2016-17 Season Recap

One year ago, I was uncertain about my future.

I had been living at my home for several months. I thought about getting a job and staying there for a while. I was happy to spend time with my family and my best mates. But when I got the funding letter from UTD, I swiftly booked a flight ticket to Dallas. I could not wait for another shot at the US and A. Ironically (and a bit sadly), I did not belong to home, not yet.

It was strange to be back at Dallas. The campus was familiar as always. I knew it like the back of my hand. Yet this time I was not a college student anymore. Now I was older, supposedly wiser, but I doubt I was any less foolish. It took me a few days to settle down. And in one unbearably hot day, so typical of Dallas, I met my graduate supervisor. He promptly made one of his graduate students cry in front of me. Wow!

Just like that, it did not take me long to decide I would need to leave this insane supervisor. The problem was he paid my tuition and stipend, so I had to wait. Soon I realized his research was not bad. My project was fun, at least I understood what I was doing. I coded everyday, and I was able to work with some interesting machine learning problems. In early November last year, I came to NYC to participate in a student competition related to my research. I prepared virtually nothing for my presentation but put on a brave face throughout. Of course I won nothing, but I liked it enough to want to give another shot next year. Somehow I thought it was okay to keep working with my supervisor.

Unfortunately, I could not escape the fact that he was truly insane. The next month, on Christmas Eve, he sent an email asking why I did not work. Then he forced me to come to the lab on New Year’s Eve. To do what? To prepare a syllabus for his class in the Spring semester. The madness did not stop there. The week after that, he threatened to fire me for not attending his lab’s weekly meeting. The only issue? That was the one and only meeting happening during the whole semester. I simply had enough. It was time for one more change.

I applied to the Computer Science department last Spring. I knew this was the right choice even though funding was not guaranteed. CS had always been my favorite subject. My best projects during college were always in CS classes. I should have moved to CS three years ago, but I thought I would enjoy being an electrical engineer, and it was a safer option since I got accepted to graduate school as an electrical engineering major. I pushed on, hoping that somehow it would work out in the end. That was perhaps my biggest mistake to date. But I do not regret making that decision. Failures and mistakes are needed because eventually they guide me towards the right way.

Now the 2016-17 school year has ended. And I’m alive. And still jobless. I tried to find some internship, or at least some on-campus job, but I cannot. The potential employers from industry are not impressed with my experience. The only “job” I’ve ever had is being a research assistant. They rather recruit a software developer with Javascript and/or Mobile Dev experience, not some daydreamer who has an empty portfolio. On-campus job? Funded graduate students are ignored. They must be thinking that the school has paid me enough money. It totally makes sense. I cannot complain. I have to do something else.

When summer began, I considered joining some program related to data science and machine learning, and one such program stood out: Udacity Self-driving Car Nanodegree. It is one thing to learn about deep learning, but learning leads to nothing without practice. I need a fun topic to apply machine learning, and I love driving cars myself, so why not try self-driving cars? Plus the self-driving car industry currently needs a lot of talents. I should give it a try. Even in case self-driving car is not for me, I can still apply my machine learning experience into another field. I cannot lose in this game.

In near future, besides the Nanodegree program, I hope to accomplish two things: (1) start a great project of my own, and (2) finish a large portion of a rigorous book (it should be Pattern Recognition and Machine Learning by Chris Bishop.) I believe there will be a lot of posts on these projects. I will write more to organize my thoughts on my study of artificial intelligence and machine learning.

A new beginning.

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Nirvana – Unplugged in New York (1994)

Although it is a great album, I am often hesitant to choose Unplugged in New York from my library. Each time I listen, it seems I can feel the pain of Kurt Cobain. Listening to the whole performance is really an experience with a man nearing his death. It is haunting and emotional.

Nirvana and Kurt Cobain choose only a few hits for the whole evening. Instead, they play covers and invite another band, Meats Puppets, to join them for three songs. It is a rare opportunity to hear Nirvana in a variety of genres and to appreciate Kurt’s versatility. Highlights among the covers include Jesus Doesn’t Want Me For A Sunbeam and The Man Who Sold The World.

While the covers show Kurt Cobain’s talent, the originals reveal his emotions and his tortured life. About A Girl, Come As You Are, and All Apologies are my favorites. For me, it is always tough to go through the middle of the album, where the most depressing moments reside.

