The Best Way to Learn Calculus
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- Опубліковано 10 лип 2023
- What is the best way to learn calculus? In this video I discuss this and give you other tips for learning calculus. Do you have advice or interesting stores to share? If so, please leave a comment below.
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Thank you:)
The only warning I give people about calculus is not to drink alcohol while studying it. Never drink and derive.
Good one
It took me a bit of time to definitely integrate this one :)
I’m 26 and I recently got back into school and I’m pursuing a comp science degree, I have a calc class that I have been procrastinating for a ridiculous amount of time. It’s thrown off all my other classes for this term, now I’m scrambling to finish calc 1 in a month. Your videos are helping me spark some motivation. I don’t have anyone else to talk about school stuff with and something like calculus although normal to some people, is completely foreign to my family, friends, and anyone else around me. Gets lonely out here lol
I went back and got a CS degree at 27. Best decision I ever made. Alternative was to become an English teacher.
If I have some advice it would be don't half-ass this new beginning. Go all out and you'll get rewarded. And get an internship at a good company if you can, as soon as you can. I had to become an intern at 27 😅 was that sort of embarrassing? Sure, but it was at a top company and they hired me on and are paying me accordingly.
I was on the Math Olympics team in high school, then my senior year I stopped taking math. I was primed to take calculus and succeed, but I thought math was not cool, or something like that. Anyway, big regrets. I started in on Comp Sci late in my college career, probably at age 24, and this required me to take calculus. I struggled with understanding only parts of it, but I could have really launched had I kept it going through high school. It is difficult but possible.
Did you finish ??
@@justadude1477 Yeah. I'm on to discrete mathematics 1 now.
I'm also 26, started school this year, and trying to get a computer science dagree. I'm also struggling with calculus. Crazy how we both went looking for an easy way to do calculus on UA-cam.
When I took Calculus, 'O so many years ago, I heard nothing but terror about Calc 2, so I came up with a plan. During the summer before the class I studied, practiced and memorized all the derivatives and integrals. I went a step further and memorized the proofs as well, along with the domain and ranges of said functions, their graphs, and a handy bucketful of trig identities. Guess what, I got a math scholarship out of it!
Totally agree with you. My son is currently learning Calculus on his own. I have purchased over 10 books to support his studies. On the other hand, when I was learning Calculus, I taught myself using an HBJ Calculus book that I borrowed from the library. I was able to pass the AP BC Calculus test. I think self-discipline is the key to learning Calculus.
Congrats and full encouragements to your son - With so many free calculus MOOCs around, you will be able to find a class that can help him.
@@freddupont3597 Thank you!
For me it was hammering precalculus to smithereens before arriving at calculus.
Then calculus at a community college and it all clicked so beautifully. Having that teacher there to help answer questions was priceless. She cared, you could tell, she loved students and she loved math. I know now looking back, she pushed me in directions that took experience. I wouldn't have followed those paths as a newby simply exploring.
Thanks for the book recommendations. I am currently in a Calc 1 course, and have realized Calc 1 isn't that bad when putting in the necessary amount of work each day. I think my biggest suggestion is for people to allow themselves to "struggle" or "not get it" and be okay with that feeling. If your okay with not knowing something right away then when trying a problem that looks very daunting you can have a more relaxed approach.
Precalc was diffintively harder for me than Calculus. Calculus is only hard because of the algebra imo. Calculus itself is conceptually very intuitive and easy to grasp and to me the methods it provides to solve problems come as a relief. I did not like math before calculus.
Dude your into to limit notion was so easy to understand! i was really intimidated by calculus because everyone says its sooo hard but you made its seem easy! thanks!
Great vid! I learned Calculus from the Howard Anton book 3rd Ed and tried my hardest to do every single problem from every section. I think that's the best way of learning any math subject... By going as many math problems as possible daily till things become just natural like taking limits, finding derivatives, integrals, volumes of solids, etc...
I learned calculus on khan academy, and it was great. Allowed me to develop a great intuition for the subject as well as practice the computation techniques.
Hi sir! Stewart book is also the most popular calc book in Brazil. The adversary is a national book commonly known as Guidorizzi because of the author, and it's way more challenging than Stewart Calc. Here I own only one half of Stewart Calc (here it is divided in two paperback volumes), but I'm only a gap year student, so I bought that to self-study (I actually didn't it till now, because I'm reviewing and deepening my knowledge in algebra and trig (a few days ago I couldn't define a polynomial). Your channel is helping me a lot, it's my reference channel in international content on math topics!
