쉐도잉 연습: Essence of linear algebra preview - 영상으로 영어 말하기 배우기
레슨 만드는 중...
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Hey everyone!
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So, I'm pretty excited about the next sequence of videos that I'm doing.
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They'll be about linear algebra, which as a lot of you know, is one of those subjects that's required knowledge for just about any technical discipline, but it's also, I've noticed,
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generally poorly understood by students taking it for the first time time.
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A student might go through a class and learn how to compute lots of things, like matrix multiplication, or the determinant, or cross products which use the determinant,
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or eigenvalues, but they might come out without really understanding why matrix multiplication is defined the way that it is,
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why the cross product has anything to do with the determinant, or what an eigenvalue really represents.
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Oftentimes, students end up well-practiced in the numerical operations of matrices, but are only vaguely aware of the geometric intuitions underlying it all.
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But there's a fundamental difference between understanding linear algebra on a numeric level and understanding it on a geometric level.
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Each has its place, but roughly speaking, the geometric understanding is what lets you judge what tools to use to solve specific problems,
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feel why they work, and know how to interpret the results.
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And the numeric understanding is what lets you actually carry through the application of those tools.
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Now, if you learn linear algebra without getting a solid foundation in that geometric understanding, the problems can go unnoticed for a while,
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until you've gone deeper into whatever field you happen to pursue, whether that's computer science, engineering, statistics, economics, or even math itself.
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Once you're in a class, or a job for that matter, that assumes fluency with linear algebra,
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the way that your professors or your co-workers apply that field could seem like utter magic.
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They'll very quickly know what the right tool to use is, and what the answer roughly looks like in a way
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that would seem like computational wizardry if you assume that they're actually crunching all the numbers in their head.
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Here, as an analogy, imagine that when you first learned about the sine function in trigonometry, you were shown this infinite polynomial.
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This, by the way, is how your calculator evaluates the sine function.
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For homework, you might be asked to practice computing approximations of the sine function, by plugging in various numbers to the formula and cutting it off at a reasonable point.
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And in fairness, let's say you had a vague idea that this was supposed to be related to triangles, But exactly how had never really been clear, and was just not the focus of the course.
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Later on, if you took a physics course, where sines and cosines are thrown around left and right, and people are able to tell pretty immediately how to apply them
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and roughly what the sign of a certain value will be, it would be pretty intimidating, wouldn't it?
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It would make it seem like the only people who are cut out for physics are those with computers for brains, and you would feel unduly slow or dumb for taking so long on each problem.
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It's not that different with linear algebra.
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And luckily, just as with trigonometry, there are a handful of intuitions, visual intuitions, underlying much of the subject.
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And unlike the trig example, the connection between the computation and these visual intuitions is typically pretty straightforward.
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And when you digest these, and really understand the relationship between the geometry and the numbers, the details of the subject, as well as how it's used in practice,
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start to feel a lot more reasonable.
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In fairness, most professors do make an effort to convey that geometric understanding.
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The science example is a little extreme.
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But I do think
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that a lot of courses have students spending a disproportionate amount of time on the numerical side of things, especially given that in this day and age,
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we almost always get computers to handle that half, while in practice, humans worry about the conceptual half.
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So this brings me to the upcoming videos.
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The goal is to create a short, binge-watchable series animating those intuitions from the basics of vectors up through the core topics
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that make up the essence of linear algebra.
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I'll put out one video per day for the next five days, then after that put out a new chapter every one to two weeks.
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I think it should go without saying that you cannot learn a full subject with a short series of videos, and that's just not the goal here.
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But what you can do, especially with this subject, is lay down all the right intuitions
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so the learning that you do moving forward is as productive and fruitful as it can be.
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I also hope this can be a resource for educators who are teaching courses that assume fluency with linear algebra, giving them a place to direct students that need a quick brush up.
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I'll do what I can to keep things well paced throughout, but it's hard to simultaneously account for different people's different backgrounds and levels of comfort,
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so I do encourage you to readily pause and ponder if you feel that it's necessary.
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Actually, I'd give that same advice for watching any math video, even if it doesn't feel too quick, since the thinking that you do on your own time is where all the learning really happens, don't you think?
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So, with that as an introduction, I'll see you next video.
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이 레슨의 어휘와 말하기 포인트
이 C1 수준 말하기 레슨은 영상 “Essence of linear algebra preview”을(를) 바탕으로 합니다. 가장 자주 반복되는 단어는 다음과 같습니다: algebra, linear, understanding, intuitions, geometric. 이 영상에는 섀도잉할 문장 47개와 단어 917개가 있습니다. 말하는 구간의 길이는 4:43입니다. 화자는 분당 약 195단어로 빠르게 말하므로 연음과 약하게 발음되는 소리가 많습니다. 영어에서 가장 많이 쓰이는 3,000단어에 속하는 단어가 81%뿐이라 어휘가 어려운 편입니다.
