#po-shen loh

[jcmarchi]

2024 Math Prize for Girls at MIT sees six-way tie

New Post has been published on https://thedigitalinsider.com/2024-math-prize-for-girls-at-mit-sees-six-way-tie/

2024 Math Prize for Girls at MIT sees six-way tie

After 274 young women spent two-and-a-half hours working through 20 advanced math problems for the 16th annual Advantage Testing Foundation/Jane Street Math Prize for Girls (MP4G) contest held Oct. 4-6 at MIT, a six-way tie was announced. 

Hosted by the MIT Department of Mathematics and sponsored by the Advantage Testing Foundation and global trading firm Jane Street, MP4G is the largest math prize for girls in the world. The competitors, who came from across the United States and Canada, had scored high enough on the American Mathematics Competition exam to apply for and be accepted by MP4G. This year, MP4G received 891 applications to solve multistage problems in geometry, algebra, and trigonometry. This year’s problems are listed on the MP4G website.

Because of the six-way tie, the $50,000 first-place prize and subsequent awards ($20,000 for second, $10,000 for third, $4,000 apiece for fourth and fifth and $2,000 for sixth place) was instead evenly divided, with each winner receiving $15,000. While each scored 15 out of 20, the winners were actually placed in order of how they answered the most difficult problems. 

In first place was Shruti Arun, 11th grade, Cherry Creek High School, Colorado, who last year placed fourth; followed by Angela Liu, 12th grade, home-schooled, California; Sophia Hou, 11th grade, Thomas Jefferson High School for Science and Technology, Virginia; Susie Lu, 11th grade, Stanford Online High School, Washington, who last year placed 19th; Katie He, 12th grade, the Frazer School, Florida; and Katherine Liu, 12th grade, Clements High School, Texas — with the latter two having tied for seventh place last year.

The next round of winners, all with a score of 14, took home $1,000 each: Angela Ho, 11th grade, Stevenson High School, Illinois; Hannah Fox, 12th grade, Proof School, California; Selena Ge, 9th grade, Lexington High School, Massachusetts; Alansha Jiang, 12th grade, Newport High School, Washington; Laura Wang, 9th grade, Lakeside School, Washington; Alyssa Chu, 12th grade, Rye Country Day School, New York; Emily Yu, 12th grade, Mendon High School, New York; and Ivy Guo, 12th grade, Blair High School, Maryland.

The $2,000 Youth Prize to the highest-scoring contestant in 9th grade or below was shared evenly by Selena Ge and Laura Wang. In total, the event awards $100,000 in monetary prize to the top 14 contestants (including tie scores). Honorable mention trophies were awarded to the next 25 winners.

“I knew there were a lot of really smart people there, so the chances of me getting first wasn’t particularly high,” Katie He told a Florida newspaper. “When I heard six ways, I was so excited though,” He says, “because that’s just really cool that we all get to be happy about our performances and celebrate together and share the same joy.”

The event featured a keynote lecture by Harvard University professor of mathematics Lauren Williams on the “Combinatorics of Hopping Particles;” talks by Po-Shen Loh, professor of math at Carnegie Mellon University, and Maria Klawe, president of Math for America; and a musical performance by the MIT Logarhythms. Last year’s winner, Jessica Wan, volunteered as a proctor. Now a first-year at MIT, Wan won MP4G in 2022 and 2019. Alumna and doctoral candidate Nitya Mani was on hand to note, during her speech at the awards ceremony, how much bigger the event has grown over the years.

The day before the competition, attendees gathered to attend campus tours, icebreaker events, and networking sessions around MIT, at the Boston Marriott Cambridge, and at Kresge Auditorium, where the awards ceremony took place. Contestants also met MP4G alumnae at the Women in STEM Ask Me Anything event.

Math Community and Outreach Officer Michael King described the event as a “virtuous circle” where alumni return to encourage participants and help to keep the event running. “It’s good for MIT, because it attracts top female students from around the country. The atmosphere, with hundreds of girls excited about math and supported by their families, was wonderful. I thought to myself, ‘This is possible, to have rooms of math people that aren’t 80 percent men.’ The more women in math, the more role models. This is what inspires people to enter a discipline. MP4G creates a community of role models.”