Although the Meats Puppets songs are very good, Kurt still has one more trick up his sleeve. Nirvana ends the show with a traditional blues song, Where Did You Sleep Last Night?, arranged by Lead Belly. Hearing Kurt screaming at the end gives me goosebumps. It is such a brilliant performance that makes me grieve his untimely death even more.

The potential is there. The talent is there. He just dies too young, too soon.

Youtube playlist (DVD version):

Tracklist: (bold = favorite)

About A Girl
Come As You Are
Jesus Don’t Want Me For A Sunbeam
The Man Who Sold The World
Pennyroyal Tea
Dumb
Polly
On A Plain
Something In The Way
Plateau
Oh, Me
Lake Of Fire
All Apologies
Where Did You Sleep Last Night?

Quái Vật Tí Hon – Đường Về (2011)

Có lẽ khoảng 6 năm qua, từ ngày bước chân vào đại học, không có album nào gây cảm xúc mãnh liệt cho tôi như Đường Về. Album này là đứa con tinh thần của Nguyễn Công Hải, hay còn gọi là Hải “Bột”. Hải Bột là một gã nghệ sĩ thích lang thang phiêu bạt. Dù từng là thành viên của ban nhạc Microwave khá nổi tiếng một thời, nhưng Hải Bột sinh ra không phải để trở thành một nghệ sĩ sáng tác và chơi nhạc để kiếm tiền. Mà kể cả anh ta có muốn thì cũng không thể. Trong thời buổi mà âm nhạc chịu ảnh hưởng của giới truyền thông và hiệu ứng đám đông nhiều như hiện nay, thật quá khó để một nghệ sĩ như Hải Bột hái ra tiền. Cũng không quá bất ngờ khi tôi chẳng mấy khi gặp một người biết về Quái Vật Tí Hon, chứ chưa nói đến yêu thích album Đường Về. Nhưng tôi đoán điều đó cũng chẳng bao giờ khiến Hải Bột bận tâm. Anh làm album này vì tình yêu cháy bỏng với âm nhạc. Đơn giản là vậy thôi.

Với Hải Bột, Quái Vật Tí Hon thuần tuý chỉ là một dự án âm nhạc. Anh tập hợp một nhóm bạn để chơi nhạc và thu âm. Vì thế nên khó có thể trông chờ về khía cạnh kỹ thuật chơi nhạc. Dù tôi không phải là người am hiểu về nhạc lý hay kỹ thuật nói chung, tôi vẫn nghĩ kỹ thuật của QVTH chỉ đạt mức chấp nhận được. Giọng hát của Hải Bột cũng không quá đặc sắc. Xuyên suốt album có thể thấy không có nhiều đoạn hát khó đòi hỏi kỹ năng hát điêu luyện. Nhưng tôi nghĩ ở Việt Nam cũng chẳng có mấy ban nhạc có khả năng chơi nhạc ở đẳng cấp cao. Điều quan trọng hơn là tất cả những nhận xét về kỹ thuật đều vô nghĩa với Đường Về. Nó là sự lên ngôi của cảm hứng sáng tác của Hải Bột. Nó thấm đẫm cảm xúc và tình người.

Quai-vat-ti-hon

Ngay từ bài đầu tiên, Qua Ô Cửa Thời Gian, tôi đã cảm nhận được ngay sự quái trong âm nhạc của Hải Bột. Âm nhạc lên xuống trầm bổng dường như chẳng theo một quy luật cụ thể nào. Những gì đọng lại trong người nghe ngoài xúc cảm trong âm nhạc là những vần thơ đậm chất Hải Bột. Anh nói về tình yêu nhưng không phải chỉ là tình yêu đôi lứa. Đây là tình yêu với cuộc sống. Tình yêu với mọi thứ xung quanh ta.

Các bài hát trong album là những câu chuyện rất người, rất thật. Hải Bột như đem những trải nghiệm sống của mình lên giấy trắng, rồi dùng âm nhạc tô điểm để biến chúng trở nên những bức tranh sinh động, gần gũi với người nghe. Từ những câu ngông nghênh như “Giờ ta mới biết mình khờ mình ngu” trong Ô Trống, đến những tình cảm trìu mến dành cho đứa con thơ trong Có Một Mặt Trời. Tôi đã từng không cầm được nước mắt khi nghe thấy tiếng đàn bầu trong đoạn cuối của Có Một Mặt Trời. Hiếm có bài hát nào lại khiến tôi nhớ cha mẹ và quê hương của mình đến vậy.