Sir,please Explain the ahistory and development of Calculus
Check out "The Calculus: A Genetic Approach" by Otto Toeplitz. It's a great history that explains a lot!
Excellent recommendation I also recommend checking out Calculus Reordered by David Bressoud for calculus history and lots of mathematics as does the book by Toeplitz.
@@John-ru4gz Or with Greeks thinking about a rabbit catching up to a tortoise! 😅
I began tutoring my son in High School about 21 years ago in his class room. (The private school had no math teacher that particular semester.) I fell in love with tutoring kids when I saw the light in their eyes when it made sense. Turned out my son didn't need my help, but plenty of others did. So I volunteered for a span of four years. Eventually, I was asked if I would be interested as a full-time teacher. I had learned so much more about mathematics while teaching these young people than I ever had dreamed. But after a few more years, I felt I should get a math degree. I used the Stewart Book in all three calc classes. I happened to be working problems in the book when I saw this video in my recommended feed. Anyway, I had to concur that Calc 2 was the most challenging of the three classes. But eventually, I got that degree and have loved each class in turn in the process.
My advice to new learners is to get at least one more copy of whatever text (different author) you're studying. I recall once during the Calc I course being stumped on a concept. (Of course now it all seems so routine...) But I found a copy of Calculus by Thomas in the used book store. I went straight to that topic in the text; it made so much sense having read it again. It said the same thing, but for some reason the diction made more sense to me. It's worth taking time to explore instead of simply spoon feeding on what is assigned. The hours you spend in research is regained in the number of hours not spent in frustration and scanning the internet for a resource that doesn't adequately support your need.
3 years ago I started learning higher mathematics.I believe being consistent is a necessary condition in learning math as it is not a one day job.
My experience with calculus was that initially I was doing good then came the monster of multivariate and vector calculus. Honestly,those were some really tough days but at last consistent was the key.
I am entirely self taught,maybe that's why I needed a little bit more time than others. But having a mentor definitely helps to save time.
Love from India.
okay idk who needs to hear this but, i started university(undergrad) yesterday. and- i was scared. nervous. anxious. bcs of how my college ended. but my anxiety has almost completely vanished after yesterday. and thats bcs i got to know that its another beginning. it is another beginning. its still in my hands to get everything together and if i try and do everydays tasks on that day, i can end up in a much better place than where i was at the end of college. and- youve got it too. whoever needs to hear this, if youre entering university, you'll be fine. this is a fresh start lifes giving you. so hopefully you and i will make the best out of it with kher, ameen.
Hello Math Sorcerer,
I love your videos, they're always so captivating and math is just amazing. I also really like the wizards on the video covers, please keep doing that as much as you can!
Best wishes, Eleonora
My college in Brasil offers a double diploma of enginnering and mathematics, Im finishing calculus now, and thinking of trying.
Sounds great, I'm checking out degrees in Scotland for my change if career. Good luck!
I took calculus in a course in college back in the late 1970's. I basically crammed for the exams back then, but also had a lot higher of an eidetic memory than now (thank God for Google coming along as I aged). I did end up with a masters in applied math (stats, operations research, numerical analysis), but I never took any of the "harder" theoretical math like advanced calc, analysis, topology, etc., like a regular graduate student in math might. I'm also almost done watching your calculus 1 lectures you did in the fall of 2019 before covid just to revisit and refresh and that was fun. (the ones you keep saying no one watches, lol).
I look forward to your videos everyday! Thank you High Supreme Induction Sorcerer!!!
Although I am not the biggest fan of how the Stewart book explains things, it by far has the best collection of problems out there. I am loving working problems from that book.
Get Spivak! Preferably if you know some calculus already, and especially if you plan on being a math major. It’s a great book!
I'm going through this process right now, thank you for this, this is a great mindset and reassurance. One of the thing that frustrates me about some of the thick books is that they don't usually have the solutions to all exercises in them, and although I know the key to learning calculus is doing the problems, I can't bring myself to move forward if I don't know that I've done a process correctly, or at least understand authoritatively what I did wrong. It feels like a risk moving forward when I may have inadvertently adopted an incorrect understanding. I guess this is something I just have to shake off.
same...
