I hate that i think that way, i try to be optimistic, and try to remind myself that it takes time to learn things, but when people tend to rush you because you have to take things a little slower, then its hard to remember that.
If you want to be able to do that, you must have MASTERED EVERYTHING that precedes the task... The language, the alphabet, the mathematical operations, set theory, relations, logic, abstraction and problem solving theory. You must be fluent in ALL OF THESE. If you are weak in the language and can't run the alphabet down quickly from backwards, master that. Read Shakespeare and ancient philosophers, learn mathematical logic, work through Principia Mathematica, get fluent in these and see yourself understanding very quickly. Understanding is about linking and combining, not just perceiving.
That is why I hate school’s pacing sometimes. College courses pack so much information into a semester that often times students don’t have time to sit down and digest all of it before they rapidly move on to another topic. Not to mention the added pressure that grades hold, oftentimes students will value their grades higher than actually learning the subject especially if they need to maintain a scholarship or a good standing with their parents etc.
@@patrick2288 That's the reason I switched fields from chemistry to visual effects. I love chemistry, and I like math too (even though I'm terrible at both) but I can't keep up with the university curriculum. So as a 21 year old, I've decided to learn on my own time instead.
The beauty of math is not that only smart people can do it, but that everyone can do it. Especially calculus, it will teach you the concept "Consistency is perfection"
What I noticed is there are always a group of people who excel at it with little effort. Took me 4 times as long for me to comprehend it compared to them. Never considered going into engineering if those were the people I am going to compete with.
I think one of the biggest problems for kids learning and understanding any kind of mathematics is that nobody ever puts it into context. A fair example is trigonometry, to me, was completely incomprehensible until I went to welding school and actually applied it to something useful. Give kids context to whatever type of math and I believe they can run with it.
The key is to give **detailed** context, not just some shallow, dumbed-down word problem. If students get to know how certain areas of mathematics are used in real-world job fields, then, and only then, can the deep motivation to learn be unlocked. This is an aspect I see so many curriculums even today still lack, and it really is a shame.
A big part of the mathematics is learning to think abstractly. Sometimes there isn't a correlation between the 'real world' and a mathematical concept.
Isn't it that humans speak this language to try to unravel the universe's mystery, instead of saying the universe has already given... hold on, let's stop before this gets philosophical.
@@gamingoptimized I've never thought of that before. If you had to use greek letters we typically use, theta, epsilon etc, do you guys still use the same thing? If you're in Greece that is.
That's only if you skip right to the end of the book like a fool. The beginning of the book has a bunch of cool pictures and some fancy equations that represent the same thing as the pictures in a more concise way.
as a 30 year old taking college calculus over the pandemic and passing it with a not-so-solid B. im happy seeing a 60 year old still be happy talking about it. And i hope im still that excised about it in 30 years from now
I can read a bit of Greek. The only reason I can, is cause I ended up majoring in math. Ironically enough, the only other creatures on campus capable of reading Greek may have been the frat boys and sorority sisters.
I got a D my first semester in college Calc I, and I think the prof was being generous. I couldn’t move on to the next level until I got at least a C, so I had to take it a second time. Somewhere in between, I found Eli Pine’s “How to Enjoy Calculus.” He laid it out so simply that it was like, “Is that all it is? Why couldn’t my professor explain it like this? Geez!” The next time I took it, I got an A. And even now, 30+ years later, it still seems pretty straightforward to me: derivatives are slope finding; integrals are area finding. I don’t remember all of the conversions, but it wouldn’t scare me to try to solve a problem.
@@jrkularatne2900 I read Eli Pine’s book and it made sense. He explained it in a way that demystified the topic. If you have a study group, I’d recommend hanging with them to see if they can assist you. But, really, derivative Calc just boils down to slope finding. You have some conversions that you’ll need to memorize and understand when to apply them, but you’re really just finding a slope at a point.
Calculus was like doing an intense workout and realizing how out of shape I was, but didn't realize it. It exposed my weaknesses in Algebra and Trigonometry, which I passed with good grades, but didn't really try hard to master those subjects. Calculus made me realize how out of shape I was with respect to those areas.
I'm taking Calc right now, and this is exactly how I feel. I got an A in College trig, and an A in college Algebra, but the hardest part of Calc for me is the trigger, and Algebra parts
Calculus best friend: Symbolab, Photomath, derivative calculator, integral calculator, Desmos, and the obvious Professor Leonard. When in doubt, check if professor Leonard went over it.
@@mannymm7887 this works long term if you're never gonna take another calc class or a science class that involves calc in the future. If you are then you're doing yourself a disservice since it will be harder and harder to understand the next class knowing you use another's brain to solve it for you. Bad advice for engineers I guess
Ex Tempetus I know a couple engineers who work industry. They all say the highest extent of math they really need on a daily basis constantly is arithmetic. Everything else can be run on a program/computer or calculator. You really only need to understand the basic concept unless you’re continuing in academia. The higher education the more shortcuts you’re allowed.
I'm taking my first calculus final right now. He was spot on when going from algebra to calculus was a huge jump. I'm in college, not high school. We have to learn the courses in 10 weeks. Not an entire high school year which makes it feel even more impossible. I've taken algebra, trig AND calculus in less than a year and my brain hurts.
Same. Within a year I’ve taken college algebra, precalc, calc 1, and now I’m taking my calc 2 final next week. Next I have linear algebra in the summer. I feel like my brain is going to explode
I failed trig and college algebra. I thought my dream of being an engineer was over since everyone in my degree was already so ahead. I applied myself and now I’m club president of the math club and never gotten anything lower than a A in any of my calculus classes . Nothing is truly hard just practice practice until it’s perfect.
Beware: the teaching and communication skilks of even the top engineering professors are WAY worse than those of mediocre math or physics teachers. So if you do go the engineering route, brace yourself..
@@jimmygeorgiev1966 i didn’t want to be behind everyone else. You either learn how to swim or you drown. It take me 1 full school year plus summer classes to get caught up to everyone. I didn’t want it to happen again especially if it’s something I’m in control of. You gotta do what you gotta do for your goals. Best wishes :)
The calculus part of calculus isn't the hard part, its the algebra. I say this because I just took it after being out of college for 8 years and managed to pull an A grade. I understood the framework of how to find derivitives and integrals. I understood how to rebuild equations to meet my needs. Yeah the notations can look confusing at first but what they represent is trivial crap you've seen before. What fucked me the hardest were the little algabraic tricks you learn in high school. Brush up on algebra and you will get through it fine.
cant agree more. im in AP calculus at the moment and really the concepts arent too hard but the rationalization and simplification from alg 1/2 is kicking my ass lol
@@defectivepikachu4582 we had a great maths teacher, she taught us in such a way that could study learn from the books and after a while, we did not need her really. we mostly discuss very difficult questions
@@marcinsobotka447 she taught us how to teach ourselves. she developed the fundamental principles so clearly and she was extremely good at expressing herself. her classes were like she was having a conversation she spends a lot of time on the fundamentals. it was not one thing she did but how she put everything together. in our school, it is the British system so at high school you could be taught pretty advanced stuff, which was up first and second-year math courses in the university. this really made my engineering maths classes pretty easy
Framing Calculus in such a mythological/representational context is kind of what I have needed, man. I've been on the fence about taking the first steps to becoming an engineer for quite some time now, and knowing Tyson was in a similar scenario for his field of science is quite inspiring. So again, ty for pulling this outa the guy man. His willingness to put in the work and the lack of fear to be a failure is probably the most inspiring and practical part of what he said. Hope I'll be on the same path soon enough
Just finished my Calculus 3 final today. Proud to have finally made it here. Neil makes a good point; looking back, what got me through these three classes wasn’t any math skills. It was simply the time I spent studying. Sure, people who are naturally good at math will learn calculus quicker. And yes, having a good professor does helps. But no matter how smart you are, or how good your professor is, it still takes time. At the end of the day, time spent studying is what brings you success. I now believe anyone can learn Calculus. You just have to be willing to put in the time. Trust me, I’m no math expert. If I can learn it, you can too 💪
@@matrxzeno476110-12 hours a week. I’m in calc 2 and I at least spend 2 hours a day reviewing concepts doing homework and practicing problems I don’t know how to do. Some areas are easier than others
Also have a study group or at least a buddy. I've worked at or been a student at highly effective learning institutions, all with different goals and timelines, and group work is one of the pillars they shared in common. It improves your motivation, it improves your morale, and it improves your ability to communicate in human terms which is useful even in abstract subjects.
@@thebravesirrobin. I personally found study groups to be less helpful. I was always more productive when studying alone, tried groups several times but I process math much slower than the average person. I usually solve problems at a slower-than-average rate or with unusual methods. Also I struggle to focus academically when other people are present. On several occasions I would leave my study group midway through so I could be more productive. I definitely think study groups can be good, but it depends on the person, the subject, and the material. For me personally they are counterproductive.
@@matrxzeno4761 Several hours before each test usually. And yeah it can be hard with other classes. I was always taking multiple other classes alongside my calculus ones. But if you can manage 5 hours personal review before each test (not necessarily all at once), you are much, much more likely to pass than if you just did like 1 hour of review.