Bốn năm đại học là bốn năm tôi nghêu ngao hát Ông Trời Cô Đơn, Ô Trống rồi cả Vợ Ơi Anh Đã Sai Rồi. Đôi lúc tôi lại say sưa với Đường Về với những suy nghĩ vẩn vơ về quê nhà. Không biết với người khác thì sao, tôi thì rất thích cái chất phiêu và chất ngông trong âm nhạc của Hải Bột. Nó có lẽ cũng là hình ảnh mà tôi luôn muốn hướng đến: sống hết mình, đôi khi ngông nghênh một chút, bất cần một chút, dám nghĩ, dám làm. Thực sự thì trong album tôi không thấy bài nào là dở cả. Tôi tin tất cả đều là những trăn trở, những ấp ủ của Hải Bột trong nhiều năm xa rời với phòng thu âm.

Trước khi dừng bút (hay dừng phím), tôi muốn nói về bài hát tôi thích nhất trong album – Đã Bao Lâu Rồi. Chắc hẳn khi lớn lên, chúng ta cũng đôi lần tự hỏi: Đã Bao Lâu Rồi chúng ta chưa có được sự bình yên trong cuộc sống. Cuộc sống vốn có biết bao nỗi lo cơm áo gạo tiền, biết bao giấc mơ còn dang dở, biết bao mồ hôi và nước mắt. Nhưng đôi lúc chúng ta vẫn phải tĩnh tâm, gạt bỏ mọi suy nghĩ, thả hồn vào khoảng không vô định. Không phải tự nhiên mà tôi rất thích nghe bài này trong những lúc đi dạo quanh trường đại học. Khi nghe Đã Bao Lâu Rồi, tôi luôn hình dung ra một ngày mùa đông. Bầu trời hơi âm u. Tôi khoác một chiếc áo rồi rảo bước với những suy nghĩ bâng quơ. Tôi chẳng biết mình nghĩ những gì trong những giây phút ấy. Chỉ cần biết khi bước về nhà lòng tôi lại nhẹ đi. Niềm vui và hạnh phúc đôi khi chỉ giản đơn vậy thôi —  tâm hồn của mình được bình yên.

Cảm ơn Hải Bột và Quái Vật Tí Hon vì tất cả. Tôi mong sẽ được thưởng thức album mới của anh trong một ngày không xa.

Playlist từ Youtube:

Tracklist: (bôi đậm = bài hát yêu thích)

  1. Qua Ô Cửa Thời Gian
  2. Ô Trống
  3. Ngày Hôm Qua
  4. Có Một Mặt Trời
  5. Đã Bao Lâu Rồi
  6. Vì Đời
  7. Kẻ Lạ Mặt
  8. Vết Nhơ
  9. Đường Về
  10. Vợ Ơi Anh Đã Sai
  11. Ông Trời Cô Đơn
  12. Cho Con Được Trở Về

Does Enjoying Music Require (A Lot Of) Money?

A friend once told me that he would never buy a pair of headphones because the stock Apple earbuds are good enough. He really does not see the point of spending money on something that would not make a difference. Meanwhile, my best friend constantly switches his audio gears. He would buy new earbuds, headphones, DAPs (digital audio players/mp3 players), and amplifiers once in a while. He always says to me things like “you must buy a good amp”, “your HD 650 sucks without an expensive amp”, “Fiio X1 is a bad DAP, only X5 can provide good sound”.

The question is between the two, who enjoys music more? Which approach leads to the musical heaven/nirvana? Unfortunately, there is no simple answer. It depends on many aspects, both technical and personal. In this article, I will give my thoughts on the issue of investing on audio gears.

Audio Gears Basics

I will focus on the most popular music playback method of today, i.e. using audio files with extensions such as mp3, m4a, and flac. The music sound (which we can hear) is converted by some machine called ADC (analog-to-digital converter) to digital files (which we obviously cannot hear) for storing purpose. From a scientific perspective, it is really magical that human can convert natural sound to a long string of ‘0’ and ‘1’.