Chris Peterson SM ’13, director of communications and special projects at MIT Admissions and Student Financial Services, agrees. “Everyone sees and appreciates the competitive function that Math Prize performs to identify and celebrate these highly talented young mathematicians. What’s less visible, but equally or even more important, is the crucial community role it plays as an affinity community to build  relationships and a sense of belonging among these young women that will follow and empower them through the rest of their education and careers.”

Petersen also discussed life at MIT and the admissions process at the Art of Problem Solving’s recent free MIT Math Jam, as he has annually for the past decade. He was joined by MIT Math doctoral candidate Evan Chen ’18, a former deputy leader of the USA International Math Olympiad team.

Many alumnae returned to MIT to participate in a panel for attendees and their parents. For one panelist, MP4G is a family affair. Sheela Devadas, MP4G ’10 and ’11, is the sister of electrical engineering and computer science doctoral candidate and fellow MP4G alum Lalita; their mother, Sulochana, is MP4G’s program administrator. 

“One of the goals of MP4G is to inspire young mathematicians,” says Devadas. “Although it is a competition, there is a lot of camaraderie between the contestants as well, and opportunities to meet both current undergraduate STEM majors and older role models who have pursued math-based careers. This aligned with my experience at MIT as a math major, where the atmosphere felt both competitive and collaborative in a way that inspired us.”

“There are many structural barriers and interpersonal issues facing women in STEM-oriented careers,” she adds. “One issue that is sometimes overlooked, which I have sometimes run into, is that both in school and in the workplace, it can be challenging to get your peers to respect your mathematical skill rather than pressuring you to take on tasks like note-taking or scheduling that are seen as more ‘female’ (though those tasks are also valuable and necessary).” 

Another panelist, Jennifer Xiong ’23, talked about her time at MP4G, MIT, and her current role as a pharmaceutical researcher at Moderna.  

“MP4G is what made me want to attend MIT, where I met my first MIT friend,” she says. Later, as an MIT student, she volunteered with MP4G to help her stay connected with the program. “MP4G is exciting because it brings together young girls who are interested in solving hard problems, to MIT campus, where they can build community and foster their interests in math.”

Volunteer Ranu Boppana ’87, the wife of MP4G founding director and MIT Math Research Affiliate Ravi Boppana PhD ’86, appreciates watching how this program has helped inspire women to pursue STEM education. “I’m most struck by the fact that MIT is now gender-balanced for undergraduates, but also impressed with what a more diverse place it is in every way.”

The Boppanas were inspired to found MP4G because their daughter was a mathlete in middle school and high school, and often the only girl in many regional competitions. “Ravi realized that the girls needed a community of their own, and role models to help them visualize seeing themselves in STEM.”

“Each year, the best part of MP4G is seeing the girls create wonderful networks for themselves, as some are often the only girls they know interested in math at home. This event is also such a fabulous introduction to MIT for them. I think this event helps MIT recruit the most mathematically talented girls in the country.”

Ravi also recently created the YouTube channel Boppana Math, geared toward high school students. “My goal is to create videos that are accessible to bright high school students, such as the participants in the Math Prize for Girls,” says Ravi. “My most recent video, ‘Hypergraphs and Acute Triangles,’ won an Honorable Mention at this year’s Summer of Math Exposition.”

The full list of winners is posted on the Art of Problem Solving website. The top 45 students are invited to take the 2024 Math Prize for Girls Olympiad at their schools. Canada/USA Mathcamp also provides $500 merit scholarships to the top 35 MP4G students who enroll in its summer program. This reflects a $250 increase to the scholarships. Applications to compete in next year’s MP4G will open in March 2025. 

[allaboutmarketing4you]

How to be a creative thinker | Carnegie Mellon University Po-Shen Loh

"Have you ever wondered whether you lack creativity? Po-Shen Loh, a social entrepreneur, illuminates issues within the education system while instructing tens of thousands of diverse students. Serving as a U.S. Math Olympiad coach and professor at Carnegie Mellon University, he endeavors to tackle these problems. He has developed a captivating educational system, reminiscent of Twitch game streaming. Explore the significant challenges and their solutions in the video."

