15 December 2015

Although there is no regular update, I will still update the IMO, Kangaroo and IOI pages.

I am not writing new articles for the time being (too much work), when time is right I will open a new blog where I’ll will write serious, well-thought-out articles on current issues, especially educational ones.

## Math Olympiad Prep Course: June 2015 School Holidays

28 May 2015

ArdentEdu will organize the MOPC during the upcoming school holidays (2-3 & 9-10 June 2015).

Please find more details in the Info Pack: Info Sheet MOPC 2015

My colleague Mr. Jonathan Ramachandran will teach the classes. He participated in IMO 2002.

If you have any questions, please email me.

## A Proof That Some Spaces Can’t Be Cut

14 January 2015

A well-written and mathematically accurate article from Quanta Magazine (no wonder, it’s published by the Simons Foundation):

https://www.quantamagazine.org/20150113-a-proof-that-some-spaces-cant-be-cut/

The question is deceptively simple: Given a geometric space — a sphere, perhaps, or a doughnut-like torus — is it possible to divide it into smaller pieces? In the case of the two-dimensional surface of a sphere, the answer is clearly yes. Anyone can tile a mosaic of triangles over any two-dimensional surface. Likewise, any three-dimensional space can be cut up into an arbitrary number of pyramids.

But what about spaces in higher dimensions? Mathematicians have long been interested in the general properties of abstract spaces, or manifolds, which exist in every dimension. Could every four-dimensional manifold survive being sliced into smaller units? What about a five-dimensional manifold, or one with an arbitrarily large number of dimensions?

Subdividing a space in this way, a process known as triangulation, is a basic tool that topologists can use to tease out the properties of manifolds. And the triangulation conjecture, which posits that all manifolds can be triangulated, is one of the most famous problems in topology.

Ciprian Manolescu remembers hearing about the triangulation conjecture for the first time as a graduate student at Harvard University in the early 2000s. Though Manolescu was considered a phenomenon when he entered Harvard as an undergraduate — he had distinguished himself as the only person, then or since, to notch three consecutive perfect scores in the International Mathematical Olympiad — trying to prove a century-old conjecture isn’t the sort of project that a wise student takes on for a doctoral thesis. Manolescu instead wrote a well-regarded dissertation on the separate topic of Floer homology and spent most of the first decade of his professional career giving the triangulation conjecture little thought. “It sounded like an unapproachable problem, so I didn’t pay much attention to it,” he wrote recently an email.

Others kept working on the problem, however, clawing toward a solution that remained stubbornly out of reach. Then in late 2012, Manolescu, now a professor at the University of California, Los Angeles, had an unexpected realization: The theory he’d constructed in his thesis eight years earlier was just what was needed to clear the final hurdle that had tripped up every previous attempt to answer the conjecture.

Building on this insight, Manolescu quickly proved that not all manifolds can be triangulated. In doing so, he not only elevated himself to the top of his field, but created a tool with enormous potential to answer other long-standing problems in topology.

_________________________________

(Yay for former IMO contestant! Many IMO participants go on to illustrious careers in mathematics and related fields.)

Manolescu’s result makes precise the “intuitive” notion that higher-dimension spaces are fundamentally different from the 2 & 3 dimensional spaces we are familiar with.

Thanks Irwan Iqbal for sending me this news.

## RIP Alexander Grothendieck (d. 2014)

12 January 2015

I just learned that Alexander Grothendieck died in November last year.

Who is Alexander Grothendieck? He was perhaps the finest mathematician of the 20th century, whose work in algebraic geometry have given birth to one of the most illuminating, productive and ambitious mathematical developments in the 20th century.

He was a colorful character who led an eventful life. His father perished in Auschwitz. He taught a prestigious mathematical seminar at IHES Paris. He was involved in radical leftist activism, which made him a pariah in Parisian academe. He gave math lectures and preached pacifism in the jungles of Vietnam during the war while Americans bombs were exploding all around him. He won the Fields Medal, the highest honor in mathematics. He decided later in his life to give up mathematics totally. Finally, in 1990, he gave up on society in general, and left behind everything he had, to live alone in the Pyrenees.

After that, his reputation took a romantic turn: popular accounts talk of a genius mind, disillusioned with worldly honors and insincere colleagues, who sought enlightenment in solitary life. He wrote screeds against what he viewed as a reactionary society, and became somewhat of a mythical figure of the French Left (Fortunately he didn’t become like the other brilliant mathematician, who stopped doing mathematics and went to live alone in ramshackle cabin in the Montana woods).

During his self-imposed exile, Grothendieck would write letters to his former departmental colleagues, to ask them to destroy anything he had ever written, whether published or not. We are lucky that they collectively decided to ignore his request, lest we would be deprived of some of the most sublime mathematical ideas ever concocted by our species.

Now that Grothendieck had passed away, mathematicians the world over are working on a mammoth task: translating the whole Grothendieck oeuvre into the major languages, so that his mathematical ideas and programs can be disseminated outside the French-speaking world. Not that these are easy to read; it is estimated that the number of people who understand his whole work is no more than ten, that including his most brilliant and most devoted proteges, like Rene Deligne.

I’m happy to see that Grothendieck is not totally forgotten, although response to his death in the English speaking media was a bit muted. I can imagine science editors the world over asking “Alexander who?”. His obituaries appeared in some major English newspapers like The New York Times, The Independent, and The Telegraph (no BBC?). There is no such problem in France. In a country that places mathematics as a source of historical pride, Grothendieck is considered a national hero. Now if only we can locate his autobiography that is rumored to exist somewhere…

He is the bald one

The best write-up on the life and work of Grothendieck that I can find online is by Pierre Cartier: http://inference-review.com/article/a-country-known-only-by-name/ .

