Nodirbek Gafforov
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PhD student in
Mathematics at
National University of Singapore

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1-Oktabr - O'qituvchi va murabbiylar kuni munosabati bilan barcha ustoz va murabbiylarni tabriklayman!

Shu fursatdan foydalanib, menga ta'lim-tarbiya bergan va yo'l-yo'riq ko'rsatgan ustozlarimga chin dildan minnatdorchilik bildiraman.

Hamisha sog'-salomat, shogirt va yaqinlaringiz hurmat va ardog'ida bo'ling, aziz ustozlar!

@ngafforov
Life hack


Wilhelm Schlagning rasmdagi(1-rasm) kitobini tasodifan kutubxonada ko'rib qolgandim. O'qib ko'rsam yaxshi kitob ekan.
Graduate Studies in Mathematics turkumidagi kitoblar bakalavrni 3-4-kurslariga yoki bakalavrni tugatib magistratura yoki PhDga qadam qo'ygan talabalarga moslangan bo'lib, qisqa, zamonaviy va eng muhim mavzularni o'z ichiga olgan bo'ladi.


Eslasangiz yuqorida Allen Hatcherning kitoblari o'z sahifasida tekin ekanligini aytkandim (https://t.me/c/2338434621/62).
Bu masalani umumiy holda ham ishlasa bo'larkan.
Ya'ni deyarli istalgan oliy matematikaga oid kitobni tekinga va qonuniy topish mumkin.
Yanayam aniqrog'i universitetda matematikadan qaysidir kursni o'qitgan o'qituvchilar o'sha kurs uchun notes tayyorlaydi va ko'pincha shu notesni pdfini o'z sahifasiga joylab qo'yadi.
Notesni topish uchun o'sha avtorning internetdagi Home Pageiga tashrif buyurish kerak.
Masalan internetga Wilhelm Schlag yoki Wilhelm Schlag Home Page deb yozsangiz Schlagning Yale universitetidagi sahifasi chiqib keladi:
https://gauss.math.yale.edu/~ws442/
U yerda uning maqolalari, kitoblari va slidelarini yuklab olishingiz mumkin.


Chapdagi kitob, Schlagning sahifasidagi Teaching sarlavhasi ostidagi Notes from a complex analysis class asosida yozilgan.
Ammo bu notesda kitobda yo'q xato va kamchiliklar bo'lishi mumkin, chunki kitob nashr qilinishidan oldin editorlar xato va kamchiliklarini tuzatadi.


Sizga sohasi qiziq bo'lgan matematiklarning ham sahifasiga tashrif buyursangiz qiziqarli slidelar, maqolalar va noteslar topishingiz mumkin.


@ngafforov
- Donu Arapura


@ngafforov
Accepting your flaws when someone points them out — without reacting defensively — is one of the hardest but most admirable things a person can do. It takes emotional maturity, humility, and self-awareness.
How can I grow into that mindset?



A prompt to ask ChatGPT.


You know what they say:
Ego is the enemy.



@ngafforov
Nodirbek Gafforov
Calculus Gilbert Strang. Yaxshi kitob. Bepul yuklab olishingiz mumkin. The reader will understand that calculus is not all sweetness and light. There is work to do. You absolutely have to solve problems—and think carefully. As one of my students said…
Gerald B. Follandning Real Analysis kitobi zamonaviy haqiqiy anlizdagi eng muhim mavzularni o'z ichiga olgan va ko'pincha PhD talabalaridan olinadigan Saralash Imtihoniga(QE) hamma shu kitobdan foydalanib tayyorlanadi, mavzularini o'qib har bitta mavzudagi 2-3ta misolni ishlab, qolgan misollarga ham kamida ko'z yugurtirib chiqish tavsiya qilinadi.


Yuqoridagi Strangning Calculus kitobi va Follandning Real Analysis kitobi orasida Follandning Advanced Calculus kitobini o'qib yuborsa bo'ladi.


Follandning sahifasidan kitobni tekin yuklab olishingiz mumkin.
Link:
https://sites.math.washington.edu/~folland/


Yaxshi kitobni olib hamma mavzusini o'qib chiqish yaxshi, albatta, ammo ba'zan mundarijaga qarab aynan sizga kerak bo'lgan mavzuni o'qib chiqishni o'zi yetarli. Bitta mavzuni tushunmasangiz boshqa kitoblardan o'qib ko'ring.
Qayerdadur Advanced Calculusga oid bilim kerak bo'lib qolsa, mundarijadan o'sha mavzuni topib o'qib olsangiz bo'ladi.


@ngafforov
Hobbilarimdan biri shaxmat 🐴 o'ynash.