Can’t do calculus but I just love it. So I am starting all over from rock bottom in maths, like -2 + -3 sort of thing to get to a doctorate. I just can’t wait to get to that bit about ‘limits’ and f(x) cos that’s the door to my ambition. Thank you Neil you are an inspiration. And I am 75 yrs old so I had better get a move on.
@@aomorgancool1775 Yes, my doctor told me I shouldn’t really be running the 5km park run every Saturday. Well I have run 35 so far, also the town’s annual 10km run. At present am In training for the Great North Run in 2021. I am fitter than very many half my age and shall never, never be forced into the form of a decrepit old woman as Society depicts us. What would you have me do? Watch ‘Love Island’ or Eastenders. God forbid! Life is for living until the moment you drop dead. As for my grandchildren , they have no need of my money, already they are far wealthier than I shall ever be.
Don’t feel bad guys if you’re bad at math. I’m a math major and got a C the first time I took calc 1. Retook it and got a B+. I just finished this semester with a B in linear algebra and a B+ in differential equations (I’ve never been an A student), just keep working hard and you’ll get through just fine guys.
@無慈悲 I am planning to go to grad school. I’ve taken all three calc classes, differential equations, linear algebra, mathematical finance and probability theory
@@jmccullough975 it’s up to you. I got a B- in calc 2, and even though I’ve now taken graduate level math courses, for me calc 2 was among the top 3 hardest math courses I’ve ever taken and I’m going to retake it for a higher grade. My concentration is in actuarial finance, but my dream is also to be a quant and want to pursue a masters in quantitative finance. I wish you good luck, you should definitely consider retaking the course if you love math like me
I just took my first calculus test and before I was like I'm never going to pass this test and got a 94. Now I'm on the next chapter and I feel the same exact way. The pace is what kills me.
Very great words. I'm in calculus 1 right now. Came back to school in the fall of 2021 after losing everything in the pandemic and 25 years removed from the classroom. It's hard, but doable, just as he says. It really boils down to how bad you want it. I'm older and more mature, so I have an advantage in that regard. Very best of wishes to anyone currently studying in college or high school and feeling discouraged. It can be a very difficult process, but you can get through it!!
@@IamFrancoisDillinger I had the privilege of taking Professor Leonard for Calculus II in person, when he used to teach back at Merced College. It was phenomenal, and quite challenging!
Keep going! You can do it! I was at a CC as well, and the tougher math courses were scary.. but no matter how challenging things might seem, one must always try to keep pushing forward. :)
You can do it man! It takes sacrifice! If you're really determined try to block out most of what you think might distract you and you'll be fine. We all go through it! Good luck!
You're absolutely right. It's a hard subject because school always rushes it. You could explain calculus to a middle schooler with little algebra experience by drawing pictures, and they would understand it.
Standardized testing for ya. It's horrible. Not everyone can learn the same material in the same amount of time. But students are expected to learn a certain thing by a certain day and expected to get 100% on a test. It's pretty lame.
for me i struggle to process what it is being taught in the class because it takes my entire processing power to just listen to the teacher speak. So if i can only focus on listening, i cant think. so i dont understand. the solution to this, for me, is to just research it on my own and think about it in my free time. i typically watch videos, pause them to think, and then play them, and then repeat. organizing it and breaking it down really helps as well
Not when he answers my emails 6 days later or never checks Piazza. :_) Some professors couldn't be bothered to help their students in the middle of a pandemic.
@Anime Sucks wow yikes i guess im just hella lucky, well some teachers are just like that, cant you somehow convince them? or mabye complain? i only mentioned USA because they are well known for their bad education system
Calculus 1 was an insane learning curve for me. I took it over the summer so the class went extremely quickly. I basically failed my first test on limits (lmao ikr?) and from that it was like I had to then make a change in perspective. I woke up and started calculus from that morning till the time I went to sleep. I essentially had to drop everything I did usually in my free time to get it done. I got the 2nd highest grade in the class, and a good start on calculus 2 after believing I was going to fail and couldn't do it. Insane learning experience all around, it helped me to finally realize the utility of all the math I've done my entire life, and showed me that the intimidating part is only the beginning.
@@tarik6694if you’re trying to learn calculus and don’t know where to start - I would recommend first getting your hands on a calculus book. Every college course you go through will be based off some book and the book is necessary because it provides a procedural approach to the topics you should look at chronologically. For example, most calculus courses and books will start with limits, then move onto derivates and then into anti-derivatives, onto integrals. You can’t understand a definite integral until you understand the limit, derivative, and anti-derivative topics because an integral is a defined limit anti-derivative and an anti-derivative is the inverse of a derivative. From there you should just utilize the resources available to us all, read the chapter on the topic, watch videos, and ask questions about that specific topic’s theory and utility. To me personally, solving problems mathematically can be rather boring, but once you actually understand the how and why, the theory and how to interpret the math, all the different pieces will fall into place. Solving things mathematically is one thing, but understanding what you’re doing is another. I hope this helps
Thank you for this. For years I have forgotten how much I love to grow learn and develop new skills. It fascinated me to feel my brain learn new things and expand. Again. Thank you for this. I remeber being like 8 or 9 and asking about calculus. At the age of like 5/6 maybe 7 I was asking my mom about multiplication and division. Unfortunately my mother had dropped out by 3rd grade to raise her own family because my grandmother one day decided to not be part of that family. Now as I see this video and these memories begging to come back, and I want to learn and strive for more all over again. This drive had left me a long time ago. Thank you!!
Something I feel newcomers should get their minds around is the fact that the concepts probably aren't going to make sense the moment they're taught to you, and sometimes you just have to take things like derivatives at face value and gradually they'll make sense to you as you progress. The learning process is significantly different.
This is advice for anything new you try in life. It won't make sense when you first learn it or try it. But given enough time and effort, it all comes together.
The problem is that in my school AP calc is squeezed into four months. This means I have little time to practice and get familiar with concepts and cannot get them in time for the test
@@sbc2954 Yeah I'm taking BC so it's basically all of Calc 1 plus a bit of Calc 2 squeezed into ~5 months. Super difficult but it's a great learning experience and helped me develop study techniques and other methods of improving since Algebra was more or less a cakewalk for me.
I remember I watched this video a year ago, just before I started calculus, A few months later I kept thinking about this video and how accurate it was! Great words Neil!
Gotta say, I just passed calc 3 with an 88. When I started my college career with basic algebra skills I didn't know how I would ever make it to this point, but i did. It's all in the work and taking things one at a time. Each new thing I learned felt like it was pushing the limits of what my brain could comprehend, but as I practiced it and learned new more complex ideas eventually they felt elementary.
Very Motivating! It all comes down to how bad you want it... and how much time and effort you're willing to sacrifice to triumph your obstacles along the way.
Calc comes with Algebra, I remember not being as good as I should have been with Algebra so I would make small mistakes in Calc class but after doing so many problems, everything starts becoming like repetitive because even if a problem look different from the other ones, we use the same methods to get the the final solution. Algebra becomes like a second nature in calc class.
I agree completely, no one can pass calculus without knowing any algebra. My professor also said that one of the most common reasons for failing calculus is poor algebra skills.
I remember feeling the exact same way when I opened a calculus book the first time. Funny how comforting all those big scary integrals become in the second semester when you learn how to use them.
I doesn’t involve calculus but.....In 1983 I graduated high school with .5 credits of math. Yes, graduated with .5 credits of math. I hated it, never understood it. I even spent time in the learning disabilities class for math. Years go by and never used any sort of math....until I got a cool job working along side some cool engineers and scientists. It inspired me to go back to school. Basic math, tech math 1, tech math II, beginning algebra, intermediate algebra, physics. Then I got into mechanical design. Material properties, statics, mechanisms, design problems. It was all math albeit still “basic”. I guess the point is you have to be willing go through the ignorant phase of learning to get better... no matter what the subject.
"Let no one deceive himself. If anyone among you thinks that he is wise in this age, let him become a fool that he may become wise." 1 Corinthians 3:18
i’m actually so thankful for how ontario’s curriculum is designed. all academic math that you learn from freshmen to senior, it’s all used to slowly transition into calculus
deGrasse Tyson's Storyteling is amazing: Talking about something abstract like calculus and he converts it into "his friend" in order to understand the universe. Hats off
I just burst into tears watching this. For what I want to achieve in my life, calculus is a necessity and I have limited time to take the courses before transfer, I get so frustrated with myself because it’s finally something I attempt to learn that completely eludes me . Japanese? Learned it with minimal problem. Calculus? Nope. So so humbling and makes me feel unintelligent UNTIL NOW. This changed my outlook. Thank you for sharing
Watch Professor Leonard. And watch the videos before lecture, so that if you have a professor who understands calculus but can't teach it, when they're done "explaining" and write the "example" for the class to "figure out and work on your own", you'll be better prepared to tackle it and you'll have a better understanding of what your grading professor's expectations will be for the exams.
Differentiation is simply the slope of a curve or function, while integration is just the area under a curve. Once you have that basic understanding, all you need to do is to solve multiple problems to gain mastery. Even the examples in textbooks can be used as exercises as long as you cover the solution and attempt to solve it first.