When we listen to music using computers or smartphones, we need to use several parts that make up an audio chain. First, we use a DAC (digital-to-analog converter) to convert digitized data back to analog signal — natural sound that human can hear. Then that signal is usually processed and amplified by an amplifier. The output of the amplifier is exactly the headphone out that we use to plug our headphones or speakers. Of course, the audio chain can get much more complicated, but basically there are two sections mentioned above: a DAC and an amplifier. Any computer, smartphone, or mp3 player that can play audio files will have a DAC and an amplifier integrated. Although the quality of audio also depends on the circuit design or circuit parts, for the sake of simplicity, let’s assume only the DAC and the amplifier will decide the final quality.

You may wonder what is the big deal with this DAC and amplifier discussion. After all, any functional computer can play audio files, right? The problem is, computer and smartphone makers have no reason to focus on the audio section of their systems. They only need it to work. As a result, designers tend to use parts with acceptable quality, but nothing that can be considered hi-fi. Size is another matter. It would be suicidal to add a big amplifier circuit to the iPhone and make it look like a cube. That said, it is wise for a beginner to invest in a good (and affordable) DAC/Amp combo, especially if you mainly listen to music via a laptop. It will make a huge difference because you probably have always used onboard sound.

Examples of affordable DACs for computers are the FiiO E10K and the AudioQuest DragonFly. I do not know about Android devices, but from my experience, the DAC from the iPhone and iPod are quite good. As long as you can get the line out (means you can bypass the built-in amplifier) and feed it to an external amplifier, you are good to go. Talking about portable devices like smartphones lead to the discussion of DAPs – Digital Audio Players. They are portable music players like the iPod, but besides playing audio files, they also try to achieve high-fidelity.

Currently I only own one DAP, an iPod Video. I used to have the Sansa Clip, Sansa Clip+ and some Rocoo DAP which I did not even remember the model name. Right now I’m happy with my iPod Video (5.5th generation) plus the CmoyBB amp (made by JDS Labs, only $59.99). I plan to buy a Fiio X1 next fall. I would like to try Fiio hardware, and it is good to have a backup DAP just in case. Note that quality players like Fiio X1 already has capable DAC and amplifier integrated so unless you have a fancy pair of headphones, you do not need to think about buying another DAC/Amp combo for a while.

To sum up, my recommendation for beginners is to buy a good-quality DAC early on. A DAC/Amp combo like the Fiio E10K is not expensive, and it will improve your computer-based audio system immensely. In case you do not want to enjoy music near a computer, a Fiio X1 or similar players, even an iPod Nano, will be enough.

Now let’s discuss the front men of the band: headphones.

What do Headphones bring to the table?

The stock earbuds by Apple are ok. Indeed for many people, these earbuds are the best sounding devices they have. I must say I like these earbuds myself. They are comfortable, they sound good, and their price are acceptable at $30. The question is: what can higher-quality headphones do that the stock earbuds cannot?

The short answer is, more expensive headphones tend to do everything better. The ultimate goal of headphones is to reproduce the music as realistic as possible. And the stock earbuds cannot satisfy that goal. While there are many aspects in sound, I will only focus on two things that quality headphones (like my HD 650) gain the upper hand.

The first thing I notice with quality headphones are the details in their sound. I will hear new things when I listen to a familiar album. With better instruments separation, for example I can focus on guitar lines in a song instead of the vocals. The musical instruments would sound much more natural as well. Some music, supposedly boring with ordinary headphones, really comes to life with quality ones. You can close your eyes and imagine the band playing in front of you. I doubt you can do the same with the stock earbuds.

Another important thing in music that I recently realize is the bass. I heard somebody said the bass is the soul of any song. The bass makes you feel the music. I don’t think I’m a bass-head, but I always miss the bass impact of the HD 650 when I listen to other headphones. The bass from the stock Apple earbuds are not only inadequate in amount, but also muddled. It is challenging to hear a bass line in a song with these earbuds. A high-quality headphones may change all that. Deep, strong yet controlled bass will keep you engaging with music for hours (and forget checking your Facebook at the same time.)

Choosing Headphones 101

I think there are roughly five tiers of headphones as followed:

~ $10: With this price, the best you can expect is something durable and functional. If I have $10, I will mainly look at earbuds. VE Monk and Fiio EM3 may be smart choices for this budget. I also owned the Koss KSC75 and was satisfied with these babies.