이 영상의 핵심 어휘
영상에서 가장 어려운 단어 15개를 발음, 뜻과 함께 정리했습니다.
| 단어 | 발음 | 뜻 |
|---|---|---|
| algebra 명사 | /ˈæl.d͡ʒɪ.bɹə/ | 대수 |
| intuition 명사 | /ˌɪn.tjuːˈɪʃ.ən/ | 직관, 직감 |
| sine 명사 | /saɪn/ | 사인, 정현 |
| determinant 명사 | /dɪˈtɜːmɪnənt/ | 행렬식 |
| fluency 명사 | /ˈfluːənsi/ | 유창 |
| multiplication 명사 | /ˌmʌltɪplɪˈkeɪʃən/ | 곱셈, 승법 |
| trigonometry 명사 | /ˌtɹɪɡəˈnɒmətɹi/ | 삼각법 |
| numerical 형용사 | /n(j)uːˈmɛɹ.ɪ.kəl/ | 수치의 |
| cosine 명사 | /ˈkoʊ.saɪn/ | 코사인, 여현 |
| intimidate 동사 | /ɪnˈtɪmɪdeɪt/ | 협박하다, 위협하다 |
| polynomial 명사 | /ˌpɑliˈnoʊmiəl/ | 다항식 |
| ponder 동사 | /ˈpɑn.dəɹ/ | 숙고하다 |
| educator 명사 | /ˈɛd͡ʒəkeɪtɚ/ | 교육자, 교육가 |
| calculator 명사 | /kæl.kjə.leɪ.tɚ/ | 계산기 |
| digest 동사 | /daɪˈd͡ʒɛst/ | 소화하다 |
영상에 나오는 구동사
| 단어 | 발음 | 뜻 |
|---|---|---|
| brush up 동사 | 연마하다 | |
| come out 동사 | /ˌkʌm ˈaʊt/ | 나오다 |
| lie down 동사 | 눕다 |
이 영상의 문법
화자가 가장 많이 쓰는 문형을 영상 속 실제 표현과 함께 정리했습니다.
| 문형 | 영상 속 표현 |
|---|---|
| 수동태 be + 과거분사 — 누가 하는지보다 무슨 일이 일어나는지에 초점 | is defined · were shown · might be asked |
| 현재완료 have/has + 과거분사 — 과거의 일이 지금도 관련이 있을 때 | I've noticed · you've gone |
주의할 발음
화자는 I'll, I'm, they'll 같은 축약형과 약화된 형태를 15번 사용합니다. 들리는 대로 짧게 발음하세요.
- “sh”와 “zh” 소리: intuition /ˌɪn.tjuːˈɪʃ.ən/, multiplication /ˌmʌltɪplɪˈkeɪʃən/, approximation /əˌpɹɑk.sɪˈmeɪ.ʃən/, computation /ˌkɑmpjʊˈteɪʃn̩/, disproportionate /dɪs.pɹəˈpɔː.ʃə.nət/
- 긴 단어 — 강세 위치에 주의: intuition /ˌɪn.tjuːˈɪʃ.ən/, geometric /ˌd͡ʒiː.əʊˈmɛt.ɹɪk/, determinant /dɪˈtɜːmɪnənt/, eigenvalue /ˈaɪ.ɡənˌvæl.ju/, multiplication /ˌmʌltɪplɪˈkeɪʃən/
한국어 화자가 어려워하는 소리:
- /f/ — ㅍ(/p/)으로 바꾸지 말고 윗니를 아랫입술에 대기: fluency /ˈfluːənsi/, fairness /ˈfɛɚ.nəs/, fruitful /ˈfɹuːtfl̩/, oftentimes /ˈɔf.ənˌtaɪmz/, straightforward /ˌstɹeɪtˈfɔː(ɹ)wə(ɹ)d/
- /v/ — ㅂ(/b/)과 구별하기: eigenvalue /ˈaɪ.ɡənˌvæl.ju/, vaguely /ˈveɪɡli/, convey /kənˈveɪ/, vague /veɪɡ/, vector /ˈvɛktɚ/
- /z/ — ㅈ이 아니라 성대를 울리는 /s/: oftentimes /ˈɔf.ənˌtaɪmz/, wizardry /ˈwɪzədɹi/, pause /pɔːz/
이 영상으로 연습하는 방법
- 먼저 말하지 않고 영상을 끝까지 듣고 모르는 단어를 적어 둡니다.
- 0.75배속으로 한 문장씩 섀도잉을 시작하고, 익숙해지면 보통 속도로 돌아갑니다.
- 자신의 목소리를 녹음해 원본과 비교하고, algebra, intuition, sine 같은 단어에 특히 주의합니다.
쉐도잉이란? 영어 실력을 빠르게 키우는 과학적 방법
쉐도잉(Shadowing)은 원래 전문 통역사 훈련을 위해 개발된 언어 학습 기법으로, 다언어 학자인 Dr. Alexander Arguelles에 의해 대중화된 방법입니다. 핵심 원리는 간단하지만 매우 강력합니다: 원어민의 영어를 들으면서 1~2초의 짧은 지연으로 즉시 소리 내어 따라 말하는 것——마치 '그림자(shadow)'처럼 화자를 따라가는 것입니다. 문법 공부나 수동적인 청취와 달리, 쉐도잉은 뇌와 입 근육이 동시에 실시간으로 영어를 처리하고 재현하도록 훈련합니다. 연구에 따르면 이 방법은 발음 정확도, 억양, 리듬, 연음, 청취력, 말하기 유창성을 크게 향상시킵니다. IELTS 스피킹 준비와 자연스러운 영어 소통을 원하는 분들에게 특히 효과적입니다.