Its such a simple point but he says it so elegantly I needed to hear it again. Quit being frustrated because you haven't mastered it quickly, keep the discipline and you'll get it. I personally beat myself up over not mastering Spanish and Mandarin but he makes such a great comparison between learning Math and a language.
With all of the lectures, books, diagrams and equations helping me learn Calculus, it was this 3 minute video that put me in the mindset to finish Calculus.
It's the 'putting in the time' bit. Trepidation at the thought of prolonged and repeated extreme boredom. That's my problem. Always has been and I end up hating myself for it
@Ne10 2718 I like that one. The real trick is to become well practiced at being uncomfortable. I really do think that being uncomfortable should be the default state for a person. Good trick for someone who was brought up in lower middle class southern England 😫
This is so encouraging! I am currently taking Calculus 1 and Calculus based Physics 1 and it's very challenging. It made me rethink my decision taking it. But I need it for my goals! Just because I don't understand it immediately, it doesn't mean I will not be great at it!!!
@@c.b.6582 yep, calc based 1 is needed before or during it to pass calc-based physics 1 successfully. Not calc 2. That's what the universities encourage too.
@@AuthenticTrading a working knowledge of the end of Calc 2 and beginning of Calc 2 is helpful in physics 1. My physics professor required us to have at least Calc 2 and Diff EQ, for his Physics 1 class, smh.
In high school, there is a class between algebra 2 and calculus, which is pre-calc. That helps a bit with bridging the gap. But the jump from those math to calculus is indeed very different. As someone who has tutored math, even though I didn't do great in my first couple of calculus classes, the biggest problem I see students having is in the algebra of the course. Factoring, simplifying, dividing, multiplying, and taking square roots of non-polynomials always became a problem.
"squiggly lines i have never seen before." Bruh... I honestly felt the same when I got to calculus in junior year. Honestly, its a good thing I started preparing months before so the transition was easier.
I’ve been a math tutor for a long time. You just need to spend time solving lots of problems. Don’t get jealous of those geniuses who don’t have to study-they’re the anomalies. Put in the time and you’ll be amazed what you can accomplish.
@@Chironex_Fleckerilmao cope. I live a very good life and I’ve tested at 4+ SD’s of IQ (exceptionally gifted). I do believe it’s disgusting to assign worth to people through their IQ, but whatever helps you sleep at night 🤷♂️
@@juanzavala9023 I'm sorry you feel the need to chime in and make your ego the internet's business. You're oversharing. I'd advice you to use a degree of discretion. Call me Mr. Bopperton if you will please. It's an odd name, right? I'm about to explain exactly why discretion is key to being professional, whether you're on company time or not. I've worked internal and external corporate recruiting. That's all. No cert sharing. No companies. No figures. Notice what I'm omitting? Keep reading. I've met a lot of people like you, managed some who always had a chip on their shoulder in zero pressure situations. You didn't have to write this comment. Neither did I. But I have a specific point to illustrate: Those statements are unfavorable statements. You know better. You're here telling on yourself, professionally speaking. Indiscretion and oversharing is normal but keep it limited to private conversations. Remember, the Company is depending on you to conduct yourself in a way that adheres to the guidelines outlined in the employee handbook. Ethics is a big part of what companies look for in their employees. Integrity. If you are someone on LinkedIn who, I don't know, posts things like "someday my family will thank me for all those nights I spent grinding at the office past 5:00pm". If that is you early in your career you're a good laugh and an easy commission for some bro sitting in PJs at his desk sipping coffee who will place you in some 100k VHCOL role with a known 90%/24mos attrition. Keep telling yourself those things. It just sounds like you're going to work for whatever manager and do what they say because you love to drink from the company's chalice. That's good. They know you'll cry multiple times in that role. Just being honest. They know it. As they hire you, if you were recruited with a 3rd party. It's all just about HC. Those people who think they're doing well and will "grind", it's bread and butter. Good luck with burning out, Mr. Zavala. If you loved your job you wouldn't have brought it up while you're supposedly relaxing on TH-cam. Remain seated. It's going to be alright, but here's the funniest thing about you posting this. Putting this in writing on the internet for people to see, Mr. Professional. You are visible here. There are so many things that these bureaus pull these days. They scrape the internet for every last drop. And here you are writing things that are signed sealed and delivered in real time permanently. That's every comment on the internet. You are a professional, aren't you? Act like the top talent and genius visionary you purport to be!!! Know these things. Keep grinding. If I heard you talking to me like that at a restaurant or company social, I'd pull you aside and have a chat out of concern. It's not professional conduct, and your likeness is an extension of what a company sees in you. They go a lot deeper than just interviews, resumes, and standard FCRA-compliant checks with all the different reporting that has changed since people started sharing everything on social media. Notice how I turned a two sentence comment into an utterly eye-glazing read? Yeah, I've written my fair share of emails at a managerial level. It's all just a game and you'll learn that making comments like yours are just limiting your own success. Genuinely mean that. There are C-Suite executives who make small talk with the facilities staff. Why? Because it's important to be able to understand others in the modern workplace environment. It's fast-paced and we need rockstar employees like you to keep doing all the legwork. Best, Bill Bopperton Senior Vice President of Informing You How Business is Conducted in 2023
Thank you to all those people who have responded to my comment inspired by the Neil De Grasse Tyson interview. Many of you have said how you struggled with maths in the beginning but found that inner strength to keep going. I am humbled by your determination and the numerous messages of encouragement too. I shall be back at my desk with maths books open shortly with a better understanding now that just because you couldn’t get it right first time doesn’t mean you are dumb, you just have to keep at it. As for my 75 years of age , well, I haven’t got time to die I am far too busy. Got the Great North Run to train for in September 2021. By the way I am English. And, teaching myself to do the ‘shuffle’, see TH-cam Elvis Presley , Sweet Surrender, Hot Girls. As for the person who asks if we could share’ books, would they message again please. Again thank you to all of you, wherever you live.
Wow how enlightening! I've never heard anyone drop such mind blowing wisdom from the stars before! This guy is a genius. Oh, wait, every parent and teacher has been telling their children and students this forever.
I love Neil deGrasse Tyson. I'll be taking Calculus next year. And I can't wait to learn it, because even though I won't get it at first, I'll work at it.
That is a wonderful perspective to learn anything in life. You don't have to be good at it in that instant. You can slowly and gradually make your way up to that skill and become really good at it eventually. You have to keep at it, you have to love it and just keep putting in your focused efforts.
@@eobardrush2112 sorry guys I tried to find the video, it was a compilation of him on the Joe Rogan podcast being incredibly rude, the video seems to be taken down. If you really care you can watch the full podcast but you won’t make it through the first hour, it’s too painful. He constantly interrupts, he tries to make joe look stupid when he asks questions. It was one of, if not the rudest displays I’ve seen broadcasted. He has a intellectual superiority complex that makes him this way, it’s very clear from the video.
i watch this a couple times out of the week. i have been so determined to learn calculus. just like Neil, i want to be able to understand the language of the universe
Pretty good advice. I've been in that situation thinking that some form of math was way too complex to learn when first looking at it, and by pushing those thoughts aside, persevering and just doing the math, came out with results in the high 90% for those exams.
My biggest hang up was interest. If you have no interest in something, or feel it has no impact on your life, it can become a mountain in your mind. It's the perspective of learning as a whole. Find the interest anyway you can. Relate it to something. Some times simply learning the process itself is what helps us navigate life. Those who are good with planning and processes tend to have great success in other areas, not just that particular subject. I struggled with this until the day I picked up Neil's Astrophysics for people in a hurry. Then Cosmos by Sagan. Then every Hawking book I could comprehend. Suddenly, I found myself learning real astrophysics from the ground up. You see, I was never a smart kid. I struggled in school, then at the age of 40, I realized how many things are so tightly bound together by physics and astrophysics, including economics, which became my ultimate passion. I now understand process, human interest and behavior, and myself, better than I ever did. It changed my life completely. Started my own business, because the idea no longer overwhelmed me. I tackled some difficult stuff in astronomy and economics, so what could possibly be a mountain to me then? I'll climb that damn mountain. Challenge accepted.
I’m struggling with a project and procrastinating rn because the due date is approaching and I just can’t wrap my head around one concept and then neil said too many people think they have to be good at something instantly to ever be good at at which gives me slme hope
I took calc 1 in high school and didnt really understand it, I was pretty lost by the end of it. Then in college i took calc 2 and suddenly all the weird integration stuff that i didnt understand just clicked with me, and i felt like i finally understood what its basically about. It also helped being in physics and learning super simplified calculus with distance vs velocity vs acceleration and seeing how its applied
i'm so bad at this, most of my life everything academic came easy and i hit pre calculus i was confused "why doesn't this make sense?" and very quickly i struggled and lost faith in my abilities and actually started to think maybe i'm bad at math and i got lucky prior. I'm still in this mindset to this day, luckily i'm very young still, but I never struggled and when it came i have no idea how to face it. Basically i was that kid telling my teachers "I don't need to study or practice" and i regret that. The fundamentals were easy to get A's on but those skills faded away as quickly because lack of use and that built over time and eventually i reached a point where it felt like i didn't know the basics anymore.
this is me, everything before pre call was easy but for sum reason my skills worsened. idk if it was because of the lockdown and having to do school online, but i can’t even get an A anymore in my math classes
I’m just starting Trigonometry on my way to become a civil engineer. I’m scared as hell but this video helped a lot. I hope to one day come back to this video and day I did it. I know the road ahead is gonna be filled with challenges, but I’m going to give it everything I’ve got.
