I enjoyed proofs a lot more than the “Solve for x” stuff. I’m going through a pre-calc workbook and realizing that I really like the logic and proof-oriented math; the exploratory stuff. It worked for me in college, and it still works for me now.
The book by Velleman inspires people who know programming languages. It teaches us to appreciate proofs the same way we appreciate solving a programming problem. I won't ever have the same opinion about proofs as before now that i'm reading this book... With this point of view, math is hard but fun!
I've been self-studying for a year to prep for grad school, and I cannot tell you how much a I appreciate your content. While self-study is a necessary process to get better at math, your channel provides an excellent supplement for the massively underrated "community" component of learning mathematics.
I’m currently 8 chapters into Chartrands proof book and have done all the exercises. I’m self studying it from the book and I feel like I’m getting proofs like never before!
You should consider writing a book on how to study mathematics. I believe that such a book would be incredibly valuable, and I think that you would be the perfect person to write it.
I love self-studying now, and I'm definitely way better at learning math now than I was even in my math masters program. BUT! there's a caveat: I'm so much better at self-study now bc I got feedback on my proofs from professors and built my foundation based on that feedback. My big piece of advice for self-studiers is to seek out quality feedback on your proofs wherever you can. Getting corrected on your mistakes will be lessons that really stick well in your brain. Also for current students, build self-study habits even within the classes you're taking as others have mentioned in the comments here. Another bit of advice: if you really want to do math as a career path, just throw your soul into the mathematics while you have the opportunity to make that time investment now. The Math Sorcerer gave great advice along these lines in a recent vid. Balance is important in life, but you're not going to have many other opportunities like you do now to just fully devote as much of your day-to-day life to mathematics like you do now, and the foundation you build from the effort you make now will pay dividends down the road. My biggest obstacle to doing math now is just not having the available time outside of my job to devote the necessary effort to it. Good luck! Learning math is worth it!
Hi, I really appreciate your devotion towards mathematics. I’m a draftsman and a 3d modeler and recently started studying programming. Through programming I discovered a much more practical mathematics and since then it gave me a huge curiosity to learn more about it. I would like to ask you, what makes you different from the other by knowing the math you know now ? How knowing math has helped in your life towards problem-solving ? And at last, but not least, what is the difference between a mathematician and a problem-solver. Thank you for your precious time. My best regards.
At the start of my Physics Undergrad (1981), I was jazzed to study the kind of stuff I enjoyed as a kid, *and* daunted at the prospect of embracing all of my ignorance laid before me as I read course descriptions, degree requirements and prowled just the Math and Physics shelves in the Science Library. Sometimes the derivative is small, but aspire to know & experience a little more today than yesterday. You can learn more than you think you can. During the past couple of years, I've had to revisit Linear Algebra and Complex Analysis for a new work assignment related to signal processing, so I could learn signal processing. Topics I found challenging in my 20's are much more self-evident now that I'm in my 20's for the 3rd time. Self-study is a great secret weapon!
Self-studying is a lot of fun. You really have the time to sit and ponder every bit you come across. You have the time to try and fail, to review your work and actually learn. Studying for an exam is a different story. Often times I find that one focuses too much on getting a good grade and you forget your primary goal must be learning the best you can to improve your craft.
Hey Sorcerer, I wanted to propose a video idea that I think many of us will benefit from. The idea is if you could perhaps display how you would study for a certain subject or topic, maybe we could simulate your style of studying. It would mean a lot; particularly to me and those of us that really struggles with our studying methods and even sometimes following instructions, a visual guide would be somewhat more defining. Maybe it’s something you could do? Thank you for everything. 🙂
I remember when I started learning calculus almost a year ago, I started by reviewing some very basic math and also by learning some requirements like trig because my math was very, very rusty at the time. And I left some topics like algebra or geometry a little bit aside, thinking that I would probably pick them up along the way (so I could focus on Calculus). And oh boy, did I struggle at the beginning. It took me quite a while to understand something as basic as to why an absolute value could have a positive or negative value, or why the solution was expressed as a system or how did it all of it work. But I tried my best to understand it. And I did understand it and kept moving on. And in the end, while doing it that way was quite painful because I didn't have a very strong foundation, it also helped me to understand how to approach my studies much better, up to a point where I don't really struggle that much anymore and I got to multivariable calculus without too much problems. It's true that I keep forgetting a lot of stuff, but maybe I do one day of reviewing and then try to move on and try to catch up with what I forget as I go. And I think I'm doing quite well, although I must admit I don't have any kind of pressure such as exams or grades, so it's probably much easier for me to do this than it will be for people who has to do exams.
Right now I'm self studying the book "Mathematics of Classical and Quantum Physics" by Byron and Fuller. I find the best way to do review basic calculus is to just go back and review topics as I need them. For example, I ran into some pretty hefty partial derivatives while studying the calculus of variations, so I picked up my copy of Thomas Calculus and reviewed them. It helped a lot.
