7,000 SUBSCRIBERS! MAJOR UPDATES FOR CITY TUTORING - PLEASE WATCH

[@quantumjunkie55.6]

Love your videos. Will definitely purchase your new book. I have a Ph.D. in Physics and I never get tired of reviewing math, always something to learn.

[@citytutoring]

Thank you! That means a lot to me! I really try to make exercises that are both rigorous and also useful. Hopefully I will be able to finish the book by February!

[@alvinshao6229]

Congrats on 7,000 subscribers. Your take on a rigorous math education is something I admire.

[@douglasstrother6584]

"The Math Sorcerer" is a big fan of "Book of Proof" and concurs that proof writing is a chronic deficiency in mathematical pedagogy.

[@apollo_gz]

u are a blessing to all the learners who come across your channel and I can tell you are Christian

[@mullerss1]

You, kind Sir, are indeed a Big person with a big heart! :) As concerning a subject for study. Well, I mean - “Topology” would be nice to cover!

[@Lettucebird1]

Congratulations, Professor Cromwell!

[@KANCHANGANGWAR-u2n]

Congratulations on 7k subscribers.I love your videos

[@petihundeuhun8950]

Congratulation! I would love to see more proof and calculus on the channel. 😊

[@julians9763]

Congratulations Professor Cromwell on reaching 7000 subscribers. May it double within the year. I like the spring season as well. Where I live is Summer. Melbourne Australia.. I look forward to watching all your encouraging videos. Make certain the students you tutor call you Sir or Professor Cromwell when addressing you or asking you questions.. From the way you speak I would say you come from a well educated family that originated from England and settled in a New England State.

[@citytutoring]

Thank you very much for your kind comment! Personally, I am indeed originally from the northeast/New England area, and yes, indeed the Cromwells originated in England! What a guess you have made! Students do in fact call me sir or Professor Cromwell...although when I visited dear friends in Scotland, I suddenly became "Alfie!" to them after they had one too many drinks! By the way, Australia is one of my favorite countries...mostly because of the "tough" (not sure now, though) reputation of the Australians. I've always felt a certain sense of brotherhood, or to use the cliche, a "special" relationship with the English speaking peoples across the world.

[@julians9763]

The question that might help your prospective students. In regards to the Metric system, to you teach it to your students with the reason that that they will need it, not only when outside the USA, but even within due sciences and international visitors? If the students are given a mathe book with the metric system, will they understand it?

[@citytutoring]

Yes, so in my Math classes we tend to use both. Normally, the metric system by default on subjects like Physics or conversions, and then the imperial system on more informal type word problems. I believe that students should learn to be comfortable and fluent in both measurement systems.

[@PaladinLeeroy42069]

Can’t wait for your book and some updates on how the class is going. I started going through The Book of Proof a few weeks ago and I’m loving it. Russell’s Paradox was awesome to reflect on, as well as the power sets of power sets!

[@citytutoring]

Yes! To me, The Book of Proof is one of the most well-written proofs textbooks for the modern age. It really breaks the topics down in a way that a student who has never been exposed to this can truly understand if done well, and patiently. I always tell my students the following, and I am very serious about it: DO NOT RUSH YOUR MATH. I would much rather a student spend MONTHS if necessary on a single chapter than rush through things sloppily. Oh, and yes, I love the power sets of power sets! When students are exposed to proper mathematics, the vast majority end up enjoying it and never realized how truly fun and thought provoking it really is!

[@PaladinLeeroy42069]

@ thank you for the advice. I’m tutoring some of my peers, and it’s hard to convince them that a better use of our time is often to work on algebra and trig than to continue integrating when their issues are with the former

[@xmvziron]

I just discovered you today, and you are the first person in 3 years to make me take a pen and paper and *willingly* solve polynomials like old times. Thank you!

[@citytutoring]

Your comment has brought me joy! Thank you! Polynomials are one of my favorite topics in Algebra.

[@ben_g_min]

Love your enthusiasm for Mathematics education, can't wait to watch this channel blow up, keep it going!

