12:42 When you talk I keep thinking yes it’s so right. I started college again at 27 and I was a total flop at 19 I didn’t have my head straight. Hated school for the longest time. When I wanted to do math, just for studying it, I have fallen in love with the material. The musical instruments analogy is awesome… I learned 8 different instruments and was in 3 band classes, one being zero period. I sucked at school though. I was amazing in band and terrible in life. But I understand why I got better all these years later. I found a real inspiration and desire to WANT to do it ONLY for the sake of doing it. I’m in Linear Algebra and your videos got me reading the textbook for HOURS. You’re a fxxking hero man!!! Screw the TH-cam academy… I’m learning algebra like the guitar… but not to impress some girl. Because I want to learn the powers of the universe and what man has created to help you get as close to it as humanly possible. The textbook has became the coolest thing instead of a big weight in my bag. The explanations of mathematics and arithmetic’s was also very helpful
I failed so many math classes due to almost every teacher I had quitting halfway through the semester due to pay. These videos help me so much with learning HOW to learn math, through a mentor that wants to help. Thank you!
Glad it was helpful! Thanks for the comment! I do a live show every morning and evening at 7:00 AM and 8:00 PM Central (Chicago USA timezone). I address all questions each day from comments here and give shoutouts to those who don't ask a question. Here is the latest live talkshow th-cam.com/users/liveORyy8-EgEX0?feature=share Thanks for commenting and being a fan! I hope to see you in the next episode. Author Jonathan David
Thank you so much! Rn I’m taking Calculus 1 class which my professor show us how to follow step by step when solving problems to help us understand. It’s better to take time to learn solving problems using skills such as Algebraic and Trigonometric skills to understand the concept problems without getting ahead.
I hope they get overrated lol. I gotta pay my bills! Thanks for being a fan Author Jonathan David If you would like to help this channel grow and show your support, here are some ways to do so- Venmo account.venmo.com/u/authorjondt CashApp cash.app/$authorjondt PayPal www.paypal.com/paypalme/authorjond Join TH-cam as a Paid Member (lots of perks!) th-cam.com/channels/dwKRgpXOHvVxlYnqYxXNzw.htmljoin The Ultimate Crash Course PDF for math and physics with a one-time purchase at payhip.com/b/hc0N9 - all future updates and editions included, so you're always equipped to excel in STEM! Thank you all so much for your continued support! Without it, this TH-cam channel would have died a long time ago. All books with access code (limited offer) payhip.com/b/hc0N9 Hardcover Cheat Sheet payhip.com/b/kQ10O Paperback payhip.com/b/VSOnC PDF payhip.com/b/lS8nY Cheat Sheets & Crash Courses Calculus 1-Differential Crash Course payhip.com/b/F437Z Both Calc 1 and 2 payhip.com/b/jkn3N How to Study payhip.com/b/pWrj3 Basic Physics payhip.com/b/y58Sr Algebra payhip.com/b/r6TmE Trigonometry payhip.com/b/LV2y8 PreCalc (alg+rig) payhip.com/b/lIbKH Calculus 1-Differential payhip.com/b/mKsLH Calculus 2-Integral payhip.com/b/OvCYE Calculus 3-Multivariable & Vector payhip.com/b/xHU6Y Linear Algebra payhip.com/b/54on7 Differential Equations payhip.com/b/b6L7k All Subjects Both Cheat Sheet and Crash Course payhip.com/b/ “The Author” Jonathan David
I left a reply for your message in this video- th-cam.com/users/liveA7PhfXfs8-k You can join me and other people from across the globe at 8:30 PM central time (Chicago US Time Zone) everyday if you would like a more in depth Q&A! Thanks for watching! Jonathan
This was me in my early years I struggled with algebra alot and with trig, but I kept grinding and starting building study habits and reconstructing my foundation in math. I left school for a while and now finishing my physics and math degree passed my calculus courses and always review my old work and looking to improve in areas I know needs work. You're right doing almost everyday and you will build the skills
Thank you for your comment! I really appreciate all the feedback. You’ll find my response in the attached video. You can listen there. th-cam.com/video/3Vz_QZyYx1s/w-d-xo.html Have a great semester! ∆ Author Jonathan David ∆ Note* This video requires membership to view for the first week, then it is released to the public.
I really appreciate your words! You’re a joy to listen to and thanks for helping my perspective on math and what I really want to do with it. Being a great teacher is magical in itself. Thanks again.