Quote from The New York Times obituary:

He avoided clever tricks that proved the theorem but did not develop insight. He likened his approach to softening a walnut in water so that, as he wrote, it can be peeled open “like a perfectly ripened avocado.”

“If there is one thing in mathematics that fascinates me more than anything else (and doubtless always has), it is neither ‘number’ nor ‘size,’ but always form,” he wrote in a long memoir in the 1980s, “Reapings and Sowings.” “And among the thousand-and-one faces whereby form chooses to reveal itself to us, the one that fascinates me more than any other and continues to fascinate me, is the structure hidden in mathematical things.”

Softening walnut in water: a brilliant heuristic. RIP, AG.

## OMK result is out

16 October 2014

The OMK 2014 (Olimpiad Matematik Kebangsaan 2014) result is out: http://persama.org.my/

Congratulations to all winners!

We hope to get more participation from schools in 2015.

Please do not contact me about the results. I am not involved in the organization of OMK, it is under the purview of the OMK coordinator.

## Malaysian Computing Challenge 2014

25 September 2014

Official MCC 2014 website:

http://ioimalaysia.org/competitions/malaysian-computing-challenge/mcc-2014/

WHAT IS MCC?

The Malaysian Computing Challenge (MCC) is an annual online competition designed for students (with no prior programming experience) to solve challenging computational problems.

ORGANIZERS

MCC is brought to you by the Malaysian Informatics and Programming Society in collaboration with the Kulliyyah of ICT, International Islamic University Malaysia.

BEYOND MCC

The MCC is the preliminary selection process of a year-long program to identify and train the top programming talents in Malaysian schools. Top scorers in MCC will be:

1. Invited to a programming camp, tentatively to be held in December 2014.
2. Upon successful completion of the camp, to be invited to the Malaysian Computing Olympiad (MCO), a real-time programming competition, to be held tentatively in April 2015.

The top scorers in MCO will be called for a series of intensive training camps conducted by experienced Olympiad participants. Students who qualify at this level will participate in Asia Pacific Informatics Olympiad (APIO), an annual online contest among countries in the Pacific Rim region. After the training camps and APIO, four students will be selected to represent Malaysia in International Olympiad in Informatics (IOI) 2015 which will take place in Kazakhstan on July 2015.

DATES AND VENUE

The MCC 2014 online competition will take place on 26-28 September 2014. Participants can submit their solutions anytime within these 3 days, starting from 12:01am on 26 September 2014 to 11:59pm on 28 September 2014.

______________________________________

In a few hours after I update this entry, the MCC 2014 will be live. I am very excited as this is the first time we are organizing an online programming-based contest (the MCC was paper-based in the last two years). Thanks to the MCC 2014 team — Shien Jin, Yi Hang, Sher Minn & Fu Yong — for your efforts to make this event happen.

To the participants: Good luck and happy coding!

22 September 2014

Now that my blog has been totally ignored for more than 4 months, I had just now taken the time to update the pages:

• The IMO page has now been updated to 2015, with full report of the 2014 events.
• Similarly for the IOI and KMC.
• Under Courses, I have updated the info on the upcoming Math Olympiad Prep Course in December.
• Much of the spam comments have been deleted.

My new book is coming out at the end of this month (it is being printed already). It is the Volume 2 of my MRSM Mathematical Olympiad series. Where else would be more suitable to launch the book than the actual MRSM Mathematical Olympiad itself, which will take place for 4 days starting 30 September at MRSM Kuala Krai, Kelantan. After the event, the book will be available for purchase. We will update our online catalog / order form.

My new project is a nationwide teachers’ workshop on Higher Order Thinking Skills (HOTS) in Mathematics. Under the latest education blueprint (Pelan Pembangunan Pendidikan Malaysia 2013-2025), the government is pushing schools to set more questions that tests HOTS in exam papers, with the goal, by next year, to have more than half of the problems in the standardized exams being HOTS problems.

Expectedly, teachers are having problems with this new push, as they are themselves unclear about what HOTS is & supposed to be, and insufficient training are being given to explain the Whats (definition and approach of HOTS) and Hows (how to set HOTS problems). There are course materials on the ministry website, but those are catered more towards to highbrow pedagogy experts in the ivory tower, not the teachers who conduct day-to-day teaching in our schools.

I have come up with a simple methodology for Math teachers to set HOTS problems which are perfectly mapped to the Malaysian mathematics school syllabus, but at the same time challenges students’ HOTS rather than memorizing and regurgitating skills. I had done several presentations to state education departments and they all seem receptive to the idea. We are doing some pilot projects in several selected states this year. I will give more updates about this project in the future.

My method consists of 15 “tools” to upgrade normal math problems into HOTS problems. Some of the tools are standard and are often used as examples when talking about HOTS, and some of the tools are borrowed from the world of competitive mathematics. I was involved in math olympiad for close to 20 years, and my wide experience as problem-setter and trainer gives me some insights into how a normal math problems can be HOTS-ified to challenge students’ thinking rather than their calculating skills.

Ultimately, developing HOTS for students depends a lot on the teachers’ ability and willingness to adapt a new paradigm for teaching. It is hard to let go of normal behaviour after teaching for decades using the same methodology. The “old school” method has run its course; it is time to give it a well-deserve rest. We should focus our efforts not to make our students A-chasers, but make them thinkers who can process new ideas and come up with novel ways to solve problems. Then only will our full educational potential be unleashed, and then perhaps, our education system can really be world-class.