I've just watched the same vid in Spanish and I can't tell which language is your native one. Learning Math is kond of loke learning a new language. You never stop learning. You need a ton of practice. You need to go through frustrating sometimes. You need to practice every day. Muchas gracias por tus videos muchachote. ¡Sigue así!
Thank you for these very insightful, inspirational/motivational videos..Lord knows the world needs more of these! For anyone with renewed enthusiasm to learn math, or for anyone that's currently in school for math, these videos are essential! Thanks again!!
Something I have noticed with math is the progression and depth of understanding of the previous or supporting subject. I mean algebra became so much easier once I was in calculus. First order calculus became easier when I took Advanced Calculus. While learning a subject, it feels difficult. However, I found the previous subjects clearer or easier to master while working at the next level. Thanks for the video.
I also noticed that. It seems like while working on the lower level subject we have many doubts about its purpose that confuse our performance, but with higher level subject we eventually figure out what is the lower one actually used for.
Hi! I hope you see this. I am trying to learn math, CS, and stats to get into a Masters of Financial Engineering degree in 3 years or less. Starting in the spring of next year, I will be taking my first math (calc 1) and CS course at the University of Houston as a visiting student. I am spending these next few months leading up to that building the foundation for my understanding of math, as I haven't taken any courses in it since undergrad in 2020. I am very excited to begin this journey and have been really enjoying your videos. Thanks for the advice in the video.
I like this advice. I feel like my perfectionism can hold me back. If you know enough but not everything you can still move on and backfill the gaps that you may have. There's definitely comfort in staying put with the material you mostly know and want to perfect.
Intellectually, providing proofs as the normal answer to exercises, with some algebraic manipulation embedded in some cases, is the real barrier. It is not the book, reading it, understanding it, taking notes, etc. In my case, my issues were (and are) a mindset problem. We assume automatically, unconsciously even, that the results and contents in every piece of Math we learn along the way, are the knowledge we are seeking for. We learnt basic algebraic manipulations, we use them for everything afterwards, we didn't stop using them after the course finished. we didn't stop using them when the topic is not about basic algebra. But we stop thinking on the results and contents from many other Math courses after we finished with them. And we don't think about them as we do with addition and subtraction, like we do with multiplication, ... but we need to think about limits, derivatives, equivalence relations, counting, cardinality, combinatorics, range, domain, injunction and disjunction,... everything you learn in every class is not only the object of study themselves. It is not there only for you to pass the course and the topic is over. They are the tools to carry on. They are your new shoes to walk the path that is ahead, to go forward. Use them, all of them, to get from the definitions available to you in every exercise topic (write them down) towards the solution that you should be able to write in full as an expression as well, or as another definition. Write them not in words only but in Mathematical notation. Go from one to the other, use small steps, like adding a number, but with your new tools as well, one step only at a time. And use your new shoes, be aware of your previous results and use them as tools like addition, subtraction and other basic tools like logic or set theory. This is the jump I needed to take to go forward.
Your are great Professor! You give a taste of math. I am in Master Finance at 51 years old. I am your fan from the Kingdom of Morocco. your are excellent. keep it up.
Thank you for making this video to help remind me of what goal I am going towards. I am self-studying Calculus 1 right now this summer because it'll keep me on track to when I am expected to graduate college in the next 3 years. I am also using your lecture videos on your channel to also help my further understanding on the topics.
I’m suffering from all the geometry I missed the first time around. Now I picked up a textbook graded for teenagers and here I am having a crack at it. 😂 “ SO THAT’S WHY!” “NOW I GET IT!” And “ OH, OF COURSE!” Are words in constantly shout now 😅
I'm reading out of Algebraic Geometry, A Problem Solving Approach by Garrity et al. The sections on divisors is beating me up, partially third time going through it and I'm not confident it'll stick with me for the rest of my life but it feels good to get through it!
This is so true. I am currently learning to write proofs via a discrete math book and it’s really rewarding. But it’s nice because the discrete math book itself has real content in it beyond simply being a ‘proofs book’.
When I found out “Hey, I actually think mathematically,” I built a roadmap. I got 2 books on mathematics (“An illustrated history of numbers: 100 ponderables” and “The Math Book” by Clifford A), studied them to self test on knowledge. I still need to complete it for the math book; I got bothered by all the name theorems because I’m just bad with names in general. But I really studied that one in a way I didn’t with the first, a bordering on research matter for me. Then, I would go back to all the stuff up to where I left off in college, with relevant materials. I’d have a knowledge base for going back to school of what’s ahead of me, with a firmer foundation in all the math before. Once I’ve finished the Pre-Calc to Calc review, it’s gonna be the proof-stuff. I also have two handbooks of mathematics; they’re very cool and provide a roadmap of their own.
