do. Usually the program and PrimeNet know the best work to assign, but it’s up to you!You can administer your account and computers on your userID’s account page. Once you complete a workunit you can track your standings on the competitive stats pages the server updates every hour (see Top Producers in the menu, left, for more stats). You can monitor each of your computers’ progress, even remote-control the work assignments they request using your userID’s CPUs page!
Linux and FreeBSD versions can also be set up to run every time you restart your computer. Ask for help at the Mersenne Forum. |

**Questions and Problems: **Please consult the readme.txt file for possible answers. You can also search for an answer, or ask for help in the GIMPS forums. Otherwise, you will need to address your question to one of the two people who wrote the program. Networking and server problems should be sent to Scott Kurowski. Such problems include errors contacting the server, problems with assignments or userids, and errors on the server’s statistics page. All other problems and questions should be sent to George Woltman, but please consult the forums first.

**Disclaimers: **See GIMPS Terms and Conditions. However, please do send bug reports and suggestions for improvements.

**Software Source Code****If you use GIMPS source code to find Mersenne primes, you must agree to adhere to the GIMPS free software license agreement**. Other than that restriction, you may use this code as you see fit.

The source code for the program is highly optimized Intel assembly language. There are many more-readable FFT algorithms available on the web and in textbooks. The program is also completely non-portable. If you are curious anyway, you can download all the source code (40.6MB). This file includes all the version 27.9 source code for Windows, Linux, FreeBSD, and Mac OS X. Last updated: December 12, 2012.

The GIMPS program is very loosely based on C code written by Richard Crandall. Luke Welsh has started a web page that points to Richard Crandall’s program and other available source code that you can use to help search for Mersenne primes.

**Other available freeware**At this time, Ernst Mayer’s Mlucas program and Guillermo Ballester Valor’s Glucas program are the best choices for non-Intel architectures. Luke Welsh has a web page that points to available source code of mostly historical interest you can use to help search for Mersenne primes.

A man goes into a store and selects four items to purchase. He walks up to the counter to pay and the clerk says “Hold on, my cash register is broken, so I have to use a calculator to get your total… okay, that’ll be $7.11″ The man pays, and as he is walking out, […]

A man goes into a store and selects four items to purchase. He walks up to the counter to pay and the clerk says “Hold on, my cash register is broken, so I have to use a calculator to get your total… okay, that’ll be $7.11″ The man pays, and as he is walking out, the clerk yells “Wait a second! I multiplied the prices together instead of adding them. Let me get the total again… hey, what do you know! It comes out the same!”

What were the prices of the four items? All of them are of the form a.bc, that is, we’re dealing with standard U.S. money, no fractions of a cent. Ignore sales taxes too.

4 | 3.16 |

2 | 1.50 |

1 | 1.25 |

1 | 1.20 |

Reblogged from The Math Less Traveled: In an idle moment a while ago I wrote a program to generate "factorization diagrams". Here’s 700: It’s easy to see (I hope), just by looking at the arrangement of dots, that there are in total. Here’s how I did it. First, a few imports: a function to do […]

Reblogged from The Math Less Traveled:

In an idle moment a while ago I wrote a program to generate "factorization diagrams". Here’s 700:

It’s easy to see (I hope), just by looking at the arrangement of dots, that there are in total.

Here’s how I did it. First, a few imports: a function to do factorization of integers, and a library to draw pictures (yes, this is the library I wrote myself; I promise to write more about it soon!).

A program to generate “factorization diagrams”.

What equals 100% in life? Here’s a little mathematical formulation that might help answer these questions. If A B C D E F G H I J K L M N O P Q R S T U V W … Continue reading →

What equals 100% in life? Here’s a little mathematical formulation that might

help answer these questions.

If

A B C D E F G H I J K L M N O P Q R S

T U V W X Y Z

is represented as

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

18 19 20 21 22 23 24 25 26.

then

H-A-R-D-W-O-R-K

8+1+18+4+23+15+18+11 = 98%

and

K-N-O-W-L-E-D-G-E

11+14+15+23+12+5+4+7+5 = 96%

But

A-T-T-I-T-U-D-E

1+20+20+9+20+21+4+5 = 100%

Therefore, one can conclude with mathematical certainty that:

**While Hard Work and Knowledge will get you close, Attitude will
get you there! **

However, consider

B-U-L-L-S-H-I-T

2+21+12+12+19+8+9+20 = 103%

So, Hard Work and Knowledge will get you close, Attitude will get you there and Bullshit will take you over the top! And look how far

A-S-S K-I-S-S-I-N-G

will take you:

1+19+19+11+9+19+19+9+14+7 = 118%

So the next time someone asks you **to give more than 100%**, you know what’s required of you!