[@apollo_gz]

U gained thousands of subs in few days and ur book is something im interested in bc i struggle learning math and solved problems helps me learn ty

[@citytutoring]

My pleasure! May I ask what grade you are currently in or college?

[@BreezeTalk]

Dropping by to say how much I appreciate you using the word please in your title. Very kind of you. Thank you.

[@walter274]

Congrats on your success. Rolle's thm is more important than most people realize. At least I didn’t really grasp it’s significance when I first learned it. The SVD and other matrix factorizations are becoming extremely important, gradients are a fundamental tool for optimization in statistical learning. Derivatives of matricies confused the hell out of me. I still have trouble interpreting the phase plane diagrams for ODEs for some reason. I was never that into ODE. In terms of more pure math, people are always going to need videos on epsilon delta. Unary operators are bit weird, not super hard, but typically underserved. Continuity is extremely important. It seems so simple, but there are still some challenges. I can't say i have a great understanding of how the reals are constructed. When i learned there were different types of infinity i was like wow. The topic is accessible, but not everyone has encountered it. I haven’t seen many videos on the analytic geometry of conics, like the coverage of them in Adams and Essex. Counter examples are always fun. I know a lot of these are niche topics. I don't know if they resonate with you or anyone else, but these are the topics that came to mind.

[@citytutoring]

Thank you! To me, Rolle's theorem is a perfect example of the mathematical art form-its beauty lies not in its utility (though there are some who will certainly value that!), but in its precision and inevitability. It’s a small masterpiece within the grand architecture of analysis, demonstrating how profoundly connected our notions of continuity and differentiability truly are. The singular value decomposition-fascinating, yes, though I must admit it strays toward the domain of applied mathematics. Nevertheless, its algebraic structure and geometric interpretation have a certain appeal. Phase plane diagrams for ODEs, however, feel more like an artifice of visualization than pure mathematical inquiry. Perhaps that’s why they might seem less compelling-an aesthetic interpretation rather than a deep dive into the equations themselves. Still, they do offer a glimpse into the behavior of systems, even if the joy of ODEs lies more in their proofs. I agree with you on counterexamples because they ensure we stay honest in our definitions and conjectures. A counterexample is a story in itself, revealing the edge cases where intuition alone cannot tread. Example: "Ohhh but if a function is continuous everywhere, it must be differentiable somewhere, right? It’s so smooth!" Oh really? The Weierstrass function enters the chat.

[@walter274]

@@citytutoring The eigen decomp and SVD are cool, because they break up a matrix, which is a linear transformation into rotate-scale- rotate. The SVD relaxes the dimention constraints on the eigen decomp. I think i'll be fine with the phase planes. I just need to a lot of them. I don;t really care about them, but i'm looking to do some tutoring and in AP calc they ask about those, and when i take practice test, to ensure i actually know what i'm talking about, i get those questions wrong. The Weierstrass function is great counter example. It shows why differentiability implies continuity, but countinuity doesn;t imply differntiability. In general we're told a lot of times what things are a vector space, or are linear operator, but more counter examples are always welcome. Lol, maybe i'm just slow.

[@sergeyart1120]

Congrats, Professor Cromwell! Sergey here. Over 6,000 subscribers in just two months-wow! Wishing you continued success in all your endeavors!

[@citytutoring]

Thank you very much! I hope you are doing well! Are you Sergey from Brooklyn? Former student?

[@sergeyart1120]

@ Yes I am!

[@gregmackinnon3663]

Congratulations on reaching 7,000 subscribers and I am sure there will be many more to come! People are yearning for a return to the standards of old in this slapdash age of ours. Mathematics is a great teacher of humility and perseverance. Qualities we need in abundance today. I enjoy your approach very much!

[@GChief117]

Congrats!!

[@citytutoring]

Thank you for your support!

[@jerryeldridge1690]

Thanks for making your videos. It would be nice to see videos on non-standard mathematics topics---those left to the learner beyond the educational system (secondary, higher-education). For example, the GRE-subject math has a category called Mathematical Models to mention something from earlier in higher education. Something like Linear Programming, Optimization, Decision Theory, Mathematical Biology, Mathematics for Neuroscience, Reinforcement Learning, Machine Learning, Optimal Control and Dynamic Programming, etc.