And make sure you understand the difference between PEMDAS and PEJMDAS. (Order of operations) on calculators and pencil & paper. . And then there's RPN; Reverse Polish Notation.
I completely agree. ☺️ I’ve been avoiding studying the mathematics behind the flatness problem in cosmology. It turns out to be based on Friedmann’s equations (which are in turn based on Einstein’s eqns). It was daunting, but I finally dove in and I’m realizing it wasnt so bad. 😅 I was suddenly happy I took a class on differential geometry in my fourth year of my Bachelor’s degree. I had to push past my discomfort.
I think it's important to treat study itself like mathematics: integrating the small skills (starting something, being resilient, being interested in learning), but deriving the big problems (time, distractions, excuses). After all, taking pleasure in learning, making what was difficult as well as easy, pleasurable. 😊
Hi Math Sorcerer, majority of my high school I was in Turkey. I was excelling at math, but when I came to US I realized something bad. When explained in English math is very complex. I am mainly talking about the names in it. For example, instead of isosceles triangle we say Twin side triangle. It is a triangle that has 2 identical sides, so twin side triangle makes sense and I instantly know what it means because the definition itself is in the name. I acquired the books you recommended and things like this slows me down. In these occasions I have to copy the word and look it up to see what it means. I think math is already complex enough, and we should not deal with Latin and unfamiliar words. I mean I can get over it, it is not the end of the world, but when names become simple, you can read and breeze through a book with ease. So yeah, I find English math books so unnecessarily hard and difficult. I don't think this is my lack of proficiency in English, I consider myself more sophisticated and articulate compared to my peers. I read regularly, but I think math should be as simple as possible to be more accessible and less intimidating for beginners. Also simplicity makes math more efficient and clear. Please let me know if you agree or not and why.
After many years I have found out the best way I learn things is to jump into the deep end and just try to figure things out. It feels like beating your head into a concrete block repeatedly in the beginning, but it is by far the most successful method for me. At the moment I'm struggling with some algebraic topology more specifically Obstruction theory and Steenrod Squares. I work as a data scientist so my aim is more deriving interesting tools than all-out proof-writing, but topology is a cool field either way.
I’m a fairly new subscriber. And I just have say that I find your videos very helpful and inspiring. Thank you for sharing yourself and creating this videos!
After years of deciding what I want to do with my life I’ve decided to go from a marketing degree to either MIS or IT. I am done with letting Math kick my ass I’m ready to do whatever it takes and this channel is giving me the greatest motivation. I seriously appreciate this channel 🫡
Funny that I'm pushing myself so much now, to learn Proofs through Sum-Formulas. I was thinking giving up for the moment but after this video: I WILL MASTER IT! I love such videos in which an expert of a subject can explain soft skills through his field of expertise... Thanks for sharing!
I guess one can divide his / her self study time into multiple sections where a lesser duration of time is devoted for recaptulation of old syllabus and more time is devoted to learn the newer challenging syllabus.
Hello, since I found your channel my interest in studying mathematics has intensified, I really appreciate you existing and doing this magnificent work. I'm addicted to books and I took many of your recommendations, I've already started studying for them. I would like to ask you to review the books in the AoPS series (Art of Problem Solving) I heard many comments praising these books, that they are more challenging than the traditional ones and very good, those who study them get very good at solving problems. It will be really cool to see a review of this book series on your channel with your comments on it, please do!
I basically learned algebra while taking calculus at uni, my algebra was really weak before that. It was definitely a ride but so rewarding once I got it, now I do calc for fun lol
That was spooky - At the beginning of the video I was on the side thinking about looking into books for functional analysis and then it was mentioned for an example a minute later.
Cuando estudié ingeniería en España, encontré 2 libros sobre Álgebra Lineal que hasta la fecha, en lo que he podido investigar, ningún otro autor lo la superado: Problemas Resueltos de Álgebra. Tomos 1 y 2. Su autor es Emilio Espada Bros. Están agotados hace años, pero se pueden conseguir de segunda mano. Si no los tienes en tu biblioteca, deberías considerarlo.
I have a degrede on mannegment, and before that i was at engeniering in the military academy, but the math i had is so useful that i am reading introdution to mathematical thinking from keith devlin
I think Feynman was 13 or something when he used that book. As a nuclear engineering PhD with a math and physics BS, I can tell that the difference not mastering proofs makes a when I am learning the math used in engineering. Yeah you do not need to know proofs to solve problems but it will help learn somethings quicker, make connections, and learn more rigorous methods. For some math topics, a lot of engineering books get repetitive and you really need a more advanced book to push your understanding.