Chess(.)comdagi rapid reytingimni vanihoyat 1500dan oshirdim va bu bilan top 3%ga kirdim.


Shaxmatni yaxshi o'ynaydigan kursdoshim sizni reytingiz 1600 atrofida ammo ba'zan juda ko'p o'ylab keyin yurasiz derdi.


@ngafforov
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STEP.


Matematika yoki Fizika yo'nalishida O'zbekistonda PhD o'qiyotgan talabalar uchun imkoniyat.


3 yil har yili 3 oydan 6 oygacha ICTP yoki rasmdagi boshqa Triestega yaqin joylashgan institutlardan biriga tashrif buyurasiz, bunda har oy 1400 yevro maosh beriladi hamda borish kelish, tibbiy sug'urta xarajatlari qoplanadi.


Xullas, faraz qilaylik, siz O'zbekistonda Matematikadan PhD o'qiyabsiz, ilmiy rahbaringiz ham bor. Mavzu ham tanlagansiz. ICTPda sizni yo'nalishizga juda yaqin sohada ishlaydigan ilmiy izlanuvchi bor. Shunda siz hujjat topshirsangiz bo'ladi, o'sha ICTPdagi ilmiy izlanuvchi sizni 2-ilmiy rahbaringiz(co-advisor) bo'ladi.
Qanday hujjatlar kerakligi va hokazolar bilan linkda tanishib olsangiz bo'ladi.


Link: https://www.ictp.it/opportunity/ictpiaea-sandwich-training-education-programme


Hujjat topshirish oralig'i:
15-noyabrdan 28-fevralgacha.


Good Luck.


P.s. Girl with glasses was a pro table tennis player.


@ngafforov
Certainly the best times were when I was alone with mathematics, free of ambition and pretense, and indifferent to the world.

- Langlands, in Mathematicians: An Outer View of the Inner World, p142.


Sizlar uchun ta'tilni maroqli o'tkazishga yordam beradigan manbalar to'plab qo'ydim.
Bu manbalarni ikki guruhga ajratamiz: Interaktiv, ya'ni ko'ngil ochar hamda advanced, ya'ni matematika sohasida o'qiydiganlarga mos.


Interaktiv: 🫡🔠🔠
1. Cut The Knot.
Boshlanishiga Geometry qismidagi Pythagorean Theorem (122 proofs)ni tavsiya qilaman. Bu yerda Pifagor teoremsining 122ta isboti bor!
Link: https://www.cut-the-knot.org/

2. Mathematical Visual Proofs.
Boshlanishiga dastlabki nta natural sonlarning yig'indisi formulasini tavsiya qilaman(https://youtu.be/eHbtc50-qXo?si=8bnW0xNsXDj4NnHL).
Link: https://youtube.com/@mathvisualproofs?si=5lZZIMTMLq3LCE7U

3. 3blue1brown.
Link: https://www.3blue1brown.com/

4. Alvaro Lozano-Robledoning YouTube kanali.
Link: https://youtube.com/@mathandcobb?si=faUkqGzqZcgKtR-J


Advanced: 👨‍💻
1. Wilhelm Schlagning homepagei https://gauss.math.yale.edu/~ws442/

2. Jerry Follandning homepagei: https://sites.math.washington.edu/~folland/

3. Terry Taoning blogi: https://terrytao.wordpress.com/

4. Gilbert Strangning Calculus kitobi: https://ocw.mit.edu/courses/res-18-001-calculus-fall-2023/pages/textbook/

5. Allen Hatcherning homepagei: https://pi.math.cornell.edu/~hatcher/#SSAT

6. J. S. Milnening homepagei: https://www.jmilne.org/math/

7. Pete L. Clarkning homepagei: https://plclark.github.io/PeteLClark/Expositions/

8. Keith Conradning homepagei: https://kconrad.math.uconn.edu/blurbs/

9. Richard Borcherdsning YouTube kanali: https://youtube.com/@richarde.borcherds7998?si=t3S08UGBJ9_Q3xQA

10. IHESning YouTube kanali: https://youtube.com/@ihesfr?si=EzVdEL1ZeGJUxUV6

11. IASning YouTube kanali: https://youtube.com/@videosfromias?si=M7RPsovW0m9yl4Ht

12. Linear Algebra Done Right by Sheldon Axler.
https://www.axler.net/
YouTube kanalida 50ta videosi ham bor: https://linear.axler.net/LADRvideos.html

Yuqorida ham aytkanimdek, juda ko'pchilik professorlar o'z sahifasiga o'zi yozgan maqola va leksiyalarni yuklaydi. Men o'zim bilgan, manbalari ko'proq va yaxshi kitoblari bor mualliflarni to'pladim.


