Pursue Your Passion and Results Will Be Unexpected — Boosting Your Career Through Independent Learning


I was trained to be a structural engineer but I want to be a theoretical physicist.

I was major in Japanese when I was a freshman in 2013. It was exciting and happy to study with so many young girls together: there are about 50 students who were major in Japanese but only five fellows! For a boy focusing on science side in high school in China, he had hardly seen over 10 girls during his whole high school life. Such a situation could not be better! Sadly, the boy read too many science popular books and was more curious about peculiar quantum mechanics, or even string theory at that time, so he decided to change his major. He first did some research on physics major in his university, but it turned out the people in the physics department look nothing like the characters in his book: Niels Bohr, Wolfgang Pauli, Richard Feynman, Albert Einstein, etc. As a result, he had to take the second best and went to civil engineering major, hoping he could meet more geek-like people there, since it was (and still is) the department with the most eminent professors and students in the country. He started his undergraduate training in structure engineering in 2014.

He got a bachelor’s degree in civil engineering in 2017 but his dream of becoming a physicist remained. It took about another two years to prepare for his physics PhD application, and finally, he got an offer from the Department of Physics of The University of Tokyo (UTokyo) on March 4, 2019. The boy is going to be a theoretical physicist! 

Yasuda Auditorium in UTokyo, image from google search

PART I: Why Do I Decide to Become a Physicist?

Cute Feynman
Feynman talking to Dirac

The thought of becoming a physicist started to haunt me when I was a high school student. I was intended to change my major to physics as mentioned above. However, the decisive moment was when I thought about what to do after graduation in the summer of 2016, when I just finished most of my undergraduate coursework in civil engineering.

I asked myself: what do you want to do as a career on which I need to spend over 8 hours a day, 5 days a week at least, of my time? It is about 8 / 24 × 5 / 7 = 0.23 ~ 1/4 of my time! I must be comfortable and happy about it, or my life will suck! The answer was not clear immediately but I tried to break the analysis piece by piece:

  • Do I want to find a structural-engineering-related job in the future? The answer was negative at that point. Structural engineering, as its name indicates, is too engineering for me. People in this subject don’t like to push the technology too much (I mean really push the technology to its boundary) because it is a very traditional subject. They care about real life problems, which I think is awesome, but the approach is just unattractive to me. After all, as long as you can build the bridge and it does not cost much, it is all right. Further scientific questions do not seem necessary in this area, most people just do not care about them too much. Of course, there are my very personal feelings. I just cannot get the interesting side of engineering. So structure engineering did not look like my game. I was and would always be a science geek, and would definitely look like a heretic in engineering area. Furthermore, I hate drawing blueprint. It is not my game.
  • Should I pursue a career to become a physicist? I was not 100% sure. Unlike civil engineering, I had not studied anything about modern physics seriously, so I was not sure whether I really enjoy physics. However, I did know many physicists, and they are all geeks, just like me. So it looked like I might want to be a physicist, or at least, to have physics-related career in the future. 
  • What should I do now? The catch here was that I was not familiar about physics so not 100% sure I should go that way. A reasonable choice was to teach myself undergraduate level physics courses on my own. When I become familiar about physics, I can make the decision. 

I started my undergraduate-level physics course self-study project in September 2016. Besides the reason stated above, another important reason for starting this project is the nature of physics learning (when choosing a career, it is better to know something about its nature in advance): there is no royal way to physics! In physics, you must build up concepts piece by piece, so there is no way I can do graduate-level physics without a thorough understanding of undergraduate-level physics. I quote Mark Weitzman, who is the best TA in all physics and mathematics online courses,  “One of the attractive features of theoretical physics is that it is tightly integrated (much more so than fields like mathematics) – and every area of physics engages in a large interaction and borrowing of techniques and concepts, from other areas of physics.“. It is very different from subjects like civil engineering, or finance, etc., where the technical entry barrier is relatively lower (I am not say other subjects are not important. They are of course very important. I am talking about some features of these careers). 

One thing I did not take into consideration at all at that point is what are the chances to be admitted to a PhD program in top institute for a student who does not have a traditional physics education background like me. I did not even ask around. One thing is that the cases of transitioning to physics from other fields are so rare, you could only find a few cases on the internet, and there were not many details about how they managed to do that (This is the main motivation for me to write this journal: I want to share my experience and hope it will be helpful to people who are physics-geeks like me but have a very non-traditional background.) The other reason is I know the answer would always be negative. The reason is simple, I quote Jim, the professor I met in a quantum mechanics online course who offered me a physics research opportunity, “The reality is doing well on the (physics) GRE but having a non-traditional background means your chances of getting into a top physics graduate school is very small, if not zero. They have no need to take a chance on you because they have so many traditional candidates available to them to pick from. Even research experience is not enough.

