@minecraftcommandnerd1280to dress well and be well presented. We had mathematicians sit in investor meetings for our funds. They dressed like him as formality can make others take you more serious.
Yes, but in a good way. He seems like a great teacher, and I bet his students will remember a lot of things he tells them about life in general, as well as in mathematics. We need more teachers like him who have a level-head and know that a good teacher also instills in their students a sense of what it means to lead a good life.
Mathematical logic allowed me to discover and enjoy the world of philosophy. As funny as it may sound at face value, it was very much the case. I am very thankful in this regard.
Professor Cromwell, I appreciate your authenticity and dedication to mathematics. I could only imagine how far along your efforts go genuinely helping people understand the basics of the subject. In my middle school I was in the 'honors' level math class and we were learning algebra. I distinctly remember fundamentally not understanding the material. Retrospectively, there was (almost) not a single concept in that class that I would have been able to derive/explain on my own. Yet, I came out of the class with the equivalent of a B or B+ as my final grade (and on the standardized NY Algebra 1 Regents Exam). This is a testament to how flawed the education system is here in the States. I went on to my freshman year of high school with the same foundation (or lack there of) and managed to keep the status quo whilst taking geometry... Every once in a while the concepts I had not grasped previously would come up and haunt me before my eyes even beyond the context of my classes. It was in those moments that deep down I knew I had to do something before my ignorance snowballed. That summer, because of the pandemic, I couldn't find a feasible job and so I took it upon myself to be somewhat productive. So it was that I decided to reteach myself all of algebra alongside certain topics from basic arithmetic from the ground up! All thanks to TH-cam content creators like yourself. Because I was on my own, free from the clutches of common core, not only did I master high/middle school algebra, but I also gained excellence in the ability to reason mathematically. Most importantly, I learned how to learn. After that episode, I returned to high school as a sophomore, in which we were to take on Algebra II. I have a fond memory of being filled with such great mathematical passion that out of sheer enthusiasm, I asked a friend of mine who I thought to be the smartest one in my class to derive the quadratic formula. And when he said the words "Why would anyone know how to do that?" I (without hesitation) took the time to explain it to him, and doing so was a truly eye opening experience. Upon realizing how far ahead I've gone relative to the curriculum, out of curiosity, and a new kind of love for learning, I taught myself calculus the same way. I had snowballed up the mountain instead of down it, which took immense effort/dedication, but it all paid off. Unfortunately, the more I learned about mathematics, the more I realized how much I did not enjoy it in pure abstraction, instead preferencing physics; and that's okay. Now I find myself studying engineering in university. To say I am glad that I have such a well rounded mathematical eye would be an understatement. It has helped me tremendously keeping me ahead of the game at all times. If all continues to go well, I'll be taking a differential geometry course this semester in pursuit of learning General Relativity at some point. So wish me good luck... I'll need it! Although your content has not directly aided me on my own mathematical journey, I'm sure another like me out there has. I cannot thank people like you enough for taking time out of their own lives to better others. Thank you!
Thank you for sharing such a thoughtful and inspiring story-it’s a privilege to hear how your dedication and curiosity propelled you forward. The image of 'snowballing up the mountain' is brilliant and perfectly captures the essence of mastering challenging concepts. Your journey from reteaching yourself algebra to delving into calculus, and now to engineering, is a testament to the power of perseverance and self-guided learning. It’s excellent how your mathematical foundation has become a tool for exploring deeper truths in physics and engineering. Differential geometry and General Relativity are no small feat, but I’m confident your passion and discipline will see you through. Remember, the curiosity that led you here will keep pushing you forward. I wish you the best, and thank you for the kind words-I hope my content inspires others as much as I have enjoyed reading about your experience!
Your story truly is amazing and one of a kind indeed, most definitely the most fascinatingly inspiring one out there. And I, too, would like to share my relationship and history with mathematics. In primary school, i used to absolutely despise said subject. Yes, i did, and i beleive that was because i wasn't taught mathematics properly, and it has been introduced to me in quite the absurd way. However, my whole perspective on that field of study completely turned upside down the moment i realized that all of what i think about not only mathematics, but any subject in general, is all in my hands, and my own will. And so, i decided to unfold my arms and prove myself that i truly can learn to love any subject, at any time, without even breaking a sweat. And i've come to beleive ever since that if you change your mindset, you change all that is around you. Mathematics, truly is a complex area of study, and that cannot be denied no further. Thus far, as the saying goes 'you cannot control what surrounds you, but you surely can control how you see it', one may still love mathematics despite its difficult demeanor and how it may come across as strict and unforgiving at times. The small drops of water form the mighty ocean, and that is true. with small, precautious careful steps you can acheive even the most absurd goals or objectives you desire. And that is quite exactly what has happened with my case. Little by little, i slowly but surely started getting better at mathematics and in a blink of an eye, i found myself being better at that very subject than ever before! All of that is thanks to consistency. Consistency is everything. Motivation or discipline stand no chance against it. It is with determination and fiery steadfastness that you reach victory in any subject, whether it be mathematics, engineering or physics, all you need to become top 1# is to never give up and keep fighting for your dreams. Upon going from the absolute worst at said subject to one of the best, if not the best at mathematics, at least in my grade, it has become crystal clear to me that it is never too late to change and get better at any area of academics, and if, a merely average human can do it, then ofcourse anyone else can, too. Thank you for sharing your experience, i will always remember it when i feel down and trust me when i say this-that the majority of the forty-eight people who have witnessed this comment of yours, has been given absolute motivation to give another chance to mathematics, stand up and start fighting once more, to hopefully share another bright story such as yours in the upcoming future.
Lately ive been studying Epictetus works on Stoicism, and he put enormous pressure on learning logic in that it is essential to truly understand and apply Stoicism.Because of that i set out to hone my logical thinking, and i will put work into understanding this course!
I am glad to find ur channel. I used to be one of those kids saying "when are we ever gonna use this" and not take maths or school too seriously but I see the value of maths now. I hope I can catch up and be good at maths from ur teachings. U say what I need to hear too I respect it🙏
Engineering student here!! I think your words at the beginning were really important. I used to suck at math back in middle/my first years of high school. I used to think I would never be able to get to the more advanced levels, and I used to blame external factors for me not being able to be successful. Like you mentioned, that's not gonna get you anywhere. I think I really started to pick up my skills again (I used to be a "gifted" math student) when I finally started blaming MYself for the grades I would receive--that's when I began to get A's, my junior/senior years. When I took pre calculus, my teacher was wonderful, but she lacked explaining the "why" to us sometimes. I ended up falling in love with trig especially because I would go home and look up the answer to my "why?" Math is beautiful because there are rules and there is discipline to it. It comes together beautifully when you follow its rules, and that's what makes me want to keep doing it.
I used "Logic and Philosophy" (4th Edition) by Howard Kahane as an Undergrad. The first half of the text covers the fundamentals of Logic, and the second covers applications.
I'VE JUST STUMBLED UPON THIS ABSOLUTE IMMACULTE & BANGER OF A VIDEO; YT PLACING IT RANDOMLY ON MY SUGGESTION FEED. WOULD'VE THOUGHT OF GETTING IT EARLIER. I LOVE WHENEVER ANY PROFFESOR GOES RIGOROUS JUST THE WAY LIKE THIS; ABSOLUTELY AMAZING TO PONDER UPON; AND ALL OF YOUR SETUP AND ALL, REALLY DEDICATES AND DEMONSTRATES HOW "TRUE" MATHEMATICIANS SHOULD BE IN A WAY OR THE OTHER. SUBSCRIBED; WOULD LOVE TO WATCH MORE OF SUCH RIGOROUS, STRAIGHT TO THE POINT, VINTAGE EMMERSED IN MODERN LIFE -STYLE-ISH VIDEOS.