Hey Sorcerer, big fan of the vids !! I’m a maths major heading into calc 1 I noticed the calculus for the practical man wasn’t on the booklist you recommended for learning calculus, should I look to pick up one of those or this book ? I had a quick read of trial ebook and did like how it was written so much pick it up anyway along with a textbook
You should do a video about the astounding power of tutoring math to others in order to increase your math skills. After finishing my physics degree i got a job tutoring math to high school kids. To my astonishment my skills improved dramatically! I felt like i became an algebra expert (when i thought i was petty good already!). I don't know what it is about tutoring, but it seems to have some sort of magical power. What you said about algebra being the foundation of doing well in calculus is so true. After tutoring i reviewed calculus and it all seemed so much clearer than it ever did in college. I only wish i could have tutored math before ever going to college. My life would have been so much easier! Now i always tell my students that algebra 2 is the most important math class they'll ever take, so take it very, very seriously.
I bought book of proof off amazon and it arrives in a month lol 😂 I dont even know if I'm ready for that level of math because i havent taken calculus yet
Yes mate, I do have that story. I landed in Mexico speaking zero Spanish. I was told that I had to teach a 6 week course on a subject I didn’t know. And everyone else left. Fortunately, I discovered I have a gift for languages. Otherwise, I’d be broke and stuck in Mexico.
Hi ! Since your a teacher I thought I'd ask. When I was a kid I didn't spend much time in school - I didn't get to learn much while I was there. But I want to know and learn at least basic math . I don't know my reading level, And I don't know how to gauge where I am at with math either. There are colleges and a university in my city. Slipping through the cracks the way I did has hurt my adult hood in some bad ways- Not sure how to go about finding the right help.
When do I know I am ready to move to a different area in mathematics? For example, say I’m learning precalculus, when do I know I am ready to learn calculus? Thank you.
Hello Mr.Sorecer, maybe you will find this interesting, im subscribe and im not studying math...im in my way of becoming a diplomat, studying international law, but your tips are really "inter exchangeables", and enjoy your aproach to study, thank you and keep doing this excelent videos!!!
Which book do you think is the better, "How to Prove It: A Structured Approach, by Daniel J. Velleman" or "Proofs: A Long-Form Mathematics Textbook (The Long-Form Math Textbook Series), by Jay Cummings". Thank you in advance for your support
Dear Math (S)orcerer, please use math to speed up my Calculus for the Practical Man book order... I swear I would be reproving the law of the cosines but unfortunately since the book hasn't come yet, I can't study....😅 Jk just lazy and anxious.. thanks for making these vids, I'll update you with any breakthroughs.... Working on making an ai math buddy in python, trying use faraday's laws to break gravity just too stoopid atm
ive done analysis not real but the delta epsilon... as someone in applied, learning some basics of physics and control are much bigger unlocks than formalization... unfortunately, maybe when i become more in depth - perhaps
What other resources are available other than Khan Academy? Edit: I dropped Calculus I, but now I’m re-learning all math from pre-school to Calculus I, and beyond! More edit: posted comment before watching the video 😅
Writing proofs is also a lot of fun after some time. It's like seeing the matrix, the structure behind, that really explains why things are true :)
I enjoyed proofs a lot more than the “Solve for x” stuff.
I’m going through a pre-calc workbook and realizing that I really like the logic and proof-oriented math; the exploratory stuff.
It worked for me in college, and it still works for me now.
The book by Velleman inspires people who know programming languages. It teaches us to appreciate proofs the same way we appreciate solving a programming problem. I won't ever have the same opinion about proofs as before now that i'm reading this book... With this point of view, math is hard but fun!
I love your channel!
A legend commenting on another legends youtube.
Hello hello and welcome! ❤❤❤❤
Yeah
The David Goggins of mathematics
I've been self-studying for a year to prep for grad school, and I cannot tell you how much a I appreciate your content. While self-study is a necessary process to get better at math, your channel provides an excellent supplement for the massively underrated "community" component of learning mathematics.
I’m currently 8 chapters into Chartrands proof book and have done all the exercises. I’m self studying it from the book and I feel like I’m getting proofs like never before!
You should consider writing a book on how to study mathematics. I believe that such a book would be incredibly valuable, and I think that you would be the perfect person to write it.
I love self-studying now, and I'm definitely way better at learning math now than I was even in my math masters program. BUT! there's a caveat: I'm so much better at self-study now bc I got feedback on my proofs from professors and built my foundation based on that feedback. My big piece of advice for self-studiers is to seek out quality feedback on your proofs wherever you can. Getting corrected on your mistakes will be lessons that really stick well in your brain.
Also for current students, build self-study habits even within the classes you're taking as others have mentioned in the comments here. Another bit of advice: if you really want to do math as a career path, just throw your soul into the mathematics while you have the opportunity to make that time investment now. The Math Sorcerer gave great advice along these lines in a recent vid. Balance is important in life, but you're not going to have many other opportunities like you do now to just fully devote as much of your day-to-day life to mathematics like you do now, and the foundation you build from the effort you make now will pay dividends down the road. My biggest obstacle to doing math now is just not having the available time outside of my job to devote the necessary effort to it.