I did not care about how my application will be not because it is not important. The reason is that it was not a good question at that time. For example, the question that whether I can be admitted by MIT or Caltech is appropriate for a high school senior year school student, but is definitely not a good question for an eight-year-old child. I had not even started my physics undergraduate training, and was much like an eight-year-old child if facing the question about graduate school applications. So I didn’t think too much any more in 2016 and started my physics self-study project anyway. There was no time for hesitation. I was literally not eight years old, I was 21 then.

PART II: How Does the Self-Study Project Work?

edX, a massive open online course provider
MIT open courseware, or MIT/OCW
Coursera, a massive open online course provider
Caltech's Physics Course Schedule and Websites

The idea of starting a self-study project was inspired by Scott H. Young’s MIT challenge. He basically finished the entire 4-year MIT curriculum for computer science in one year. Then I thought to myself: I basically finished the entire 4-year Tongji curriculum for civil engineering in three years, so a challenge like Young’s looked very interesting. As a result, I started the physics challenge. 

Next decision was whether I should study physics using Chinese or English material. After some research, I found there were much more excellent learning materials in English than in Chinese. What’s more, the big treasure for  all independent learners (not necessarily for physics or computer science learners), MIT/OCW, has all its learning material in English, so my decision was to learn physics using English materials directly.

The main sources I used are the pictures I listed above (clicking on the pictures will take you to the corresponding websites). edX and Coursera are two massive open online courser providers (MOOC providers). MIT/OCW is the source Young used to accomplish his MIT challenge. Most courses in MIT/OCW provide syllabus, reading materials, assignments and their solutions, and exams. Some courses even provide lecture videos. A few courses (mostly first-year college courses like Calculusbasic physicsbiologychemistry, or basic programming) has the so-called OCW scholar version, whose learning materials are integrated carefully to make the study convenient for independent learners (the course number of such courses have an SC suffix). The truth is as long as you have basic English skills (high school level is enough for foreign learners), MIT/OCW is a fascinating place to learn college-level courses and to boost your life experience. A good lecturer knows about his/her audience and never assumes the audience knows everything, and will work you through all the details. You will find most lectures of courses in MIT/OCW are such good lectures. For physics learners, Caltech’s Physics Course Schedule and Websites is also a good place to find learning materials. 

How to study independently if given these sources? Different source formats have different learning experiences, but as learning process, the basic spirit is the same. Think about how we study in a college (or a high school). There are roughly three steps: attending lectures, completing assignments, and taking exams. The first two steps are crucial for independent learners. Since there is no lectures to attend, we will watch video lectures if the course provides, or read the textbooks. Then do the exercises. Doing exercises is the most important step. Nobody learns only by attending lectures or reading books, especially for science and engineering subjects. Practice makes perfect. Since doing exercises is important, it is recommended for the beginners to find courses providing assignments solutions, or to find the books with solution manuals. For exams, if the course (or the book) provides one, take it, if not, just forget it. Specifically, 

  1. For MOOCs and OCW scholar version courses, just take them as ordinary courses you take in school. They organize the material carefully for you. They are the best version for independent learners. 
  2. For courses on MIT/OCW and Caltech’s course schedule and websites, do what I suggested above.

One additional suggestion about independent learning. Most independent learners will have their own jobs to do on workdays. I was in structure engineering graduate school of Tongji while carrying on my self-study project. There was much work to do in graduate school. For a serious independent learner, it is necessary to plan carefully and write the learning tasks into your schedule. Another useful trick is to keep timing your learning process. It will give you an idea about how much work you spend into the self-study project. I typically spend 3 – 4 hours a day during workday on my self-study project, and about 5 – 7 hours a day during weekend. I had spent about 3000 hours on physics by the time I got UTokyo’s offer.

Timing my physics study
Timing my physics study

PART III: What Courses Did You Study Specifically?

For those who want to study physics on their own, I list all the courses I have finished, or partly finished in my undergraduate-level physics course self-study project.
(note: If the link below gives you an archived mode course in edX, you can search the course in edX to see whether there is a current-running version.)

