How to Self Teach and Prepare for Calculus
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- Опубликовано: 10 сен 2024
- In this short video I answer a question I received from a viewer. He is trying to learn calculus on his own so that he can prepare for his calculus course. Do you have any advice? If so, please leave a comment below.
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The best preparation for calculus is a solid understanding of college algebra and trigonometry- the sole purpose for the course entitled “pre-Calc” is to prep you for the Calculus. Pre- Calc is the first calculus course! This reminds me of the aphorism “if you want to learn algebra, take a course in Calculus!” The message is that algebra and trig are the bedrock principles for Calculus. If you have weaknesses in either subject, it will be revealed when you take a course in Calculus since so much of this beautiful theory requires proficiency in algebra and trig. When you open almost any book on Calculus you’ll find the first chapters will cover topics in algebra and trig, the subjects covered in pre-Calc.
Dan Rosser
Yes, definitely, absolutely.
Oh, and study graphs. I noticed this *_heavily_* upon starting and retroactively.
My dad gave me the same advice as both of you. He was right and so are you. Ugh.. and here I am 25 years later 😂 but I'm getting it finally.
I'm in my mid 50's and have been casually learning the basics of calculus because I simply missed out in my younger years and I want to see what all the fuss is about...! 😋 My advice is to get some solid context behind calculus, learn some of the history and philosophy behind it and how and why it came to be. The universe is best described by how much and how fast it changes in relative terms rather than describing it in absolutes and calculus is the best tool we have to this end. This was my starting point. There are a lot of videos on RUclips that give you "the big picture" and I would recommend these. There is no doubt that learning any subject in a contextualised way helps dramatically.
do you feel like you feel the same way about today's youth as your parents and grandparents did about you when you were younger?
I think you’ll enjoy reading the book titled Calculus Reordered by David Bressoud
@@mastershooter64 One of the ancient Greek philosophers made a note about the "arrogance" of youth. They noted how they themselves were dismissive of their elders and in later life how the youth were dismissive toward them. Thats when it hits you that you're getting older. I think "difficult" teenagers are put on this Earth to remind us of the limited time we have.... 😋. Nothing about this dynamic has changed since then.... 😉
@@danielmrosser I'll check it out 👍😁
That's me! OMG! I'm so happy that I'm not alone. Thank God. Thank you for sharing this with us/me.
Without a doubt be solid with algebra and trig. I’ve seen so many students stuffer in calculus because they have a very weak algebra/trig foundation. “You can always be better in algebra”
Total immersion, and don't skip around subjects. Calculus is highly structured, so every concept is dependent on what comes before. Start from the beginning and don't proceed until you are totally proficient with the current lesson. If you have difficulty understanding a concept, find another source of instruction. When I self-studied Calculus I was using at least 6 different sources of information including online textbooks, university lecture series, online testing programs, and tutorial videos. I did the same thing for linear algebra. Then do lots of problems, and don't quit until you have solved the problems and understand your mistakes and where you had trouble. By the end of the process I was proof-reading Calculus 3 content for an online textbook.
A book has many advantages: no batteries required (still works w/o WiFi); it's tangible (make notes); it's structured (start at the front), unlike search engine results; and it should have a bibliography, if you want to explore subjects in more detail or from a different perspective.
Skim through the whole thing, cover to cover (preface to index), before diving into the first chapter. The geometric nature of Calculus makes it easier to digest than other branches of higher mathematics; so learn how to draw examples of definitions, theorems, problems, etc.
Learning Math, Physics or any other stuff like this is little different that learning a musical instrument or a sport. At first, you'll feel clumsy, but with practice, you'll be surprised how much you can learn.
Turn all of your electronics off, and find a quiet place to work. Watch "Attitude, Concentration & Effort", by The Math Sorcerer, then turn your electronics off!
And writing down notes and doing actual problems from a book reinforces the learning that you don't acquire simply by watching videos.
I'm starting calculus in Italy next Fall. Here it's called mathematical analysis. Can't wait!
awesome!
I started recently with calc III on my own and am hoping to go through linear algebra, DEs, and then Analysis over the summer. I have a bit of olympiad experience (I got top 5 in Canadian Math Olympiad and top 20 in the USA Math Olympiad this year), but I really haven't formally gone past HS math. I honestly am just excited to go further in Math in uni come September :)
my advice for people that people must follow you because you worth😊
thank you:)
what's mean worth it's mean legendary ? or something like that?