It's hard to disagree with what you said, but I fear it may come off a bit rigid. I started with Serg Lang Basic Math for high school algebra trig in a 'pure math' context. Ignoring everything else until I finished it. However as a self-studier, I've found the more fundamental things become easier to learn when you have dipped your toe in other areas 'farther' ahead. Now when I learn I am cycling and touching all different areas, I've found that this usually leads me back to Basic Math except this time with purpose for a particular point or subtlety. After having had more anchor points of relevance, and really realising how shallowly I had previously understood it, when I go back to it (with a different perspective given to me by jumping ahead or around somewhere), then I really know it, and it's almost hard to forget. So in the extreme case, I agree with you, someone literally has no foundation in math they just have to get the most basic stuff down, but I would try to include a caveat for people who have the trunk of the tree, the next levels of branching shouldn't follow the same pattern, in my experience at least, it should become much more free - but maybe that's a personality / cognitive quirk of mine. I think we sometimes don't sell math right, when it comes down to it, the difference between what mathematicians do vs. what maths is in the minds of most people is feels almost like an injustice. A lot of people don't know that it is an intellectual exploration, diving in the midnight zone assembling all these alien-looking life-forms through reason alone. I think at some level, showing people things before they have any idea how to work with them is good, it has a level of mystery, similar to how calculus might for the students you mention. But of course in any discussion, wilingness to Do The Work has to be assumed. All I know is, without being aware of all these cool mysterious things up ahead, I probably wouldn't have had a good reason to work myself.
As someone that is majoring in general science but wants to become an astronomer and is going to take a pre-calc course and a physics non-calc course next semester, this definitely helps. Great video 👍
You're super interesting and fun to listen to. I'm about to enter community college this fall for my first ever semester. I'm not super sure how college works but your video on how to navigate as a STEM major gave me a better view on college. It makes me more enthusiastic that i must depend on my self to actually learn and understand the professor, i really didn't like high-school at all i felt like i had no freedom and i didn't have the skills and habits to go through the motions however i'm building those skills and i feel like this new form of school gives me more of a feeling of control and being able to differentiate myself. Unfortunately i don't come from a super rich family where i can afford to choose just any major without having to worry about job/financial security and if i did i would probably do pure mathematics and physics and become a researcher, that's fine though because math is a skill i intend to use/learn for the rest of my life.
Just make sure that you treat everything with respect and you’ll be fine. Keep yourself a few chapters ahead of each lecture and it’ll be a walk in the park.
8/23/24 Thanks for commenting. Here is my daily video addressing your question or comment. If it was not a question, I gave you a shout out! th-cam.com/users/livekKOi0DsjImU Thanks for being a fan! ∆ Author Jonathan David ∆
I think your selling yourself short a bit but message received. Your right that becoming an expert in something is not as mystical as it seems. Still I find people that are experts in anything impressive simply because not everyone is willing to put in the necessary amount of work, even under ideal conditions. I admit though most of the time learning math and physics doesn’t feel like work, it feels like self indulgent puzzle solving. Especially outside of University it’s not a chore, it’s just fun.
Anything is impressive when it takes a lot of work to do. My point is just not to idolize someone that spent 10 years doing something just because you didn’t do it. Because most people have done a lot of things that they’ve mastered that other people haven’t we just pick and choose which things we think are better than others. Thanks for being a fan!
Edit: Revised grammar. You sound like someone who has been deluded by the societal narrative of STEM field, wanting to receive validation on the work they've put in for their past self-inflicted masochistic behaviors. And to your point about people not wanting to put in the necessary amount of work: Why the f**k would anyone want to put in the work when they are rarely provided opportunities to form an intrinsic value system concerning STEM education? Do you even have a faint understanding of personal interest formation in the context of the broader educational structure? Also, what do you mean by "ideal conditions"? When you say "ideal conditions", are you even self-aware enough to see that personal CONTEXT may affect the learning process more than you might think? How do you know what you consider to be an "ideal condition" in another person from YOUR perspective is also ideal in THEIR perspective? -- Good luck reaching any depth in a personally meaningful way in whatever field you are pursuing with that attitude. Yeah, I admit. I'm hella projecting. But I feel it is because I've dealt with many people who think like you do, who tend to perpetuate toxic learning environments outside the educational setting. Case in point: Are you going to find it "simply impressive" of an engineer who became an expert in their respective field to invent a technology just for their own monetary gain or to feed their ego at the cost of YOUR suffering? That's not to say we should vilify and/or abandon the role that money or ego plays in our lives. To me, however, the only imaginable scenario in which you would answer yes to my last question is if you are not wise enough to think for yourself or you share similarities with the hypothetical individual I've described.