~ $50: Believe it or not, you can get musical headphones for roughly $50. They will be upgrade from the stock earbuds. The Koss Portapro used to be my dream when I was in high school. Though I never listened to it, I think I would love it because they are mostly known as good dark headphones (translate: bassy and musical headphones). Another example: Sennheiser PX-200.

~ $150: I bought the Audio Technica ATH-M50 when I was a freshman in college. It is still very popular in this price range. But another headphones that I own, Sennheiser HD 598, cost only $150 nowadays. They are both very good all-round headphones, and there are many many other choices in this range. You should expect better details, clarity, and bass from the $50 tier.

~ $400: This is the current price of the HD 650. You may question the big jump from $150 to $400. It is normal. You need to invest more and more money to reach another stage in the headphones game. I will write about my beloved HD 650 in more details later. For now, I will just say, they are worth every penny even though they are $400. In this price range, many headphones can be considered hi-fi, and most of you can forget about buying another pair of headphones. Also, this is the end game for all-round headphones. More expensive headphones will be designed towards a unique sound that you may not like. Other examples: Hifiman HE-400i, NAD Viso HP50, Philips Fidelio X2.

> $800: I doubt I will buy these expensive headphones anytime soon. I know next to nothing about the expensive headphones, so just skip reading this article if you have this much money to burn.

For me, the headphones are the most important section in the audio chain. If I have $400, I would spend on the HD 650 instead of the ATH-M50 plus a DAC/Amp combo. The HD 650 may not reach its potential with an iPod or a smartphone, but it still sounds better than the ATH-M50 does. As I mentioned in earlier paragraphs, an acceptable DAC/Amp combo that can drive the HD 650 is not expensive. It is better to prioritize the headphones instead of DAC/Amp/DAP.

Instead of giving you advice or recommendation about headphones because each of you has a different taste of music, I will discuss my method of choosing headphones for myself. I like to focus on music so my ideal listening setting must be comfortable and quiet. That means I like enjoying music at home. It leads me to prefer full-size headphones. For me it is the most comfortable type of headphones.

I like many genres of music, and I want to discover other genres so I like all-round headphones. I also want deep bass along with laid-back and musical sound, not analytical and crystal clear sound. The reason is I want to feel the music without fatigue (analytical headphones tend to cause fatigue). That might be the reason I am a fan of Sennheiser headphones. They make quality, open-back, comfortable, dark headphones geared towards home use. As simple as that.

Back to the Title Question…

I believe listening to music is actually a cheap hobby if you spend money wisely. A simple yet very musical system (for example, Fiio E10K + Koss Portapro) may cost only a little over $100. You can even just buy the Koss Portapro and forget about DAC/Amp at the moment. Unless you are unlucky, audio stuffs are reliable and will keep working for a long time. Let’s assume you will enjoy that system for two years, then $100 is next to nothing when compared to other expenses in your life. Just remember to prioritize the headphones when building a system.

A common reason that people are reluctant to spend money is they cannot see the improvement in the sound. For some newcomers, the Koss Portapro might even sound worse than the familiar Apple earbuds. It is not surprising and easy to explain. If you never listen to a variety of headphones before, your ears will not be very sensitive to different frequencies of sound. Take your time. Gradually you will begin to hear new details. Sooner rather than later you discover that your favorite albums just sound better. No doubt you will be happy in the long run.

Though I am not an audiophile nor an expert, these days I usually have a beaming smile on my face each time I put the HD 650 over my ears. Music with them is just wonderful. Indeed, at these moments everything is wonderful. I’m glad that all the years with this hobby have paid off.

If you want to read more:

What we hear – Nwavguy
The dark HD650 – Headfonia
Closed headphones round-up – Headfonia
CmoyBB – Headfonia
Thoughts on DAP – Headfonia

New Direction for My Blog: Music

It has been months since I wrote anything on this blog. Truth be told, my life in the last year could be called madness. I went through a lot for the last 10 months or so. But I will not write anything about it. I learn that I tend to share my personal stories, or sometimes I like to write about self-improvement. I must be influenced by authors/bloggers like Cal Newport and Scott Young. Sadly, I am not really good at improving myself, and my personal stories are not interesting, at least at the moment. I know you don’t care about it either, so I will not waste more of your time as well as mine.