Ulashgan manbalarimning barchasi ingliz tilida! Ammo;
Interaktiv qismidagi vizual isbotlarni tushunish uchun deyarli til bilish talab qilinmaydi.
Pifagor teoremasining 122ta isbotida ko'p isbotlar vizual.


Interaktiv qismdagi manbalardan maktabda dars o'tadigan o'qituvchilar foydalanishi mumkin.


Shuningdek, ba'zan bo'sh vaqtingizda interaktiv saytlarga kirib(cut the knot, yoki shunga o'xshash) qiziqarli boshqotirmalarni oila a'zolaringiz bilan ishlasangiz bo'ladi.
I loved math when I was growing up. Nobody in my family was a scientist, but my father loved doing puzzles. So we did a lot of puzzles.


Men ulg'ayayotganimda matematikani juda yaxshi ko'rardim. Oilamizda hech kim olim bo'lmagan, lekin dadam boshqotirmalarni ishlashni yoqtirardi. Shuning uchun biz ko'p boshqotirmalar ishlaganmiz.

- Jennifer Doudna, Kimyo yo'nalishida Nobel mukofoti sohibasi.

Ushbu manbalar ro'yxatini uzaytirib borishga harakat qilaman.
Ta'tilingiz maroqli o'tsin.


@ngafforov
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Nodirbek Gafforov
The heart has two eyes to perceive that which is not visible to the eye. One is the 'Sun Eye', which sheds a bright light on our understanding of things from a rational and logical perspective. The other is the 'Moon Eye', which perceives things through instinct…
she asks, 'Ryo, dear, have you ever thought about what makes the world go round?'
'Rr . . . rr, love, I guess.'
'Oh, that's priceless!' she cries. 'You never cease to amaze me, Ryo, but that's what I love about you. I believe it is trust,'
she adds.
'Trust?'
'Yes, trust. Anything you do - borrowing money from a bank, commissioning a piece of work, sending or receiving a parcel, making a plan with friends, ordering food at a restaurant - all those things can only happen because of mutual trust on both sides.'

tarjima:
U so‘raydi:
“Ryo, azizim, hech o‘ylab ko‘rganmisan — dunyoni nima aylantirib turadi?”

— “Rr… rr, muhabbat, shekilli,” deydi u.

— “Voy, bu juda ajoyib!” — deb qichqiradi u. — “Sen meni hech qachon hayratga solishni to‘xtatmaysan, Ryo. Aynan shuning uchun seni yaxshi ko‘raman. Ammo menimcha, bu — ishonch,” deya qo‘shimcha qiladi u.

— “Ishonch?”

— “Ha, ishonch. Qarasang, bankdan qarz olish, biror ishni buyurtma qilish, posilka yuborish yoki qabul qilish, do‘stlar bilan reja tuzish, restoranda ovqat buyurtma berish — bularning barchasi faqat ikki tomon o‘rtasidagi o‘zaro ishonch tufayli amalga oshadi.”



@ngafforov
I just had an amazing meeting with my coursemates from ICTP. We caught up with each other; asked some questions, like “Are you still single?” and “What are you working on?”

It was hard to find a time that fits all, as usual everywhere, but we did it - even though one of us couldn't join.
Special thanks to Danielle for organising!


@ngafforov
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Chekli maydonlar nazariyasi so‘nggi 60 yil ichida yangi qo‘llanilishlar sababli katta ahamiyat kasb etdi. Chekli maydonlarning qo‘llanilish sohalariga kodlash nazariyasi, kombinatorika, kommutatsiya sxemalari, chekli geometriyalar orqali statistika hamda kompyuter fanining ayrim yo‘nalishlari kiradi.

Fundamentals of Abstract Algebra, D.S. Malik, et. al.

@ngafforov
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After taking some uneven photos, I was just about to leave Jewel. Then this happened.

@ngafforov
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Nodirbek Gafforov pinned «Certainly the best times were when I was alone with mathematics, free of ambition and pretense, and indifferent to the world. - Langlands, in Mathematicians: An Outer View of the Inner World, p142. Sizlar uchun ta'tilni maroqli o'tkazishga yordam beradigan…»
Yaqinda IQ haqida ikki kishini suhbatini videosini ko'rdim.
Unda birinchi odam ikkinchisidan aholisining IQsi eng kuchli davlatlar ro'yxatini so'radi.

- 1-o'rinda Singapur bo'lsa kerak
- Ha, albatta, Singapurga borsang sen yo'l belgilarini ham tushunishga aqling yetmay qolsa kerak😂 hahaha


Rasmdagi yo'l belgisini ma'nosini topishga urinib ko'ringchi :)
Men ham boshida tushunmagandim.


@ngafforov
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