I'm a high school student taking calc, and my best friend is taking it with me and his dad is a civil engineer. I'd say you don't have to worry that much: try to get good at solving the equations but also try to understand them too. Some things will never make sense- math is easy to learn to do but sine, cosine, and tangent have never "made sense" in the same way that 2+3=5 does. Make sure you ask your teachers questions, and it's also important to have at least one friend in the class that you can go back and forth with for help. Sometimes there will be small holes in your understanding, but just try to fill in as many of them as you can and the rest will fix themselves later. I did trigonometry and precalculus stuff last year, and it's honestly about the same difficulty as calculus itself in my opinion. You just need to stay on top of your game, learn one concept after another, and stay confident. What high school has taught me so far is that if you play your cards right math will be the easiest subject.
don't slack on that trig, because you'll need that shit in calculus lol. calculus isn't actually hard, it's remembering all the trig and algebra you forgot that makes it tough.
I’m in calculus and I find it absolutely fascinating, I’m not really like a “nerd” and I don’t even get the best grades in a lot of classes, but I love math
higher level math is very straight forward as long as your instructors/profs actually give a good geometric intuition behind it. learning math by memorizing formulas is like trying to learn a language by reading its dictionary: you get a spotty understanding a few specific concepts but you can't really see the whole picture. calculus 1/2 were actually first math classes i ever found easy because my prof was very heavy on geometric intuition BEFORE rigorous proofs and derivations. one of the most memorable sayings of his was: "if you don't understand it geometrically, you don't really understand it". after having taken that advice to heart it completely transformed the way i look at math and i've now taken several graduate level math courses and gotten 95%+ in them. obviously you need to study and do practice problems too, but i think anyone studying math can massively, MASSIVELY cut down on the amount of "grinding" they need to do by spending more time on geometric/spatial understanding of what they're dealing with, rather than just seeing math as some slog of symbolic manipulations. math is the language we use to understand the universe, and the universe is a spatial thing, not a symbolic thing.
One of the first things I learned in calculus was a vastly easier way to do something that was challenging in advanced algebra. I was mad at first for having to slog through it in algebra when it was easier in calculus, but then I realized if I hadn't slogged through it in algebra I would not have been in a position to understand it in calculus. Sometimes there's a reason to wax on wax off.
I majored in math and completed my degree. I can definitely say Calculus I was the most foreign and bizarre subject I ever learned. I wouldn't say it was the hardest, but was very hard at first. I ended up taking tons of calculus courses. But it "opened my brain up" in a way I had never experienced.
Thank you so much for this Dr. Tyson. I’m a 2nd year physics major with a dream to be a theoretical physicist, currently struggling in Calc 2 honors, after thinking the regular Calc 1 section was too easy. When you said “I don’t understand this yet, but the universe is speaking this language” I felt that so hard. Thank you for being a great example of how you learn something slowly, not all at once. I’ll go back to my studying now, so that I can achieve my goals.
My suggestion when starting any new area of mathematics is to focus on simple memorization of how to arrive at the correct answer, as opposed to focusing on true understanding. Just plug and chug, and through repetition, understanding will inevitable come in time. This little tidbit of wisdom was given to me by a friend. I'm forever grateful for it and pass it along whenever I can because without it, I never would have made it through any of my algebra, geometry, or calculus classes. Hope it helps someone else as it did for me.
"And every bit of yourself you invest helps to dissipate that fog." I love the fog analogy. It's not a binary on/off switch of understanding. Learning complicated things is done through thousands of popcorn kernels being popped.
Need this because I felt so smart going into AP calc AB and I’m currently failing because of mini mistakes and sometimes the concepts are hard for me to grasp it’s only been 1 month and we just started L’Hopital chapter 3 so we’ll see how this goes hopefully I can bring my grade up to at least a B- by the end of the semester I have a little over 2 months
His shared experience is a good perspective for beginners struggling with calculus. Unfortunately most students do not have the luxury of tutors for challenging subjects. For this we have TH-cam.
Sadly, many people are turned off math snd science on account of professors who are bad teachers. Many professors simply don’t have a passion for teaching.
I remember when I did Calculus, the fog slowly started becoming radioactive fallout
🤣❤️
i alughed way too hard for this
Noice
Hahahahaa
fog was supposed to clear when you did composition of functions
"Too many people think that they have to be instantaneously understand something to be good at something."
I hate that i think that way, i try to be optimistic, and try to remind myself that it takes time to learn things, but when people tend to rush you because you have to take things a little slower, then its hard to remember that.
If you want to be able to do that, you must have MASTERED EVERYTHING that precedes the task...
The language, the alphabet, the mathematical operations, set theory, relations, logic, abstraction and problem solving theory.
You must be fluent in ALL OF THESE.
If you are weak in the language and can't run the alphabet down quickly from backwards, master that.
Read Shakespeare and ancient philosophers, learn mathematical logic, work through Principia Mathematica, get fluent in these and see yourself understanding very quickly.
Understanding is about linking and combining, not just perceiving.
That is why I hate school’s pacing sometimes. College courses pack so much information into a semester that often times students don’t have time to sit down and digest all of it before they rapidly move on to another topic. Not to mention the added pressure that grades hold, oftentimes students will value their grades higher than actually learning the subject especially if they need to maintain a scholarship or a good standing with their parents etc.
@@patrick2288 That's the reason I switched fields from chemistry to visual effects. I love chemistry, and I like math too (even though I'm terrible at both) but I can't keep up with the university curriculum. So as a 21 year old, I've decided to learn on my own time instead.
@@spidaxtreme amazing!!That's the spirit dude.
The beauty of math is not that only smart people can do it, but that everyone can do it. Especially calculus, it will teach you the concept "Consistency is perfection"
The problem is finding the motivation to learn that
The thing is that i may understand the algorithm to solve it , but sadly i cannot understand them in real world..
@@waltuh771 do you mean the application of calculus?
What I noticed is there are always a group of people who excel at it with little effort. Took me 4 times as long for me to comprehend it compared to them. Never considered going into engineering if those were the people I am going to compete with.
Everyone, can do it! I promise you all can. I got a B in calc I and I am currently going through calc II stay in your journey! 😌
I think one of the biggest problems for kids learning and understanding any kind of mathematics is that nobody ever puts it into context. A fair example is trigonometry, to me, was completely incomprehensible until I went to welding school and actually applied it to something useful. Give kids context to whatever type of math and I believe they can run with it.
this this this!
Exactly, trig made a lot more sense after I took physics and geophysics.
This should be the number one comment. I've been saying this for years. Nice job!
The key is to give **detailed** context, not just some shallow, dumbed-down word problem. If students get to know how certain areas of mathematics are used in real-world job fields, then, and only then, can the deep motivation to learn be unlocked. This is an aspect I see so many curriculums even today still lack, and it really is a shame.
A big part of the mathematics is learning to think abstractly. Sometimes there isn't a correlation between the 'real world' and a mathematical concept.
"But I need to know this because the universe speaks this language".
exactly this ia how I am feeling now
@@athul_c1375 sammeeeee
Neil Tyson is literally a quotes factory.
Imagine some genius proving that it actually ain't the universe's equation.....he will be like "ah...here we go again"
Isn't it that humans speak this language to try to unravel the universe's mystery, instead of saying the universe has already given... hold on, let's stop before this gets philosophical.
"Half the greek alphabet is in there" calculus summed up 😂😂😂
@@gamingoptimized I've never thought of that before. If you had to use greek letters we typically use, theta, epsilon etc, do you guys still use the same thing? If you're in Greece that is.
That's only if you skip right to the end of the book like a fool. The beginning of the book has a bunch of cool pictures and some fancy equations that represent the same thing as the pictures in a more concise way.
as a 30 year old taking college calculus over the pandemic and passing it with a not-so-solid B.
im happy seeing a 60 year old still be happy talking about it.
And i hope im still that excised about it in 30 years from now
I can read a bit of Greek. The only reason I can, is cause I ended up majoring in math. Ironically enough, the only other creatures on campus capable of reading Greek may have been the frat boys and sorority sisters.
It's all Greek to me...
(Obvious joke. Sorry.).
I got a D my first semester in college Calc I, and I think the prof was being generous. I couldn’t move on to the next level until I got at least a C, so I had to take it a second time. Somewhere in between, I found Eli Pine’s “How to Enjoy Calculus.” He laid it out so simply that it was like, “Is that all it is? Why couldn’t my professor explain it like this? Geez!” The next time I took it, I got an A. And even now, 30+ years later, it still seems pretty straightforward to me: derivatives are slope finding; integrals are area finding. I don’t remember all of the conversions, but it wouldn’t scare me to try to solve a problem.
