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)

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.

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.

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!

PhD Comprehensive Exams

What a stressful week!

I sat for the Topology exam on August 19 and the Analysis counterpart on August 21. Comprehensive exams (sometimes referred to as qualifying reviews or preliminaries) are 3-hour exams, each covering two-semester course material in the introductory graduate-level curriculum at UNC Chapel Hill. For example, the Analysis exam I took is a cumulative exam for Math 653 and Math 656, Real and Complex Analysis respectively. In short, it’s about cramming a year worth of material, for each subject. Passing these PhD comprehensive exams are crucial to moving towards your PhD candidacy. These exams are administered twice a year (in January and August).

I have to pass three exams in total — Analysis, Algebra, and Topology. I hope that I can pass both I just sat for. However optimistic I am trying to be, I am well aware that I did not prepare well for my Topology exam. While I keep my fingers crossed, it is certainly likely that I have to retake my Topology comprehensive exam early next year.

If you are interested in taking a peek at the questions, click here: UNC Analysis and Topology Comprehensive Exams (Fall 2009).

AAB is now Tun

We shall address the outgoing Prime Minister of Malaysia by Tun Abdullah Ahmad Badawi from today onwards.

As Najib takes over Abdullah’s position, I attended a seminar today on Malaysian politics at UNC. The talk, titled The Najib Administration: The Politics of Reform in Malaysia by Dr James Chin was organized by the Carolina Asia Center. He gave a brief background on UMNO, which ran a gamut from the Malay supremacy (ketuanan Melayu) to money politics. He discussed several prominent issues that are going to beleaguer Najib as soon as he takes the oath at the Istana Negara, which includes, but not limited to, the New Economic Policy (which he wittily dubbed at the Never Ending Problem), stronger opposition, the rising of SAPP etc. He briefly mentioned Anwar Ibrahim and his sodomy charges. After the seminar, I could not help but thinking that Malaysia would serve as the best option for a political science student who needs a case study to work on.

Dis-moi, lune d’argent

Lately, I listened to a French song in my French class, as required by the syllabus. The lyrics was rather bizarre and maybe a little disturbing. Otherwise the song was fine. Guess what — the tune is stuck in my head now. Ahh…

I shall bestow you the opportunity to enjoy the music. Then, if you would like to understand the lyrics, scroll down; I provided both French and the translated English version (quoted from elsewhere).

***

J’ai recemment écouté une chanson française pour mon cours de français, comme requis par le programme. Les paroles étaient plutôt bizarres et peut-être un peu inquiétants. Sinon, la chanson était bien. Maintenant, la musique est resté gravé dans ma tête ! Oh la la …

Je vous partage la musique. Si vous voulez comprendre les paroles, regardez à la fin de journal; je fournis les deux versions des paroles.

Click here to listen. Cliquez ici pour écouter.

En français (in French):

Idiot qui ne comprend pas
la légend’ qui comme ça
dit qu’une gitane
implora la lune
jusqu’a lever du jour
Pleurant elle demandait
un gitan qui voudrait
l’épouser par amour

Tu auras ton homme, femme brune
du ciel repondit la pleine lune,
mais il faut me donner
ton enfant le premier
dès que te sera né
cell’qui pour un homme
son enfant inmole
bien peu l’aurait aimé

Refrain:
Lune tu veux être mère
tu ne trouves pas l’amour
qui exauc’ ta prière
dis-moi lune d’argent
toi qui n’as pas de bras
comment bercer l’enfant
Hijo de la luna

D’un gitan canelle
naquit l’enfant
tout comme l’hermine
il ètait blanc
ses prunelles grises
pas couleur olive
fils albinos de lune
Maudit soit-tu bâtard!
t’es le fils d’un gadjo
t’es le fils d’un blafard

Refrain

Le gitan se croyant déshonoré
couteau en main sa femme alla trouver
l’enfant n’est pas de moi
tu m’as trompé je vois
à mort il la blessa
Et l’enfant dans ses bras
la colline il monta
là-haut l’abandonna…

Refrain

Et les soirs oú l’enfant joue et sourit
de joie aussi la lune s’arrondit
et lorsque l’enfant pleure
elle décroit pour lui faire
un berceau de lumière

En anglais (in English):

Foolish is he who doesn’t understand.

A legend tells of a gypsy woman
Who pleaded to the moon until dawn.
Weeping she begged
At the break of dawn
To marry a gypsy man.

“You’ll have your man, tawny skin,”
Said the full moon from the sky.
“But in return I want your first child
Whom you have with him.
Because she who sacrifices her child
So that she is not alone,
Isn’t likely to love it very much.”

Chorus:
Moon, you want to be mother,
But you cannot find a love
Who makes you a woman.
Tell me, silver moon,
What you intend to do
With a child of flesh.
A-ha-ha, a-ha-ha,
Son of the moon.

From a cinnamon-skinned father
A son was born,
White as the back of an ermine,
With gray eyes instead of olive –
Moon’s albino child.
“Damn his appearance!
This is not a gypsy man’s son
And I will not put up with that.”

Chorus

Believing to be dishonored,
The gypsy went to his wife,
A knife in his hand.
“Whose son is this?
You’ve certainly fooled me!”
And he wounded her mortally.
Then he went to the woodlands
With the child in his arms
And left it behind there.

Chorus

And the nights the moon is full
It is because the child
Is in a good mood.
And if the child cries,
The moon wanes
To make it a cradle.

Solution – Convergence of A Sequence

So here you go – the solution to my previously posted problem. You may download it in any two formats:

• PDF
• TeX

Have fun!

Please let me know if I make any mistake. Thanks!

Convergence

Hey folks!

I have been super busy of late. I shall write more on my graduate school experience (as a neophyte) later in a separate post during fall break. In the mean time, I have an interesting problem to share with you:

To all readers with single-variable calculus background (US Calculus II equivalent; UMICH Math 116 equivalent; UNC Math 232 equivalent): Determine whether the following sequence converges or diverges. Justify your answer.

I shall reveal the answer in a week or so. Happy attempting!

How Dreadful!

For the past week, I have been trying to savor the excitement of being at a new place, a new school, a new campus, and a new environment. I look forward to getting acquainted with my fellow graduate students, especially the first-year students. I have been attending graduate level mathematics classes. However, I was (and still am) rather overwhelmed by some of my classes, especially my favorite analysis.

My analysis homework (and lectures) inundates my first week with pressure, stress, and to some extend, fear. The professor speaks at the speed of light, even when he presents unfamiliar proofs of new theorems and/or propositions. I am lost in the class. The homework is a nightmare. The problems assigned are excruciatingly difficult. They macerate my confidence in shreds. I could spent countless hours on a single problem and ended up not knowing where to even start. It certainly does not feel good.

Last week, when I first felt really down (and before I spoke to anyone), I experienced a mild depression. I was feeling blue for the rest of the evening (after sitting in a 1.5 hours long lecture not understanding a single thing), and I experienced insomnia that night. I tried not to think of what happen – but my instinct told me this is “alarming” and I worried nonstop.

Thank goodness I spoke to a couple of people about what happen. Most of them, especially my former professor whom I consider a friend, gave me useful advices. I managed to stay more positive and I have been starting to feel better…

Wish me luck. I really need them this time…