@@TheMathSorcerer I love you and I wish I could to meet you
@@hatemalkd1633👍 well done my english is extremely poor
Easy! Go to Khan Academy!!! Take precal and master Algebra II. Then take the whole calculus. Sal Khan teaches deeply into intuitive stuff plus rigorous proving. Then combining practice, you will get fluid and deep understanding of subject. Yeah, buy a book, read other resources, watch youtube videos like in this channel. Actually not that easy but entirely doable. I was stupid at math until I did this. One year later I am helping physics graduates in their calculations.. I will be freshmen this coming month and I hope I'm ready!!
Math Sorcerer, you are the "BESTEST!!!!!" Love ALL your videos!!! Thanks for hosting, producing and posting THIS ONE!!!! :) :) :) :)
Get good at Precalculus. A textbook at a thrift store can be picked up for a few bucks.
Get the gist of a subject by scanning the table of contents. I take notes all in my texts. do what works for you. after you finish a section. review concepts using your own words, rework some examples. get a clear picture of why the answers worked the way they did. then work a few problems to test you knowledge while getting practice. Mistakes are OK, they show you where you are slipping up. Keep trying.
tutorial videos such as The Math Sorcerer's can fill in gaps and save time.
Later, in class you'll have a level of proficiency during lectures while half of the class is catching up,. that's an addictive feeling.
I'm 28 and applied to study physics at uni next year. I'm working through algebra 2 as a reminder and then working through pre-calc and then calc one. I find the for dummies books are very good and college algebra and trigonometry is very much a must for anyone looking after doing calculus. As I work through trig and algebra, I'm watching videos on calc to see how my subject relates to calculus helping me to get a deeper understanding
im 28 as well. glad to hear another 20something year old still learning
Get a little study group together, even if it's just with one friend, and/or at least find a mentor. The key here is to learn how to TALK about math and make your lessons and studies be as conversational as possible! This makes it all more understandable, memorable and meaningful!
I would have avoided so many pitfalls if only I had a second pair of eyes giving me feedback, or even just to help me feel better when stressed or lonely.
Conversation can be its own form of high-frequency, low-stakes self-testing. And that's essentially the most potent way to learn and grow that I know.
And personally, I recommend trying to make your studies as interdisciplinary as possible, at least as a long-term plan. Making connections between disciplines can be another fun and meaningful form of high-frequency, low-stakes self-testing, and it can also be done through conversation.
Learn how to cycle between high, medium and low levels of difficulty. It's probably best to spend most of your time at whatever's only moderately difficult for you. But easier topics and problems can help you perfect what you already know and prepare you for challenges that really make you grow. Harder topics can make you more motivated to do the less challenging stuff necessary for mastery, and the harder stuff can give you guidance, too.
This is exactly what I think I need. I'm learning Calculus on my own and I'm struggling to understand it, especially since I am really bad in Math. But I think that if I have someone to learn Calculus with, I am definitely sure I can understand it more clearly. Great advice.
I'm 67, at least for the next 2 months, and have been trying to teach myself math with a goal of learning enough math to work my way through a university level physics books. I live on a fixed income and was able to scrape up enough money to buy a few used math books and a ti-84 plus CE calculator. I think for my the most frustrating thing is getting answers to only odd numbered problem but get curves thrown my way on the harder even numbered exercises. For example yesterday I was working on exercises about simplifying expressions with imaginary number and putting them in a+bi form. I do fine then get toward end of the exercises and sure enough I get an even numbered problem involving irrational square roots. I will search RUclips for help but often those RUclips videos just show the easier problems I can already solve. Is there any advice on how to deal with those or should I just grind on?
I'm doing exactly the same thing! And I’m even older than you. I’m thrilled to come across someone else who’s interested in learning physics, at our advanced age. Should we maybe keep in touch?
You guys are inspiration for the youngsters. In this age you're still learning. It's amazing. Best wishes for you.
You don't have to finish all problems.
Maybe try to give approxomation or narrow down the set of possible solutions? That can be fun and worth doing.
If it's too frustrating find some other book and then return that one later.
Some books are more begginer friendly.
Some are more focused on drilling, some on those aha! moments.
I’d think that all the problems would be about irrational square roots, what with the imaginary number “i”being the square root of -1, which doesn’t exist in the system of real numbers. I studied math in college and still mess around with math as a daily treat.