I’m currently failing calculus how did you do it
@@jrkularatne2900 I read Eli Pine’s book and it made sense. He explained it in a way that demystified the topic. If you have a study group, I’d recommend hanging with them to see if they can assist you. But, really, derivative Calc just boils down to slope finding. You have some conversions that you’ll need to memorize and understand when to apply them, but you’re really just finding a slope at a point.
I got so excited thinking how to enjoy calculus was a TH-cam video
@@letsstudy3579 😄 Though it’s not a bad idea.
Im taking ap calc ab in junior year you are giving me a heart attack
"But I need to know this because the universe is speaking this language" thats probably the best motivation to push through day in and day out
Calculus was like doing an intense workout and realizing how out of shape I was, but didn't realize it. It exposed my weaknesses in Algebra and Trigonometry, which I passed with good grades, but didn't really try hard to master those subjects. Calculus made me realize how out of shape I was with respect to those areas.
It’s just genetics to favor math at the age of 6.
I'm taking Calc right now, and this is exactly how I feel. I got an A in College trig, and an A in college Algebra, but the hardest part of Calc for me is the trigger, and Algebra parts
experiencing that rn, send help 🥲
Factss‼
100% right
Calculus best friend: Symbolab, Photomath, derivative calculator, integral calculator, Desmos, and the obvious Professor Leonard. When in doubt, check if professor Leonard went over it.
Wolfram Alpha and Geogebra too
Paul notes
Patrickjmt
@@mannymm7887 this works long term if you're never gonna take another calc class or a science class that involves calc in the future. If you are then you're doing yourself a disservice since it will be harder and harder to understand the next class knowing you use another's brain to solve it for you. Bad advice for engineers I guess
Ex Tempetus I know a couple engineers who work industry. They all say the highest extent of math they really need on a daily basis constantly is arithmetic. Everything else can be run on a program/computer or calculator. You really only need to understand the basic concept unless you’re continuing in academia. The higher education the more shortcuts you’re allowed.
I'm taking my first calculus final right now. He was spot on when going from algebra to calculus was a huge jump. I'm in college, not high school. We have to learn the courses in 10 weeks. Not an entire high school year which makes it feel even more impossible. I've taken algebra, trig AND calculus in less than a year and my brain hurts.
*cries in UCSD*
Same here :)
i took calc 1 in 5 weeks last semester after failing algebra 2 in highschool. in cal 2 class and I'm so glad i didnt cheat
Same. Within a year I’ve taken college algebra, precalc, calc 1, and now I’m taking my calc 2 final next week. Next I have linear algebra in the summer. I feel like my brain is going to explode
@@gabriellebron9968 How did calc 2 finish out? taking it over the summer now and linear algebra in the fall.
I failed trig and college algebra. I thought my dream of being an engineer was over since everyone in my degree was already so ahead. I applied myself and now I’m club president of the math club and never gotten anything lower than a A in any of my calculus classes . Nothing is truly hard just practice practice until it’s perfect.
Beware: the teaching and communication skilks of even the top engineering professors are WAY worse than those of mediocre math or physics teachers. So if you do go the engineering route, brace yourself..
Yeah the comment that replied to you is right…. Goodluck buddy
How did you manage to turn it arounf?
@@jimmygeorgiev1966 i didn’t want to be behind everyone else. You either learn how to swim or you drown. It take me 1 full school year plus summer classes to get caught up to everyone. I didn’t want it to happen again especially if it’s something I’m in control of. You gotta do what you gotta do for your goals. Best wishes :)
@@Madam2012are you an engineer now? Or are you almost done?
The calculus part of calculus isn't the hard part, its the algebra. I say this because I just took it after being out of college for 8 years and managed to pull an A grade. I understood the framework of how to find derivitives and integrals. I understood how to rebuild equations to meet my needs. Yeah the notations can look confusing at first but what they represent is trivial crap you've seen before. What fucked me the hardest were the little algabraic tricks you learn in high school. Brush up on algebra and you will get through it fine.
cant agree more. im in AP calculus at the moment and really the concepts arent too hard but the rationalization and simplification from alg 1/2 is kicking my ass lol
@@conraddgg6800 I’m in the exact same spot; sometimes I’ll completely miss easy simplifications and get confused.
@@rando5673 we were just doing implicit and double derivative implicit and yeah those were interesting to say the least
I disagree,hardest part about calc is the trig
let alone the unit circle
it was taught in my high school, once you study and have a good teacher you are good
the teachers makes all the difference
@@defectivepikachu4582 we had a great maths teacher, she taught us in such a way that could study learn from the books and after a while, we did not need her really. we mostly discuss very difficult questions
@@midnightwatchman1 what did she do that made her good?
@@marcinsobotka447 she taught us how to teach ourselves. she developed the fundamental principles so clearly and she was extremely good at expressing herself. her classes were like she was having a conversation she spends a lot of time on the fundamentals. it was not one thing she did but how she put everything together. in our school, it is the British system so at high school you could be taught pretty advanced stuff, which was up first and second-year math courses in the university. this really made my engineering maths classes pretty easy
Steve Spence calculus is watered down in high school. You'll have to retake it at the University.
Framing Calculus in such a mythological/representational context is kind of what I have needed, man. I've been on the fence about taking the first steps to becoming an engineer for quite some time now, and knowing Tyson was in a similar scenario for his field of science is quite inspiring. So again, ty for pulling this outa the guy man. His willingness to put in the work and the lack of fear to be a failure is probably the most inspiring and practical part of what he said. Hope I'll be on the same path soon enough
Just finished my Calculus 3 final today. Proud to have finally made it here. Neil makes a good point; looking back, what got me through these three classes wasn’t any math skills. It was simply the time I spent studying. Sure, people who are naturally good at math will learn calculus quicker. And yes, having a good professor does helps. But no matter how smart you are, or how good your professor is, it still takes time. At the end of the day, time spent studying is what brings you success.
I now believe anyone can learn Calculus. You just have to be willing to put in the time. Trust me, I’m no math expert. If I can learn it, you can too 💪
How much time we talking here cuz remember students usually are taking several other courses alongside their math courses
@@matrxzeno476110-12 hours a week. I’m in calc 2 and I at least spend 2 hours a day reviewing concepts doing homework and practicing problems I don’t know how to do. Some areas are easier than others
Also have a study group or at least a buddy. I've worked at or been a student at highly effective learning institutions, all with different goals and timelines, and group work is one of the pillars they shared in common. It improves your motivation, it improves your morale, and it improves your ability to communicate in human terms which is useful even in abstract subjects.
@@thebravesirrobin. I personally found study groups to be less helpful. I was always more productive when studying alone, tried groups several times but I process math much slower than the average person. I usually solve problems at a slower-than-average rate or with unusual methods. Also I struggle to focus academically when other people are present. On several occasions I would leave my study group midway through so I could be more productive.
I definitely think study groups can be good, but it depends on the person, the subject, and the material. For me personally they are counterproductive.
@@matrxzeno4761 Several hours before each test usually. And yeah it can be hard with other classes. I was always taking multiple other classes alongside my calculus ones. But if you can manage 5 hours personal review before each test (not necessarily all at once), you are much, much more likely to pass than if you just did like 1 hour of review.
Can’t do calculus but I just love it. So I am starting all over from rock bottom in maths, like -2 + -3 sort of thing to get to a doctorate. I just can’t wait to get to that bit about ‘limits’ and f(x) cos that’s the door to my ambition. Thank you Neil you are an inspiration. And I am 75 yrs old so I had better get a move on.
Viel Glück und viel Spaß
Viel erfolgreiches
You’re 75 and you’re trying to get a PhD in math?
Joan you shouldn't have tried to get a phd. You are too old for it, and it would be better if you have that money to your grandchildren.
@@aomorgancool1775
Yes, my doctor told me I shouldn’t really be running the 5km park run every Saturday. Well I have run 35 so far, also the town’s annual 10km run. At present am In training for the Great North Run in 2021.
I am fitter than very many half my age and shall never, never be forced into the form of a decrepit old woman as Society depicts us. What would you have me do? Watch ‘Love Island’ or Eastenders. God forbid!
Life is for living until the moment you drop dead.
As for my grandchildren , they have no need of my money, already they are far wealthier than I shall ever be.
Don’t feel bad guys if you’re bad at math. I’m a math major and got a C the first time I took calc 1. Retook it and got a B+. I just finished this semester with a B in linear algebra and a B+ in differential equations (I’ve never been an A student), just keep working hard and you’ll get through just fine guys.
Yep same here calc 2 was easy for me but calc 3 was so abstract that I thought I would fail it. But I somehow pulled through
@@foreverskeptical1 weird, Calc 2 for me was easily twice as hard as calc 3
@無慈悲 I am planning to go to grad school. I’ve taken all three calc classes, differential equations, linear algebra, mathematical finance and probability theory
I just failed calc 2 should I retry it for an quantitative finance/actuary career or move onto sonethong else like management info systems
@@jmccullough975 it’s up to you. I got a B- in calc 2, and even though I’ve now taken graduate level math courses, for me calc 2 was among the top 3 hardest math courses I’ve ever taken and I’m going to retake it for a higher grade. My concentration is in actuarial finance, but my dream is also to be a quant and want to pursue a masters in quantitative finance. I wish you good luck, you should definitely consider retaking the course if you love math like me
I just took my first calculus test and before I was like I'm never going to pass this test and got a 94. Now I'm on the next chapter and I feel the same exact way. The pace is what kills me.