I subscribed so quickly to this channel your advice is so genuine and you convey it in a way where I really absorb it, definitely a hidden gem in TH-cam! I’m starting off a STEM degree and this exact philosophy is the reason I chose to take it easy and understand a notch lower to calc before I take it.
I agree that people often overlook the importance of basic arithmetic and algebraic manipulation, but I don’t necessarily agree that students who want to take higher level math courses is a bad thing. For me I’ve always been looking forward to what’s next in math and that’s what’s sustained my interest in math and helped me improve my skills. Specifically in calculus I found a lot of what I didn’t understand in algebra became illuminated within the context of calculus problems. Things like vertex forms of quadratic functions, slopes of functions, exponential functions, etc. Currently I’m taking my second course in Real Analysis and I wouldn’t be studying math right now if I didn’t have that consistent interest in what’s yet to come.
Nice video. I completely agree with you when it comes to studying algebra and trig rigorously prior to taking calculus. I was fortunate enough to study my butt off in college algebra II and trigonometry, which made my calculus journey a lot easier. However, I find that the real monster is differential equations!
8/23/24 Thanks for commenting. Here is my daily video addressing your question or comment. If it was not a question, I gave you a shout out! th-cam.com/users/livekKOi0DsjImU Thanks for being a fan! ∆ Author Jonathan David ∆
i struggle alot with learning math because in my school the books are very bad and skip subjects way too quickyl the books are only workbooks so no explanations and the teacher is always busy
As the science major, your job is to be a problem solver. It sounds like you have a problem you need to solve. Author Jonathan David Support your learning journey and help keep this educational channel thriving by leaving a tip - every contribution empowers me to create more valuable content to help you succeed! Join this channel for $9.99/ month or $24.99/month youtube.com/@authorjond/join Donate- Leave a Thanks on TH-cam Venmo account.venmo.com/u/authorjondt Cashapp cash.app/$authorjondt PayPal www.paypal.com/paypalme/authorjond Patreon www.patreon.com/authorjonathandavid Check out my custom formula cheat sheets! They are pretty great! • How to Study payhip.com/b/pWrj3 • Basic Physics payhip.com/b/y58Sr • Algebra payhip.com/b/r6TmE • Trigonometry payhip.com/b/LV2y8 • PreCalculus payhip.com/b/lIbKH • Differential Calculus payhip.com/b/mKsLH • Integral Calculus payhip.com/b/OvCYE • Multivariable Calculus payhip.com/b/xHU6Y • Linear Algebra payhip.com/b/54on7 • Differential Equations payhip.com/b/b6L7k • Differential Calculus Crash Course payhip.com/b/F437Z • All Subjects and Crash Course (BONUS Access Code to Download all PDF books) payhip.com/b/aw0b9
i really enjoyed this video. Im a mechanical engineering major getting into calculus. I really like calculus cause it makes me feel like a genius, but i hit a brick wall. I realized that my algebra skills are terrible. Time to go back to Algebra and learn the fundamentals very well. Not in any terrible rush. Do you think I should stress the fundamentals heavily for this field, or just learn what I need and move onto the engineering. I like math but I prefer mechanical
The absolute best way to do this is to take one simple topic, and master it. Then move onto another simple topic and master it. Take it slow at first, and then it will become very easy to master every topic going forward. It’s no different than building any solid foundation.
Interesting on the YT algorithm. I've actually had the same Idea. I'm starting a CS degree in the fall, instead of jumping directly into Precalculus / Calculus. I decided on taking College Algebra first. Just to make sure I have the fundamentals down first. I've also been self-studying Algebra, Trig, Geometry.
Your plan is pretty much what I recommend to anyone entering stem. I left college the first time 1 class and a capstone away from a chemistry degree, now I'm in my 30s returning to school for electrical engineering and I started my math self study preparation/review at algebra, despite having passed all the calc classes in the past. I forget what TH-camr said it, but someone described learning science as building and filling a barrel, each topic is a board on the side of the barrel and water is being dumped into the top. It will fill as high as the lowest board, so as someone just starting, you need to ensure the boards you put on first are tall enough that they don't become the limiting factor later. I hope that metaphor was descriptive enough.