Last year, I tried to write another blog on music but failed. The approach was wrong. I wanted to mimic music review sites without having any deep knowledge of music. I should have written about my favorite music, not things that I think would impress readers. I will write again though. The reason is my Sennheiser HD 650 headphones. These babies surprise me even though I own several so-called hi-fi (or mid-fi if you like) headphones before. They are so addicted that I usually stay up late just to listen more music. They are so musical that I believe it is worthwhile to share my joy with others. It makes me believe writing a blog about music is a great way to relax.

As I said above, I like to have something personal in my blog. After all, I do not want my blog to be another newspaper. It should reflect my thoughts and my personality. On the other hand, I hate to write about my personal life. Music will be a nice solution. By discussing my favorite albums, you will be able to learn more about who I am and how I think. Maybe you will understand me much more than ever before because music is a big, big part of me. It is also great if I can make friends with people who share my passion for music.

I also debate with myself whether I should write my blog in Vietnamese. Writing in Vietnamese will make it easy to read for the majority of my friends. Maybe it is a good thing. However, most of my friends don’t care about my taste of music. Those who are serious will need to read in English anyway since most in-depth articles on the internet are only available in English. Remember, English is the universal language. There is no way escaping it. If I talk about a Vietnamese album or a Vietnamese artist, I will still use Vietnamese. I think it is quite self-explanatory.

Besides this blog, I think in the future I will focus more on music in general. I have decided that I must be good at playing a musical instrument. I will save up money to buy an instrument again. I always dream that I can wow people with music. Before you judge, please, just let me dream.

Book: Intelligence by Stuart Richie

My Old Impression of Intelligence

I used to ridicule the IQ test. To me, it is nothing more than another test, and I hate tests. The IQ test also does not help its cause by sharing common segments with other standardized tests I have taken like SAT (for college) and GRE (for graduate school). Personally I have not seen much correlation between high scores in standardized test and intelligence. I have met people with impressive test-taking skill but not-so-impressive ability to do complex work. In short, I never bothered to think about the IQ test.

I even did not care much about intelligence. I like to believe most of us could achieve anything by working hard and working smart. Of course, being smart does not hurt, but intelligence should not be so important that it can make or break a career. However, my belief is dismissed by Stuart Richie in his book Intelligence: All That Matters. Stuart uses many research results spanning from the 19th to 21st century to make his point: people have different intelligence, and intelligence matters.

Intelligence Does Matter (sometimes, a lot)

Before trying to understand about intelligence, we should have a clear and succinct definition of intelligence. Here is the definition of intelligence given by Gottfredson, an expert in intelligence research:

Intelligence is a very general mental capability that, among other things, involves the ability to reason, plan, solve problems, think abstractly, comprehend complex ideas, learn quickly, and learn from experience. It is not merely book-learning, a narrow academic skill, or test-taking smarts. Rather, it reflects a broader and deeper capability for comprehending our surroundings, ‘catching on’, ‘making sense’ of things, or ‘figuring out’ what to do.

Great, the definition alone answers several of my questions about intelligence. From my experience with people, the not-so-smart ones almost always have serious troubles with abstract and complex ideas, and they seemed to be hopeless with reasoning and learning from experience. The definition also explains about the people who could easily outsmart standardized tests but could do not much else. I have also wondered why some people repeatedly interpret information, even straightforward ideas and facts, in the wrong way. It is frustrating because they could not learn much from books even if they spend considerable time and effort on reading. After all, “Making sense” of things is an important part of intelligence.

Can We Improve Our Intelligence?

Okay, intelligence varies from person to person but is there any way to improve our intelligence? Stuart answers the question using a chapter called “The easy way to raise your IQ”, only that he does not mention any way at all. (He admits that the chapter title is just a bait). At the current state, researchers around the world still do not know which is the easiest and most convenient method to raise our IQ. Should we feel depressed?

Sadly, for some people, the answer is yes. It is because the best way to raise the IQ, in my opinion, is to read good books, take good courses, learn from great people, and learn from experience. However, for a person who is not intelligent enough, how on earth can he differentiate a good book from a bad one? From my somewhat cynical point of view, the same person probably also listens and follows other stupid people. He will not learn anything from his experience and keep repeating his mistakes. That is the dilemma of intelligence. If he could do better, then he would not have needed to raise his IQ so badly.