Very great words. I'm in calculus 1 right now. Came back to school in the fall of 2021 after losing everything in the pandemic and 25 years removed from the classroom. It's hard, but doable, just as he says. It really boils down to how bad you want it. I'm older and more mature, so I have an advantage in that regard. Very best of wishes to anyone currently studying in college or high school and feeling discouraged. It can be a very difficult process, but you can get through it!!
Needed this after failing calculus 1 and intro to physics. Getting my associates in computer science..
@@IamFrancoisDillinger I had the privilege of taking Professor Leonard for Calculus II in person, when he used to teach back at Merced College. It was phenomenal, and quite challenging!
Keep going! You can do it! I was at a CC as well, and the tougher math courses were scary.. but no matter how challenging things might seem, one must always try to keep pushing forward. :)
I appreciate your guys’ support and useful links. Thanks for the encouragement!
You can do it man! It takes sacrifice! If you're really determined try to block out most of what you think might distract you and you'll be fine. We all go through it! Good luck!
Aha same here brother
For me it felt like school expected me to get it quickly, instead of break things down in a logical that made sense.
best comment For me I have to say it
You're absolutely right. It's a hard subject because school always rushes it. You could explain calculus to a middle schooler with little algebra experience by drawing pictures, and they would understand it.
this is exactly how it felt to me
Standardized testing for ya. It's horrible. Not everyone can learn the same material in the same amount of time. But students are expected to learn a certain thing by a certain day and expected to get 100% on a test. It's pretty lame.
for me i struggle to process what it is being taught in the class because it takes my entire processing power to just listen to the teacher speak. So if i can only focus on listening, i cant think. so i dont understand.
the solution to this, for me, is to just research it on my own and think about it in my free time. i typically watch videos, pause them to think, and then play them, and then repeat.
organizing it and breaking it down really helps as well
Dr. Tyson is so inspirational. This experience/lesson is applicable to any academic challenge that I can think of.
As a first year engineering student thank you cause I feel the same way when I see what I’ll be learning in the years to come
this is how : study study study, and if you still cant get it in, make your teacher help you, thats what they are paid for
Not when he answers my emails 6 days later or never checks Piazza. :_) Some professors couldn't be bothered to help their students in the middle of a pandemic.
@@PaulyM856 U from USa?
@Anime Sucks wow yikes i guess im just hella lucky, well some teachers are just like that, cant you somehow convince them? or mabye complain? i only mentioned USA because they are well known for their bad education system
“Make your teacher help you” -guy who went to a private school
@@zugzug733 nope never went to one... i tihnk im just lucky to have good teachers
Calculus 1 was an insane learning curve for me. I took it over the summer so the class went extremely quickly. I basically failed my first test on limits (lmao ikr?) and from that it was like I had to then make a change in perspective. I woke up and started calculus from that morning till the time I went to sleep. I essentially had to drop everything I did usually in my free time to get it done. I got the 2nd highest grade in the class, and a good start on calculus 2 after believing I was going to fail and couldn't do it.
Insane learning experience all around, it helped me to finally realize the utility of all the math I've done my entire life, and showed me that the intimidating part is only the beginning.
Nice man!
Mind sharing how you studied it ?
@@tarik6694if you’re trying to learn calculus and don’t know where to start - I would recommend first getting your hands on a calculus book.
Every college course you go through will be based off some book and the book is necessary because it provides a procedural approach to the topics you should look at chronologically. For example, most calculus courses and books will start with limits, then move onto derivates and then into anti-derivatives, onto integrals. You can’t understand a definite integral until you understand the limit, derivative, and anti-derivative topics because an integral is a defined limit anti-derivative and an anti-derivative is the inverse of a derivative.
From there you should just utilize the resources available to us all, read the chapter on the topic, watch videos, and ask questions about that specific topic’s theory and utility.
To me personally, solving problems mathematically can be rather boring, but once you actually understand the how and why, the theory and how to interpret the math, all the different pieces will fall into place. Solving things mathematically is one thing, but understanding what you’re doing is another.
I hope this helps
Hollywood David my class started with 60 students. There was 8 students left for the final.
@@tarik6694 You grind problems and depending on the difficulty of your teacher, you do great or terrible.
Thank you for this. For years I have forgotten how much I love to grow learn and develop new skills. It fascinated me to feel my brain learn new things and expand. Again. Thank you for this. I remeber being like 8 or 9 and asking about calculus. At the age of like 5/6 maybe 7 I was asking my mom about multiplication and division. Unfortunately my mother had dropped out by 3rd grade to raise her own family because my grandmother one day decided to not be part of that family. Now as I see this video and these memories begging to come back, and I want to learn and strive for more all over again. This drive had left me a long time ago. Thank you!!
Love this story, Neil.❤ I failed Calculus 3 (twice) but ended up teaching it multiple times over my career..
The fact that I’m taking calculus right now in the same grade that he did is giving me so much more confidence and hope that I can do it
U got it fam 💪
@@figurefiguras4104 I got this while doing calc homework, perfect motivation lol
don't measure yourself against Neil. he's a fraud and he's a TERRIBLE math student
I'm not from America. What ages do students start to take calculus as a subject
@@okenough2124 as soon as they are able
Something I feel newcomers should get their minds around is the fact that the concepts probably aren't going to make sense the moment they're taught to you, and sometimes you just have to take things like derivatives at face value and gradually they'll make sense to you as you progress. The learning process is significantly different.
Currently on chapter of derivatives as i read this comment 😵
This is advice for anything new you try in life. It won't make sense when you first learn it or try it. But given enough time and effort, it all comes together.
The problem is that in my school AP calc is squeezed into four months. This means I have little time to practice and get familiar with concepts and cannot get them in time for the test
@@sbc2954 exactly. The exam is gonna destroy my áss, but getting used for more examples does help
@@sbc2954 Yeah I'm taking BC so it's basically all of Calc 1 plus a bit of Calc 2 squeezed into ~5 months. Super difficult but it's a great learning experience and helped me develop study techniques and other methods of improving since Algebra was more or less a cakewalk for me.
I remember I watched this video a year ago, just before I started calculus, A few months later I kept thinking about this video and how accurate it was! Great words Neil!
This was much needed for me. Thank You Neil❤️
I swear this man has the most soothing voice ever
Gotta say, I just passed calc 3 with an 88. When I started my college career with basic algebra skills I didn't know how I would ever make it to this point, but i did. It's all in the work and taking things one at a time. Each new thing I learned felt like it was pushing the limits of what my brain could comprehend, but as I practiced it and learned new more complex ideas eventually they felt elementary.
Congrats bro, calc 3 was absolute brutal for me
Dustin Jensen good job.
@@MinecraftisC00lSometimes yep same here somehow passed it but it was extremely brural
I feel like the difference between single-variable calculus and calc 3 is greater than the difference between algebra and calc 1
@@mickrobertson7782 completely agree. The concepts were too abstract and I had a hard time visualizing it.
Very Motivating! It all comes down to how bad you want it... and how much time and effort you're willing to sacrifice to triumph your obstacles along the way.
I ljust love how Neil always breaks it down for you to understand and relate. Thanks again. Neil Degrasse Tyson
Calc comes with Algebra, I remember not being as good as I should have been with Algebra so I would make small mistakes in Calc class but after doing so many problems, everything starts becoming like repetitive because even if a problem look different from the other ones, we use the same methods to get the the final solution. Algebra becomes like a second nature in calc class.
I agree completely, no one can pass calculus without knowing any algebra. My professor also said that one of the most common reasons for failing calculus is poor algebra skills.
Jose Rodriguez getting a good grade in pre-calculus is a good indicator on how well someone does in calculus.
I agree. The most I got out of calc was a complete mastery of algebra.
Bro i just now realize how lucky i am to be good at math
Exactly this. Every equation has the exact same steps to it as the next one does, more or less.
I've been studying Calculus the whole day, and this is the inspiration I need to keep going.
I remember feeling the exact same way when I opened a calculus book the first time. Funny how comforting all those big scary integrals become in the second semester when you learn how to use them.
I am 3 years drop out and restarted my University in ECE. I was about to lose it but this video just got me motivated and gave me confident.
I doesn’t involve calculus but.....In 1983 I graduated high school with .5 credits of math. Yes, graduated with .5 credits of math. I hated it, never understood it. I even spent time in the learning disabilities class for math. Years go by and never used any sort of math....until I got a cool job working along side some cool engineers and scientists. It inspired me to go back to school. Basic math, tech math 1, tech math II, beginning algebra, intermediate algebra, physics. Then I got into mechanical design. Material properties, statics, mechanisms, design problems. It was all math albeit still “basic”.
I guess the point is you have to be willing go through the ignorant phase of learning to get better... no matter what the subject.