10:11 MAN do i love this man, from the outfit, from the background, from the accent, from the attitude. But greatest of all is the math content otherwise i wouldnt find myself here, and that really is the cherry on top. Keep doing what you do man you got supporters behind you
Looks like a good start for a logic course. Discussing propositional logic (syntax, semantics, proof system), first order logic, important properties of those logics like soundness, completeness and compactness.
In case anyone's not satisfied with why p->q must be True when p is False, I recommend the section on Conditionals from the first chapter of "How To Prove It" by Daniel J. Velleman. You will find the arguments there quite convincing.. (I wish this textbook, or at least some distilled version of it, could be taught as standard curriculum early on in high school or even in middle school.)
I asked my teacher why logic was not taught at an earlier age. Their response was that it would intimidate kids. That’s not a good enough answer. Logic is important to understand truths of mathematics. I wasn’t introduced to the subject until college. It was from logic that I developed a deeper understanding of mathematical structure. When I was younger I found math challenging. I believe if I was introduced to logic earlier it would have made a world of difference. Thank you for discussing logic. 🙏
Thank you for your comment. One of the major problems is precisely what you mention - by the time students get to college, they are completely lost because they do NOT have any training at all in logic. Schools used to teach "Logic and Rhetoric", but now? They're too busy fixating over whether the teachers use the right "pronouns" and say the government approved talking points rather than actual teaching and learning. The politicians who have run our schools to the ground are not in any way interested in having an educated population. An educated population would not tolerate the abuse and illegal behavior we have seen from our governments for decades.
Professor Cromwell I still honestly don't get some of those comments you mentioned about people attacking your work. You were literally the kindest professor I had who never cut off a student who wanted to learn. I remember how youd even stay past your office hours just to talk about math and actually was the only professor I had who even asked me about me personally and my well being. You also tutored my brother (Luis the Hispanic kid with the thick accent lol) but you made it a point to help everyone with Math. People can be so awful smh. But I know you dont need my help to defend yourself!
Good ol' Euclidian Geometry (High School Sophomore Year) finally turned-on my "Math Lightbulb". The visual and tactile nature of straightedge & compass constructions allowed me to see the logical structure of proofs.
YOU NEED MATHEMATICAL LOGIC! It is the very first video that I stumbled upon. Before I start my comment I must firstly introduce myself. So I am a 10th grade student from India studying in the CENTRAL BOARD of SECONDARY EDUCATION (CBSE) where the national curriculum starts from 9th grade (Before that all of the syllabi are handled by the schools individually or under some corporation in the case of private schools). I am the type of person who has been very much interested in physics, Not the mathematical one but the one where mathematics are not involved like that of encyclopedias, pictures, black hole related TH-cam videos, rockets and their launches, history of science and much more. But as soon as I started to grow up, I realized that many of what I was doing is not sustainable for a long run if i were to top my 10th class final exams then I must rewire my brain with the help of mathematics. Which i did and at the present time while my friends are all cobbled up in remembering the formulas, i fondly remember all of the mathematical formulas with some being able to derive it, Like basic trigonometry identities of sin^2A+cos^2A=1 is derivable by using Pythagoras theorem and their own more derivatives, visual representations of exponential and linear graphs, the sine, cosine, and tangential waves in the Cartesian plane, and much more. In accordance to the syllabus, I have not gone much further due to two main reasons 1.I will get far more opportunities and a good environment in 11th and 12th grade for my preparation of JOINT ENTRANCE EXAMINATION (JEE), as it will also eliminate most of the worthless people to stay with. 2.Also due to some of my bad habits, negligence and laziness, which has happened to stop me from getting the top positions. I have truly not studied throughout the entire year, I am here is just again relearning what my teachers has taught me in the classes, but still I could retain more than my friends and add more to it. I have the scientific and mathematical capability, just waiting for it to get exploited. And that sums up my position in my academics( I have not talked about history, civics, political science and economics along with my Indian literature with English and computer science as it is irrelevant to my introduction here). I want to do something in quantum computing when i will grow up, as it is the future and there will be more demand of highly skilled and interdisciplinary thinkers like me and similar like minded people. Timestamp(9mins into the video) In this section, I really liked on how you instead of starting about mathematical logic, you started out with the need to talk on it, as not only in the US bur also in India we are having the similar problems, which you can read more in this article www.21kschool.com/in/blog/problems-in-indian-education-system/. That how you presented the problems faced by my generation, where distractions like social media has truly done damage to the minds, souls and culture of the people all around the world. Unfortunately, as of now I was writing it for the comment but due to some project related problems i cannot fully write it, So sir please accept my apology and I just wanted to have a little bit of talk with you since from you the video you have presented yourself as a no-nonsense guy and i really like it, So sir if possible can i get your email ID through which I can contact you and share some ideas from the other side of the world.
bhai you wrote a essay ;-; , but appreciated your effort i too like theoretical physics and about the last part that u said ' i am gonna eliminate some people" can u also help me how to eliminate because lately i am going in wrong directions , and its boards for me too next year i am hella scared tbh
This was a greatly enjoyable video! Having taken an intro to logic course, this video was review for me, but I do look forward to the rigorous introduction of the "for all" and "there exists" operators! I've self studying linear algebra, and although I can use these symbols to great effect, I've never taken the time to ground my understanding in this respect, and it's especially important to me as a prospective math major. Beyond the math, your demeanor and philosophy on work and life is quite refreshing. The simple joy of "southern barbecue" brought a smile to my face. Regarding your point about the deterioration of grammar and cursive, although I was taught both in elementary and middle school, the maintenance of such machinery of communication has not been a top priority. Nevertheless, last year I took it upon myself to re-learn cursive, and this year I feel that philosophy class and AP Latin have together pushed me to sharpen my grammar. On an unrelated note, I tossed a quarter and noted the result 395 times over the course of this video. I got tails 56.3% of the time and heads 43.7% of the time. From my stats class I can deduce that there is approximately a 0.61% chance this happened purely by chance. Neat.
Thank you for your comment and support! Yes, we will be covering all of that in this series. Cursive is a great skill to maintain, because there is nothing wrong with balancing old skills even if they may not be "needed" (whatever that means!) nowadays. I use it daily, and it improves memory and taking good notes. 395 times eh? That’s commitment! A 0.61% chance, you say? Perhaps the universe is playing a cosmic joke, or that quarter has a preference for tails!
I would greatly appreciate a series on mathematical logic. Im currently a college student and I have just learned how important logical thinking is and school has always taught me that mathematics is a memory game. I just started solving different AIME-AMC12 questions for fun and have been doing it for a month now.
Thank you! Check out my latest video if that helps. All the logic videos I am doing are under the playlist called "Mathematical Logic/Proofs". AIME-AMC12? Beautiful! Keep at it!
@@citytutoring Please continue with this series of explaining mathematical logic, I JUST CAN'T GET ENOUGH OF THEM, EVER, please professor, you are doing in a sense, a "holy" duty for science, since logic is foundation of everything. I also think that all of mathematics(and everything else, since everything else is mathematics) is nothing else but Logic and Set Theory, ...
I’m looking forward to this course on logic. I like to study my material so that it overlaps; if I want to learn something I’ll try 2 books and a TH-cam course minimum. This is definitely the series I’ll be following.
My fondest memory is doing pages of proofs, and labeling the logical reasoning for each step. It's one of those things I wish I could do in exchange for room, board, insurance, and currency.
Truly apreciate your words. I'm an italian uni student, and I can say with certainty that Italy is also becoming a lost country, where emotions matter more than facts. Discipline and respecting rules are slowly becoming a thing of the past.
Thank you for your comment! Such a shame isn't it? A beautiful country like Italy, with a rich history...and all going down due to the same poisonous attitudes. I do have hope though that there are still people around the world waking up to this reality and hopefully if we work together we can at least change some attitudes.
I have simple and basic knowledge abt the english language but i can definitely say that learning and doing maths helps me get better logic especially jee main or advance problems since and its because of them i am able to have much more borader choices and can think of a solution very quickly or just try to solve the problem at hand.
