An Inequality Problem

A while ago, Khoon Yu posted a math problem involving inequality. If you are interested, do give it a try:

Given numbers and such that . Prove that .

The solution I wrote: An Inequality Problem – Khoon Yu Tan’s blog (14 October 2009)

A Quick Update

Looking at the date of my last post, I was like — “Gosh? Has it been that long since I last blogged?”

My enrollment in the reading course has kept me busy most of the time. It was such a relief when Fall break arrived a month ago, giving me a short hiatus I much needed. A couple of friends and I rented a car for a one-day shopping trip, groceries and otherwise. I bought a winter jacket from my favorite store Banana Republic; the price tag was definitely not kind towards my credit card, for it was a new arrival item which I love so much. We had a late yet wonderful lunch at P.F. Chang Restaurant and pampered ourselves with a piece of cheesecake from the Cheesecake Factory.

Three weeks ago, Indrani Rao (a colleague of mine) invited me to an Indian-cuisine-themed Halloween dinner at her apartment. A small group of graduate students from the Mathematics Department (duh!) joined us and we had a very wonderful curry (thanks Indrani!) as well as a very intellectually stimulating and interesting (I am not talking about math here) conversation. In fact, the dinner started at about half past seven and we stayed there till about 01:00 in the morning! My body was bloated since I had a lot of stomach food and “brain food.”

 

Indrani's Halloween Dinner

Then November rolled in while October left the door step quietly, and so did Daylight Saving Time. I adjusted all of my unsynchronized clocks around me before going to bed. An extra hour of sleep, I uttered the cliché to myself. The sun has been setting earlier, and the weather has become noticeably colder. Last week, it started raining like Portland, Oregon. At first, I welcomed the rain drops with a warm heart. But after three consecutive days of nonstop raining, I got annoyed by its continuous presence.

Now, it is the end of November. Time flies by so quickly while I labored as a math graduate student. Thanksgiving is around the corner and once again, I look forward to having a short break. Even though I have a lot of studying to do during the break, I appreciate the lack of hectic schedule and pounding deadlines for about five days or so. Plus, I get to work from home, sitting at my comfortable desk next to the window, with the sight of falling autumn leaves as zephyr gently breeze through the neighborhood from time to time.

Oh, and I had myself vaccinated for the H1N1 Influenza last Tuesday. It was administered using a nasal spray. So I had two flu vaccinations this autumn.

Nobel Peace Prize to Barack Obama

My heartiest congratulations to the forty-fourth President of the United States Barack Obama; he was bestowed the 2009 Nobel Peace Prize by the Norwegian Nobel committee this morning.

Everyone is surprised — there was no discussion of Obama being a possible candidate prior to this announcement. His “extraordinary efforts to strengthen international diplomacy and cooperation between peoples” has landed him this amazing honor, which is indeed an extraordinary recognition for such a young president.

Again, congratulations Mr Obama. Félicitation, Monsieur Obama.

• New York Times — In surprise, Nobel Peace Prize to Obama for Diplomacy
• Le Monde — Barack Obama Prix Nobel de la paix

Distribution Theory

Last week, I was talking to several professors whose research area is analysis because I was hoping to start a reading course.

One of them is currently on sabbatical; the other is currently supervising three PhD students. At the end, I narrowed down to two options — functional analysis or distribution theory.

Personally, I do not know much about both fields. (I guess that’s why I chose to do a reading course at the first place, duh!) So the decision making relied heavily on the 30-minute brief preview of what I would be doing should I decide to have them as my adviser. As the title of this post suggests, I picked the latter.

I am now reading with Professor Mark Williams. By choosing distribution theory, I am positioning myself closer to the field of partial differential equations (PDE). As an undergraduate at the University of Michigan (UM), I did not take a PDE class; instead, I enrolled in a Fourier analysis course as an elective. Like every other people to whom I spoke, Professor Williams said that basic background in PDE can always be built through additional readings.

A reading course, more commonly known as an independent study at UM, is a 3-credit-hour “course” without the traditional classroom settings. There are neither lectures nor deadlines for homework or exams. Instead, a text was chosen by the professor and there will be a weekly meeting where I will present what I have self-studied and difficulties (which arise from problems I choose to attempt). As my adviser, Professor Williams will facilitate my learning by filling in gaps (e.g. lines in between proof which I do not comprehend) and sharing germane remarks (in addition to that of the text). The text that I am using is Introduction to the Theory of Distributions by Friedlander and Joshi.

Flu Shot

I got my seasonal flu shot this afternoon. Even though the vaccine is not too expensive, I am glad that it is covered under my Blue Cross Blue Shield insurance.

Next injection — H1N1 influenza shot.

My Teaching Observed

Last Friday, I was observed by Ellen Gasparovic (Senior Teaching Fellow, Department of Mathematics) and the following are the comments I received from her:

• Board work is beautifully organized.
• Your examples are good and your explanations are clear.
• Engaged your class by asking questions often and getting them involved, even at 8am!
• Good pace, volume, and tone of voice!
• I liked the fact that you gave them a problem to try on their own.
• Good work!

Needless to say I was a euphoric bloke after the observation/review!

An Eventful Weekend

Yesterday, I went to the department’s fall picnic in the afternoon and John Helm’s party in the evening.

