به نظر شما با توجه به آثار به جا مانده از خیام نیشابوری، او بیشتر چگونه شخصیتی دارد؟!
Anonymous Poll
61%
عقلانی
6%
مذهبی
33%
عرفانی
تعاریف ریاضی را با مثال‌های شهودی به کودکان بیاموزیم.
@harmoniclib
@harmoniclib
مطالب جذاب ریاضی مورد نظرتان را برای ما بفرستید تا با هشتگ اختصاصی خودتان در کانال قرار دهیم.
👇👇👇👇👇
@meisami_mah
👇👇👇👇👇
@meisami_mah
گروه اپلای ریاضی با ۹۰۰ عضو واگذار می شود.
افرادی که مایل هستند می توانند در خصوصی پیام دهند.
👇👇👇
@meisami_mah
افرادی که مایل هستند می توانند در خصوصی پیام دهند.
👇👇👇
@meisami_mah
از چت جی‌بی‌تی پرسیدم بهترین کتاب ها برای مطالعه‌ی خودخوان آنالیز ریاضی چیست!؟
جواب داد:
1. Principles of Mathematical Analysis by Walter Rudin
2. Understanding Analysis by Stephen Abbott
3. Calculus by Michael Spivak
4. Real Analysis: Modern Techniques and Their Applications by Gerald Folland
5. Introduction to Real Analysis by William F. Trench
6. Analysis I and II by Terence Tao
7. Advanced Calculus: A Differential Forms Approach by Harold Edwards
8. A Course in Pure Mathematics by G.H. Hardy
9. The Art of Mathematics: Coffee Time in Memphis by Béla Bollobás
10. Mathematical Analysis: An Introduction to Functions of Several Variables by Mariano Giaquinta and Giuseppe Modica.
@harmoniclib
جواب داد:
1. Principles of Mathematical Analysis by Walter Rudin
2. Understanding Analysis by Stephen Abbott
3. Calculus by Michael Spivak
4. Real Analysis: Modern Techniques and Their Applications by Gerald Folland
5. Introduction to Real Analysis by William F. Trench
6. Analysis I and II by Terence Tao
7. Advanced Calculus: A Differential Forms Approach by Harold Edwards
8. A Course in Pure Mathematics by G.H. Hardy
9. The Art of Mathematics: Coffee Time in Memphis by Béla Bollobás
10. Mathematical Analysis: An Introduction to Functions of Several Variables by Mariano Giaquinta and Giuseppe Modica.
@harmoniclib
در استقرا همیشه گام بعد از n
n+1
نیست.
لزومی ندارد گام‌ها در همه‌ی مسائل یکی یکی طی شوند. ممکن است فرض n باشد و حکم n+k .
@harmoniclib
n+1
نیست.
لزومی ندارد گام‌ها در همه‌ی مسائل یکی یکی طی شوند. ممکن است فرض n باشد و حکم n+k .
@harmoniclib
اخبار و کتاب های ریاضی
منتظر مثال‌های جالب ارسالی شما در قسمت کامنت‌ها هستیم. @harmoniclib 👇👇👇
نظر ارسالی
یکی از انواع بسیار جالب استقرا
استقرای رفت و برگشتی هست
برای نمونه میتونید به اثبات نابرابری میانگین حسابی - هندسی مراجعه کنید
در این استقرا ابتدا برای تایپ خاصی از اعداد طبیعی حکم رو ثابت میکنید(مثلا توان های ۲) و بعد نشون میدید برای هر عدد کوچکتر از یک توان ۲ حکم برقرار هست.
@harmoniclib
یکی از انواع بسیار جالب استقرا
استقرای رفت و برگشتی هست
برای نمونه میتونید به اثبات نابرابری میانگین حسابی - هندسی مراجعه کنید
در این استقرا ابتدا برای تایپ خاصی از اعداد طبیعی حکم رو ثابت میکنید(مثلا توان های ۲) و بعد نشون میدید برای هر عدد کوچکتر از یک توان ۲ حکم برقرار هست.
@harmoniclib
نظرات ریاضیدان بزرگ تری تائو در مورد چت جی‌بی‌تی
Mathematician Terence Tao Comments on ChatGPT
Apr 10, 2023, 23:11pm Pandaily
Terence Tao, an Australian-American mathematician of Chinese ethnicity and Fields Medal winner, recently announced that he has decided to try incorporating AI tools into his workflow in different ways, including GPT-4 and others. On April 10, Tao wrote on the decentralized social network Mastodon: “Today was the first day that I could definitively say that GPT-4 has saved me a significant amount of tedious work. I am now looking forward to native integration of AI into the various software tools that I use, so that even the cut-and-paste step can be omitted.”