Most important subject for students who want to do physics. Most of the students struggle with subjects like classical mechanics and electromagnetism mainly because they don't have solid understanding of concepts in calculus.
Hey I've watched all of your math lecture and am learning thanks and your funny also God bless you ❤
Calc 1 was tough at first because my first calc professor was a visiting one from another university, and told us all about what calculus means conceptually (awesome) but virtually none of the steps on how to solve the equations that were on the test lol
The second time I took it, the professor stuck mostly to the book. Read the chapter before class, and his lecture would be word for word, even the examples were the same. For whatever reason this was much easier for my brain.
Calc 2 was tough particulary when it came to Integration by parts, and knowing when to use it, but I slogged my way through a summer cram course.
Calc 3 was by far the most interesting, and I loved how everything built on itself, but the first time I took it, I had calc 3 back to back with Intro To Mathematical Proofs, and it was all too much at once. I passed proofs, but failed calc 3 (or didn't get a high enough grade for it to count by a little bit).
The second time I took calc 3, my professor was a really cool guy who hunted mushrooms, and had worked with NASA for a bit, and biked everywhere. I ended up passing it the second time with a better grade.
Even though I got my minor in Mathematics, I feel like my calc skills are not as strong as I'd like, especially since I want to continue and learn Differential Equations. (I graduated university in 2020)
Calculus was and still is my favourite course , it is the fundamental of all fields the hart of science!!!!!
Badass beard dude, I'm growing my father time biker level stuff hopefully... Back in engineering school I thought calc 2 was the worst, diff eq smashed my ass right outta the program but I'm still grasping them as an older math enthusiast and artist... Thanks for making these, just forced myself through reading the first couple chapters of Calc for Practical Man, reads well... I got Steward's transcendental version way back in 04, they used it for calc 1-3 back then....... Please stop showing books, I'm starting to become a math book hoarder who can barely prove the fundamentals 😂 peace 🕊️ Getting Euler's calc books next!
After taking level classes through school (i didnt know about yhe diferent levels), i chose to take AP calculus my senior year of highschool. I also took it along with AP physics. I felt so out of place my first day and throughout the school year. However, while some topics didnt make complete sense i was thrilled to find topis that I recognized from taking level couses and even new ones that were really interesting. Now im 28 and plan to go to college for electrical engineeing and want to brush up my knowlege.
I agree with you that the Stewart Calculus is amazing. There are both advanced problems, as well as for beginners, excellent book!
The other day I was looking through my library and looking at my college books...I found these two gems:
Linear Algebra - Insel, Friedberg and Spence.
A Logical Approach to Discrete Math - Gries and Schneider.
If you don't have them, I suggest you take a look at them, specially the latter one!
I am getting ready to go back to school for my Bachelor's in Computer Science and I have to take Calculus with Limits (whatever that means) and I am terrified! I was always really bad with math in high school and the highest math I ever took was Algebra and that's after failing it my junior year. Then when I got my Associate's degree, I had to take algebra and trig I and II and I absolutely fell in LOVE with it! I learned that it was 150% because of the instructor! I'm the kind of person that learns technical programs by learning every single step to get to a correct answer and she literally taught us to that level. I even got to learn some geometry with her. I am a dominant right brain person and while I work in a very technical field (Sr. GIS Analyst in ITS), I am way stronger when it comes to the creative side of the world. Thankfully my education and professional experience has allowed me to be very successful in my industry. I'm still TERRRRRRIFIED of having to take Calculus at any level and my first time being to get my Bachelor's. 😕
I started at university last week, I'm trying to graduate on Physics and we take calculus classes, your videos have been helping me a lot to have the motivation to go and study everyday! I love math and physics but I often have a hard time with it (specially with math) but this year I decided to dedicate myself to at least study 1h everyday or solve 1 problem per day, so far I have been consistent with it (I'm also using that James Stewart book). Your channel is helping me a lot with my studies!
The strategy he suggests about setting the bar super low is gold. If you say “I’ll just do one problem today, or I’ll just do 25 minutes today”, it becomes easier to convince your mind to get started. After you start then the law of motion is in your favor and often you may want to keep going. And if not, at least you got through one problem or one 25 minute session
What's been working for me is exactly what is described in this video. My college uses Larson, so I got an older used copy if Larson and have been teaching myself over the summer. I try to do a minimum of an hour of calculus every day. And since the end of the spring semester I have learned about 2/3 of a Calc 1 course.