Swarnava Mukhopadhyay, Daniel Orr, and Eric Fu

Like last year, there were hamburgers, salad, chips, and drinks. It was nice talking to some of the first-years. At 20:45, my roommate and I headed to John Helm’s party. His apartment was rather crowded since he invited a lot of people. I had the opportunity to meet Andrew’s and Emmanuel’s roommate — Henry. Joanna, Carole, and I were talking to Henry most of the time. He was very friendly and approachable.

My Saturday was unusually filled; while it was fun, it also equalled to a nonproductive day.

Bits and Pieces

I have recently made my photos on Flickr private. Please understand this is a sheer privacy concern — if we know each other, you are definitely more than welcome to browse through my photo albums. Log in Flickr with your existing Yahoo! account and request to add me as a friend. Once I approve your request, you will be my Flickr buddy and henceforth granted access to view my photos. If your username does not reflect your name, it would be very helpful if you could include your name so that I can identify your accurately. I apologize for any inconvenience and certainly appreciate your patience.

***

"Goodies" from UNC Campus Heath Service

I am finally done with this tedious routine. What a relief! Yahoo!

***

Last Friday, I was stressed out after attending a notationally heavy class which I did not understand. Symbols such as and were driving me nuts. I would need some time to imagine/visualize what these sets are; but the professor seemed to think that they should register in less than 2 seconds, and moved on with lecturing without pausing.

So, after class, a bunch of my classmates (apparently I was not alone) decided to get some beer on Franklin Street. I was rather tired, so I did not join them. But I decided to get a bottle of wine while I do my grocery shopping before heading home. I got myself a bottle of sauvignon blanc, and when the cashier rang it up, I handed her my driver’s license for ID verification. She politely declined; when I perused the receipt, the spot that usually indicates the customer’s date of birth stated instead “Cashier has bypassed age verification.“

My goodness, I am not even in my late 20s, yet!

***

My teaching is going well thus far. Even though Math 110 (College Algebra) covers elementary material, but introducing the notion of quadratic equations to first-time learners does require considerable amount of effort. Students generally find completing the square absurdly hard to perform. Nonetheless I am enjoying this experience, since deep down of a corner of my heart, I am passionate about being an educator.

***

Last weekend was the Labor Day weekend. I was in the mood of hosting a small and simple dinner with some of my friends in the Mathematics Department. I invited two friends, Carole Agyeman-Prempeh and Indrani Rao, to my humble abode.

Almost done cooking

Carole arrived before I was even done preparing the meal, which was nice, as I had someone to chat with while cooking.

Boston lettuce, drunken chicken, and seafood platter

Voilà! The dinner I prepared consisted of three main entrées: Boston lettuce with oyster sauce, Chinese style drunken chicken (a cold dish), and seafood platter with tamarind sauce. I had a pot of herbal chicken soup to complement these dishes.

Myself, Carole, and Indrani

After dinner, we went over to Indrani’s apartment (she lives in a neighborhood which is 15 minutes walk away) to taste some chocolate cake that she baked. It was a wonderful way to spend a relaxing evening.

An Avalanche

A hiker had trained for months before he hiked a steep mountain. As he ascended, he was hopeful that he could reach the peak and fly his flag there. He was quite optimistic and he certainly had the support he needed from his friends and family.

Unfortunately, the thing happened — an unexpected avalanche swept him a few thousands feet down. Gravity, avalanche’s best buddy, was not shy in providing assistance for sure. When the hiker thought that he was close enough to the peak, he was suddenly rather far apart from it.

At the bottom of the hill, he strives to make a comeback. He is determined to go through another round of self training and attempt to climb the mountain again four months later. He tries to be sanguine about the prospects; but at the same time, he might have to give up on climbing this very dream mountain should the second attempt failed.

C’est la vie maybe?

A New Semester

Today marks the first day of Fall 2009, the beginning of the second year of my graduate education.

I am enrolled in three mathematics courses. They are

• Math 676 — Modules and Linear Algebra
• Math 753 — Measure and Integration
• Math 781 — Differentiable Manifolds

I shall spare you the description of these courses. A few years back, I would have never imagined myself saying “I am taking some 700-level math classes.” Aside from these math classes, I am also taking Grad 810, a course titled “Communication for International Teaching Assistants.” I am not sure how this class is going to benefit me, but I should be able to gauge a week or two into the semester. I am seeking for a seminar which focuses on teaching tips and techniques as well as classroom culture, instead of the language barrier in English. I can always drop it if the emphasis is otherwise.

Furthermore, I am continuing my French language education. Je veux améliorer mon français (I want to improve my French). I spoke to the instructor of French 300, French Composition and Grammar, and she had graciously allowed me to sit in her class. As much as I would like to enroll as a regular student, I think I am better off without the extra stress from my obligations in my French class. If I have the time, I shall try to submit the assignments; after all, doing your homework and getting feedbacks on them are the best approaches in any language learning, I reckon.

Apart from my being a student in a classroom, I have the opportunity to play the role of an instructor. I have been assigned to teach Math 110 — Algebra this fall. Section 001 runs on Mondays, Wednesdays, and Fridays from 08:00 through 08:50 (See UNC Course Catalog — Mathematics). I do not know how exciting the material is going to be, but I am definitely thrilled to assume an instructor’s role officially for the first time.

As the new semester begins, I hope that the following four months will not be as rough as last fall semester, and I look forward to teaching Math 110 and to spicing up my French!