Good luck! Learning math is worth it!
Great !
❤❤ thank you
Hi, I really appreciate your devotion towards mathematics. I’m a draftsman and a 3d modeler and recently started studying programming. Through programming I discovered a much more practical mathematics and since then it gave me a huge curiosity to learn more about it. I would like to ask you, what makes you different from the other by knowing the math you know now ? How knowing math has helped in your life towards problem-solving ? And at last, but not least, what is the difference between a mathematician and a problem-solver.
Thank you for your precious time. My best regards.
At the start of my Physics Undergrad (1981), I was jazzed to study the kind of stuff I enjoyed as a kid, *and* daunted at the prospect of embracing all of my ignorance laid before me as I read course descriptions, degree requirements and prowled just the Math and Physics shelves in the Science Library.
Sometimes the derivative is small, but aspire to know & experience a little more today than yesterday. You can learn more than you think you can.
During the past couple of years, I've had to revisit Linear Algebra and Complex Analysis for a new work assignment related to signal processing, so I could learn signal processing. Topics I found challenging in my 20's are much more self-evident now that I'm in my 20's for the 3rd time. Self-study is a great secret weapon!
Self-studying is a lot of fun. You really have the time to sit and ponder every bit you come across. You have the time to try and fail, to review your work and actually learn. Studying for an exam is a different story. Often times I find that one focuses too much on getting a good grade and you forget your primary goal must be learning the best you can to improve your craft.
No. Not if you have a fulltime job and a family and bills to pay
@@kolyxixstarting a family was your first mistake
@@kolyxixwhat does any of that got do with anything? 😳
Hey Sorcerer,
I wanted to propose a video idea that I think many of us will benefit from. The idea is if you could perhaps display how you would study for a certain subject or topic, maybe we could simulate your style of studying. It would mean a lot; particularly to me and those of us that really struggles with our studying methods and even sometimes following instructions, a visual guide would be somewhat more defining.
Maybe it’s something you could do?
Thank you for everything. 🙂
I remember when I started learning calculus almost a year ago, I started by reviewing some very basic math and also by learning some requirements like trig because my math was very, very rusty at the time. And I left some topics like algebra or geometry a little bit aside, thinking that I would probably pick them up along the way (so I could focus on Calculus). And oh boy, did I struggle at the beginning. It took me quite a while to understand something as basic as to why an absolute value could have a positive or negative value, or why the solution was expressed as a system or how did it all of it work. But I tried my best to understand it. And I did understand it and kept moving on. And in the end, while doing it that way was quite painful because I didn't have a very strong foundation, it also helped me to understand how to approach my studies much better, up to a point where I don't really struggle that much anymore and I got to multivariable calculus without too much problems. It's true that I keep forgetting a lot of stuff, but maybe I do one day of reviewing and then try to move on and try to catch up with what I forget as I go. And I think I'm doing quite well, although I must admit I don't have any kind of pressure such as exams or grades, so it's probably much easier for me to do this than it will be for people who has to do exams.
I wish I could live two lifetimes to understand all the maths
Right now I'm self studying the book "Mathematics of Classical and Quantum Physics" by Byron and Fuller. I find the best way to do review basic calculus is to just go back and review topics as I need them. For example, I ran into some pretty hefty partial derivatives while studying the calculus of variations, so I picked up my copy of Thomas Calculus and reviewed them. It helped a lot.
I've just watched the same vid in Spanish and I can't tell which language is your native one. Learning Math is kond of loke learning a new language. You never stop learning. You need a ton of practice. You need to go through frustrating sometimes. You need to practice every day. Muchas gracias por tus videos muchachote. ¡Sigue así!
Thank you for these very insightful, inspirational/motivational videos..Lord knows the world needs more of these! For anyone with renewed enthusiasm to learn math, or for anyone that's currently in school for math, these videos are essential! Thanks again!!
Something I have noticed with math is the progression and depth of understanding of the previous or supporting subject. I mean algebra became so much easier once I was in calculus. First order calculus became easier when I took Advanced Calculus. While learning a subject, it feels difficult. However, I found the previous subjects clearer or easier to master while working at the next level. Thanks for the video.
I also noticed that. It seems like while working on the lower level subject we have many doubts about its purpose that confuse our performance, but with higher level subject we eventually figure out what is the lower one actually used for.
It is like you knew what I was thinking lately and gave the advice and push I needed. Thank you.
Thank you math sorcerer.
Watching your videos awakens my mathematical senses.
It gives love, courage and determination to do maths.