During the past few days, he discovered many hidden features of ChatGPT, such as searching for formulas, parsing documents with code formatting, and rewriting sentences in academic papers. For example, sometimes ChatGPT can perform a semantic search on an unfinished mathematical problem to generate some hints. Tao also asked ChatGPT to identify Kummer’s theorem from its description. Although it could not provide the correct answer, it gave an approximate answer based on Legendre’s formula. Regarding this matter, Tao said that AI plays a role in mathematics by providing an initial approximate answer which can then be combined with traditional search engines to easily find the correct answer.
Tao also discovered the highlights of ChatGPT in handling mathematical problems, which can describe the recommended pronunciation of proper nouns in various languages, in a manner that does not require knowledge of phonetics. In addition, ChatGPT can be requested to convert a pile of references obtained from MathSciNet and format them as .\bibitems in the LaTeX bibliography environment.
However, in a proof problem about the infinitude of primes, Terence Tao found that the answer given by ChatGPT was not entirely correct. On the other hand, he discovered that the AI argument does imply that the infinitude of squarefree numbers implies the infinitude of primes, and the former statement can be proven by a standard sieve argument.
Terence Tao also released some further minor use cases for ChatGPT that he has discovered recently. “Firstly, it is quite good at parsing documentation for a code format (in this case the API for arXiv search) and then returning a correctly formatted query for that code (and it also later provided some working python code to call this API in the fashion I requested, although I had to manually install a package to make it run).”
“Secondly (and not pictured here), I asked it to come up with some questions that a bright student might ask in an undergraduate linear algebra class (for which I provided a few sample topics), and it came up with some good examples that stimulated ideas for possible directions for the course, as well as potential assignment questions.”
“In general, I am finding that while these AI tools do not directly assist me in core tasks such as trying to attack an unsolved mathematical problem, they are quite useful for a wide variety of peripheral (but still work-related) tasks (though often with some manual tweaking afterwards).”
@harmoniclib
Mathematician Terence Tao Comments on ChatGPT
Apr 10, 2023, 23:11pm Pandaily
Terence Tao, an Australian-American mathematician of Chinese ethnicity and Fields Medal winner, recently announced that he has decided to try incorporating AI tools into his workflow in different ways, including GPT-4 and others. On April 10, Tao wrote on the decentralized social network Mastodon: “Today was the first day that I could definitively say that GPT-4 has saved me a significant amount of tedious work. I am now looking forward to native integration of AI into the various software tools that I use, so that even the cut-and-paste step can be omitted.”
During the past few days, he discovered many hidden features of ChatGPT, such as searching for formulas, parsing documents with code formatting, and rewriting sentences in academic papers. For example, sometimes ChatGPT can perform a semantic search on an unfinished mathematical problem to generate some hints. Tao also asked ChatGPT to identify Kummer’s theorem from its description. Although it could not provide the correct answer, it gave an approximate answer based on Legendre’s formula. Regarding this matter, Tao said that AI plays a role in mathematics by providing an initial approximate answer which can then be combined with traditional search engines to easily find the correct answer.
Tao also discovered the highlights of ChatGPT in handling mathematical problems, which can describe the recommended pronunciation of proper nouns in various languages, in a manner that does not require knowledge of phonetics. In addition, ChatGPT can be requested to convert a pile of references obtained from MathSciNet and format them as .\bibitems in the LaTeX bibliography environment.
However, in a proof problem about the infinitude of primes, Terence Tao found that the answer given by ChatGPT was not entirely correct. On the other hand, he discovered that the AI argument does imply that the infinitude of squarefree numbers implies the infinitude of primes, and the former statement can be proven by a standard sieve argument.
Terence Tao also released some further minor use cases for ChatGPT that he has discovered recently. “Firstly, it is quite good at parsing documentation for a code format (in this case the API for arXiv search) and then returning a correctly formatted query for that code (and it also later provided some working python code to call this API in the fashion I requested, although I had to manually install a package to make it run).”
“Secondly (and not pictured here), I asked it to come up with some questions that a bright student might ask in an undergraduate linear algebra class (for which I provided a few sample topics), and it came up with some good examples that stimulated ideas for possible directions for the course, as well as potential assignment questions.”
“In general, I am finding that while these AI tools do not directly assist me in core tasks such as trying to attack an unsolved mathematical problem, they are quite useful for a wide variety of peripheral (but still work-related) tasks (though often with some manual tweaking afterwards).”
@harmoniclib
اخبار و کتاب های ریاضی
نظرات ریاضیدان بزرگ تری تائو در مورد چت جی‌بی‌تی Mathematician Terence Tao Comments on ChatGPT Apr 10, 2023, 23:11pm Pandaily Terence Tao, an Australian-American mathematician of Chinese ethnicity and Fields Medal winner, recently announced that he has decided…
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