Shadowing Practice: Essence of linear algebra preview - Learn English Speaking with Video
Ders oluşturuluyor...
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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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Bu dersin kelimeleri ve konuşma notları
Bu C1 seviyesindeki konuşma dersi “Essence of linear algebra preview” videosuna dayanıyor. En çok tekrarlanan kelimeler: algebra, linear, understanding, intuitions, geometric. Bu videoda gölgeleme çalışması için 47 cümle ve 917 kelime var. Konuşma bölümü 4:43 sürüyor. Konuşmacı hızlı konuşuyor, dakikada yaklaşık 195 kelime; bu yüzden birbirine bağlanan ve zayıflayan sesler duyacaksınız. Kelimelerin yalnızca %81’i İngilizcede en sık kullanılan 3.000 kelime arasında, bu yüzden kelime dağarcığı zorlayıcı.
Bu videodaki önemli kelimeler
Videodaki en ileri düzey 15 kelime, telaffuzu ve anlamıyla:
| Kelime | Telaffuz | Anlam |
|---|---|---|
| algebra isim | /ˈæl.d͡ʒɪ.bɹə/ | cebir |
| intuition isim | /ˌɪn.tjuːˈɪʃ.ən/ | görü, sezgi |
| compute fiil | /kəmˈpjuːt/ | hesaplamak |
| fluency isim | /ˈfluːənsi/ | akıcılık |
| multiplication isim | /ˌmʌltɪplɪˈkeɪʃən/ | çarpma işlemi |
| trigonometry isim | /ˌtɹɪɡəˈnɒmətɹi/ | trigonometri |
| numerical sıfat | /n(j)uːˈmɛɹ.ɪ.kəl/ | sayısal, sayıca |
| animate sıfat | /ˈæn.ə.mət/ | canlı, diri |
| cosine isim | /ˈkoʊ.saɪn/ | kosinüs |
| intimidate fiil | /ɪnˈtɪmɪdeɪt/ | sindirmek, yıldırmak |
| polynomial isim | /ˌpɑliˈnoʊmiəl/ | polinom |
| ponder fiil | /ˈpɑn.dəɹ/ | düşünüp taşınmak |
| vaguely zarf | /ˈveɪɡli/ | belli belirsiz, belirsiz bir şekilde |
| calculator isim | /kæl.kjə.leɪ.tɚ/ | hesap makinesi |
| binge isim | /bɪnd͡ʒ/ | alem, içki alemi |
Duyacağınız deyimsel fiiller
| Kelime | Telaffuz | Anlam |
|---|---|---|
| put out fiil | çıkarmak | |
| come out fiil | /ˌkʌm ˈaʊt/ | çıkmak |
| lie down fiil | yatmak |
Bu videodaki dil bilgisi
Konuşmacının en çok kullandığı yapılar, videodaki sözcüklerin aynısıyla:
| Yapı | Videoda |
|---|---|
| Edilgen yapı be + fiilin üçüncü hâli — kimin yaptığı değil, ne olduğu önemli | is defined · were shown · might be asked |
| Present perfect have/has + fiilin üçüncü hâli — geçmişte olan ama şimdi de önemli olan bir eylem | I've noticed · you've gone |
Dikkat edilecek telaffuzlar
Konuşmacı I'll, I'm, they'll gibi kısaltılmış biçimleri 15 kez kullanıyor. Bunları duyduğunuz gibi kısa söyleyin.
- “sh” ve “zh” sesleri: intuition /ˌɪn.tjuːˈɪʃ.ən/, multiplication /ˌmʌltɪplɪˈkeɪʃən/, approximation /əˌpɹɑk.sɪˈmeɪ.ʃən/, computation /ˌkɑmpjʊˈteɪʃn̩/, disproportionate /dɪs.pɹəˈpɔː.ʃə.nət/
- Uzun kelimeler — vurguyu doğru yere koyun: intuition /ˌɪn.tjuːˈɪʃ.ən/, geometric /ˌd͡ʒiː.əʊˈmɛt.ɹɪk/, determinant /dɪˈtɜːmɪnənt/, eigenvalue /ˈaɪ.ɡənˌvæl.ju/, multiplication /ˌmʌltɪplɪˈkeɪʃən/
Türkçe konuşanların zorlandığı sesler:
- /w/ — dudaklar yuvarlak, /v/ değil: wizardry /ˈwɪzədɹi/, straightforward /ˌstɹeɪtˈfɔː(ɹ)wə(ɹ)d/
- Kelime başındaki ünsüz kümesi — araya ünlü eklemeyin: fluency /ˈfluːənsi/, numeric /n(j)uːˈmɛɹɪk/, trigonometry /ˌtɹɪɡəˈnɒmətɹi/, numerical /n(j)uːˈmɛɹ.ɪ.kəl/, fruitful /ˈfɹuːtfl̩/
- /æ/ — “e”den daha açık: algebra /ˈæl.d͡ʒɪ.bɹə/, eigenvalue /ˈaɪ.ɡənˌvæl.ju/, animate /ˈæn.ə.mət/, calculator /kæl.kjə.leɪ.tɚ/, analogy /əˈnæləd͡ʒi/
Bu videoyla nasıl çalışılır
- Videonun tamamını konuşmadan bir kez dinleyin ve bilmediğiniz kelimeleri not edin.
- 0,75× hızla başlayın, cümle cümle tekrar edin ve kolaylaşınca normal hıza dönün.
- Kendinizi kaydedin ve orijinaliyle karşılaştırın; algebra, intuition, compute gibi kelimelere özellikle dikkat edin.
Gölgeleme Tekniği Nedir?
Gölgeleme, başlangıçta profesyonel tercüman eğitimi için geliştirilen ve çok dilli Dr. Alexander Arguelles tarafından popüler hale getirilen, bilim destekli bir dil öğrenme tekniğidir. Yöntem basit ama güçlüdür: ana dili İngilizce olan bir sesi dinler ve hemen yüksek sesle tekrar edersiniz — konuşmacıyı 1-2 saniye gecikmeyle takip eden bir gölge gibi. Pasif dinleme veya dilbilgisi alıştırmalarının aksine, gölgeleme beyninizi ve ağız kaslarınızı gerçek konuşma kalıplarını eşzamanlı olarak işlemeye ve yeniden üretmeye zorlar. Araştırmalar, telaffuz doğruluğu, tonlama, ritim, bağlı konuşma, dinleme anlama ve konuşma akıcılığını önemli ölçüde geliştirdiğini göstermektedir — bu da onu IELTS Konuşma hazırlığı ve gerçek dünya İngilizce iletişimi için en etkili yöntemlerden biri yapar.