That sounds like a solid plan! Starting with College Algebra before diving into Precalculus or Calculus is a smart move, especially if you want to make sure your fundamentals are rock-solid. Algebra is the foundation for so many concepts you'll encounter later on, and having a strong grasp of it will definitely make the transition to more advanced topics smoother. It's great that you're also self-studying Algebra, Trig, and Geometry. These subjects are all interconnected, and your self-study will give you a head start as you begin your CS degree. Having a good understanding of these areas will not only help with Calculus but also with many concepts in computer science. It's awesome that you're taking the initiative to build a strong mathematical foundation-it's going to pay off big time!
Thanks for the encouragement! I’m really hoping that starting with College Algebra will help solidify my understanding before tackling more advanced topics. It’s reassuring to know that building a strong foundation now will make things easier down the road. I’ve been finding the connections between Algebra, Trig, and Geometry pretty fascinating, especially as I start seeing how they all fit together. I’m excited to see how this groundwork will help me with both Calculus and my computer science courses. Thanks again for the support-it’s definitely motivating to keep pushing forward!
Super interesting video! I've taught myself Calc 1, 2 and now on Calc 3. I plan to learn the math that comes after that i.e. Diff EQs, Linear Algebra, etc. From what I understand Algebra will show up in almost all the further math courses and is needed to tackle advanced topics, is there a book you would recommend for someone to really solidify their understanding of Algebra?
Every course beyond algebra is just applied algebra. And a lot of the stuff in algebra was derived from further applications of algebra lol. Sullivan algebra and trigonometry book is good. Pretty much any algebra book but I like their flow is very straightforward.
I`ve had many of these similar thoughts...I as well started with physics and switched to math. I definitely agree with arrogance aspect, when I go to social gatherings I`ve learned not to bring up my research and other things I do. As for pure math and applications, I believe some of the most advanced mathematical physics is tending towards utilizing a lot of ideas from Langlands program. Math to me is beautiful but becoming more of a hobby and prefer to work with my hands. Modeling systems, software, finance, etc. is just very boring to me and i`ve dabbled in a bit of it all. You should consider making a series out of this relative topic I enjoyed it quite a bit!
Sometime around the 8 minute mark you say something like: I’m not an applied mathematician because I wasn’t trained as one, I was trained to teach people the foundations of math so they can go and be applied mathematicians. But don’t you think you should know how to do applied math a little? Love the video !❤
So, I haven't been in school for 11 years and I'm finally quitting my job to go after my dream degree in physics. I feel I need a restart/refresh on math(starting Algebra again in college instead of jumping into pre-cal). I've had a couple friends who tells me precal covers algebra and to just dive in. Should I dive in, or stick my toes in the water starting fresh?
Thanks for the comment! Here is my reply- th-cam.com/video/Uh471yPtdoA/w-d-xo.html ∆ Author Jonathan David ∆ Please support this channel by ordering an "Ultimate Cheat Sheet for Math and Physics" payhip.com/b/aw0b9 [NOTE- I do live Q&A sessions every night about 8:00 PM Central (US Chicago Time).] Order by the subject for $9 per subject • How to Study Guide payhip.com/b/pWrj3 • Basic Physics payhip.com/b/y58Sr • College Algebra Cheat Sheet payhip.com/b/r6TmE • Trigonometry Cheat Sheet payhip.com/b/LV2y8 • Precalculus payhip.com/b/lIbKH • Differential Calculus or Calculus 1 Cheat Sheet payhip.com/b/mKsLH • Integral Calculus or Calculus 2 Cheat Sheet (includes sequence and series) payhip.com/b/OvCYE • Vector Calculus, Several or Multivariable Cheat Sheet or Calc 3 payhip.com/b/xHU6Y • Linear Algebra Cheat Sheet payhip.com/b/54on7 • Differential Equations Cheat Sheet payhip.com/b/b6L7k Request a Custom Solution authorjonathandavid.com Donate via Venmo account.venmo.com/u/authorjondt Donate via Patreon patreon.com/authorjonathandavid Donate via Cashapp cash.app/$authorjondt Donate via PayPal paypal.com/paypalme/authorjond
Yeah, yeah. I deleted the live stuff. It was messing with the algorithm behind-the-scenes. Everything’s gonna be pre-recorded now except for my life book signing.