[@talishjain9354]

Good morning / evening sir, congratulations on reaching this milestone of 7000+ subscribers, I have a hard time understanding complex numbers, I hope you would cover it in the future.

[@citytutoring]

Thank you! Ah yes, I definitely plan to do videos on the set of complex numbers.

[@yusuf7376]

Maybe you could possibly do some videos on going back to some basic math like Pre-Algebra, thanks for the great channel!

[@Obell3]

I’m pursuing my degree in mathematics thanks for your videos and book recommendation

[@citytutoring]

I wish you the very best in your studies! We need more people doing what you are doing in our colleges and universities!

[@JuanManuelPlaceres]

You have an amazing channel, please keep it up like this!!! As a fellow math student, i fully support your project.

[@citytutoring]

Thank you very much for your support!

[@spaceman688]

I have been teaching american students (mostly undergrads), and let me share some topics that they lack knowledge of (as an outside perspective): 1) Set theory. I do not mean that undergrads should learn about transitive sets, forcing etc... but Zorn lemma (,induction, and choice) is just used everywhere. Also, ultrafilters and ordinals are also very useful. 2) Descriptive set theorical results. I am not talking about the very deep results. But the notion of completeness, separability, compactness, Baire category etc... just make our life a lot easier and help us understand results in analysis and topology a lot better. 3) Modules/ categories/ homological algebra. I don't think I need to explain the applications. Also, some of my students have quite a good understanding of groups/rings/vectorspaces, which is nice (that s why I excluded them). So I think these are some topics where they lack good sources. I think you have some very nice videos, and I hope my perspective helped. Keep ut the excellent work :).

[@citytutoring]

You are right! Set theory has been utterly neglected in the past decades. The last time schools made a serious effort to teach sets was from the 1960s to about the early 1980s in most districts. After the early 1980s, there were noticeable and verifiable declines in nearly all schools in America. I was "blessed" because my high school, though not perfect, still had very tough teachers who were of the "old school" and taught inductive reasoning, but by the time I got to senior year, there was a decline as well. Thank you for your suggestions and for your support. Your perspective most certainly helps!

[@AvisBell-m5g]

Thanks, Have you seen the Math Books for elementary school books for students.

[@citytutoring]

No, I have not, as I am not specialized in elementary education. However, I do know that in some school districts they are, unfortunately, using what they call "scripted lessons" and "Illustrative Mathematics", which have both been disastrous.

[@dicksonrk]

Words of encouragement: math is hard, teaching math is harder, making video supplements...herculean! By the way I fed your exponential problem set thru gemini ai. It scored 9/12!

[@citytutoring]

Thank you! Ha! I appreciate you telling me that -- it means that I was somewhat "on to something" with the claim that some of my problems can be "ai proof"!

[@bterry101]

Great channel! What level of prerequisite is set for your upcoming book?

[@citytutoring]

Thank you! For my upcoming book, you should be comfortable with Precalculus topics at the very minimum. What grade/course are you in?

[@bterry101]

@@citytutoring College tech Calc 2 - one of those who didn't care and 'C' ed my way through (40 years ago) now I'm ready to retire and properly start learning with fascination, what I skated through then. Hoping to take on Math and Science as a retirement hobby to keep my lame brain from totally rusting out. Appreciate your approach - you are a blessing to many folks!

[@brunnocarvalho1941]

🌻🌻

[@cmdstraker]

It's a bit of a speciality topic, but I would appreciate a video on generalized eigenvectors.

[@citytutoring]

OK, I will make a note of it. Will do my best to discuss it at some point!

[@cmdstraker]

Government-run education is in pretty bad shape all over the West, not just the U.S. Which just makes high-quality private tutoring institutions like yours more important than ever.

[@cmdstraker]

The guy calling you an elitist under the last video was particularly funny. He probably didn't realize these are basic concepts required for any kind of engineering job.

[@citytutoring]

I had a good chuckle with that one! Ah well, I've been called worse...

[@Alex-h4z2u]

Han har ju banne mig en Montefjanton-fåtölj!!