From September 2016 to June 2017
Even though I know much about freshman level physics, I started my self-study project with two MIT’s freshman physics courses 8.01 and 8.02, mainly to get myself familiar with the whole self learning process and to get myself used to English environment. (one bonus fact: studying courses with video lectures and assignments in English is extremely useful for getting a high TOEFL score. I took my first try on TOEFL before the self-study project in May 2016 after preparing for three months and got 96. My second TOEFL exam was in April 2017, half a year after starting my project, without preparing for the exam specially, and I got 105.) Here are the courses I studied:

  1. 8.01.1x – 3x, Physics I, Classical Mechanics. I was lucky that edX version for 8.01, first introductory physics course about mechanics, was launched for the first time. It covers Newton’s vector formulation of mechanics. First you draw the forces and then do some analysis. As always, conservation laws are emphasized: linear momentum conservation, angular momentum conservation and energy conservation. Easy piece for me, and my final grade is (99+100+92)/3=97.
  2. 8.02Physics II, Electricity and Magnetism. I took the version lectured by Professor Walter Lewin. For some reason, Prof. Lewin’s lectures are not available on MIT/OCW anymore, but he kindly put all the video lectures on YouTube. The assignments and solutions can also be found in the introduction section of each video. Electricity and Magnetism is like magic in science, and Prof. Lewin’s demonstration shows the magic before your own eyes. I recommend this course for all people who are interested in engineering and science. It’s just exciting to see how electricity and magnetism work! BTW, there is a edX version 8.02x, but I haven’t taken it, you can take a look at it if you are interested. My final grade is 95.8
  3. 8.03Physics III, Vibrations and Waves. I took the version lectured by Professor Walter Lewin. There is a OCW Scholar Version of 8.03 on MIT/OCW now. I still strongly recommend Prof. Lewin’s lectures. Basically, this course deals with second order differential equations, wave equations and electromagnetic waves, from a physics perspective. Like 8.02, this course has lots of demonstrations, one of which is that your tune of speaking will become very high, and you will sound like a character in anime after inhaling the Helium. 8.03 will have many applications in engineering. One of my course on structural dynamics covers the similar material, less fundamental but more engineering. I nailed the structural dynamics course with knowledge I learned in 8.03 and got 98 in the exam. My final grade for 8.03 is 89.
  4. 18.031xIntroduction to Differential Equations. An excellent mathematics course that covers the simplest ordinary differential equations. It is normally taken by sophomore students in MIT. This course deals with second order differential equations too, but from a mathematical point of view. I recommend taking it with 8.03. I think it is a course that should be taken by every science and engineering major student. The world around us is described by the language of differential equations and this course is the first baby step to study them. I wonder why such a course is not in the curriculum for civil engineering in my university. My final grade is 99.
  5. An introductory course on complex analysis. A short course (less than 2 months) on basic complex analysis. Necessary for physics major students, but I am not sure its applications in other engineering disciplines. Surely enough electric engineering use complex analysis heavily, but structural engineering does not use it that much. This course covers analytical functions, contour integrals, residual theorem, and an introduction to fractal (something like Mandelbrot set). My final grade is 96.4.
  6. 6.00.1x – 2xIntroduction to Computer Science and Programming Using Python and Introduction to Computational Thinking and Data Science. Nice introductory level programming course and is suitable for all people who want to start learning to program. Better than any courses available in my home university. (our course is too old, c++ is suitable for professional programmers, not other people.) My final grade is (99+96)/2=97.5.
  7. Understanding Einstein: The Special Theory of Relativity. This Stanford course takes one step further from what you learn in freshman-year physics course about special relativity. It is designed for ordinary audience, high school level math is enough to learn this course. For physics-oriented students, this course can help you build up intuitions before diving deep into this subject. Not only does this course introduce many famous paradoxes in special relativity and their proper explanations, it also emphasizes the geometry side of special relativity: it is all about invariance of spacetime length for different observers, but not about “everything is relative”!
Spacetime diagram analysis for the twin paradox, screenshot of Stanford's special relativity course
Mandelbrot set, picture from Wikipedia
Alder and Wainwright's event-driven Molecular Dynamics algorithm (1957). (Animation by Maxim Berman).

From June 2017 to December 2017
I graduated in late June 2017, but had to continue my self-learn project. Poor me! 🤭🤭