It's not easy. There are many days I feel like I'm just not getting it. But I push on and usually experience some breakthroughs.
I have taught myself from beginner algebra to calculus by doing this. Again, it's not easy, but it has been worth it imo. Plus my professors really appreciate how prepared I am when I get to class. So that's a nice ancillary benefit.
Thank you❤
im a math major student and im struggling with calculus 1 when you said that 1:27 i literally cried
calc is fun, theres many a different flavors of calc - which just use small extensions
matrix calc : university of Minnesota has a nice primer -pdf- if you're reading Elements Statistical Learning
stochastic calc: useful for stochastic processes, im using parzen but saw initially in finance
thank you
Udemy just has a huge sale. I bought some of your courses. I also bought a bunch of other courses so this will take me some time to navigate through your courses. Thank you for what you do.
I actually do have mneumonic for the unit circle. First, understand the concept of "reference angles". Second, "He asked for a 13 but they drew a 31" Everything else is 2 and everything in the numerator is a radical. You see, He wanted to represent MS-13 but the tattoo artist spelled it wrong, so he drew a 31, instead: ua-cam.com/video/QtTR-_Klcq8/v-deo.html
I say go out and get Calculus Made Easy by Sylvanus P. Thompson. The unabridged version. It's a paperback. It's a good start.
I got a D in Calc 2 about a quarter century ago and never took another math class again, so it was definitely the hardest I ever took. Anyway, I'm taking it again this fall as a one-off at community college, so I will probably be looking for some supplemental problem books, thanks for the suggestions.
Calc 3 I flunked.
Then flunked again.
Then analysis - easy
Then topoligy - aced
Then calc3 - passed with a 50.
How to Enjoy Calculus by Eli Pine
Forgotten Calculus by Barbara Bleau. She reviews algebra in chaps 1-9. Scour thrift stores for used math books. if you find a textbook, get the solution manual for that edition. Sometimes, i find a solution manual first and then get the textbook that goes with it.
We got shown the basic patterns first , without even being told that it was a maths class.
On the left a graph of 2x^3
On the right a graph of 3×
Then x^5 on the left, 5×^4 on the right.
The challenge for each team of three was to be able to guess the left from the right, or vice versa.
Thanks for the useful content you make
Is better to read mcmullen's books before reading a thick book? Or what is the order you suggest?
Yes. I have a copies of books of all the authors you’ve named📚
wow, I believe I used that Silverman book in the late 70's!
Highly recommend creating a custom Anki deck for calculus. Its algorithm helps you learn with repetition and active recall.
Could you please make a video about the reasons and differences between normal calculus books and their Early Transcendental versions? Thank you for your great videos! It is very inspiring to learn calculus!
Haven't done a Maths major but definitely, other than Calculus (all calculus courses), thought Mathematical proofs and statistics is definitely the hardest we have done. But everyone is different.
At 24 years old, the last class I had taken was Alg 2 in 2016 - after transitioning out of the military, the best thing that could have happened for me to learn calculus was to fail my first semester of calculus. It lit me up and gave me the drive to try again and do it right the second time. Now I'm in Calculus 2 and using discipline as a tool - it blew my mind to realize being good at math isn't a talent, it's a muscle.
You are the best.
As a predental student at the University of South Florida ( 1965-1969 ) we had required courses one of which was calculus. I had a very limited math background and I found this course very difficult. I attended the University of Maryland School of Dentistry and graduated in 1972.
I presently practice dentistry in Miami Beach and am the author of the book " Understanding First Class Dental Care". I am also the founder of the David Hamilton Music Project.
I recently started questioning what made calculus so difficult for me and I came upon The Math Sorcerer web site. I like his presentation but when I tried to find a really basic web site it was still difficult......maybe I need to go back to basic math....2 plus 2 stuff.
Thanks sir
Hello ! I really enjoyed doing the yellow calculus book from Pr. McMullen.
I will buy the multiple variables workbook aswell.
I was wondering tho if there were equivalent workbooks for higher calculus ? For example I've studied a bit the Taylor expensions to find limits but I struggle a lot with all the maths when I try to expend complex/composed functions and I do a lot of mistakes. Having a workbook that could help me solve that with a lot lot lot of solved exercices would be a huge help to prepare my second year during those 2 months of vacation.