What you've said is undoubtedly true, sir, i wasn't even aware of thing like proof theory and mathematical proof writing until i was at my final year in Posgrad. This says so much the lackings in our mathematical educational system, we are only groomed into solving problems without understanding and experience true mathematical maturity
Sir, thank you for your attempt to stop the Visigoths. I appreciate the time and effort you expend to create your outstanding videos. Please employ a lecture classification system to facilitate my ability to go back to a previous lecture, that you reference, to delve further into the point you are focused on. Also, the classification system would help keep the lectures in sequence. Thanks for your consideration of this request. Shortly after the Civil War, my seventh-grade English course spent about a month diagramming sentences. It helped my reading and writing considerably.
Thank you for your comment! All the videos will be numbered in the order of post. Is that what you mean? I am glad that you learned about diagramming sentences! I was also taught how to diagram, although in my case it was before the Civil War.
I’m an older student and I have ASD. I’ve been blessed by some of the best professors ever, who not only got excited when I asked to see the proof, but readily showed it to me either in or out of class depending on how long it might take. I taught myself math up to Calculus 2 (still had to take both) from older math books that did show a lot of the proofs, so I’ve always used them to understand how or why a specific function or formula exists. You’re absolutely right, though, the mass produced thinking of “just learn my steps” is sad and insane to me. I need to know why and how first. I’m going to add in mathematical logic and game theory to my schedule. That’s two videos in two days that will cost me thousands of dollars. 😂
A formal logic course would be great. The closest I've ever come to one was Boolean Algebra as part of my electronics training. In my youth, I encountered people who could not learn mathematics because they lacked the humility to accept there were things they did not know.
I fondly remember a Symbolic Logic course [offered by the Philosophy Dept]. We had to derive certain truth statements given an initial statement using LOGICAL TOOLS. It was fascinating. Understanding quantifiers and the NEGATION of quantifiers is essential to math. Also, the understanding of contrapositives.
you look like clark kent sir 😅 , but yes i agree , we're just fed concepts , never asked how or where did this come from . please do upload more videos like this , you've earned my subscription
Nice timing. I’m reading How To Prove It along with tackling some linear algebra proofs. I’m also reading a book on term-functor logic (as opposed to propositional logic). Yet, I’ve noticed my attention span is destroyed. It helps to tell myself the lie that I have an imaginary class with imaginary tests such that I can muster up the urgency to study automatically.
Interesting when you mentioned about identity, I think there needs to be that encouragement of creativity for newer students, especially in the US, how they see themselves when faced with mathematics (or any difficult discipline) how they can incorporate the discipline to make a definitive argument based on independent thought and seeing their contribution on a universal impact, empowerment and validation for themselves. Few thoughts 💭
Creativity is one thing, but saying "because I am (insert constructed identity in the blank), then I am exempt from an assignment, or from consequences for my behavior". Here in the US, in our public schools, there are serious discipline problems as a result of that. For example, a student will claim he has "mental health" issues, and will expect a teacher to excuse them. Teachers are not therapists. Teachers are there to teach and give assignments under certain syllabus conditions to all. If a student is not up to task, then he needs to check out or get the help he needs instead of using identity as a crutch or, worse, an excuse for what in many cases is nothing more than bad behavior.
TikTok is owned by a Singaporean company… Not seeing the connection between the general point of the video and this point. And I think he should make a distinction between logic and critical thinking. Logic is very rigid and sequential, while critical thinking is much more flexible and tangible. Critical thinking is the tool for understanding logic, that without it no one would understand.
I see your point, but I respectfully disagree with the distinction you're making between logic and critical thinking. Logic isn't inherently rigid; it provides a structured framework for reasoning, which can be applied in both flexible and creative ways. Meanwhile, critical thinking is more of a broader cognitive process that involves evaluating, analyzing, and interpreting information-often employing logic as one of its key tools. The two are deeply interconnected, but critical thinking doesn't necessarily "understand" logic; rather, it uses logic to form coherent and well-reasoned conclusions. Would you mind elaborating on what you mean by "flexible and tangible"?
I agree with a lot of the points he's made regarding the education system, only thing is, this dude is acting loopy, with an odd pessimist connotation in every word he says. It's almost like watching a video of him ranting, as opposed to presenting a reasonable and focused criticism.
that's just not true. If apple hired a danish ceo one day, that would not make apple a "danish" company. At the end of the day Tiktok is owned by a chinese company (Bytedance) and has to take orders from the CCP
@ That’s a fair point! His critiques of the education system are insightful, but the way he presents them might come across as more of a rant than a structured argument.
@ Thanks! Stumbling upon your channel is like a breath of fresh air. I have aspirations to teach children and adults alike in mathematical thinking-for reasons you mentioned in this video. I am trying to work out a program with our local rep to the House here in GA. I have even showed my friend your video to give them an idea of what I mean!
You are correct about mathematical logic. It is very much needed in today’s schools. I find myself needing to teach at least some of it. Our state had the genius idea of trying to put every student with or without Algebra 1 into Geometry. And our state standards writers thought that in their infinite wisdom they knew more than Euclid. So they took out most all the proofs and logic out of Geometry. And they wonder why the kids fall apart in AP math when it is no longer copy and paste, paint by numbers style calculation oriented math. So yes, I teach it and do it as often as I can. But this is sometimes going off standard. It’s not exactly in the AP CED and not exactly in the state standards before it, but you cannot accomplish the CED outcomes without instilling some of it.
As someone who has a great deal of logic textbooks, I think Hurley's "A Concise Introduction to Logic" is the best introductory text I've come across. It was an excellent starting point for me for formal/symbolic logic. It gives you a solid foundation from propositional/sentential thorough predicate/quantifier logic, before you get into the real weeds of more advanced mathematical logic and set theory. I think any edition is great, which you can order for a couple of dollars online used. It also has a great deal of informal/inductive logic. If you're looking for something slightly more advanced, "Logic and Philosophy"/"Elementary Symbolic Logic" are both excellent. And if you want something pretty advanced/hardcore, "The Logic Book" might be the one.
To those curious toward the philosophical branch of "Logic", I reccomend Immanuel Kant's "Critique Of Pure Reason", and Harry J Gensler's "Introduction To Logic". Syllogism, is one of the things discussed in the latter aforementioned, which is what is explored in this video. Exploring the tenets of semiotics also doesn't hurt - there's a lot of overlap in the signs, symbols and denotations used in any kind of language (which is used to represent this, that or the other). Mr. "Citytutoringmath" if you can reccomend other texts and/or resources, feel free to mention them. I'm always looking for new knowledge, and you just happened to appear on my TH-cam feed by chance.
I love it when you post! Perfect timing too, there are a lot of really weird finitists in my recommended who hate mathematicians lol. They claim we should only account for things if they exist in the physical world. Ironically, despite claiming this outlook makes no assumptions, they assume that the empirical sense data they mentally process is congruent to the reality around them... lol... the truth is that these things all exist only because of god, and the infinite exists in his boundless mind.
Thank you! Actually, you're one of the commenters I always remember and it's always a pleasure to read your feedback. Ah, the finitists-equivalent to flat-earthers who think the horizon is the edge of reality. It’s amusing how they claim to dodge assumptions while standing on a mountain of them! Your point about God is spot on, though: the infinite isn’t some quirky abstraction, it’s the signature of the divine. Trying to limit mathematics to what’s physically measurable is like insisting Beethoven only exists because you can hear him on Spotify.
@@citytutoring Brilliant response! And I'm so happy to hear that! I find your channel to be very inspirational, and I love your style. Just to let you know, even when I'm not in the comments I'm always here!
@@JR-uc3nk I am not very well-read on religion (yet!) to be honest, however we do not need god for infinity type axioms to be justified (I mean, unless you precieve logic as a divine thing, which you can do... but as I said, I don't know much about it). So as a pure technicality, if we assume the contradiction of the infinity axiom in ZFC for example (you can do it in other systems, but I mostly care about ZFC interpretations) then there is a statement sequence that directly contradicts the law of induction which is WILD.