Just make sure you have a super solid foundation of algebra. Spend more time in college algebra than anything else, and the rest of the courses will be a breeze. If you google a college algebra or you can find a PDF for a college algebra trigonometry or pre-calculus PDF by Michael Sullivan that’s a great book to study. You can master everything in that book, the rest of math will be a walk in the park. The rest of math is applied algebra.
2:45 That's not really true... :/ I started learning calculus when I was maybe around the age of 15 or 16? Because I was really curious as to how the sine function was calculated. They just told me "this is a sine function" and I was like "but how though?" That's a difficult starting point for learning calculus I think, but nonetheless I still became super infatuated with the subject and I still learned it all the same. As long as you get excited every time you discover mathematics you haven't learned yet, you can learn a difficult subject even without knowing prior subjects very well. What you do whenever you find a reference to something you don't know, is you just go look it up, and then learn whatever that is. And then if there's something in that tutorial you don't know, you go look up that concept until you're familiar. You can go learn algebra as you need to when it comes to calculus, you don't need to be a master at it. edit: Maybe you'll argue that I don't really know calculus intimately, because I learned it that way. I mean, every technique and theorem, I know the proof to. If you ask me, "What's the proof for chain rule?" I could take you step by step. I know the proof for integration by parts, or the fundamental theorem of calculus. Is that still surface level?? I'm not trying to brag or anything btw. I definitely agree that calculus is not impressive, higher level algebra and analysis is impressive. Calculus is just a simplified and boxed up condensation of those two subjects. I'm just bringing this up because I feel arguments concerning personal experience and evidence would be the most valid arguments to make here. I think, personally, if you want to learn calculus before algebra, go for it man. That goes for any subject. Just try it regardless of how advanced it is. Don't go in with expectations, don't judge yourself or others for not understanding the subject immediately. Just learn the subject because you personally want to, and don't worry about anything. You're spending your time wisely educating yourself.
You certainly can. Without going into extraordinary detail, depending on which advanced subject you choose, it may turn out to be a rabbit hole. There might be so much foundational knowledge you would need to know before you could even begin to understand or start operating confidently in that subject. I agree that it's sort of a gray area. His thing was music, my thing is weight lifting. You might not be able to lift 200 lbs initially. You would keep adjusting the weight until it's a weight you can bear, but it's also challenging for you. Then you attempt to lift a heavier weight again once you become more comfortable with the weight setting you chose. I was the arrogant guy. I got through calc 1 in high school and got a 4 on my AP exam. Skipped to Calc 2, then I did Calc 2, Calc 3, linear algebra, differential equations 1, and statistics by the end of the first semester of my sophomore year. Would I say that I knew these subjects well? Not really. I was doing a bunch of classes around them too (about 18 credit hours a semester + I was an undergraduate research assistant.) I just rehearsed enough that I could pass. I was also a computer science major, so I was trying to jump ahead in my CS course work. I think I was on junior level classes really early and was set to graduate a semester earlier. I jumped into a machine learning course in which they would prove out a bunch of the basic machine learning concepts, and I would see integrals everywhere and gradients. But I wasn't ready for that. I played the music, but I didn't understand the music. I think you understand math best when you're forced to prove something is true as opposed to going through the motions. My math really leveled up when I took proofs and proof intensive courses. Had I took fewer classes and dedicated more time to honing my math, I probably wouldn't have struggled in machine learning. Anyway, my take on this is, if you choose an advanced subject (for which you may be unprepared,) don't make it your entire focus. Focus on your core mostly but also in the background building up your knowledge around the target field. It'll bite you in the ass eventually otherwise. Also, at some point, you begin to think a lot of what you learned was unimpressive/uninteresting. Oh huh, groups, rings, polynomial rings, fields... pretty trivial honestly.. You might know and understand these things, but they're a mere fraction of the things you would need to know to make a real contribution to anything in mathematics.