Whenever I were stuck on problems I will go to tutoring at my college or talk about it with friends that are more mature than me on the subject, best of luck 🙏🏼
For learning pre-calculus, preliminary algebra (Higher algebra by Bernard Child), geometry (Elements of Coordinate Geometry by S.L. Loney), trigonometry (Plane Trigonometry by S.L. Loney) and basics of linear algebra (RUclips lectures / Linear Algebra : A modern introduction by David Poole) should be thoroughly studied in the same order. For building self confidence in calculus through practice one may study Schaum's 3000 solved problems by Elliott Mendelson. Most beginner calculus books are usually isomorphic.
Does this work if im trying to relearn math from the ‘beginning’? (‘Beginning’ = 9th grade)
Mason, especially if you have not taken a math class in seven years, you might want to start at the _super_-basic level. Allow me to recommend:
-- Calculus for Dummies
-- Calculus for Dummies Workbook
-- Calculus II for Dummies
For me i started my long journey with calculus when i totally stop caring about school and was so excited to learn some pure math , i stopped caring and just foxed on having fun while learning ,i got an A+ in all my exams, calculus is amazing just give yourself time to learn
Hi Mason (and everyone looking to learn something)! I have advice for you. I don't know much math, but I am currently learning C# programming to make games in unity and this advice can apply to math. What I do is two main things
1. I watch the whole video first and THEN I do. I find this so much better than continuously pausing the video every few seconds to then do whatever the instructor did. Watch the whole video first. Just watch. Then do the problem(s) in the video.
2. Drill it in your mind. By this I mean - repeat, repeat, repeat. After you got one topic right, keep doing it again and again and again. Some may not like this advice as they may say to not take too long on a particular problem and subject. Although it is true that you do need to move on to the next topic eventually, drilling the topic into your mind by doing it again and again and watching the same videos again and again can really just make sure everything sticks in your brain and you don't forget it. Just don't overdo it to the point where you never move on. Watch the same video perhaps 3 times. The first time just watch. Then watch a second time and after the second watch actually do the problems in the video. For the third watch, once again watch and then do the problems in the video.
Good luck, C# is dope 👌
@@slayz_sa thanks very much!
My comment was deleted for some reason :( I just want to say how much I appreciate your calculus courses. I survived calculus 2 because of you. (I got A+ for calc 2.)
thanks man! Strange that it was deleted:) I rarely even delete spam comments hehe
Please do more videos like these 😭😭😭 i really need this motivations
I have gotten through Calculus I-III with B average but still feel I need to go back and be great at writing proofs and logic before going further. I would love for there to be a thorough course from basic logic and proofs through more complex at the level of math majors.
Have you studied Discrete Math?
Funny you mention that as most colleges require that kind of course for math majors before they can move on to courses like Analysis and Modern Algebra
Meason, I like the advice given by The Math Sorcerer. Just get a used book even if an earlier edition of the book that will be used by the professor in that class and read and study the book and do the exercises. There are many math channels where you can watch the videos and study the same topic in the book you have. If you use this approach I am sure you will do well. Just word of advice make sure you have a good sound background in algebra, trigonometry and basic geometry before self studying Calculus. Good luck!
I'm 72 and I can think of no better way to keep ones mind from turning to jelly than do math and physics.
i just sit on the computer watch math videos with a notebook and pencil all day- works for me.
Good evening Math Sorcerer thanks for all the highly informative videos. I am currently an undergraduate Computer Scientist studying Computer Science at my University. Im currently taking Calculus 1 so far and am enjoying it pretty well. You make mathematics fun and intriguing to approach and I love the subject quite a bit.
You can use calculus by Thomas and Finney and believe me it's a great book I learned calculus using this book by I was 15 years old
Hi professor
Please introdious mathematica books for writing code.
Internet and technology is a great tool
I would think that to ensure that you survive a course, your best bet would be to buy your prescribed book/s now, and at least scan over it to see what the ground ahead looks like. Then, if you can get hold of a syllabus (maybe ask?) you could mark the parts of the book that apply to your current course (a lot of text books cover more than just a single course's material) and try initially to see if you can get the gist of what it will entail. (Don't be put off by things that are a complete mystery right now. Just write them down, and look them up later, probably best, in their course order.)
That will at least put you on the track of following the course's path through calculus.