@@spaceman688 You should look into jay dyer. He has good videos on philosophy. But essentially, no world view can be philosophically reconciled without god, especially not the view of the arrogant and clueless empiricists we have seen since the 1600s. Look at Jay's transcendental argumentations though.
I'm a Brazilian with 14 years old and I pretend to study logical mathematics, to have a more easily preparation for mathematics in ITA's exam, the most hard exam of Brazil, basiclly. Sorry for the english, btw😅 I gonna improve that with the book "Grammar in Use" and with the study of the book "How to Prove It" to learn logical mathematics thinking In really, it's not to just get aproved in the exam, is that because i love mathematics and conhecimento ( knowdelege) idk how to write that😅
Would you recommend to study "Intro to mathematical Logic, Intro to Mathematical proofs and Intro to abstract algebra" before jumping into real, complex, functional analysis, topology etc....?
"The best lack all conviction, while the worst are full of passionate intensity"- W.B. Yeats. I thought this quote to be germane to your plea for logic and discipline.
Honestly, there isn't a better thing than mathematical competitions in this day and age where people from a younger grade could get exposed to a proof-styled testing format at such an early time in life. I'm happy to say that after doing many math, physics and programming contests that the combinatorial and number theoretic problems are my favorite because when they give you those problems, most of the time, they are not in the form of equations, just a bit of information with a few rules and it's your job to disect what you're trying to accomplish into little bits and solve it all at once. You don't need any prerequisite knowledge for those types of questions, pure logic.
Hello, I just discovered your channel and really enjoy what you're saying. I was a high school math teacher and taught symbolic logic to 10th grade students! I used the book by Irving Copi, 5th edition. We got through most of propositional logic before I moved on to other topics. I taught logic, or tried to, because I realized the students couldn't do proofs in geometry, in fact, they had no idea how to think in that way. The Copi book was too advanced for them, probably, but it was the only textbook I had. Interestingly, some of the female students did quite well. Later, I found a web site called The Art of Problem Solving, I was wondering if you've heard of it? All the best to you!
I'm from Canada, but the same thing applies. I wish high school at least included logic and proofs at a rudimentary level as part of the math curriculum. I was only introduced to proof writing in my second year of university.
True but remember Godel’s work. Not every logical statement can be definitively categorized as true or false. Even though I think Godel’s work and Cantor’s work need a rethink and maybe a bounded finite system of maths is preferable I still believe we should be clear about what the limitations of current logical systems are.
but we do this kinda, we always put emphasis whether the theorem is constructive or not or we redo theorems for automated theorem provers (they sometimes require more rigorous constructions) working mathematicians live in this world where there are 3 levels of scrutiny big picture hand-waving, slight formalism, proved with the help of automated provers with the separate dimension of whether the result is constructive or not all of them are good
Great channel and content. I'm a happy subscriber. However, it is a bit hypocritical of you to vilify people who disagree with you politically while you present yourself as a "know-it-all" regarding Sino-American politics. Blanket calling China an "enemy" and reducing the Tik-Tok issue to a simplistic one-dimensional buzzword such as "patriotism" is, ironically, quite illogical. I understand you are passionately against Tik Tok, and for good reason, but this shouldn't limit your assessment of complex geopolitical issues. Ne supra crepidam, if you will. It goes to show that expertise in formal logic does not translate into real-world wisdom and application, since too many personal biases get involved, not to mention the mountains of data one has to sift through. Regardless, I do very much enjoy your rigorous, academic content. Cheers.
Nice video :), I have some pathological but true statements (I will also ellaborate why they are special). It is a nice exercise to think about them. 1) All the (tautologically) false statements are eqvivalent to eachother. (intuition for indirect proofs) 2) We call a set cute if all of its elements are fluffy (whatever these words mean). Then the empty set is cute. (intuition examples: that is why the empty set is closed, open etc...) 3) Every unicorn likes Polish literature. (intuition for contrapositive arguments, also we assume that there are no unicorns )-: )
@spaceman688: Indeed, the equivalence of all tautologically false statements is a marvelous exercise in vacuity-a universal party where falsehood reigns supreme. Surely, '2+2=5' must feel quite at home mingling with 'the empty set contains a pink elephant.' As for unicorns and their literary predilections, this sounds like the perfect setup for a contrapositive proof: Should we find a unicorn unfamiliar with Sienkiewicz, we shall be forced to revise their very existence! But alas, unicorns are as fictional as a consistently fuzzy Zorn's Lemma!
Professor Cromwell, every time I listen to you I think of that actor Tony Randall and I don't mean it as an insult but rather a complement. Your voice and mannerisms are very similar. Anyway, can you recommend a basic math book for a finance degree? Thanks in advance.
Thank you for your observation! A basic math book for a finance degree? I would need to know what specifically you are being tested on to give you a better answer.
Thank you for emphasising discipline as a key foundational element for a person to build life. Thousands of kids come through my university. After a few lectures I know which ones have the self discipline and character to make it through. I will say that it is a very tiny percentage. Like you, I too blame the parents for the part they played. The laissez faire approach to nurturing children has not panned out well. Many of the students, even at the university level have not developed enough discipline to master and excel what it is that they put their minds to work on. Shallowness and viewing everything as a chore, that should have been easy to begin with, is now deeply weaved in their minds. Effort is to be sneezed at. Instead the term "smart" is being used as a magical word. Study smarter, work smarter etc.
This man looks exactly like how a mathematician would look like.
As a maths undergrad, why the hell would any mathematician voluntarily wear a tie and a suit? We're not programmers, but we're not businessmen either.
@minecraftcommandnerd12804:25
@minecraftcommandnerd1280to dress well and be well presented. We had mathematicians sit in investor meetings for our funds. They dressed like him as formality can make others take you more serious.
no
This guy teleported from 1968 to complain about brainrot
Hero
This man sounds and looks like he was teleported from the 50s
bertrand russell reincarnate
Trans-Atlantic accent, get used to it.
😂
Lol you should see his office! It's like stepping back to the Guilded Age!
Yes, but in a good way. He seems like a great teacher, and I bet his students will remember a lot of things he tells them about life in general, as well as in mathematics. We need more teachers like him who have a level-head and know that a good teacher also instills in their students a sense of what it means to lead a good life.
Mathematics is truly the ultimate cornerstone of logic and understanding in our world. I admire your style-so inspiring! Wishing you all the best!
Can you help me understanding a symbol? Its like an arch with two columns. Used in discrete math! You are awesome sir. 👍🏻
@@zephyrr108 are u talking abt the cap notation? as in the intersection of sets?
I'm dumb , so please keep uploading to teach me how to think
Do the correct thing. By correct I don't mean morally
Mathematical logic allowed me to discover and enjoy the world of philosophy. As funny as it may sound at face value, it was very much the case. I am very thankful in this regard.
Professor Cromwell, I appreciate your authenticity and dedication to mathematics. I could only imagine how far along your efforts go genuinely helping people understand the basics of the subject.
In my middle school I was in the 'honors' level math class and we were learning algebra. I distinctly remember fundamentally not understanding the material. Retrospectively, there was (almost) not a single concept in that class that I would have been able to derive/explain on my own. Yet, I came out of the class with the equivalent of a B or B+ as my final grade (and on the standardized NY Algebra 1 Regents Exam). This is a testament to how flawed the education system is here in the States. I went on to my freshman year of high school with the same foundation (or lack there of) and managed to keep the status quo whilst taking geometry... Every once in a while the concepts I had not grasped previously would come up and haunt me before my eyes even beyond the context of my classes. It was in those moments that deep down I knew I had to do something before my ignorance snowballed.