"Let no one deceive himself. If anyone among you thinks that he is wise in this age, let him become a fool that he may become wise." 1 Corinthians 3:18
i’m actually so thankful for how ontario’s curriculum is designed. all academic math that you learn from freshmen to senior, it’s all used to slowly transition into calculus
this is analogous to learning anything new. shouts out to neil degrasse tyson for being so inspirational!
deGrasse Tyson's Storyteling is amazing: Talking about something abstract like calculus and he converts it into "his friend" in order to understand the universe. Hats off
I just burst into tears watching this. For what I want to achieve in my life, calculus is a necessity and I have limited time to take the courses before transfer, I get so frustrated with myself because it’s finally something I attempt to learn that completely eludes me . Japanese? Learned it with minimal problem. Calculus? Nope. So so humbling and makes me feel unintelligent UNTIL NOW. This changed my outlook. Thank you for sharing
Watch Professor Leonard.
And watch the videos before lecture, so that if you have a professor who understands calculus but can't teach it, when they're done "explaining" and write the "example" for the class to "figure out and work on your own", you'll be better prepared to tackle it and you'll have a better understanding of what your grading professor's expectations will be for the exams.
@@ggsilik thank you for this. I appreciate any help
Differentiation is simply the slope of a curve or function, while integration is just the area under a curve. Once you have that basic understanding, all you need to do is to solve multiple problems to gain mastery. Even the examples in textbooks can be used as exercises as long as you cover the solution and attempt to solve it first.
find another line of work. calculus isn't hard.
@@RobertMJohnson for you
Its such a simple point but he says it so elegantly I needed to hear it again. Quit being frustrated because you haven't mastered it quickly, keep the discipline and you'll get it. I personally beat myself up over not mastering Spanish and Mandarin but he makes such a great comparison between learning Math and a language.
With all of the lectures, books, diagrams and equations helping me learn Calculus, it was this 3 minute video that put me in the mindset to finish Calculus.
I’m posting this for my Calculus classes ASAP. Thank you!!!
It's the 'putting in the time' bit. Trepidation at the thought of prolonged and repeated extreme boredom.
That's my problem. Always has been and I end up hating myself for it
@Ne10 2718 I like that one. The real trick is to become well practiced at being uncomfortable. I really do think that being uncomfortable should be the default state for a person. Good trick for someone who was brought up in lower middle class southern England 😫
If it’s boring then you won’t do it... so make it important. If it’s not important don’t do it.
@@dadyasuo8151 That's a good one too. I'll take all the motivation I can get
That’s true. It’s just that it just doesn’t feel like it’s worth it sometimes you know?
@@lucasargandona4658 Right. It's always feelings and never reasoning. Always a bad idea to rationalise not doing something because it feels bad.
This is so encouraging! I am currently taking Calculus 1 and Calculus based Physics 1 and it's very challenging. It made me rethink my decision taking it. But I need it for my goals! Just because I don't understand it immediately, it doesn't mean I will not be great at it!!!
You need Calc 1 or 2, to be better prepared for Calc based physics 1. Wish you the best.
@@c.b.6582 yep, calc based 1 is needed before or during it to pass calc-based physics 1 successfully. Not calc 2. That's what the universities encourage too.
@@AuthenticTrading a working knowledge of the end of Calc 2 and beginning of Calc 2 is helpful in physics 1. My physics professor required us to have at least Calc 2 and Diff EQ, for his Physics 1 class, smh.
In high school, there is a class between algebra 2 and calculus, which is pre-calc. That helps a bit with bridging the gap. But the jump from those math to calculus is indeed very different. As someone who has tutored math, even though I didn't do great in my first couple of calculus classes, the biggest problem I see students having is in the algebra of the course. Factoring, simplifying, dividing, multiplying, and taking square roots of non-polynomials always became a problem.
1:23 HOLY SHIT, HE HAS BECOME SELF AWARE. LADIES AND GENTLEMEN, HISTORY HAS BEEN MADE!!!!
"squiggly lines i have never seen before." Bruh... I honestly felt the same when I got to calculus in junior year. Honestly, its a good thing I started preparing months before so the transition was easier.
I’ve been a math tutor for a long time. You just need to spend time solving lots of problems. Don’t get jealous of those geniuses who don’t have to study-they’re the anomalies. Put in the time and you’ll be amazed what you can accomplish.
Plus life is give and take. The math wiz is going to have some other trouble somewhere in life or learning that you don't. So all the more reason
@@Chironex_Fleckerilmao cope. I live a very good life and I’ve tested at 4+ SD’s of IQ (exceptionally gifted). I do believe it’s disgusting to assign worth to people through their IQ, but whatever helps you sleep at night 🤷♂️
@@juanzavala9023 I'm sorry you feel the need to chime in and make your ego the internet's business. You're oversharing. I'd advice you to use a degree of discretion. Call me Mr. Bopperton if you will please. It's an odd name, right? I'm about to explain exactly why discretion is key to being professional, whether you're on company time or not.
I've worked internal and external corporate recruiting. That's all. No cert sharing. No companies. No figures. Notice what I'm omitting?
Keep reading. I've met a lot of people like you, managed some who always had a chip on their shoulder in zero pressure situations. You didn't have to write this comment. Neither did I. But I have a specific point to illustrate:
Those statements are unfavorable statements. You know better. You're here telling on yourself, professionally speaking. Indiscretion and oversharing is normal but keep it limited to private conversations. Remember, the Company is depending on you to conduct yourself in a way that adheres to the guidelines outlined in the employee handbook. Ethics is a big part of what companies look for in their employees. Integrity.
If you are someone on LinkedIn who, I don't know, posts things like "someday my family will thank me for all those nights I spent grinding at the office past 5:00pm". If that is you early in your career you're a good laugh and an easy commission for some bro sitting in PJs at his desk sipping coffee who will place you in some 100k VHCOL role with a known 90%/24mos attrition. Keep telling yourself those things. It just sounds like you're going to work for whatever manager and do what they say because you love to drink from the company's chalice. That's good. They know you'll cry multiple times in that role. Just being honest. They know it. As they hire you, if you were recruited with a 3rd party. It's all just about HC. Those people who think they're doing well and will "grind", it's bread and butter. Good luck with burning out, Mr. Zavala. If you loved your job you wouldn't have brought it up while you're supposedly relaxing on TH-cam. Remain seated. It's going to be alright, but here's the funniest thing about you posting this.
Putting this in writing on the internet for people to see, Mr. Professional. You are visible here. There are so many things that these bureaus pull these days. They scrape the internet for every last drop. And here you are writing things that are signed sealed and delivered in real time permanently. That's every comment on the internet. You are a professional, aren't you? Act like the top talent and genius visionary you purport to be!!! Know these things. Keep grinding.
If I heard you talking to me like that at a restaurant or company social, I'd pull you aside and have a chat out of concern. It's not professional conduct, and your likeness is an extension of what a company sees in you. They go a lot deeper than just interviews, resumes, and standard FCRA-compliant checks with all the different reporting that has changed since people started sharing everything on social media.
Notice how I turned a two sentence comment into an utterly eye-glazing read? Yeah, I've written my fair share of emails at a managerial level. It's all just a game and you'll learn that making comments like yours are just limiting your own success. Genuinely mean that. There are C-Suite executives who make small talk with the facilities staff. Why? Because it's important to be able to understand others in the modern workplace environment. It's fast-paced and we need rockstar employees like you to keep doing all the legwork.
Best,
Bill Bopperton
Senior Vice President of Informing You How Business is Conducted in 2023
good looking out Tys, i definitely need to take this advice.
Solid encouragement! What one man can do another can! Don't give up!
Thank you to all those people who have responded to my comment inspired by the Neil De Grasse Tyson interview. Many of you have said how you struggled with maths in the beginning but found that inner strength to keep going. I am humbled by your determination and the numerous messages of encouragement too. I shall be back at my desk with maths books open shortly with a better understanding now that just because you couldn’t get it right first time doesn’t mean you are dumb, you just have to keep at it. As for my 75 years of age , well, I haven’t got time to die I am far too busy. Got the Great North Run to train for in September 2021. By the way I am English. And, teaching myself to do the ‘shuffle’, see TH-cam Elvis Presley , Sweet Surrender, Hot Girls. As for the person who asks if we could share’ books, would they message again please. Again thank you to all of you, wherever you live.
The difference between Tyson and myself is that the fog just doesn’t disappear even after 5 years.
Lol 😂
He explains that at the end of the clip. Did you watch the full thing?
i mean look at your username tyson studied more in 5 days then you did in 5 years simple
Wow, I didn't know we could simply gauge the capacity of studying just by someone's name. Do have any research that supports this fact of yours.
@@evanurena8868 i was joking as he is called rob the procrastinator bruh
I needed this.
Wow how enlightening! I've never heard anyone drop such mind blowing wisdom from the stars before! This guy is a genius. Oh, wait, every parent and teacher has been telling their children and students this forever.
I love Neil deGrasse Tyson. I'll be taking Calculus next year. And I can't wait to learn it, because even though I won't get it at first, I'll work at it.
Needed this right now, that was a very inspiring and relatable story.