Hi! I hope you see this. I am trying to learn math, CS, and stats to get into a Masters of Financial Engineering degree in 3 years or less. Starting in the spring of next year, I will be taking my first math (calc 1) and CS course at the University of Houston as a visiting student. I am spending these next few months leading up to that building the foundation for my understanding of math, as I haven't taken any courses in it since undergrad in 2020. I am very excited to begin this journey and have been really enjoying your videos. Thanks for the advice in the video.
I like this advice. I feel like my perfectionism can hold me back. If you know enough but not everything you can still move on and backfill the gaps that you may have. There's definitely comfort in staying put with the material you mostly know and want to perfect.
I love these videos, you've been really helpful for me throughout my journey and I am really grateful for you and what you do in here. ♥♥♥♥♥
Intellectually, providing proofs as the normal answer to exercises, with some algebraic manipulation embedded in some cases, is the real barrier. It is not the book, reading it, understanding it, taking notes, etc. In my case, my issues were (and are) a mindset problem.
We assume automatically, unconsciously even, that the results and contents in every piece of Math we learn along the way, are the knowledge we are seeking for. We learnt basic algebraic manipulations, we use them for everything afterwards, we didn't stop using them after the course finished. we didn't stop using them when the topic is not about basic algebra.
But we stop thinking on the results and contents from many other Math courses after we finished with them. And we don't think about them as we do with addition and subtraction, like we do with multiplication, ... but we need to think about limits, derivatives, equivalence relations, counting, cardinality, combinatorics, range, domain, injunction and disjunction,... everything you learn in every class is not only the object of study themselves. It is not there only for you to pass the course and the topic is over.
They are the tools to carry on. They are your new shoes to walk the path that is ahead, to go forward.
Use them, all of them, to get from the definitions available to you in every exercise topic (write them down) towards the solution that you should be able to write in full as an expression as well, or as another definition. Write them not in words only but in Mathematical notation. Go from one to the other, use small steps, like adding a number, but with your new tools as well, one step only at a time. And use your new shoes, be aware of your previous results and use them as tools like addition, subtraction and other basic tools like logic or set theory.
This is the jump I needed to take to go forward.
Your are great Professor!
You give a taste of math. I am in Master Finance at 51 years old. I am your fan from the Kingdom of Morocco. your are excellent. keep it up.
I love your videos, they are so motivating and real. Thank you!
I’m loving your Udemy algebra course. I’m learning new techniques and I like the way you organise questions without too much of a jump in difficulty.
Thank you for making this video to help remind me of what goal I am going towards. I am self-studying Calculus 1 right now this summer because it'll keep me on track to when I am expected to graduate college in the next 3 years. I am also using your lecture videos on your channel to also help my further understanding on the topics.
I’m suffering from all the geometry I missed the first time around. Now I picked up a textbook graded for teenagers and here I am having a crack at it. 😂 “ SO THAT’S WHY!” “NOW I GET IT!” And “ OH, OF COURSE!” Are words in constantly shout now 😅
Thanks sir it was really needed. Love from India❤
Love the quotes! Keep them coming
I'm reading out of Algebraic Geometry, A Problem Solving Approach by Garrity et al. The sections on divisors is beating me up, partially third time going through it and I'm not confident it'll stick with me for the rest of my life but it feels good to get through it!
This is so true. I am currently learning to write proofs via a discrete math book and it’s really rewarding. But it’s nice because the discrete math book itself has real content in it beyond simply being a ‘proofs book’.
What's the title of that book , I want to start learning discrete math too , thank you ❤
Great talk, Math Sorcerer!
When I found out “Hey, I actually think mathematically,” I built a roadmap.
I got 2 books on mathematics (“An illustrated history of numbers: 100 ponderables” and “The Math Book” by Clifford A), studied them to self test on knowledge. I still need to complete it for the math book; I got bothered by all the name theorems because I’m just bad with names in general. But I really studied that one in a way I didn’t with the first, a bordering on research matter for me.
Then, I would go back to all the stuff up to where I left off in college, with relevant materials.
I’d have a knowledge base for going back to school of what’s ahead of me, with a firmer foundation in all the math before.
Once I’ve finished the Pre-Calc to Calc review, it’s gonna be the proof-stuff.
I also have two handbooks of mathematics; they’re very cool and provide a roadmap of their own.
This is a really cool vid. Good pointers good motivation.. Thanks a lot!
Your my motivation to do math everyday !!! Thanks for inspiring 🙏 people like me who are not interested in math and made it into daily habit !!🎉❤
And make sure you understand the difference between PEMDAS and PEJMDAS.
(Order of operations) on calculators and pencil & paper.
.
And then there's RPN; Reverse Polish Notation.
I completely agree. ☺️ I’ve been avoiding studying the mathematics behind the flatness problem in cosmology. It turns out to be based on Friedmann’s equations (which are in turn based on Einstein’s eqns). It was daunting, but I finally dove in and I’m realizing it wasnt so bad. 😅 I was suddenly happy I took a class on differential geometry in my fourth year of my Bachelor’s degree. I had to push past my discomfort.