That summer, because of the pandemic, I couldn't find a feasible job and so I took it upon myself to be somewhat productive. So it was that I decided to reteach myself all of algebra alongside certain topics from basic arithmetic from the ground up! All thanks to TH-cam content creators like yourself. Because I was on my own, free from the clutches of common core, not only did I master high/middle school algebra, but I also gained excellence in the ability to reason mathematically. Most importantly, I learned how to learn. After that episode, I returned to high school as a sophomore, in which we were to take on Algebra II. I have a fond memory of being filled with such great mathematical passion that out of sheer enthusiasm, I asked a friend of mine who I thought to be the smartest one in my class to derive the quadratic formula. And when he said the words "Why would anyone know how to do that?" I (without hesitation) took the time to explain it to him, and doing so was a truly eye opening experience.
Upon realizing how far ahead I've gone relative to the curriculum, out of curiosity, and a new kind of love for learning, I taught myself calculus the same way. I had snowballed up the mountain instead of down it, which took immense effort/dedication, but it all paid off. Unfortunately, the more I learned about mathematics, the more I realized how much I did not enjoy it in pure abstraction, instead preferencing physics; and that's okay. Now I find myself studying engineering in university. To say I am glad that I have such a well rounded mathematical eye would be an understatement. It has helped me tremendously keeping me ahead of the game at all times. If all continues to go well, I'll be taking a differential geometry course this semester in pursuit of learning General Relativity at some point. So wish me good luck... I'll need it!
Although your content has not directly aided me on my own mathematical journey, I'm sure another like me out there has. I cannot thank people like you enough for taking time out of their own lives to better others. Thank you!
Thank you for sharing such a thoughtful and inspiring story-it’s a privilege to hear how your dedication and curiosity propelled you forward. The image of 'snowballing up the mountain' is brilliant and perfectly captures the essence of mastering challenging concepts. Your journey from reteaching yourself algebra to delving into calculus, and now to engineering, is a testament to the power of perseverance and self-guided learning.
It’s excellent how your mathematical foundation has become a tool for exploring deeper truths in physics and engineering. Differential geometry and General Relativity are no small feat, but I’m confident your passion and discipline will see you through. Remember, the curiosity that led you here will keep pushing you forward.
I wish you the best, and thank you for the kind words-I hope my content inspires others as much as I have enjoyed reading about your experience!
I stood up and clapped
Your story truly is amazing and one of a kind indeed, most definitely the most fascinatingly inspiring one out there. And I, too, would like to share my relationship and history with mathematics.
In primary school, i used to absolutely despise said subject. Yes, i did, and i beleive that was because i wasn't taught mathematics properly, and it has been introduced to me in quite the absurd way. However, my whole perspective on that field of study completely turned upside down the moment i realized that all of what i think about not only mathematics, but any subject in general, is all in my hands, and my own will. And so, i decided to unfold my arms and prove myself that i truly can learn to love any subject, at any time, without even breaking a sweat. And i've come to beleive ever since that if you change your mindset, you change all that is around you. Mathematics, truly is a complex area of study, and that cannot be denied no further. Thus far, as the saying goes 'you cannot control what surrounds you, but you surely can control how you see it', one may still love mathematics despite its difficult demeanor and how it may come across as strict and unforgiving at times.
The small drops of water form the mighty ocean, and that is true. with small, precautious careful steps you can acheive even the most absurd goals or objectives you desire. And that is quite exactly what has happened with my case. Little by little, i slowly but surely started getting better at mathematics and in a blink of an eye, i found myself being better at that very subject than ever before! All of that is thanks to consistency.
Consistency is everything. Motivation or discipline stand no chance against it. It is with determination and fiery steadfastness that you reach victory in any subject, whether it be mathematics, engineering or physics, all you need to become top 1# is to never give up and keep fighting for your dreams. Upon going from the absolute worst at said subject to one of the best, if not the best at mathematics, at least in my grade, it has become crystal clear to me that it is never too late to change and get better at any area of academics, and if, a merely average human can do it, then ofcourse anyone else can, too.
Thank you for sharing your experience, i will always remember it when i feel down and trust me when i say this-that the majority of the forty-eight people who have witnessed this comment of yours, has been given absolute motivation to give another chance to mathematics, stand up and start fighting once more, to hopefully share another bright story such as yours in the upcoming future.
That was a legendary introduction. I subbed within the first 3 minutes. I look forward to learning from you!!
I'm about to gain +50 knowledge with this one.
Cheers from Brazil! I got positively surprised as I was listening to the audio, so I subscribed.
I adore your professionalism and as a European student finding prosperity in math, science I love this video, looking forward to more, thank you
This is my first time watching your video and I loved the first 10 minutes of your video when you talked about good foundation.
Thank you!
Lately ive been studying Epictetus works on Stoicism, and he put enormous pressure on learning logic in that it is essential to truly understand and apply Stoicism.Because of that i set out to hone my logical thinking, and i will put work into understanding this course!
I am glad to find ur channel. I used to be one of those kids saying "when are we ever gonna use this" and not take maths or school too seriously but I see the value of maths now. I hope I can catch up and be good at maths from ur teachings. U say what I need to hear too I respect it🙏
I do not agree with many of your views but I'd honestly probably enjoy a debate/conversation with you, as you seem like such a respectable man.
Thank you! I am always happy to debate/converse with anyone. It's great to exchange ideas, in a logical way.
Engineering student here!! I think your words at the beginning were really important. I used to suck at math back in middle/my first years of high school. I used to think I would never be able to get to the more advanced levels, and I used to blame external factors for me not being able to be successful. Like you mentioned, that's not gonna get you anywhere. I think I really started to pick up my skills again (I used to be a "gifted" math student) when I finally started blaming MYself for the grades I would receive--that's when I began to get A's, my junior/senior years.
When I took pre calculus, my teacher was wonderful, but she lacked explaining the "why" to us sometimes. I ended up falling in love with trig especially because I would go home and look up the answer to my "why?" Math is beautiful because there are rules and there is discipline to it. It comes together beautifully when you follow its rules, and that's what makes me want to keep doing it.
Hats off to this man🥸
I used "Logic and Philosophy" (4th Edition) by Howard Kahane as an Undergrad.
The first half of the text covers the fundamentals of Logic, and the second covers applications.
I'VE JUST STUMBLED UPON THIS ABSOLUTE IMMACULTE & BANGER OF A VIDEO; YT PLACING IT RANDOMLY ON MY SUGGESTION FEED.
WOULD'VE THOUGHT OF GETTING IT EARLIER.
I LOVE WHENEVER ANY PROFFESOR GOES RIGOROUS JUST THE WAY LIKE THIS; ABSOLUTELY AMAZING TO PONDER UPON; AND ALL OF YOUR SETUP AND ALL, REALLY DEDICATES AND DEMONSTRATES HOW "TRUE" MATHEMATICIANS SHOULD BE IN A WAY OR THE OTHER.
SUBSCRIBED; WOULD LOVE TO WATCH MORE OF SUCH RIGOROUS, STRAIGHT TO THE POINT, VINTAGE EMMERSED IN MODERN LIFE -STYLE-ISH VIDEOS.
This guy is a real character
10:11 MAN do i love this man, from the outfit, from the background, from the accent, from the attitude. But greatest of all is the math content otherwise i wouldnt find myself here, and that really is the cherry on top. Keep doing what you do man you got supporters behind you
Gay
I'm definitely looking forward to meet you as a student, some day. You're literally an incarnation of the mathematics i love.
Thank you for your kind comment! If you are ever in Lynchburg, Virginia, please give me a call!
@citytutoring if I ever visit USA (though I don't see any chances in the next 5 years) I will be sure to do so.
Logic + Coffee = Truth aggressively in your face. Sign me up, bro.
Looks like a good start for a logic course. Discussing propositional logic (syntax, semantics, proof system), first order logic, important properties of those logics like soundness, completeness and compactness.
Sir you tell it how it is, and that is why fools get angry. Thank you for being an amazing teacher.
Thank you very much for your support! It's amazing how those foolish commenters actually prove my point!
Valid crashout. Commendable work.
In case anyone's not satisfied with why p->q must be True when p is False, I recommend the section on Conditionals from the first chapter of "How To Prove It" by Daniel J. Velleman. You will find the arguments there quite convincing..
