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Ordered, thank you!

There's so little physics for a physics exam - in my country, the math is a separate and now obligatory exam (basic level is mandatory, but you can take advanced level which is significantly harder in comparison) - I'm quite shocked but also positively surprised at what qualities it checks. I'd love for Tom to have a crack at one from my home country, especially the older type - the equations and constants are provided so I'm sure it can provide a different kind of challenge.

🙏 Thank you

Small math book = {small set of topics, a very difficult topic}

I remember the Graham Schmidt Orthogonalization in linear algebra and Legendre polynomials from differential equations

This is a nice little read. Jackson should have written one for his "Classical Electrodynamics" text as well.

Ming has been working up to this gradually through all his previous videos: you can't do quantum anything without a cat. Makes sense: the mental and spiritual properties of the cat are useful in communicating Out There into Quantum Reality.

Warning: there is a vicious carnivorous animal lurking in your office.

"Partial Differential Equations in Physics" by Arnold Sommerfeld is based on his lectures on Theoretical Physics. It, like other volumes in the series, illustrates the thought-processes of a truly great mind; he was one of the strong bridges between Classical and Quantum Mechanics. (The exercises are at the back of the book.)

NICE BOOK AND SUBJECT IN TRUTH THERES MANY DIMENSIONS WHEN WE UNDERSTAND THE REALITY OF GOD AND VALUE OF WOMAN, THEN WE BE ABLE TO UNDERSTAND MATHEMATICS AND THE MECHANICS OF IT THE PARALLEL UNIVERSES OF GOD Honorable Elijah Muhammad WHO MET GOD IN PERSON " SUPREME BEING " and Honorable Minister Farrakhan Taught us GOD IS SELF CREATED AND STUDY HIMSELF AND FOUND ANOTHER SELF CALLED WOMAN THAN MANY MAN AND WOMAN SPREAD WOMAN IS POWERFUL ! SECOND SELF OF GOD, CO-CREATOR ! THIS BEFORE CREATION OF UNIVERSES Taught us! GOD ORIGINATOR FIRST ! ORIGINATED THE UNIVERSES ( TOWARD ) PERFECTION UNTIL ONE WAS BORN OF MAN AND WOMAN SINCE 78 TRILLION YEARS AGO THE SCRIPTURES BIBLE, QURAN, SACRED BOOKS OF THE WORLD TALKS ABOUT THE (COMING ) OF GOD SCRIPTURES SAYS THIS ONE WILL MAKE A NEW PARALLEL UNIVERSES OR HEAVEN SO SUPREME IN WISDOM, KNOWLEDGE AND POWERS INTO THE INIFINTY, " THE BEST KNOWER OF ALL. " THE SUPREME BIENG A HUMAN BEING " FOR EXAMPLE THEIR ALWAYS WILL BE ONE HAS THE CAPACITY OF KNOWING, AND APPLYING MORE " WHETHER ITS ELEMENTARY, HIGH SCHOOL, COLLEGES OR ANY FIELD DISCIPLINE ALWAYS BE ONE ON TOP , NOT BIAS! BUT THAT IS TRUTH COMES FROM WOMB OF WOMAN THAT ARITHMETIC KEEPS GOING IN GENERATIONS OR INTO MILLENNIUM Taught us ! GOD SAYS THEIR 60,000 HIGHER MATHEMATICS KNOWN WE GAVE ONE TO THE WORLD DID A GREAT JOB BUILDING CIVILIZATIONS AND OUT OF THAT ONE CAME CALCULUS AND OTHER MATHEMATICS MORE TO COME, BECAUSE GOD IS ETERNAL AND INFINITE WOMAN MUST BE EDUCATED IN SCIENCE, MATHEMATICS, MOTHERING AND TALENTS WOMAN IS CORNERSTONE OF FAMILY MARRIAGE IS SCIENCE OF FAMILY " MALE AND FEMALE " SCIENCE OF DATING OR MATING " WHO TO CHOOSE " , BASE ON HEART AND INTELLIGENCE GOD LOVE IS UNIVERSAL TO ALL HUMANITY AS WELL IN PARALLEL UNIVERSES GOD LOVE IS THE HIGHEST ORDER AND THAT LOVE TRANSCEND COLOR AND ITS NOTHING WRONG KEEPING IT PURE WITH OWN KIND (PAIRS) THAT IS ALSO LOVE TOO BUT WITH RESPECT TOWARD OTHERS OR EACH OTHER ! DOING BUSINESS AND TRADE, UNDERSTANDING TRUTH AND PEACE WOMAN IS THE KEY ALSO TO THE KINGDOM OF GOD OR HEAVEN MENS WE ARE GREAT TOO ! WE HAVE A ROLE TOO! BUT WITHOUT THE MIND AND WOMB OF WOMAN WE CAN'T ADVANCED OR BEYOND HER WOMB RESEMBLES THE DARKNESS OF SPACE WHICH GOD SELF CREATED AND EVERYTHING CAME INTO EXISTENCE WOMAN WOMB PRODUCES MENTAL GIANTS MALE AND FEMALE= GODS, SCIENTISTS , MATHEMATICIAN, ENGINEERS, ARCHITECTURES, KINGS AND QUEENS, PEOPLE OF VALUE ETC .... SCIENCE OF MARRIAGE, MATHEMATICS, SCIENCE AND ENGINEER BUILDS CIVILIZATIONS Artical " HEAVEN LIES AT THE FOOT OF MOTHER " Artical " THE REALITY OF GOD " Artical " PURPOSE OF EDUCATION "