I just graduate from 1st year and will go in 2nd year with pure maths. I'm in France, so I don't know if what I did is about calc 2 or 3
I'm a biologist and I had calculus I e II (differential equations and modelling). And they were the hardest classes for me. I'm 52 years old and trying to overcome my difficulties in mathematics just for fun. I don't like doing exercises (I'm a bit lazy to writing), I like reading. I think this is the biggest problem. I understand the explanations, but when I try to solve a problem, I struggle to even get started on it and I feel discouraged to go on.
Mathematics involves doing problems and proving theorems and what not so it's imperative that you write.
Calculi of knowledge!
from now on my goal will be "at least a page in the morning, at least a page in the evening"! lol it is true that it is easy to get started, but being consistent is tough!
This is a most inspiring channel. Do you mean that calculus is difficult because differentiating and integrating complex functions is difficult or because the understanding of the concept of for example differential equations describing physical phenomena like heat flow, electricity transmission, gravitational forces is difficult to comprehend?
For the self learner, could you talk about when to use a different book? Like if one is struggling a lot with a book, when is it a you provlem or a problem with the author.
I would say that if you have an absolute thorough command of Algebra you will find Calculus much easier to understand.
No truer words.
Bob Miller (former Lecturer at City College of New York) wrote a series of books that are excellent
I'm taking calc 2 right now, at my school we use Stewart too but we use the Essential Calculus version. Other than calc the only other hard math class I have to take is Linear Algebra, maybe it's not hard but it's a foreign concept to me right now.
How did I learn it? I tried to do every problem in the book as I went along. Also had a study group for Calc I. It was fun, although you had to put in the effort.
Starting in late February, I've been self-studying for almost every day. I started with a book called _Teach Yourself Geometry_ , then proceeded into _Teach yourself Trigonometry_ (Both by some British dude called Abbott). I mostly read those and did very few exercises. Then I read through _Algebra and Trigonometry for College Students_ by some McKeauge and did most odd numbered exercises.. I skipped systems of equations and a chapter on matrices.. About a month ago I started reading Stewart's Calculus and doing exercsises.. I only do the odd numbered exercises (Odd among the first 50 or 60) and no word problems unless the chapter is about applications or something interesting!! I am about finishing trig substitution and might start on partial fractions tomorrow!! I don't know how much more free time I can afford so I am trying to chew through as much of the book as I can, but this chapter 9 (Techniques of Integration) is by far the toughest and some exercises made me really think I might be just wasting my time.
keep going bro, you got this
A precalculus course should include creating functions from independent and dependent values in terms of different operations.
f(a) = r, f(b) = s, f(c) = t, ..., f(x) = y
I want to read Spivak or Apostol after Stewart. Which one should I get?
Hi Math Sorcerer I'm doing first year in uni and statistics is my major. I'm really struggling with probability,any books that you can recommend for a beginner?
Hello Math Sorcerer. What do you think of the book "Calculus" by David Patrick from the aops series. I used it to learn Calc and I personally really like it, but its meant more for competitive maths rather than university maths.
Brother I'm not gonna lie, I don't watch your videos. But I just wanted to say great job on uploading so many vids on a daily basis, I can clearly see that you put effort into this channel ❤.
Please, can you provide some book names about mathematical logic?
Do you or does anyone else here have an opinion of Thomas & Finney’s Calculus And Analytic Geometry?
Calc I was a weeder class. Calc II was brutal, but good. Calc III was a breeze!
Good description hehe
First time I took a calculus course , I failed so miserably, I didn't understand anything, difficulty to motivate myself. The second time, I bought calculus made easy and I did maybe half of the book before I took the university course again. Maybe it's the way the teacher motivate the student that count, seeing that calculus could be easy to do was a big motivator for me. Often the teacher said oh it's '' hard '' not everybody could do it blah blah, but it's negative for a lot of people just to hear that. Anyway, the second time it was more easy in the class to keep up with the teacher and his exercise but I succeed my calculus course who was a requirement for my other computer science math class. A lot of my best teachers I encounter in my student life, the stuff they taught is easy (maybe it's the words or the way they used the stuff to make the student follow them, when people got passion for a subject, it's easy to tell ) and they encourage anybody to follow their path and they could do it like they did.