Infinity is the longest rabbit hole Each day I respond to comments live as it is easier to do than writing text that gets misunderstood and leads to anger. You can join or view here th-cam.com/users/liveeXBAvqGlkHY?feature=share
This is semi-decent advice if you are not actually that interested in math. If you are only looking at the applications of math, sure you want a really good foundation of basic subjects like high school algebra and trigonometry so that you can do quick calculations and understand applications. However, if you are actually interested in pure mathematics there is no reason to stay in algebra for an extended period of time, if you understand the basic concepts you can move on. You said in your video "algebra is way more complicated than calculus" which is... odd. I would not like to really compare the "complicatedness" of any given math subject because you can basically go as deep as you like. I am a number theorist and thus work with a lot of algebra (specifically galois theory) and my coworker and close friend works in analysis; I would never tell him that his field is "less complicated" than mine because every field of math is complicated, you can just go as deep or as shallow as you want. Your argument is that what you learn in an elementary algebra course is just the applications of deeper algebra which is true, but the same applies for introductory calculus: you are just learning the results of real analysis. I think foundations are important but don't be afraid to move on. When I was an undergraduate I skipped my school's intro to proofs class and multivariable calculus to jump straight into undergraduate real analysis and never looked back. I would absolutely recommend others to do the same if they feel they truly love mathematics and are ready for that leap.
I haven’t watched the full video yet but i’s just like to say, as one of those people you’re referring to, it’s not just about looking intelligent, it’s also because i don’t want to interact with people Sad, i should tend to that, but yeah
![[TH] 2024 PMGC League | Survival Stage วันที่ 1 | PUBG MOBILE Global Championship](http://i.ytimg.com/vi/FVFT-PFwU80/mqdefault.jpg)
12:42
When you talk I keep thinking yes it’s so right. I started college again at 27 and I was a total flop at 19 I didn’t have my head straight. Hated school for the longest time. When I wanted to do math, just for studying it, I have fallen in love with the material. The musical instruments analogy is awesome… I learned 8 different instruments and was in 3 band classes, one being zero period. I sucked at school though. I was amazing in band and terrible in life. But I understand why I got better all these years later. I found a real inspiration and desire to WANT to do it ONLY for the sake of doing it. I’m in Linear Algebra and your videos got me reading the textbook for HOURS. You’re a fxxking hero man!!! Screw the TH-cam academy… I’m learning algebra like the guitar… but not to impress some girl. Because I want to learn the powers of the universe and what man has created to help you get as close to it as humanly possible. The textbook has became the coolest thing instead of a big weight in my bag. The explanations of mathematics and arithmetic’s was also very helpful
Bro u are deadass very interesting to listen to
couldn’t have said it much better myself
I appreciate that!
I failed so many math classes due to almost every teacher I had quitting halfway through the semester due to pay. These videos help me so much with learning HOW to learn math, through a mentor that wants to help. Thank you!
Happy to help!
America?
Glad it was helpful! Thanks for the comment! I do a live show every morning and evening at 7:00 AM and 8:00 PM Central (Chicago USA timezone). I address all questions each day from comments here and give shoutouts to those who don't ask a question. Here is the latest live talkshow th-cam.com/users/liveORyy8-EgEX0?feature=share
Thanks for commenting and being a fan! I hope to see you in the next episode.
Author Jonathan David
Thank you so much! Rn I’m taking Calculus 1 class which my professor show us how to follow step by step when solving problems to help us understand. It’s better to take time to learn solving problems using skills such as Algebraic and Trigonometric skills to understand the concept problems without getting ahead.
Glad it helped!
these videos are so underrated. lowkey hoping you stay under radar because im a selfish stem major 😭
I hope they get overrated lol. I gotta pay my bills! Thanks for being a fan
Author Jonathan David
If you would like to help this channel grow and show your support, here are some ways to do so-
Venmo account.venmo.com/u/authorjondt
CashApp cash.app/$authorjondt
PayPal www.paypal.com/paypalme/authorjond
Join TH-cam as a Paid Member (lots of perks!) th-cam.com/channels/dwKRgpXOHvVxlYnqYxXNzw.htmljoin
The Ultimate Crash Course PDF for math and physics with a one-time purchase at payhip.com/b/hc0N9 - all future updates and editions included, so you're always equipped to excel in STEM!
Thank you all so much for your continued support! Without it, this TH-cam channel would have died a long time ago.