Where is the proof for "In principle, all proofs can be written in a two column format" lol? Suppose a proof of such does exist, but the proof of which isn't representable in a two column format, then the statement "all proofs can be written in a two column format" is falsified, since at least 1 proof is not representable in a two column format. Now if a proof of such does exist, and is representable in a two column format, then the proof itself would be self-referential and thus incomplete. For one can not prove a statement, with the statement itself.

Mathematicians gotta eat too! Now you've made me hungry!

I have the German original.

Is there a connections between civil engineered trusses and atomic structures? This video shows a natural quantized effect using a version Euler’s Contain Column Theory? This video of an engineering test models the quantum physics problem called “Particle in a Box”. The wave function is used to predict the location of quantum particles, atomic structure and molecules. th-cam.com/video/wrBsqiE0vG4/w-d-xo.htmlsi=J5jCMxq3pRe_P-gG Very stable trusses and truss core panels have been fabricated using the process shown in the video. The video shows how materials naturally respond to induced stresses in a “quantized“ manor. The process’s load/deflection’s sawtooth curve with its exponential fit in the engineering study shows the previously unknown bifurcation between quantum jumps. The effect has been used to make light weight structures and shock mitigating/recoiled reduction systems and earthquakes isolation systems. The model shows why with the, exponential load increase and loss of resistance at phase change, quantum jumps are so very fast.

oops that is theta, not phi

Triangle has 180 degrees. Psi plus phi plus something equals 180 degrees. Here pi is the something.

I absolutely love your channel! Amazing content!

Thank you so much!

Beautiful video! Thanks!

Thank you so so so much, but physical next time, please! I hate computer stuff. It's not weird to make a video that includes you flipping pages and writing. That's just more natural and real (pun intended)!

Offbeat and interesting.

The ancient fascination with spirals, "it's always NOW", and Cosmology in perspective maps suggests that knowledge of Math-Physics is cyclical and epicyclical to the e-Pi-i sync-duration 1-0-infinity instantaneous limits, from which ideas such as Hilbert's Infite Hotel accommodation of mono-dualistic rooming scenarios are emergent phenomena and worthy of numerical analysis of derivatives.. "You just look (listen, hear and see), and you notice" all those entangled aspect-versions of coordination-identification positioning systems derived like the Hotel of Conjecture. I very much doubt German Math-Physics is in any way inhibited outside of politics.

Great rant and love the cat! I wish more books on proof would address what I consider to be the central issue right out of the gate. That is proofs are tree structures with certain constraints imposed by the inference rules. Velleman does this to some extent, but one of the best books for explaining proof trees is Using Z by Woodcock and Davies. They use Gentzen style natural deduction which is pretty easy to understand.

Whether or not you loathe baby rudin, it is indeed a must-read for everyone

It's such a waste. The author could have used the opportunity to give a glimpse into more advanced topics in continuity, limits etc. They could have said "...this is not a proof that the continued fraction approaches 2; in fact, we don't even have a clear concept of what 'approaches' means; for that, we need a more rigorous approach, which is what analysis does...". Sure, one might say these are just middle/high school students, but students are naturally curious. Offering a peek and motivation into more advanced topics is likely to pique the interest of at least some students.