Source: EO

#mktmarketing4you#corporatestrategy#marketing#M4Y#lovemarketing#IPAM#ipammarketingschool#ContingencyPlanning#virtual#volunteering#project#Management#Economy#ConsumptionBehavior#BrandManagement#ProductManagement#Logistics#Lifecycle

#Brand#Neuromarketing#McKinseyMatrix#Viralmarketing#Facebook#Marketingmetrics#icebergmodel#EdgarScheinsCultureModel#GuerrillaMarketing#STARMethod#7SFramework#gapanalysis #AIDAModel #SixLeadershipStyles #MintoPyramidPrinciple #StrategyDiamond #InternalRateofReturn #irr #BrandManagement #dripmodel #HoshinPlanning #XMatrix #backtobasics #BalancedScorecard #Product #ProductManagement #Logistics #Branding #freemium #businessmodel #business #4P #3C #BCG #SWOT #TOWS #EisenhowerMatrix #Study #marketingresearch #marketer #marketing manager #Painpoints #Pestel #ValueChain # VRIO #marketingmix

[eros-vigilante]

a man named Po-Shen Loh simplified the quadratic formula (link is to a video of him explaining the formula)

[n2qfd]

https://www.novid.org

Public health officials have cited contact tracing as a key part of lifting lockdowns and continuing to prevent the spread of the coronavirus; a new app developed at Carnegie Mellon University could make the effort easier.

NOVID launched in the Apple app store and Google Play last week. It’s the first app of its kind made in the United States, according to creator and CMU math professor Po-Shen Loh.

NOVID traces users and warns them about exposure risks in their network. If a user tells the app if they’ve tested positive for the virus, people that have come into contact with that user recently will receive a notification. After a user reports positive, their network is only alerted once. Then those users can decide whether or not it’s in their best interest to get tested or go near a relative who could be at higher risk for severe effects of the virus.

Loh said it's all anonymous.

"It doesn't ask you for your phone number, it doesn't ask you for your name. It doesn't even ask you for a username and password," he said. It does require permission to use a device’s Bluetooth and microphone.

[niazbinsiraj]

সূত্র ছাড়াই সমাধান করুন দ্বিঘাত সমীকরণ - Actual Explanation of Po-Shen Loh Method

সূত্র ছাড়াই সমাধান করুন দ্বিঘাত সমীকরণ – Actual Explanation of Po-Shen Loh Method

“চার হাজার বছর পর দ্বিঘাত সমীকরণের নতুন সমাধান” – এই টাইটেলে প্রথম আলোতে রিসেন্টলি একটা লেখা পাবলিশ হওয়ার পর থেকে এ নিয়ে নানা রকমের আলোচনা সমালোচনা শুরু হয়ে গেছে। ফেসবুকের কমেন্ট সেকশনে দেখা মিলছে অনেক সাহিত্যিক, কবি এবং গণিতবিদের।

সমালোচনা কারীর একটাই কথা, এটা কোনো নতুন সমাধান না। এটা আগের সমাধানটিরই ভিন্ন রূপ। এবং হ্যাঁ, আমি সমালোচনা কারীর বক্তব্যের সাথেও একমত যে এটা আসলেই একদম নতুন কোনো সমাধান…

[todaynationnews]

US Olympic Mathematics head coach Roboshen has a unique teaching method for the US to win four championships

US Olympic Mathematics head coach Roboshen has a unique teaching method for the US to win four championships

Since the American Olympiad National Team was led by the Chinese head coach Po-Shen Loh, it has won four international team championships. Before that, it had not won the championship for more than a decade. Therefore, many Chinese parents have turned to Luo Boshen. Ask for education methods. Luo Boshen recently returned to Southern California where he used to study and plans to share his…

[munove]

¿Te enseñaron a resolver la ecuación de segundo grado así?