Thanks for the Daily Motivation 💪🏾
I think it's important to treat study itself like mathematics: integrating the small skills (starting something, being resilient, being interested in learning), but deriving the big problems (time, distractions, excuses). After all, taking pleasure in learning, making what was difficult as well as easy, pleasurable. 😊
I study books & Practice, when self studying 💯
Great advice. The fundamentals
Hi Math Sorcerer, majority of my high school I was in Turkey. I was excelling at math, but when I came to US I realized something bad. When explained in English math is very complex. I am mainly talking about the names in it. For example, instead of isosceles triangle we say Twin side triangle. It is a triangle that has 2 identical sides, so twin side triangle makes sense and I instantly know what it means because the definition itself is in the name. I acquired the books you recommended and things like this slows me down. In these occasions I have to copy the word and look it up to see what it means.
I think math is already complex enough, and we should not deal with Latin and unfamiliar words. I mean I can get over it, it is not the end of the world, but when names become simple, you can read and breeze through a book with ease. So yeah, I find English math books so unnecessarily hard and difficult.
I don't think this is my lack of proficiency in English, I consider myself more sophisticated and articulate compared to my peers. I read regularly, but I think math should be as simple as possible to be more accessible and less intimidating for beginners. Also simplicity makes math more efficient and clear. Please let me know if you agree or not and why.
After many years I have found out the best way I learn things is to jump into the deep end and just try to figure things out. It feels like beating your head into a concrete block repeatedly in the beginning, but it is by far the most successful method for me. At the moment I'm struggling with some algebraic topology more specifically Obstruction theory and Steenrod Squares. I work as a data scientist so my aim is more deriving interesting tools than all-out proof-writing, but topology is a cool field either way.
I’m a fairly new subscriber.
And I just have say that I find your videos very helpful and inspiring.
Thank you for sharing yourself and creating this videos!
After years of deciding what I want to do with my life I’ve decided to go from a marketing degree to either MIS or IT. I am done with letting Math kick my ass I’m ready to do whatever it takes and this channel is giving me the greatest motivation. I seriously appreciate this channel 🫡
Thank you, this was very helpful. I hope you have a great day my good sir:)
Thomas Taylor's "Theoretic Arithmetic" is a phenomenal book.
Funny that I'm pushing myself so much now, to learn Proofs through Sum-Formulas.
I was thinking giving up for the moment but after this video:
I WILL MASTER IT!
I love such videos in which an expert of a subject can explain soft skills through his field of expertise...
Thanks for sharing!
Thank you.
I guess one can divide his / her self study time into multiple sections where a lesser duration of time is devoted for recaptulation of old syllabus and more time is devoted to learn the newer challenging syllabus.
didn't even know there was such a thing as pure math
Hello, since I found your channel my interest in studying mathematics has intensified, I really appreciate you existing and doing this magnificent work. I'm addicted to books and I took many of your recommendations, I've already started studying for them. I would like to ask you to review the books in the AoPS series (Art of Problem Solving) I heard many comments praising these books, that they are more challenging than the traditional ones and very good, those who study them get very good at solving problems. It will be really cool to see a review of this book series on your channel with your comments on it, please do!
I basically learned algebra while taking calculus at uni, my algebra was really weak before that. It was definitely a ride but so rewarding once I got it, now I do calc for fun lol
Aguardando os vídeos em espanhol 😊
Thank you for the inspiration
What must be even better would be doing math together. I wish there were a club I could join.
Self study is the best.Specially for maths.I still do it to learn new topics.
That was spooky - At the beginning of the video I was on the side thinking about looking into books for functional analysis and then it was mentioned for an example a minute later.
you look a little tired today, hope everything is well. great video as always! hope you mention us statistics guys more in later videos :)
Cuando estudié ingeniería en España, encontré 2 libros sobre Álgebra Lineal que hasta la fecha, en lo que he podido investigar, ningún otro autor lo la superado: Problemas Resueltos de Álgebra. Tomos 1 y 2. Su autor es Emilio Espada Bros. Están agotados hace años, pero se pueden conseguir de segunda mano. Si no los tienes en tu biblioteca, deberías considerarlo.
Great advice for a Math Noob like me ,
Thank you
I have a degrede on mannegment, and before that i was at engeniering in the military academy, but the math i had is so useful that i am reading introdution to mathematical thinking from keith devlin
This gentleman at 90 years old will still be kicking PhD candidates butts in the lecture halls.
I had to learn logic and reason from the ground up in order to even begin to truly learn how to do proofs
Please consider doing a review of the book “The Cartoon Guide to Calculus” by Larry Gonick.
Neat book. 😊
Connect three dots is a vector to me the clock and stuff you know the circle.