All books with access code (limited offer) payhip.com/b/hc0N9
Hardcover Cheat Sheet payhip.com/b/kQ10O
Paperback payhip.com/b/VSOnC
PDF payhip.com/b/lS8nY
Cheat Sheets & Crash Courses
Calculus 1-Differential Crash Course payhip.com/b/F437Z
Both Calc 1 and 2 payhip.com/b/jkn3N
How to Study payhip.com/b/pWrj3
Basic Physics payhip.com/b/y58Sr
Algebra payhip.com/b/r6TmE
Trigonometry payhip.com/b/LV2y8
PreCalc (alg+rig) payhip.com/b/lIbKH
Calculus 1-Differential payhip.com/b/mKsLH
Calculus 2-Integral payhip.com/b/OvCYE
Calculus 3-Multivariable & Vector payhip.com/b/xHU6Y
Linear Algebra payhip.com/b/54on7
Differential Equations payhip.com/b/b6L7k
All Subjects
Both Cheat Sheet and Crash Course payhip.com/b/
“The Author”
Jonathan David
You have a nice way of wording things, it helps to hear layman terms instead of unnecessary jargon.
Thank you for recognizing that. I try to make sense of difficult things.
@@authorjond That’s a wise and intelligent way of teaching. There’s always brilliance in the basics.
Thanks!
im in school currently and watching your videos is helping a lot in developing as a person in college and in the real world. love your videos!
I left a reply for your message in this video- th-cam.com/users/liveA7PhfXfs8-k
You can join me and other people from across the globe at 8:30 PM central time (Chicago US Time Zone) everyday if you would like a more in depth Q&A!
Thanks for watching!
Jonathan
This was me in my early years I struggled with algebra alot and with trig, but I kept grinding and starting building study habits and reconstructing my foundation in math. I left school for a while and now finishing my physics and math degree passed my calculus courses and always review my old work and looking to improve in areas I know needs work. You're right doing almost everyday and you will build the skills
Thank you for your comment! I really appreciate all the feedback. You’ll find my response in the attached video. You can listen there.
th-cam.com/video/3Vz_QZyYx1s/w-d-xo.html
Have a great semester!
∆ Author Jonathan David ∆
Note* This video requires membership to view for the first week, then it is released to the public.
I really appreciate your words! You’re a joy to listen to and thanks for helping my perspective on math and what I really want to do with it. Being a great teacher is magical in itself. Thanks again.
Thanks 😊 I appreciate the feedback
I am halfway through calculus 1. Great video
That's great! Good luck!
It's hard to disagree with what you said, but I fear it may come off a bit rigid.
I started with Serg Lang Basic Math for high school algebra trig in a 'pure math' context. Ignoring everything else until I finished it.
However as a self-studier, I've found the more fundamental things become easier to learn when you have dipped your toe in other areas 'farther' ahead. Now when I learn I am cycling and touching all different areas, I've found that this usually leads me back to Basic Math except this time with purpose for a particular point or subtlety. After having had more anchor points of relevance, and really realising how shallowly I had previously understood it, when I go back to it (with a different perspective given to me by jumping ahead or around somewhere), then I really know it, and it's almost hard to forget.
So in the extreme case, I agree with you, someone literally has no foundation in math they just have to get the most basic stuff down, but I would try to include a caveat for people who have the trunk of the tree, the next levels of branching shouldn't follow the same pattern, in my experience at least, it should become much more free - but maybe that's a personality / cognitive quirk of mine.
I think we sometimes don't sell math right, when it comes down to it, the difference between what mathematicians do vs. what maths is in the minds of most people is feels almost like an injustice.
A lot of people don't know that it is an intellectual exploration, diving in the midnight zone assembling all these alien-looking life-forms through reason alone. I think at some level, showing people things before they have any idea how to work with them is good, it has a level of mystery, similar to how calculus might for the students you mention. But of course in any discussion, wilingness to Do The Work has to be assumed.
All I know is, without being aware of all these cool mysterious things up ahead, I probably wouldn't have had a good reason to work myself.
I'm a rigid guy!
I found a gold. Thanks keep making contents Sir.
More to come!
As someone that is majoring in general science but wants to become an astronomer and is going to take a pre-calc course and a physics non-calc course next semester, this definitely helps. Great video 👍
Awesome! Thanks for being a fan! @authorjond
You're super interesting and fun to listen to. I'm about to enter community college this fall for my first ever semester. I'm not super sure how college works but your video on how to navigate as a STEM major gave me a better view on college. It makes me more enthusiastic that i must depend on my self to actually learn and understand the professor, i really didn't like high-school at all i felt like i had no freedom and i didn't have the skills and habits to go through the motions however i'm building those skills and i feel like this new form of school gives me more of a feeling of control and being able to differentiate myself. Unfortunately i don't come from a super rich family where i can afford to choose just any major without having to worry about job/financial security and if i did i would probably do pure mathematics and physics and become a researcher, that's fine though because math is a skill i intend to use/learn for the rest of my life.