(I wish this textbook, or at least some distilled version of it, could be taught as standard curriculum early on in high school or even in middle school.)
I asked my teacher why logic was not taught at an earlier age. Their response was that it would intimidate kids. That’s not a good enough answer.
Logic is important to understand truths of mathematics. I wasn’t introduced to the subject until college. It was from logic that I developed a deeper understanding of mathematical structure.
When I was younger I found math challenging. I believe if I was introduced to logic earlier it would have made a world of difference.
Thank you for discussing logic. 🙏
Thank you for your comment. One of the major problems is precisely what you mention - by the time students get to college, they are completely lost because they do NOT have any training at all in logic. Schools used to teach "Logic and Rhetoric", but now? They're too busy fixating over whether the teachers use the right "pronouns" and say the government approved talking points rather than actual teaching and learning. The politicians who have run our schools to the ground are not in any way interested in having an educated population. An educated population would not tolerate the abuse and illegal behavior we have seen from our governments for decades.
Professor Cromwell I still honestly don't get some of those comments you mentioned about people attacking your work. You were literally the kindest professor I had who never cut off a student who wanted to learn. I remember how youd even stay past your office hours just to talk about math and actually was the only professor I had who even asked me about me personally and my well being. You also tutored my brother (Luis the Hispanic kid with the thick accent lol) but you made it a point to help everyone with Math. People can be so awful smh. But I know you dont need my help to defend yourself!
Good ol' Euclidian Geometry (High School Sophomore Year) finally turned-on my "Math Lightbulb".
The visual and tactile nature of straightedge & compass constructions allowed me to see the logical structure of proofs.
Vivek Ramaswamy was right it means about the levels at which US schools have fallen
YOU NEED MATHEMATICAL LOGIC!
It is the very first video that I stumbled upon.
Before I start my comment I must firstly introduce myself. So I am a 10th grade student from India studying in the CENTRAL BOARD of SECONDARY EDUCATION (CBSE) where the national curriculum starts from 9th grade (Before that all of the syllabi are handled by the schools individually or under some corporation in the case of private schools). I am the type of person who has been very much interested in physics, Not the mathematical one but the one where mathematics are not involved like that of encyclopedias, pictures, black hole related TH-cam videos, rockets and their launches, history of science and much more. But as soon as I started to grow up, I realized that many of what I was doing is not sustainable for a long run if i were to top my 10th class final exams then I must rewire my brain with the help of mathematics. Which i did and at the present time while my friends are all cobbled up in remembering the formulas, i fondly remember all of the mathematical formulas with some being able to derive it, Like basic trigonometry identities of sin^2A+cos^2A=1 is derivable by using Pythagoras theorem and their own more derivatives, visual representations of exponential and linear graphs, the sine, cosine, and tangential waves in the Cartesian plane, and much more. In accordance to the syllabus, I have not gone much further due to two main reasons
1.I will get far more opportunities and a good environment in 11th and 12th grade for my preparation of JOINT ENTRANCE EXAMINATION (JEE), as it will also eliminate most of the worthless people to stay with.
2.Also due to some of my bad habits, negligence and laziness, which has happened to stop me from getting the top positions. I have truly not studied throughout the entire year, I am here is just again relearning what my teachers has taught me in the classes, but still I could retain more than my friends and add more to it. I have the scientific and mathematical capability, just waiting for it to get exploited.
And that sums up my position in my academics( I have not talked about history, civics, political science and economics along with my Indian literature with English and computer science as it is irrelevant to my introduction here). I want to do something in quantum computing when i will grow up, as it is the future and there will be more demand of highly skilled and interdisciplinary thinkers like me and similar like minded people.
Timestamp(9mins into the video)
In this section, I really liked on how you instead of starting about mathematical logic, you started out with the need to talk on it, as not only in the US bur also in India we are having the similar problems, which you can read more in this article www.21kschool.com/in/blog/problems-in-indian-education-system/. That how you presented the problems faced by my generation, where distractions like social media has truly done damage to the minds, souls and culture of the people all around the world.
Unfortunately, as of now I was writing it for the comment but due to some project related problems i cannot fully write it, So sir please accept my apology and I just wanted to have a little bit of talk with you since from you the video you have presented yourself as a no-nonsense guy and i really like it, So sir if possible can i get your email ID through which I can contact you and share some ideas from the other side of the world.
bhai you wrote a essay ;-; , but appreciated your effort i too like theoretical physics and about the last part that u said ' i am gonna eliminate some people" can u also help me how to eliminate because lately i am going in wrong directions , and its boards for me too next year i am hella scared tbh
I seriously loved this video ! Thankyou for making it
This was a greatly enjoyable video! Having taken an intro to logic course, this video was review for me, but I do look forward to the rigorous introduction of the "for all" and "there exists" operators! I've self studying linear algebra, and although I can use these symbols to great effect, I've never taken the time to ground my understanding in this respect, and it's especially important to me as a prospective math major.
Beyond the math, your demeanor and philosophy on work and life is quite refreshing. The simple joy of "southern barbecue" brought a smile to my face.
Regarding your point about the deterioration of grammar and cursive, although I was taught both in elementary and middle school, the maintenance of such machinery of communication has not been a top priority. Nevertheless, last year I took it upon myself to re-learn cursive, and this year I feel that philosophy class and AP Latin have together pushed me to sharpen my grammar.
On an unrelated note, I tossed a quarter and noted the result 395 times over the course of this video. I got tails 56.3% of the time and heads 43.7% of the time. From my stats class I can deduce that there is approximately a 0.61% chance this happened purely by chance. Neat.
Thank you for your comment and support! Yes, we will be covering all of that in this series. Cursive is a great skill to maintain, because there is nothing wrong with balancing old skills even if they may not be "needed" (whatever that means!) nowadays. I use it daily, and it improves memory and taking good notes.
395 times eh? That’s commitment! A 0.61% chance, you say? Perhaps the universe is playing a cosmic joke, or that quarter has a preference for tails!
I would greatly appreciate a series on mathematical logic. Im currently a college student and I have just learned how important logical thinking is and school has always taught me that mathematics is a memory game. I just started solving different AIME-AMC12 questions for fun and have been doing it for a month now.
Thank you! Check out my latest video if that helps. All the logic videos I am doing are under the playlist called "Mathematical Logic/Proofs". AIME-AMC12? Beautiful! Keep at it!
Thank you Sir, I learnt something new today, especially the part about Reuleaux polygons which really fascinates me now that I know!
I m a computer scientist and I always hates when I use any mathematical result or theorem with understanding why it is true
I like your style.
Thank you!
@@citytutoring Please continue with this series of explaining mathematical logic, I JUST CAN'T GET ENOUGH OF THEM, EVER, please professor, you are doing in a sense, a "holy" duty for science, since logic is foundation of everything. I also think that all of mathematics(and everything else, since everything else is mathematics) is nothing else but Logic and Set Theory, ...
I’m looking forward to this course on logic. I like to study my material so that it overlaps; if I want to learn something I’ll try 2 books and a TH-cam course minimum. This is definitely the series I’ll be following.
Thank you! I truly hope the series will be of benefit to anyone interested in taking Logic seriously.
My fondest memory is doing pages of proofs, and labeling the logical reasoning for each step. It's one of those things I wish I could do in exchange for room, board, insurance, and currency.
"This channel is a goldmine for anyone interested in mathematical logic! Keep up the great work!"
Truly apreciate your words.
I'm an italian uni student, and I can say with certainty that Italy is also becoming a lost country, where emotions matter more than facts. Discipline and respecting rules are slowly becoming a thing of the past.
Thank you for your comment! Such a shame isn't it? A beautiful country like Italy, with a rich history...and all going down due to the same poisonous attitudes. I do have hope though that there are still people around the world waking up to this reality and hopefully if we work together we can at least change some attitudes.
Both important, emotions and facts.
Thank you sir I really enjoyed your video
I have simple and basic knowledge abt the english language but i can definitely say that learning and doing maths helps me get better logic especially jee main or advance problems since and its because of them i am able to have much more borader choices and can think of a solution very quickly or just try to solve the problem at hand.