I think Feynman was 13 or something when he used that book.
As a nuclear engineering PhD with a math and physics BS, I can tell that the difference not mastering proofs makes a when I am learning the math used in engineering. Yeah you do not need to know proofs to solve problems but it will help learn somethings quicker, make connections, and learn more rigorous methods.
For some math topics, a lot of engineering books get repetitive and you really need a more advanced book to push your understanding.
Hey Sorcerer, big fan of the vids !!
I’m a maths major heading into calc 1 I noticed the calculus for the practical man wasn’t on the booklist you recommended for learning calculus, should I look to pick up one of those or this book ? I had a quick read of trial ebook and did like how it was written so much pick it up anyway along with a textbook
You should do a video about the astounding power of tutoring math to others in order to increase your math skills. After finishing my physics degree i got a job tutoring math to high school kids. To my astonishment my skills improved dramatically! I felt like i became an algebra expert (when i thought i was petty good already!). I don't know what it is about tutoring, but it seems to have some sort of magical power.
What you said about algebra being the foundation of doing well in calculus is so true. After tutoring i reviewed calculus and it all seemed so much clearer than it ever did in college. I only wish i could have tutored math before ever going to college. My life would have been so much easier! Now i always tell my students that algebra 2 is the most important math class they'll ever take, so take it very, very seriously.
“5 integrals is a great way to start the day” YESSS!!! 😂
I bought book of proof off amazon and it arrives in a month lol 😂 I dont even know if I'm ready for that level of math because i havent taken calculus yet
I thought I was the only one who smelled his books. Books and some types of paper smells amazing!
Yes mate, I do have that story.
I landed in Mexico speaking zero Spanish. I was told that I had to teach a 6 week course on a subject I didn’t know.
And everyone else left.
Fortunately, I discovered I have a gift for languages. Otherwise, I’d be broke and stuck in Mexico.
Thanks sir for this as I'm an advocate for self study. By the way where do you lecture?
Hi ! Since your a teacher I thought I'd ask.
When I was a kid I didn't spend much time in school - I didn't get to learn much while I was there.
But I want to know and learn at least basic math . I don't know my reading level,
And I don't know how to gauge where I am at with math either.
There are colleges and a university in my city.
Slipping through the cracks the way I did has hurt my adult hood in some bad ways-
Not sure how to go about finding the right help.
I'm struggling so much in pre algebra
Suggest some easiest books of learning to write proofs, for a high school student.
Sounds to me like writing proofs is like writing music - rather than learning other people’s songs
Seattle shirt. Do you live in Seattle? From there?
I'm almost buying the How To Prove It.. but it's just 1/4 of the minimum wage in my country lol
Active learning vs Passive learning
best video rectified my mistake
I just bought "how to prove it" after watching this video :)
Fuck, fine! I’m buying the proof book tonight 😤
Self studying is great but writing these proofs at the beginning is really hard 😅
When do I know I am ready to move to a different area in mathematics? For example, say I’m learning precalculus, when do I know I am ready to learn calculus? Thank you.
Hello Mr.Sorecer, maybe you will find this interesting, im subscribe and im not studying math...im in my way of becoming a diplomat, studying international law, but your tips are really "inter exchangeables", and enjoy your aproach to study, thank you and keep doing this excelent videos!!!
Which book do you think is the better, "How to Prove It: A Structured Approach, by Daniel J. Velleman" or "Proofs: A Long-Form Mathematics Textbook (The Long-Form Math Textbook Series), by Jay Cummings". Thank you in advance for your support
Dear Math (S)orcerer, please use math to speed up my Calculus for the Practical Man book order... I swear I would be reproving the law of the cosines but unfortunately since the book hasn't come yet, I can't study....😅 Jk just lazy and anxious.. thanks for making these vids, I'll update you with any breakthroughs.... Working on making an ai math buddy in python, trying use faraday's laws to break gravity just too stoopid atm
I guess math really is the rational imagination. A beautiful thing that most of us don't appreciate very well.
ive done analysis not real but the delta epsilon...
as someone in applied, learning some basics of physics and control are much bigger unlocks than formalization...
unfortunately, maybe when i become more in depth - perhaps
Great
Pls sir, what are the various topics to study as a complete beginner in mathematics
What other resources are available other than Khan Academy?
Edit: I dropped Calculus I, but now I’m re-learning all math from pre-school to Calculus I, and beyond!
More edit: posted comment before watching the video 😅
It's time to mention that "Learning Mathematics" is not simply "Learning of Methods", rather it's learning the language of rational imagination...
4:56 And then, I just realize something I should have done earlier
Do you have an upper limit of how much you want to spend per book?
Who would need to learn to write proofs other than a mathematician? I'm in college for computer science or possibly engineering.
👍
Why social secuirty numbers and name are turned in with your bench labs assignments
When did you stopp reading Spidey?