That is a wonderful perspective to learn anything in life. You don't have to be good at it in that instant. You can slowly and gradually make your way up to that skill and become really good at it eventually. You have to keep at it, you have to love it and just keep putting in your focused efforts.
He is such an inspiration. great guy!
This guy is amazing, I love this guy
All is fundamental, is only a genius, is descomplicating things up.
@@pedro134953 I could 100% make you think differently about him, he can be extremely rude and arrogant
@@kevinreynolds3594 Do it.
@@kevinreynolds3594 Try me
@@eobardrush2112 sorry guys I tried to find the video, it was a compilation of him on the Joe Rogan podcast being incredibly rude, the video seems to be taken down. If you really care you can watch the full podcast but you won’t make it through the first hour, it’s too painful. He constantly interrupts, he tries to make joe look stupid when he asks questions. It was one of, if not the rudest displays I’ve seen broadcasted. He has a intellectual superiority complex that makes him this way, it’s very clear from the video.
I'm glad this was recommended to me. I felt like the video was made for me
this almost made me cry, made me remember my first classes in uni
Excellent. Thank you.
i watch this a couple times out of the week. i have been so determined to learn calculus. just like Neil, i want to be able to understand the language of the universe
Pretty good advice. I've been in that situation thinking that some form of math was way too complex to learn when first looking at it, and by pushing those thoughts aside, persevering and just doing the math, came out with results in the high 90% for those exams.
Taking my calc final tomorrow after studying for 7 hours today. Needed this!
There's no such things someone else being "born a genius". Genius are created through commitment.
what about savants
My biggest hang up was interest. If you have no interest in something, or feel it has no impact on your life, it can become a mountain in your mind. It's the perspective of learning as a whole. Find the interest anyway you can. Relate it to something. Some times simply learning the process itself is what helps us navigate life. Those who are good with planning and processes tend to have great success in other areas, not just that particular subject. I struggled with this until the day I picked up Neil's Astrophysics for people in a hurry. Then Cosmos by Sagan. Then every Hawking book I could comprehend. Suddenly, I found myself learning real astrophysics from the ground up. You see, I was never a smart kid. I struggled in school, then at the age of 40, I realized how many things are so tightly bound together by physics and astrophysics, including economics, which became my ultimate passion. I now understand process, human interest and behavior, and myself, better than I ever did. It changed my life completely. Started my own business, because the idea no longer overwhelmed me. I tackled some difficult stuff in astronomy and economics, so what could possibly be a mountain to me then? I'll climb that damn mountain. Challenge accepted.
I got through calculus already, idk why I'm here
Props to you!
Cause Neil degrass. Calc is ez. I learned it all in 5-6 days. How? I just read the text book for 5-6 days.
@@ineverchangemyplayericon3016 how to delete comment
Because neil
@@ineverchangemyplayericon3016 if only it worked that way ;_;
the video description really helped me understand what's going on
I’m struggling with a project and procrastinating rn because the due date is approaching and I just can’t wrap my head around one concept and then neil said too many people think they have to be good at something instantly to ever be good at at which gives me slme hope
I took calc 1 in high school and didnt really understand it, I was pretty lost by the end of it. Then in college i took calc 2 and suddenly all the weird integration stuff that i didnt understand just clicked with me, and i felt like i finally understood what its basically about. It also helped being in physics and learning super simplified calculus with distance vs velocity vs acceleration and seeing how its applied
don't yell at me
i'm so bad at this, most of my life everything academic came easy and i hit pre calculus i was confused "why doesn't this make sense?" and very quickly i struggled and lost faith in my abilities and actually started to think maybe i'm bad at math and i got lucky prior. I'm still in this mindset to this day, luckily i'm very young still, but I never struggled and when it came i have no idea how to face it. Basically i was that kid telling my teachers "I don't need to study or practice" and i regret that. The fundamentals were easy to get A's on but those skills faded away as quickly because lack of use and that built over time and eventually i reached a point where it felt like i didn't know the basics anymore.
this is me, everything before pre call was easy but for sum reason my skills worsened. idk if it was because of the lockdown and having to do school online, but i can’t even get an A anymore in my math classes
Such a great message. Love this.
thank you youtube recommended for this gem
I’m just starting Trigonometry on my way to become a civil engineer. I’m scared as hell but this video helped a lot. I hope to one day come back to this video and day I did it. I know the road ahead is gonna be filled with challenges, but I’m going to give it everything I’ve got.
I'm a high school student taking calc, and my best friend is taking it with me and his dad is a civil engineer. I'd say you don't have to worry that much: try to get good at solving the equations but also try to understand them too. Some things will never make sense- math is easy to learn to do but sine, cosine, and tangent have never "made sense" in the same way that 2+3=5 does. Make sure you ask your teachers questions, and it's also important to have at least one friend in the class that you can go back and forth with for help.
Sometimes there will be small holes in your understanding, but just try to fill in as many of them as you can and the rest will fix themselves later. I did trigonometry and precalculus stuff last year, and it's honestly about the same difficulty as calculus itself in my opinion. You just need to stay on top of your game, learn one concept after another, and stay confident.
What high school has taught me so far is that if you play your cards right math will be the easiest subject.
don't slack on that trig, because you'll need that shit in calculus lol. calculus isn't actually hard, it's remembering all the trig and algebra you forgot that makes it tough.
I’m in calculus and I find it absolutely fascinating, I’m not really like a “nerd” and I don’t even get the best grades in a lot of classes, but I love math
Thank you Wise one
This really inspires me to keep watching random youtube videos for hours on end
higher level math is very straight forward as long as your instructors/profs actually give a good geometric intuition behind it. learning math by memorizing formulas is like trying to learn a language by reading its dictionary: you get a spotty understanding a few specific concepts but you can't really see the whole picture. calculus 1/2 were actually first math classes i ever found easy because my prof was very heavy on geometric intuition BEFORE rigorous proofs and derivations. one of the most memorable sayings of his was: "if you don't understand it geometrically, you don't really understand it". after having taken that advice to heart it completely transformed the way i look at math and i've now taken several graduate level math courses and gotten 95%+ in them.
obviously you need to study and do practice problems too, but i think anyone studying math can massively, MASSIVELY cut down on the amount of "grinding" they need to do by spending more time on geometric/spatial understanding of what they're dealing with, rather than just seeing math as some slog of symbolic manipulations. math is the language we use to understand the universe, and the universe is a spatial thing, not a symbolic thing.
One of the first things I learned in calculus was a vastly easier way to do something that was challenging in advanced algebra. I was mad at first for having to slog through it in algebra when it was easier in calculus, but then I realized if I hadn't slogged through it in algebra I would not have been in a position to understand it in calculus. Sometimes there's a reason to wax on wax off.
i know that feeling. it feels funny to be able to understand something that you couldn't understand weeks or months ago
Calculus books are ENORMOUS. and they are HEAVY!!! I love this story so much 💕
I majored in math and completed my degree. I can definitely say Calculus I was the most foreign and bizarre subject I ever learned. I wouldn't say it was the hardest, but was very hard at first. I ended up taking tons of calculus courses. But it "opened my brain up" in a way I had never experienced.
Was calc 1 harder than calc 2 for you?
@@elmozwrldtaken For me calculus 3 was the hardest. Calc 1 is probably easier than calc 2 depending on your level of trig knowledge
Thank you so much for this Dr. Tyson. I’m a 2nd year physics major with a dream to be a theoretical physicist, currently struggling in Calc 2 honors, after thinking the regular Calc 1 section was too easy. When you said “I don’t understand this yet, but the universe is speaking this language” I felt that so hard. Thank you for being a great example of how you learn something slowly, not all at once. I’ll go back to my studying now, so that I can achieve my goals.
My suggestion when starting any new area of mathematics is to focus on simple memorization of how to arrive at the correct answer, as opposed to focusing on true understanding.
Just plug and chug, and through repetition, understanding will inevitable come in time.
This little tidbit of wisdom was given to me by a friend. I'm forever grateful for it and pass it along whenever I can because without it, I never would have made it through any of my algebra, geometry, or calculus classes.
Hope it helps someone else as it did for me.
motive is everything
"And every bit of yourself you invest helps to dissipate that fog." I love the fog analogy. It's not a binary on/off switch of understanding. Learning complicated things is done through thousands of popcorn kernels being popped.
Need this because I felt so smart going into AP calc AB and I’m currently failing because of mini mistakes and sometimes the concepts are hard for me to grasp it’s only been 1 month and we just started L’Hopital chapter 3 so we’ll see how this goes hopefully I can bring my grade up to at least a B- by the end of the semester I have a little over 2 months
good luck!
Thanks I needed to hear that it was helpful.
Gratitude
His shared experience is a good perspective for beginners struggling with calculus. Unfortunately most students do not have the luxury of tutors for challenging subjects. For this we have TH-cam.
Sadly, many people are turned off math snd science on account of professors who are bad teachers. Many professors simply don’t have a passion for teaching.
Once the idea of a limit clicked for me, everything else fell into place.
Mind sharing good resources for that?
What a orator!!
literally watching this while doing my calc 3 final, its been a while since ive watched this.