What you've said is undoubtedly true, sir, i wasn't even aware of thing like proof theory and mathematical proof writing until i was at my final year in Posgrad. This says so much the lackings in our mathematical educational system, we are only groomed into solving problems without understanding and experience true mathematical maturity
Sir, thank you for your attempt to stop the Visigoths. I appreciate the time and effort you expend to create your outstanding videos. Please employ a lecture classification system to facilitate my ability to go back to a previous lecture, that you reference, to delve further into the point you are focused on. Also, the classification system would help keep the lectures in sequence. Thanks for your consideration of this request. Shortly after the Civil War, my seventh-grade English course spent about a month diagramming sentences. It helped my reading and writing considerably.
Thank you for your comment! All the videos will be numbered in the order of post. Is that what you mean? I am glad that you learned about diagramming sentences! I was also taught how to diagram, although in my case it was before the Civil War.
I’m an older student and I have ASD. I’ve been blessed by some of the best professors ever, who not only got excited when I asked to see the proof, but readily showed it to me either in or out of class depending on how long it might take. I taught myself math up to Calculus 2 (still had to take both) from older math books that did show a lot of the proofs, so I’ve always used them to understand how or why a specific function or formula exists. You’re absolutely right, though, the mass produced thinking of “just learn my steps” is sad and insane to me. I need to know why and how first. I’m going to add in mathematical logic and game theory to my schedule. That’s two videos in two days that will cost me thousands of dollars. 😂
A formal logic course would be great. The closest I've ever come to one was Boolean Algebra as part of my electronics training.
In my youth, I encountered people who could not learn mathematics because they lacked the humility to accept there were things they did not know.
I fondly remember a Symbolic Logic course [offered by the Philosophy Dept]. We had to derive certain truth statements given an initial statement using LOGICAL TOOLS. It was fascinating. Understanding quantifiers and the NEGATION of quantifiers is essential to math. Also, the understanding of contrapositives.
I appreciate your courage to tell the Truth.
Enjoyed your video. And I like your closing comments and your overall ethics! Ty!
Bro you should invest in a graphic tablet. Life changer really. One tutor to another.
This guy is a beast
A lot of love from India to your maths☺
this guy sounds so old school xD
you look like clark kent sir 😅 , but yes i agree , we're just fed concepts , never asked how or where did this come from . please do upload more videos like this , you've earned my subscription
I really like set theory.
Nice timing. I’m reading How To Prove It along with tackling some linear algebra proofs. I’m also reading a book on term-functor logic (as opposed to propositional logic).
Yet, I’ve noticed my attention span is destroyed. It helps to tell myself the lie that I have an imaginary class with imaginary tests such that I can muster up the urgency to study automatically.
The teacher i wish i had in my school.
close enough, welcome back atticus finch
Interesting when you mentioned about identity, I think there needs to be that encouragement of creativity for newer students, especially in the US, how they see themselves when faced with mathematics (or any difficult discipline) how they can incorporate the discipline to make a definitive argument based on independent thought and seeing their contribution on a universal impact, empowerment and validation for themselves. Few thoughts 💭
Creativity is one thing, but saying "because I am (insert constructed identity in the blank), then I am exempt from an assignment, or from consequences for my behavior". Here in the US, in our public schools, there are serious discipline problems as a result of that. For example, a student will claim he has "mental health" issues, and will expect a teacher to excuse them. Teachers are not therapists. Teachers are there to teach and give assignments under certain syllabus conditions to all. If a student is not up to task, then he needs to check out or get the help he needs instead of using identity as a crutch or, worse, an excuse for what in many cases is nothing more than bad behavior.
@@citytutoring oh yes no doubt when the identity is used as an excuse to saying “because I am therefore I can’t do this” is not good
TikTok is owned by a Singaporean company… Not seeing the connection between the general point of the video and this point.
And I think he should make a distinction between logic and critical thinking. Logic is very rigid and sequential, while critical thinking is much more flexible and tangible. Critical thinking is the tool for understanding logic, that without it no one would understand.
I see your point, but I respectfully disagree with the distinction you're making between logic and critical thinking. Logic isn't inherently rigid; it provides a structured framework for reasoning, which can be applied in both flexible and creative ways. Meanwhile, critical thinking is more of a broader cognitive process that involves evaluating, analyzing, and interpreting information-often employing logic as one of its key tools. The two are deeply interconnected, but critical thinking doesn't necessarily "understand" logic; rather, it uses logic to form coherent and well-reasoned conclusions. Would you mind elaborating on what you mean by "flexible and tangible"?
I agree with a lot of the points he's made regarding the education system, only thing is, this dude is acting loopy, with an odd pessimist connotation in every word he says. It's almost like watching a video of him ranting, as opposed to presenting a reasonable and focused criticism.
that's just not true. If apple hired a danish ceo one day, that would not make apple a "danish" company. At the end of the day Tiktok is owned by a chinese company (Bytedance) and has to take orders from the CCP
@ That’s a fair point! His critiques of the education system are insightful, but the way he presents them might come across as more of a rant than a structured argument.
A proud mathematical logician here 🎉
Welcome! We need more people like you!
@ Thanks! Stumbling upon your channel is like a breath of fresh air. I have aspirations to teach children and adults alike in mathematical thinking-for reasons you mentioned in this video. I am trying to work out a program with our local rep to the House here in GA. I have even showed my friend your video to give them an idea of what I mean!
"foreign enemy government" i belive that for america china is a competitor not an enemy,afterall it is 21 century not some Middle Ages
This is the best channel ever
You are correct about mathematical logic. It is very much needed in today’s schools. I find myself needing to teach at least some of it. Our state had the genius idea of trying to put every student with or without Algebra 1 into Geometry. And our state standards writers thought that in their infinite wisdom they knew more than Euclid. So they took out most all the proofs and logic out of Geometry. And they wonder why the kids fall apart in AP math when it is no longer copy and paste, paint by numbers style calculation oriented math. So yes, I teach it and do it as often as I can. But this is sometimes going off standard. It’s not exactly in the AP CED and not exactly in the state standards before it, but you cannot accomplish the CED outcomes without instilling some of it.
It seems as though, to get anything 'done', we must *presuppose* some stable form of logic like this.
Based Teacher! 😆 I like this guy! "Kahn Academy-ing your way through life."....🤣 Guilty as charged! Lol
Please do a books recommendations video for Logic. Thank you
As someone who has a great deal of logic textbooks, I think Hurley's "A Concise Introduction to Logic" is the best introductory text I've come across. It was an excellent starting point for me for formal/symbolic logic. It gives you a solid foundation from propositional/sentential thorough predicate/quantifier logic, before you get into the real weeds of more advanced mathematical logic and set theory. I think any edition is great, which you can order for a couple of dollars online used. It also has a great deal of informal/inductive logic. If you're looking for something slightly more advanced, "Logic and Philosophy"/"Elementary Symbolic Logic" are both excellent. And if you want something pretty advanced/hardcore, "The Logic Book" might be the one.
Vid starts at 9:10 btw
respect from Iraq, UOB math dept
thank you sir.
To those curious toward the philosophical branch of "Logic", I reccomend Immanuel Kant's "Critique Of Pure Reason", and Harry J Gensler's "Introduction To Logic". Syllogism, is one of the things discussed in the latter aforementioned, which is what is explored in this video. Exploring the tenets of semiotics also doesn't hurt - there's a lot of overlap in the signs, symbols and denotations used in any kind of language (which is used to represent this, that or the other). Mr. "Citytutoringmath" if you can reccomend other texts and/or resources, feel free to mention them. I'm always looking for new knowledge, and you just happened to appear on my TH-cam feed by chance.
I love it when you post! Perfect timing too, there are a lot of really weird finitists in my recommended who hate mathematicians lol. They claim we should only account for things if they exist in the physical world. Ironically, despite claiming this outlook makes no assumptions, they assume that the empirical sense data they mentally process is congruent to the reality around them... lol... the truth is that these things all exist only because of god, and the infinite exists in his boundless mind.