Recientemente he leído sobre un nuevo método de resolución de las ecuaciones de segundo grado elaborado por el Dr. Po-Shen Loh, profesor asociado de Matemáticas en la universidad Carnegie Mellon. El método no necesita el uso de la famosa fórmula de resolución de la ecuación de segundo grado que todos aprendimos en la escuela. Hace ya tiempo que yo les explico a mis alumnos de instituto otro método que tampoco requiere el uso de la famosa fórmula y que se basa en el utilizar la fórmula del cuadrado del binomio.

etiquetas: ecuaciones, segundo grado

» noticia original (dayinlab.com)

[sciencespies]

Math genius has come up with a wildly simple new way to solve quadratic equations

https://sciencespies.com/humans/math-genius-has-come-up-with-a-wildly-simple-new-way-to-solve-quadratic-equations/

Math genius has come up with a wildly simple new way to solve quadratic equations

If you studied algebra in high school (or you’re learning it right now), there’s a good chance you’re familiar with the quadratic formula. If not, it’s possible you repressed it.

By this point, billions of us have had to learn, memorise, and implement this unwieldy algorithm in order to solve quadratic equations, but according to mathematician Po-Shen Loh from Carnegie Mellon University, there’s actually been an easier and better way all along, although it’s remained almost entirely hidden for thousands of years.

In a 2019 research paper, Loh celebrates the quadratic formula as a “remarkable triumph of early mathematicians” dating back to the beginnings of the Old Babylonian Period around 2000 BCE, but also freely acknowledges some of its ancient shortcomings.

“It is unfortunate that for billions of people worldwide, the quadratic formula is also their first (and perhaps only) experience of a rather complicated formula which they must memorise,” Loh writes.

That arduous task – performed by approximately four millennia worth of maths students, no less – may not have been entirely necessary, as it happens. Of course, there have always been alternatives to the quadratic formula, such as factoring, completing the square, or even breaking out the graph paper.

But the quadratic formula is generally regarded as the most comprehensive and reliable method for solving quadratic problems, even if it is a bit inscrutable. This is what it looks like:

That formula can be used to solve standard form quadratic equations, where ax2 + bx + c = 0.

In September 2019, Loh was brainstorming the mathematics behind quadratic equations when he struck upon a new, simplified way of deriving the same formula – an alternative method which he describes in his paper as a “computationally-efficient, natural, and easy-to-remember algorithm for solving general quadratic equations”.

“I was dumbfounded,” Loh says of the discovery. “How can it be that I’ve never seen this before, and I’ve never seen this in any textbook?”

In Loh’s new method, he starts from the standard method of trying to factor the quadratic x² + bx + c as (x −   )(x −   ), which amounts to looking for two numbers to put in the blanks with sum −b and product c. He uses an averaging technique that concentrates on the sum, as opposed to the more commonly taught way of focusing on the product of two numbers that make up c, which requires guesswork to solve problems.

“The sum of two numbers is 2 when their average is 1.” Loh explains on his website.

“So, we can try to look for numbers that are 1 plus some amount, and 1 minus the same amount. All we need to do is to find if there exists a u such that 1 + u and 1 − u work as the two numbers, and u is allowed to be 0.”

According to Loh, a valid value for u can always be determined per Loh’s alternative quadratic method, in an intuitive way, making it possible to solve any quadratic equation.

In Loh’s paper, he admits he would “be very surprised if this approach has entirely eluded human discovery until the present day, given the 4,000 years of history on this topic”, but says the alternative technique – which combines steps pioneered by Babylonian, Greek, and French mathematicians – is “certainly not widely taught or known (the author could find no evidence of it in English sources)”.

However, since first sharing his pre-print paper describing the simple proof online in October, Loh says his attention has been drawn to a 1989 research article that is the most similar previous work he has found – going some way to justify his disbelief that this alternative method had not been identified before now.

“The other work overlapped in almost all calculations, with an apparent logical difference in assuming that every quadratic can be factored, and a pedagogical difference in choice of sign,” Loh explained to ScienceAlert in an email.

All that remains to be solved then, is the mystery of why this technique hasn’t become more widely known previous to this, since it gives us, in Loh’s words, “a delightful alternative approach for solving quadratic equations, which is practical for integration into all mainstream curricula”.

(Not to mention, of course, that it might just mean that nobody need ever again memorise the quadratic formula.)

We still don’t know how this escaped wider notice for millennia, but if Loh’s instincts are right, maths textbooks could be on the verge of a historic rewriting – and we don’t take textbook-changing discoveries lightly.