I've been brushing up on algebra to get into calculus, what parts of algebra should I be fluent in before moving on?
hey sir, i was wondering if you are thinking about making an intro linear algebra course on udemy or youtube or anything? I have noticed that it is very difficult to find good linear algebra courses on the internet and was wondering if you would consider creating one yourself
i cant wait to pass calculus because up until where im at in pre calculus i dont think there's been anything truly difficult. i want to really make great accomplishments in math
This man understands the psychology of pedagogy.
Pls do a video for linear alg and diffy Q!🙏🏿
I have seen many videos on learning calculus but none seem to go from what I understand in algebra 1 and 2, for example graphing, to applying calculus to the graphs I already understand.
I've never taken Calculus. I heard from some of the people I'm close to that they had so much difficulty with it. I only ever had one Math subject during my freshman year in college. Even that I find difficult as well. Math just feels too foreign to me. Like it's an encrypted message that I find hard to decode. I've heard people say that it takes a lot of practice to understand Mathematical concepts. My father had no problems with Math. He had earned a Master's degree in Engineering from the University of Auckland. Never once did I see him sit down and actually study. Maybe it's due to that big brain of his.
The biggest problem I see is that people don't understand how to read mathematics. They see a bunch of symbols and start freaking out because wtf does this mean?
If threw a language you did not speak in front of your face and told you to read it to me you probably wouldn't be able to do it for the same reason as above. You don't know how to read the language.
Once you understand the proper way to read math, then you can start to properly think about math, and only then can you start to get a slim understanding of math.
It just takes a calm mind and a strong will to learn and understand mathematics. Just don't get frustrated and expect the subject to consume a *lot* time of your time. peace x
Explain the Lost Mathematical Inventions From History, Sir prepare a Video about It?
I’m 32 now and going back to school for a Computer Science degree. Praying it’s worth it in the end. Lol
Thanks. How does an average student in elementary Mathematics learn Calculus?
Would love to hear your thoughts on a book, A Programmer's Introduction to Mathematics by Jeremy Kun.
I remember when i studied calculus was a loooong summer, it was me and the stewart, in like 2 months i learned how to do integrals, now im in college :DD
How about a maths placement test? I want to know where i should begin personally as I've been so far separated from maths.
Are your Udemy courses a good place to start ?
Bro you look different in a good way
Sir can you please make a video on books on trigonometry
I took calculus the first quarter of my freshman year of college. It was a 7 am class, I rarely woke up in time, and I failed miserably. The next year I took it again, still didn't pay much attention, and earned a D. The next year I switched my major to English and that D in calculus was enough to satisfy all my math requirements. It wasn't until ten years later that I found myself back in school and taking it seriously for the first time as a biology major. I took calculus again and turned that D into an easy A. The big difference? I actually went to class and did my homework.
"Thickness matters." - Math Sorcerer 2023
What made me frustrated is that sometimes I have to read one specific book in mathematics and that book skip steps.... I hope there could be a computer program that can generate missing steps :(
It doesn't happen in the UK system ,where the A-level Physics has no calculus on it, as far as I am aware.
But I found years ago, that using Physics is a great complimentary way of learning Calculus really well, developing all the intuitions.
Some educational systems time ago used this double approach. Being out of touch, I don't know if it is feasible anymore.
Do you think visualisation is a great tool for beginners so use of softwares like Mathematica or matlab or maple or some apps on mobile like desmos. May be you can make a video of how to use these software to enhance and suppliment and even get a sense of experimentation and play to what we are learning. This is what learning is all about anyways. Finally also talk on how to maintain a notebook physical or digital like one note or app like anki flashcards. Where the difficult problem once encountered are all categorised and solution along with insights or any graphs that was created using the software is saved. This abridged note of difficult problems if revised daily twice once before going to sleep and once immediately on waking up will be a game changer. It can also be reviewed on any mobile device during commute. Will 10X performance and expertise. Please make a video elaboting and showing how these tools can be leveraged
Topology kick my butt
Calc 2 was insane.
I'm probably going to have to take calc 1 a third time. It was either finish college or stay in the marine corps.
Im just starting a computer science degree at 28 and im not good at math…any advice 😊
is it a good idea to learn this stuff at 15 (im very bored)
m only here coz youe voice is relaxing..😂🤌