Thank you! Actually, you're one of the commenters I always remember and it's always a pleasure to read your feedback. Ah, the finitists-equivalent to flat-earthers who think the horizon is the edge of reality. It’s amusing how they claim to dodge assumptions while standing on a mountain of them! Your point about God is spot on, though: the infinite isn’t some quirky abstraction, it’s the signature of the divine. Trying to limit mathematics to what’s physically measurable is like insisting Beethoven only exists because you can hear him on Spotify.
@@citytutoring Brilliant response! And I'm so happy to hear that! I find your channel to be very inspirational, and I love your style. Just to let you know, even when I'm not in the comments I'm always here!
@@JR-uc3nk I am not very well-read on religion (yet!) to be honest, however we do not need god for infinity type axioms to be justified (I mean, unless you precieve logic as a divine thing, which you can do... but as I said, I don't know much about it). So as a pure technicality, if we assume the contradiction of the infinity axiom in ZFC for example (you can do it in other systems, but I mostly care about ZFC interpretations) then there is a statement sequence that directly contradicts the law of induction which is WILD.
@@spaceman688 You should look into jay dyer. He has good videos on philosophy. But essentially, no world view can be philosophically reconciled without god, especially not the view of the arrogant and clueless empiricists we have seen since the 1600s. Look at Jay's transcendental argumentations though.
@JR-uc3nk I believe in god I am just not very good at theology. I will take a look, thanks for the recommendation.
I'm a Brazilian with 14 years old and I pretend to study logical mathematics, to have a more easily preparation for mathematics in ITA's exam, the most hard exam of Brazil, basiclly.
Sorry for the english, btw😅 I gonna improve that with the book "Grammar in Use" and with the study of the book "How to Prove It" to learn logical mathematics thinking
In really, it's not to just get aproved in the exam, is that because i love mathematics and conhecimento ( knowdelege) idk how to write that😅
Me too. I am 20 and I will be entering university this year.
Parabéns irmão, continue na jornada
Man youtube recomended this and I m gonna watch it
Boss ngl as if late. I've scared myself bc i don't know, even my x tables. imma start working on my math .
i couldn`t agree more
Subscribed
Would you recommend to study "Intro to mathematical Logic, Intro to Mathematical proofs and Intro to abstract algebra" before jumping into real, complex, functional analysis, topology etc....?
"The best lack all conviction, while the worst are full of passionate intensity"- W.B. Yeats. I thought this quote to be germane to your plea for logic and discipline.
Love you sir ❤❤
Honestly, there isn't a better thing than mathematical competitions in this day and age where people from a younger grade could get exposed to a proof-styled testing format at such an early time in life. I'm happy to say that after doing many math, physics and programming contests that the combinatorial and number theoretic problems are my favorite because when they give you those problems, most of the time, they are not in the form of equations, just a bit of information with a few rules and it's your job to disect what you're trying to accomplish into little bits and solve it all at once. You don't need any prerequisite knowledge for those types of questions, pure logic.
Ribs + Math = Road Trip!
I thought I'm the problem until I saw this.
Hello,
I just discovered your channel and really enjoy what you're saying.
I was a high school math teacher and taught symbolic logic to 10th grade students! I used the book by Irving Copi, 5th edition. We got through most of propositional logic before I moved on to other topics. I taught logic, or tried to, because I realized the students couldn't do proofs in geometry, in fact, they had no idea how to think in that way. The Copi book was too advanced for them, probably, but it was the only textbook I had. Interestingly, some of the female students did quite well.
Later, I found a web site called The Art of Problem Solving, I was wondering if you've heard of it?
All the best to you!
how did you tie your tie? :D
I have a book by Dociani I’m working through that introduces how to conduct proofs in the first chapter. And she’s very good at teaching the method.
Yes! Modern Introductory Analysis? If you are interested, I reviewed the book here: th-cam.com/video/usLkuFlmNew/w-d-xo.html
@@citytutoring Modern Algebra and Trigonometry 2: Structure and Method. I’ll definitely check out your review. Thank you.
Thank you! I have that one too. All her books are excellent for serious Math students.
I'm from Canada, but the same thing applies. I wish high school at least included logic and proofs at a rudimentary level as part of the math curriculum. I was only introduced to proof writing in my second year of university.
Bro's a mathematician from the 1960s
I like your style sir
Im so invested here!! xD
I'm gonna be honest, we need congeniality school and then logic school. Make them boarding schools, imo, no phones-allowed on campus, only linux PCs.
True but remember Godel’s work. Not every logical statement can be definitively categorized as true or false. Even though I think Godel’s work and Cantor’s work need a rethink and maybe a bounded finite system of maths is preferable I still believe we should be clear about what the limitations of current logical systems are.
but we do this kinda, we always put emphasis whether the theorem is constructive or not
or we redo theorems for automated theorem provers (they sometimes require more rigorous constructions)
working mathematicians live in this world where there are 3 levels of scrutiny
big picture hand-waving, slight formalism, proved with the help of automated provers
with the separate dimension of whether the result is constructive or not
all of them are good
Great channel and content. I'm a happy subscriber.
However, it is a bit hypocritical of you to vilify people who disagree with you politically while you present yourself as a "know-it-all" regarding Sino-American politics. Blanket calling China an "enemy" and reducing the Tik-Tok issue to a simplistic one-dimensional buzzword such as "patriotism" is, ironically, quite illogical. I understand you are passionately against Tik Tok, and for good reason, but this shouldn't limit your assessment of complex geopolitical issues.
Ne supra crepidam, if you will.
It goes to show that expertise in formal logic does not translate into real-world wisdom and application, since too many personal biases get involved, not to mention the mountains of data one has to sift through.
Regardless, I do very much enjoy your rigorous, academic content. Cheers.
Logical was a really enjoyable course for me last semester, although it stopped short of predicate logic, which was disappointing.
x2=15-30=-15
Nice video :), I have some pathological but true statements (I will also ellaborate why they are special). It is a nice exercise to think about them.
1) All the (tautologically) false statements are eqvivalent to eachother. (intuition for indirect proofs)
2) We call a set cute if all of its elements are fluffy (whatever these words mean). Then the empty set is cute. (intuition examples: that is why the empty set is closed, open etc...)
3) Every unicorn likes Polish literature. (intuition for contrapositive arguments, also we assume that there are no unicorns )-: )
@spaceman688:
Indeed, the equivalence of all tautologically false statements is a marvelous exercise in vacuity-a universal party where falsehood reigns supreme. Surely, '2+2=5' must feel quite at home mingling with 'the empty set contains a pink elephant.'
As for unicorns and their literary predilections, this sounds like the perfect setup for a contrapositive proof: Should we find a unicorn unfamiliar with Sienkiewicz, we shall be forced to revise their very existence! But alas, unicorns are as fictional as a consistently fuzzy Zorn's Lemma!
Professor Cromwell, every time I listen to you I think of that actor Tony Randall and I don't mean it as an insult but rather a complement. Your voice and mannerisms are very similar. Anyway, can you recommend a basic math book for a finance degree? Thanks in advance.
Thank you for your observation! A basic math book for a finance degree? I would need to know what specifically you are being tested on to give you a better answer.
Nice to hear some truth through the noise
Thank you for emphasising discipline as a key foundational element for a person to build life. Thousands of kids come through my university. After a few lectures I know which ones have the self discipline and character to make it through. I will say that it is a very tiny percentage. Like you, I too blame the parents for the part they played. The laissez faire approach to nurturing children has not panned out well. Many of the students, even at the university level have not developed enough discipline to master and excel what it is that they put their minds to work on. Shallowness and viewing everything as a chore, that should have been easy to begin with, is now deeply weaved in their minds. Effort is to be sneezed at. Instead the term "smart" is being used as a magical word. Study smarter, work smarter etc.