“I wanted to share it as widely as possible with the world,” Loh says, “because it can demystify a complicated part of maths that makes many people feel that maybe maths is not for them.”

The research paper is available at pre-print website arXiv.org, and you can read Po-Shen Loh’s generalised explanation of the simple proof here.

A version of this article was first published in December 2019.

#Humans

[wozziebear]

3Blue1Brown

3Blue1Brown (real name Grant Sanderson) is my favourite maths YouTuber. He animates his videos with a software he created called Manim, which is now also used by VcubingX and Reducible. Even if you didn’t understand anything he was talking about, 3B1B’s videos are still worth watching for the pure art and enthusiasm. My favourite videos of his are the ones about error-correcting codes, Dirichlet’s theorem and his interactive quaternion explainer. He has recurring series on deep learning, differential equations, linear algebra and calculus, all of which are excellent high-level overviews of the respective topics.

Numberphile

This is the most well-known maths channel. It’s possible that 3B1B’s new releases get more attention, but Numberphile has been going for longer and has a much larger archive. I enjoyed their recent series of videos featuring Neil Sloane, the founder of the Online Encyclopaedia of Integer Sequences. Some classics include the video on the Josephus problem, the interview with Terence Tao, and the videos with Ron Graham. It’s worth mentioning that James Grime and Katie Steckles, frequent contributors to Numberphile, also have their own channels.

Stand-up Maths

Matt Parker describes himself as a stand-up mathematician: part comedian and part mathematician. He first received wide recognition from his Numberphile appearances and now he does live shows with his group Festival of the Spoken Nerd. His best videos are: his stand-up routine about spreadsheets, his videos about the hilarious superpermutation saga, and his investigation into whether “land area” assumes a country is perfectly flat. He also has a second channel, the highlight of which is the time he ran untested viewer-submitted code on his Christmas tree.

Mathologer

Another excellent channel. This one is of intermediate production value between the guy-with-whiteboard channels and the 3B1B cinematic masterpieces. He has a great video addressing the infamous Numberphile claim that the sum of all natural numbers is -1/12. Mathologer is strongest in animating proofs. I am especially pleased by his Simpsons-themed videos.

PBS Infinite Series (discontinued)

This is (or rather was) an underrated channel. I particularly enjoyed their exploration of voting systems and the Condorcet paradox (which I wrote about in my Beginning of Infinity review). Their video on the assassin puzzle is also good and it’s what introduced me to the idea of representing shapes as lattices. Finally, here is this post’s obligatory link to a quantum computing video.

Mathmaniac

The first video I saw from this channel was his mathematical analysis of whether the YouTuber Dream was cheating in his now-infamous Minecraft speedrun (Matt Parker also made a video on the same subject!). Mathmaniac also has a series about group theory, inspired by 3B1B’s series about calculus and linear algebra.

Blackpenredpen

Blackpenredpen is probably the channel I’ve watched the second most after 3B1B. While the production value is significantly lower, he makes up for it with sheer quantity. He’s particularly strong in algebra and calculus. Highlights of the channel include the time he livestreamed solving integrals for six hours straight, his videos about Oxbridge interview questions (which include a collaboration with Tom Rocks maths), and his recent conversation with Po Shen Loh.

Michael Penn

Another channel with a simple style. I enjoy his videos about geometry. Like many of these channels, Penn has videos where he works through Olympiad problems and problems from other famous exams like the Putnam.

Flammable Maths

Flammable Maths is one of the most active members of the YouTube maths community. The level of assumed knowledge varies massively between videos and even within them. He also has a meme-y aesthetic and sense of humour that can become a bit much at times. His Christmas specials are good: these two videos featured many other well-known maths personalities, and he goes through problems every day during ‘Papa Flammy’s advent calendar’.

MindYourDecisions

Presh Talwalkar, or MindYourDecisions, is the clickbait of maths on YouTube. Did you know that only 6% of Korean 11-year-olds could solve this problem?! All of his videos have the same basic format of working through some problem, animated with Powerpoint. Some random ones I liked: the 25 horses problem and some deceptively simple geometry problems.

Jan Misali

This guy really only has one video about maths, but it’s shockingly good.