I think if I am intelligent enough, but not successful as I might like, then my problem is likely not about my intelligence. Maybe the problem is about my perception, my vision, my friends, my character, my habits, et cetera. Heck, even if I am not smart, I will try to solve other problems anyway.

Another point Stuart makes in his book is that even among highly intelligent people, intelligence still matters. What if I am not as intelligent as my competitors? I will try to do two things: think and do.  Regardless of the problem, the more I think about it, the better chance I will solve it. Maybe my competitors are smarter and they can solve the problem faster, but they still have to spend time. They still could not do it in an instant, and there is a chance that they will not even solve the problem at all. No matter what others do, I will continue to reap the rewards by working hard. It might be more difficult for me, but it should not matter. As long as I have fun doing what I do, I will be happy. At least in my field of science and engineering, experience is as important as intelligence.

The bottom line: There will be people who are more intelligent than you, it is okay, and it is natural. Just do your best and enjoy your work. Improvement, however small you think of it, will count in the end.

Linear Algebra (LAFF) by UT Austin – Course Review

Course profile:

  • Link:                LAFF at edX
  • Professor:       Robert A. van de Geijn
  • Institution:     The University of Texas at Austin
  • Date:                Summer 2015
  • Platform:        edX

Linear Algebra was the first real mathematics course I decided to take for my current project. While the importance of linear algebra cannot be overstated, it is not exactly an accessible subject. I already took a Linear Algebra course in college, but I did not learn much (as usual, sadly). From my memory it was just another frustrating class that I stood in only to fulfill my degree requirements.

How It Went Wrong at College

My Linear Algebra professor at college focused the entire course on the techniques of linear algebra. These techniques included simple matrix-matrix multiplication, Gauss-Jordan elimination, projection, orthogonality, fundamental spaces, linear least-square, and eigen-blahblah. If you have some experience with the subject (and you really remember it), you should find those topics familiar. So in a way, my professor did teach everything he was supposed to teach. Except he did not.

The techniques, while indeed important to master, do not tell the whole story of Linear Algebra. It is not about applications either. I appreciated that my professor made some effort to give a recitation each week (most courses in my college did not even have recitation). He and the teaching assistants gave several presentations about the cool applications of linear algebra, such as image compression in JPEG file. Still this information did not help the students, including me, at all. The one thing that my professor forgot to teach, or deliberately avoided, is the same thing that should have made students fall in love with linear algebra: the insight.

Why LAFF Works for Me (and For You)

Techniques make up only a small part of LAFF (Linear Algebra: Foundations to Frontiers). This should not be surprising. With the ubiquity of matrix libraries as good as MATLAB, we can use a computer to apply the techniques. What we should do instead is teaching the computer to solve problems for us. In addition to computation techniques, this goal requires a deep understanding of linear algebra.

Prof. Robert van der Geijn, who teaches LAFF, insists that insight can only be gained by doing mathematics. In this class, that means understanding proofs and proving theorems. In fact, Robert make all the answer keys available at the beginning of the course. A student who just wants a certificate (like the old me in college) could just enter all the answers and get a good-looking piece of paper without even knowing what Linear Algebra is. The reason for this approach is it makes absolutely no sense to use the techniques without understanding the proofs. Proofs are not created for a specific kind of creatures called mathematician. They are important for anyone who wants to learn mathematics the right way.

Admittedly I did not dare to read even one proof in the linear algebra class in college. I even did not remember the professor mentioned any proof, or whether he included proofs in the homework and exams. (He did not!) Sadly, it was and remains the standard teaching method of mathematics nowadays. I will definitely write more about the topic of mathematics teaching in near future.

Back to the course, it was the first time I tried to make proofs by myself, without any external motives like homework or exam. It may sound extremely nerdy, but math has changed me, inside out. I’m a changed man. Suddenly I find myself interested in reading and understanding proofs. My attitude towards Linear Algebra and Math in general turns a complete 360 degrees. Now I am eager to learn more. It’s crazy, but finally it seems I have found my favorite subject.

Studying math should be like this. It should be about thinking, exploring, proving, arguing and imagining. It should be a creative process, not a mechanical one like what is taught in school.

I want to thank Prof. Robert van der Geijn, his wife, and his assistants for an excellent course. Really they taught me to love math.

(Image Source: http://ulaff.net)