That stuff is for an old-fashioned quantum mechanics course, which is annoying for young math students because they take it before they can learn it rigorously. It's much more satisfying to start with quantum information theory and quantum computation, which is much more accessible mathematically.

Dammit! Now I have to buy this one too😅

I propose a proof language that is keyboard friendly in this paper: "Towards a coding-like experience for mathematical proof writing". The language is based on Fitch and supports comments, macros, object abbreviations and other syntactic conveniences. As a person who is clearly passionate about proof I would love to hear your feedback.

I am currently a 1st year math student at university. When I was in my last 2 years of highschool, I didn't really like how math is taught so I taught myself how to write proofs using books like book of proof and the one by Chartrand.. By 12th grade I have mastered the majority of the material. Reflecting on that, I believe that some proofs should at least be taught to highschool students, It is completely achievable by anyone with knowledge of basic algebra and the way if thinking it requires is very useful to everyday Life.

A very unique calculus text.

can u and ur cat do vol II

… and that’s how a book review is done! Loved the video, congrats! Have you heard about ‘The Calculus. A genetic approach’, by Toeplitz? It’s also a very interesting introduction to the subject.

BTW, Courant's first cousin, Edith Stein, was also a student in Göttingen at the same time. She studied under Husserl and followed him later to Freiburg. She converted to Catholicism, became a nun, and was later rounded up and sent to Auschwitz and murdered. One of her fellow philosophy students, Roman Ingarden was from Poland. He returned after WW1 and became a teacher in Krakow. One of his students later was Karol Woytyla who later as Pope John Paul II, canonized Edith Stein and made her patroness of Europe.

Thanks for the video, my favorite calculus/analysis book is mathematical analysis by Vladimir A. Zorich

The German causally says "but later they moved to the United States." NO. They were Jews who had to escape Nazi-Germany. Rewrite the Holocaust out of history. Don't mention their Jewish heritage. Now the hateful antisemitic comments can come.

What a masterpiece

I had never heard of this book, but it looks fantastic! Calculus is one of those areas which are often brushed off as "too basic" by students (myself included) who are eager to go on to higher math. The older I've grown, however, the more I have come to appreciate the incredible conceptual sophistication that basic calculus has. The breadth of applications, depth of theorems, and usefulness of the skills trained. You're never too advanced to learn something enriching from picking up a good calculus book!

Nice video. There are so many good books on calculus that this one Will struggle to survive in the book market. For this type of books the most accepted one is Spivak's calculus (expensive). The three dimensións or faces of calculus are: integrals, derivatives and series. However, this is a dover book it may have an opportunity.😂

Courant-Hilbert is a well regarded book. Courant was a 'master' of the variational approach. Courant style is a little bit terse and 'verbose' at times. The problem with this book is that it is outdated, it was written before the invention or creation of functional analysis. Courant tried to update it by adding appendixes and a third volumen on numerics but it was not an easy task and he got old and died. Nice video👍

Mu favorite calculus text is introduction to calculus and analysis by courant and john.

Hello Mr.Ming is it possible to ask for your email id to write to you?

Hello boss, do you need a Math PHD to learn from these books?

Thank you very much

Respected Sir! Thank you very much for your very thoughtful presentations of various books in mathematics. I have not only enjoyed this paricular presentation, but also the one on "Mathematics for Physicists by Hilbert and Courant". Please keep it up! Shiva.

i have spent my life skipping the exercises, and also puzzling why my progress in maths was so slow

it is sad, that the general public do not realise the important interplay between mathematicians and physics. The average person can probably name a few famous physicists, Newton, Einstein, Heisenberg but struggle to name any famous mathematciains. Mathematics can seem very abstract and obscure, but it is the language that we use to try and understand the physical world.Biographies of mathematicians such this one, bring them to life and help to redress the balance

Exercise 1: This book has no exercises. Dear reader, take your time and figure out witty exercises for each chapter.

선배, 따봉올려드려요. 매번마다 좋은 가르침을 항상 올려서 수학과 과학의 진전이 기대되는 나날들까지 더해서, 같이 많은걸 배우곤 갑니다..

What editor were you using? I liked it.