Veritasium

Watching Veritasium videos was a not insignificant part of what first got 13-year-old me into science. Here are his videos about the logistic map, the Collatz conjecture and Gödel’s incompleteness theorem.

Vsauce

Vsauce is perhaps the most popular educational YouTuber, and he has touched on maths a number of times. I recommend his videos on the Banach-Tarski paradox, the napkin ring problem, and the brachistochrone. I have to say, I respect how much detail he goes into, especially in the Banach-Tarski video. It has so many views that it’s plausible that, of all people in the world who know what the Banach-Tarski paradox is, more than 50% of them learned it from Vsauce.

Andrew Dotson

Andrew Dotson is a bit like the physics equivalent of Flammable Maths. A lot of his videos are vlogs, for people who want to see what life is like as a physics graduate student (hint: it’s shit). The videos of his where he does actual maths include finding the eigenvalues of a Möbius strip, integrating with Feynman’s technique and the “you laugh you differentiate” challenge.

Tibees

Tibees became popular through her ‘exam unboxing’ series (see for example professors reacting to India’s JEE Advanced exam). Now she makes videos about what famous mathematicians and physicists were reading or writing, and occasionally she’ll make a video of her solving a problem herself.

Simon Clark

Simon Clark studied physics at Oxford and is the messiah for physics A-level students applying to Oxbridge. He’s made a number of videos about admissions (playlist here) and if you’re thinking about applying then definitely watch his videos. The most explicitly maths-related videos he has include a brief history of pi and a video about the etymology of sin and cos. The videos of his I like the most are the ones where he talks about his favourite books (click here for the playlist).

TED-Ed

TED-Ed has a puzzle series which includes videos on the prisoner hat riddle, the Mondrian squares riddle, and a variation upon the blue-eyed islander problem. They also have videos about Hilbert’s hotel and where maths symbols come from.

A guide to fun mathematics YouTube channels

https://samenright.com/2021/08/31/a-laymans-guide-to-recreational-mathematics-videos/ Comments

[biofunmy]

Why Mathematicians Hate That Viral Equation

Math can be useful. It can also be elegant, even beautiful — a word you’ll often hear mathematicians say when they describe the discovery of a nugget of surprising insight.

That seemingly simple equation that ricocheted across the internet recently was neither useful nor elegant. By now, you’ve likely seen it:

8 ÷ 2(2+2) = ?

“I HATE this,” Amie Wilkinson, a mathematician at the University of Chicago, commented on a Facebook post by a colleague about the equation, echoing the disdain felt by many mathematicians for the trending question.

Kenneth Ribet of the University of California, Berkeley described it as “irksome.”

“I didn’t care. I wasn’t interested,” said Greg Kuperberg of the University of California, Davis. “I stared at it a little bit and moved on.”

You might think that mathematicians would be happy about a rare instance when people are enthusiastically talking about math.

That was the assumption of Rachel Pulido Oakley, a former writer on “The Simpsons” and an old college friend of Dr. Wilkinson’s. She texted Dr. Wilkinson — “Amie Amie Amie … urgent question!” — asking which of two common calculating procedures was the correct one to use.

“Secretly, it enraged me, but I didn’t actually take it out on Rachel fully,” Dr. Wilkinson said.

Instead, she texted back to Ms. Pulido Oakley: “LOL. That’s not math.”

[Like the Science Times page on Facebook. | Sign up for the Science Times newsletter.]

For mathematicians, equations like this one — something that looks like what you learned in school, but which has been twisted with intentionally ambiguous notation — reinforce the trope that the core of math consists of memorized recipes of calculation.

“It implies that the point of mathematics is to trip up other people with stupid rules,” Dr. Wilkinson said.

The ruckus was like expounding the exceptions to “i before e except after c” and wondering why a Shakespearean scholar is not sharing your excitement in discussing the English language.

Interpret the expression one way, you get 1.

Interpret it the other way, you get 16.

There’s no aha moment, just confusion and discord.

“No one in good spirits would ever want to inflict it on anyone else,” Dr. Ribet said.

In isolation, without context, mathematical expressions like this say nothing. But equations really can solve problems when they describe a question you want to answer.