I don't know at what stage it would become helpful, but alternative views of some of the the aspects might be handy at some stage, if you want (and have the time for) a wider (not deeper, I don't think) view of it. You'll find a physics text book goes through quite a lot of calculus, fast, with a context that gives you something material to connect it to. A numerical methods book will give you another view of differentiation and integration, for one thing. The broadest alternative view can be found by searching the web for "Strang Calculus". That should take you to Gilbert Strang's PDF at MIT. The print can get a bit blurry at times, but it's readable, and different to most courses.
Any binary theory is easily substituted with a calc app in the windows OS
Get a book, solve it thoroughly and then get a different book bam you go......Don't ask for help and get your own personalized solutions. Spend time visualizing your answers. That's all.
Hi Mason, It has already been 9 months and I think you've already finished your course. I need suggestions from you, I'm a highschool student fascinated by the mathematical world and learning few every day.
In what order do you recommend I go down the learning udemy list and also do you think i should cover the statistics portion for calculus?
Doing this to prep for calculus 3 next semester. Dropped it this semester due to feeling rushed for exams that were literally 2 weeks apart… 3 at most. I kid you not, our first exam was 2 weeks after class started on first 6 chapters. I rushed through homework and notes not really learning and bombed the exam bad. I don’t want to just get by calculus. I want to understand it to help me with my engineering classes in the future. I need to know the how, why and when.
Hello sir my name is kamleshdutt. Sir these days I am having bad days, I am not able to solve maths question. I feel like tearing the book and throwing it, please answer in 2 days .
Please reply my answer through the veido
Hello, I'm a college calculus 1 student at the moment. For context, I have a disability that affects the speed at which I am able to retain information and be able to recall it. I have a professor currently that, when interacting with me, has far more often than not just left me with a snide, derisive, or otherwise condescending comment from them, making me feel inferior to everyone else. Is there any advice that might help here? I welcome any input from anyone!
The problem is, how can I study and read the book effectively? Should I read everything and solve every problem? It will costs so much time :[ any ideas please?
Just commenting for the algorithm
Hello, do you have any advice to study probability and statistics? It's not like mathematics and I'm having big troubles
❤❤
Sir plz make a video for cylinderical cordinate and spherical cordinate system...
I want to start my advance course but I don't know where to start for COVID my study sequence collapsed and my results wasn't good as I expected but now I am thinking I wan to start my study to clear my P.hd entrance exam so I can start my pH.d but sir, when I am starting I couldn't understand anything like from differential geometry, functional analysis category theory, Field extension, Graph theory and advanced number theory. Where should I start from it also sir I have a deep study on spaces topological space and topological groups, measure theory and linear algebra and Differential equations but for PhD entrance I have to do those parts too! Like I saw a Riesz theorem trying to understand but couldn't so where should I start from?
Bro I am 18 years boy studying in 12th standard. I find that I am weak in maths but if I keep studying then can I can become good at maths I am giving 7 hrs daily to mathematics.
I swear go to khan academy
could you make a video about using R or Python for Data Science or general coding?
Sir you are looking like a Isaac newton
Hollow sir email you but you did not reply to me through the veido
Khan Academy!
I just tried to buy a course and I keep getting an error message saying my email,address isn’t valid. It’s a gmail address I’ve used since gmail started! Help!!!
aww that's weird! sorry!
@@TheMathSorcerer so,what can I do? I also sent you email from your website, and that had no trouble with my email address. Improbably won’t see any answer you send until tomorrow as I,live in France and it’s night here.
How do I ask him a question of my own?
go to my website mathsorcerer.com and click contact
Calculus is ❤️
Absolutely👍
I have a mental block for calculus.
How remember all theory of real analysis? And how to prepare myself for Real analysis?😁
kisses for Brazil
I've big question why calculus is so important?
It's the mathematics of change. Many things change
@@zaydmohammed6805 yeah I know but I need a comprehensive picture thank you
If you want to study any of the sciences, you’ll need to know calculus. Science is about how the world works and the world works by changing constantly. Thing move, things grow, things shrink and you’ll need to be able to understand and measure how those changes happen and at what speed, how often, all that. Calculus is the math for doing just that.
@@21ruevictorhugo Wow is fantastic
Calculus and your answer are you professor?
@@hatemalkd1633 No, but I studied mathematics and love it. Before I retired I was a computer programmer. Best of luck in your studies.
Step 1) Pick up Tom Apostol Calculus Volume 1.
Step 0) Remortgage Your House
And y'all saying Newton's dead.?.
Are You a Professor of Mathematics, Sir'?
Heard the news. Too many things are and have changed, and not for the good.