  1. 18.03LTransfer Functions and the Laplace Transform and 18.032xDifferential Equations: 2×2 Systems. The two courses are in the same series course as 18.031x. I recommend them to all science and engineering major students. My final grade is (100+99)/2 = 99.5.
  2. Astronomy: Exploring Time and Space. Introduce basic ideas in modern astronomy. It is a relatively easy course.
  3. Statistical Mechanics: Algorithms and Computations. Excellent introductory level course on computational physics. It focuses on Markov Chain Monte Carlo (MCMC) sampling technique. There are three weeks  focusing on quantum statistical mechanics. My PhD work is very likely to focus on this kind of quantum Monte Carlo method. My finale grade is 88.6. The picture, Alder and Wainwright’s event-driven Molecular Dynamics algorithm, shown above is in one of the homework examples.
  4. 8.033Relativity. I was doing this archived version 8.033 because there were full assignments and solutions. It looks they are not available now. However, if you want to do this version, I can share the assignments and solutions since I downloaded all the materials. I only finished the special relativity part of this course, that is first 6 of total 9 assignments. The textbook of this course is Special Relativity by A. P. French. It is a lovely book. 
  5. 8.044Statistical Physics. This MIT/OCW course has full assignments and solutions. The lecture notes are very nice and I mainly followed these notes. I didn’t go through the course textbook, Kerson Huang’s Statistical Mechanics. I didn’t finish the exam for reasons I forget now. All in all, this is a nice course!
  6. W3003Mechanics. This is a course on slightly high-level classical mechanics, somewhat between freshman mechanics course and Goldstein’s Classical Mechanics. The original website does not work anymore, but archive has a back-up version. The textbook of this course is John R. Taylor’s Classical Mechanics. I enjoyed reading this book. The course website provides full assignments and solutions. 
  7. 6.041xIntroduction to Probability: Part I – The Fundamentals. It was the first part of MIT’s probability course. I highly recommend this course. The lecturer makes the concepts in probability theory crystal clear. In addition, Mark also recommend the probability course provided by Harvardx in edX. If you prefer Harvard to MIT, you should try that one. 

Year 2018
I described my physics study in 2018 in my journal  in detail here. Besides the ordinary coursework, Professor Jim Freericks and I worked on a research project, which was my first research in physics. I started my physics graduate school application in late 2018.

PART IV: How Do You Get the Offer from UTokyo?

Professor James K. Freericks
Professor James K. Freericks
Professor Naoki Kawashima
Professor Naoki Kawashima

It was mentioned before that the chances for an applicant with non-traditional educational background of getting into a top graduate school are very small. I was trained as a structural engineering but how do I get into the Department of Physics of UTokyo? 

I would say the crucial part is Professor Jim Freericks’s letter of recommendation. Jim and I worked on a research project in the second half of 2018, which is the only physics research experience I have. I describe this experience in my journal here.

Professor Naoki Kawashima, whom I chose as my supervisor in UTokyo is an acquaintance of Jim, so Jim’s letter means a lot to him. I believe this is the reason why UTokyo gives me one offer. I was actually not aware of such fact when I sent email to Prof. Kawashima. The reason why I found Prof. Kawashima is that I felt very interested in his research area. It was the course Statistical Mechanics: Algorithms and Computations provided by École Normale Supérieure that gave me such motivations.  

Everything comes naturally from my self-study project, though the most crucial ones come quite unexpectedly. However, that is why life is interesting, you never know what would happen. Hard work is necessary, and luck is also indispensable. 

2019 is a lucky year for me and I am going to be a theoretical physicist!

Give physics a huge hug!

Xinliang (Bruce) Lyu

Working on my way to become a theoretical physicist!

This Post Has 11 Comments

  1. Piyawat Jityen

    This is really inspiring my friend. Cheers from Thailand. Now I’m interesting in blockchain/quantum computing technology and I majored in philosophy at the undergraduate level. Now I’m working as a full stack developer. I will try to follow in your footsteps and pursue a graduate education in the field that I mentioned above.

  2. Amal

    Hi, what app did you use to track your self-study project?

    1. Xinliang (Bruce) Lyu

      Hi. I probably used a markdown software to keep track of the project back then. It is very easy to create a to-do list. One possible such markdown software is Joplin. But, there are other choices.

  3. Raf

    Hello, what an inspiring article to read! To pursue a phd in my intended institution, I am required to hold a bachelors degree in physics, do you have suggestions as to how I may receive a certified degree at a low cost within a 1 year timeframe ?
    I’ve been struggling to find a programme of this nature

    Thank you!

    1. Xinliang (Bruce) Lyu

      Hi, glad that you like the post. I have no idea about such programs. But, it is not necessary to insist to one single institution. There are many good PhD programs all around the world.

  4. Sherlock

    您好,在自学gr和搜索8.962的solution的过程中看到你的网站,收获颇丰!我很喜欢你自学的规划,也很羡慕你的效率和决心。我常常发现自己选做的题目难度不够好,也不能很好帮助我理解想要理解的东西,反而做8.962上有的problem sets会感觉学习到很多,但是网络上唯一有的solution(在知乎上)是自制的,也有一些小的错误。因此我想请教一下,在学习mit的8.962(gr and cosmology)的过程中,您的exercise是都选取的schutz的教材中的问题吗?您是直接刷完了所有的题目,还是有选择地进行练习?您选择题目是否有一些自己的窍门呢?期待您的答复,谢谢!

    1. Xinliang (Bruce) Lyu


  5. Armando

    Such an inspiring journey that you have. After 15 years away from physics I am trying to do the same.
    I wish you all the best

    1. Xinliang (Bruce) Lyu

      We are very luck to live in an internet era and so many high-quality learning resources can be found online.

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