Consider this word problem:

A restaurant employs 8 waiters who split into two equal sized shifts, each waiter earning $2 in wages and $2 in tips per hour.

How much per hour does a shift of waiters earn in total?

Translating the words into an equation yields:

(8/2)(2+2) = ?

In this context, the alternative interpretation of the expression makes no sense and so there is no ambiguity.

When the problem is set up properly and the equation is written down properly, it’s easily solved — $16 per hour — and there’s no controversy, although these servers are clearly exploited and under-tipped.

But a simple, straightforward problem wouldn’t give the internet anything to fight over. So here’s a different math problem to debate and discuss that doesn’t rely on ambiguity in stating the problem. It doesn’t even include any mathematical symbols.

The diagram below, of six intersecting lines, none parallel to each other, comes from Po-Shen Loh, a mathematics professor at Carnegie Mellon University in Pittsburgh and coach of the United States Math Olympiad team.

Ready?

How many triangles are there?

Image

CreditPo-Shen Loh

You can count and fight over who’s a better counter. But the beauty of this problem is that it provides a nifty insight into combinatorics — another area of math that figures out the number of ways things can be shuffled. And once learned, that’s a mathematical tool that can be applied to other problems.

That’s the kind of problem that makes mathematicians smile.

A hint from Dr. Loh: “You can think about counting triangles in a completely different perspective, which is very cool. A triangle is made of three lines. So if I have six lines, then the whole question becomes how can I pick three lines out of those six lines?”

Sahred From Source link Science

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[coolcatteacher]

Inspiring Math Excellence in the Classroom with Po-Shen Loh

Inspiring Math Excellence in the Classroom with Po-Shen Loh

Po-Shen Loh @poshenloh, National Math Coach and Carnegie Mellon Professor gives us a refreshing take on teaching math. From giving kids problems with the right level of difficulty to solving problems with students, learn how to take any math student to the next level. You’ll also learn about the open source resource, Expii invented by Po-Shen Loh and how you can use it.

[callout]Thank you,…

[totumat]

¿Una nueva fórmula cuadrática?

¿Una nueva fórmula cuadrática? Esta fórmula ha estado frente a nuestras narices y no nos habíamos dado cuenta. ¡Veamos qué plantea Po-Shen Loh!

El Doctor en Matemáticas Po-Shen Loh, ha descubierto una nueva forma — ¡más simple! — para deducir la fórmula cuadrática y así calcular la solución de las ecuaciones cuadráticas, es decir, aquellas que se expresan de la forma . Esta fórmula ha estado frente a nuestras narices y no nos habíamos dado cuenta.

Perdón, ¿quién?

Po-Shen, quien obtuvo su título como matemático en el Instituto de…

[mastcomm]

This Professor’s ‘Amazing’ Trick Makes Quadratic Equations Easier

The quadratic equation has frustrated math students for millenniums. But a math professor at Carnegie Mellon University in Pittsburgh may have come up with a better way of solving it.

“When I stumbled on this, I was just completely shocked,” said the professor, Po-Shen Loh.

Quadratics, which are introduced in elementary algebra classes, pop up often in physics and engineering in the calculating of trajectories, even in sports. If you had wanted to estimate how far a pass thrown by Patrick Mahomes would travel during the Super Bowl, you’d be solving a quadratic equation. The equations also show up in calculations for maximizing profit, a key consideration for anyone who wants to succeed in business.

Dr. Loh has not discovered something entirely new. Indeed, his method mixes together ideas dating back thousands of years to the Babylonians. But this is not how modern algebra textbooks present the topic.

“To find out that there’s this trick from thousands of years ago that you can import into here is amazing to me,” Dr. Loh said. “I wanted to share that as widely as possible.”

Dr. Loh mentors some of the top high school math students in the country as coach of the United States Mathematical Olympiad team. But he also wants to improve the teaching of all math students.

“Everyone assumes the only people I work with are Olympiad students,” said Dr. Loh, who is the founder of the educational website Expii. “That’s not true. My passion is everyone.”

A few months ago, Dr. Loh posted online a paper describing his method, and teachers have already tried it in their classrooms.

“I was really surprised that most of them were getting it,” said Bobson Wong, a math teacher at Bayside High School in Queens, New York, who used the approach in an algebra class where many students fear math. “They were able to do it on their own.”

The burst of pedagogical discussion about quadratic equations highlights the ability of the internet to spread new teaching ideas quickly.

“It’s innovation in education that’s being pursued the right way,” said Michael Driskill, chief operating officer of Math for America, an organization that recognizes top teachers and provides forums for them to exchange ideas. (Mr. Wong is one of the people that Math for America has designated as a master teacher.)

Mr. Driskill said Dr. Loh did not proclaim that he had something definitively better, but instead, “He put it out to teachers and asked, ‘Does it work in classroom?’”

Quadratics and Parabolas 101

First, a quick review about quadratic equations and parabolas.

What algebra students currently learn

Before students are presented with the quadratic formula, they’re taught a simpler method to solve certain equations. For simplicity, we’ll consider an equation where a = 1.

x² – 4x – 5 = 0

You might recall your teacher asking you to factor the jumble of symbols. That is, you hoped to find two numbers r and s such that

x² – 4x – 5 = (x – r)(x – s) = 0

Multiplying out (x – r)(x – s) produces x² – (r + s)x – rs.

The key is to find r and s such that the sum of r and s equals 4 (that is, r + s = 4), and multiplying r and s produces –5 (r × s = –5). If they exist, then r and s are the two and only two solutions.

Figuring out the factors that work is essentially trial and error. “The fact that you suddenly have to switch into a guessing mode makes you feel like maybe math is confusing or not systematic,” Dr. Loh said.

Guessing also becomes cumbersome for quadratics with large numbers, and it only works neatly for problems that are contrived to have integer answers

Dr. Loh’s method eliminates this guessing game. But for many algebra students, the jumble of algebraic symbols is still confusing. So Mr. Wong tells them to sketch a parabola.

“If you graph it, it’s much easier for the kids to understand what’s going on,” he said.

How the new method works

This alternate method for solving quadratic equations uses the fact that parabolas are symmetrical.

The same method also works for equations that are not readily factorable.

That’s when students turn to the quadratic formula. But they often misremember it — the usual derivation is a bit convoluted involving a technique called “completing the square” — and get the wrong answers.

Dr. Loh’s method allows people to calculate the answers without remembering the exact formula. (It also provides a more straightforward proof.)

“Math is not about memorizing formulas without meaning, but rather about learning how to reason logically through precise statements,” Dr. Loh said.

Mr. Wong said Dr. Loh’s version is easier for students because it, “provides one method for solving all kinds of quadratic equations.”

A technique with ancient roots

Dr. Loh delved into mathematics history to find that the Babylonians and Greeks had the same insights, although their understanding was limited because their math was limited to positive numbers. It was only later that people came up with the concepts of negative numbers, zero and even more esoteric concepts like imaginary numbers — the square roots of negative numbers.

He even found out that a math teacher in Sudbury, Canada, named John Savage came up with a similar approach 30 years ago. An article by Mr. Savage in the journal The Mathematics Teacher in 1989 laid out almost the same procedure, although Dr. Loh filled in some nuances of logic in explaining why it works.

“I honestly can’t remember exactly where the eureka moment was,” Mr. Savage said in a phone interview. But it seemed to be an improvement over the usual way of teaching the subject.

He continued using that approach, as did some other teachers he knew. But the internet was still in its infancy, and the idea faded away.

“It never caught on,” Mr. Savage said. “Looking back on it, I should have pushed it a little more. I think it’s so much easier than the traditional way.”

Mr. Savage said he was excited to see the same idea revived 22 years after he had retired. “I was quite interested to read it now,” he said of Dr. Loh’s paper. “It’s quite interesting that he basically came up with the same idea.”

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Math Genius Has Devised a Wildly Simple New Way to Solve Quadratic Equations

Math Genius Has Devised a Wildly Simple New Way to Solve Quadratic Equations

If you studied algebra in high school (or you’re learning it right now), there’s a good chance you’re familiar with the quadratic formula. If not, it’s possible you repressed it.  

By this point, billions of us have had to learn, memorise, and implement this unwieldy algorithm in order to solve quadratic equations, but according to mathematician Po-Shen Loh from Carnegie Mellon University,…