Just make sure that you treat everything with respect and you’ll be fine. Keep yourself a few chapters ahead of each lecture and it’ll be a walk in the park.
Amazing take. I've had the same opinion for a long time but it's the first time I've heard someone say it so elegantly.
8/23/24 Thanks for commenting. Here is my daily video addressing your question or comment. If it was not a question, I gave you a shout out!
th-cam.com/users/livekKOi0DsjImU
Thanks for being a fan!
∆ Author Jonathan David ∆
I think your selling yourself short a bit but message received. Your right that becoming an expert in something is not as mystical as it seems. Still I find people that are experts in anything impressive simply because not everyone is willing to put in the necessary amount of work, even under ideal conditions. I admit though most of the time learning math and physics doesn’t feel like work, it feels like self indulgent puzzle solving. Especially outside of University it’s not a chore, it’s just fun.
Anything is impressive when it takes a lot of work to do. My point is just not to idolize someone that spent 10 years doing something just because you didn’t do it. Because most people have done a lot of things that they’ve mastered that other people haven’t we just pick and choose which things we think are better than others. Thanks for being a fan!
@@authorjond Of course. Your very interesting to listen to, even though I've already graduated from University.
Why thanks 😊
Edit: Revised grammar.
You sound like someone who has been deluded by the societal narrative of STEM field, wanting to receive validation on the work they've put in for their past self-inflicted masochistic behaviors. And to your point about people not wanting to put in the necessary amount of work: Why the f**k would anyone want to put in the work when they are rarely provided opportunities to form an intrinsic value system concerning STEM education? Do you even have a faint understanding of personal interest formation in the context of the broader educational structure?
Also, what do you mean by "ideal conditions"? When you say "ideal conditions", are you even self-aware enough to see that personal CONTEXT may affect the learning process more than you might think? How do you know what you consider to be an "ideal condition" in another person from YOUR perspective is also ideal in THEIR perspective? -- Good luck reaching any depth in a personally meaningful way in whatever field you are pursuing with that attitude.
Yeah, I admit. I'm hella projecting. But I feel it is because I've dealt with many people who think like you do, who tend to perpetuate toxic learning environments outside the educational setting. Case in point: Are you going to find it "simply impressive" of an engineer who became an expert in their respective field to invent a technology just for their own monetary gain or to feed their ego at the cost of YOUR suffering? That's not to say we should vilify and/or abandon the role that money or ego plays in our lives. To me, however, the only imaginable scenario in which you would answer yes to my last question is if you are not wise enough to think for yourself or you share similarities with the hypothetical individual I've described.
Thanks for the analysis!
I subscribed so quickly to this channel your advice is so genuine and you convey it in a way where I really absorb it, definitely a hidden gem in TH-cam! I’m starting off a STEM degree and this exact philosophy is the reason I chose to take it easy and understand a notch lower to calc before I take it.
Welcome aboard!
Awesomely clear exposition of math foundations and understanding in pure math context. Love the rough plastered wall behind you 🎉 . New sub
Glad you enjoyed it! It’s supposed to be a foundation for brick to block sound but the pandemic put a pause on the remodel 😎
I agree that people often overlook the importance of basic arithmetic and algebraic manipulation, but I don’t necessarily agree that students who want to take higher level math courses is a bad thing. For me I’ve always been looking forward to what’s next in math and that’s what’s sustained my interest in math and helped me improve my skills. Specifically in calculus I found a lot of what I didn’t understand in algebra became illuminated within the context of calculus problems. Things like vertex forms of quadratic functions, slopes of functions, exponential functions, etc. Currently I’m taking my second course in Real Analysis and I wouldn’t be studying math right now if I didn’t have that consistent interest in what’s yet to come.
Thanks for the comment! I did a response here th-cam.com/video/mIU3atkABto/w-d-xo.html
thank you for the reality check
You are welcome
Nice video. I completely agree with you when it comes to studying algebra and trig rigorously prior to taking calculus. I was fortunate enough to study my butt off in college algebra II and trigonometry, which made my calculus journey a lot easier. However, I find that the real monster is differential equations!
What's hard about differential equations?
8/23/24 Thanks for commenting. Here is my daily video addressing your question or comment. If it was not a question, I gave you a shout out!
th-cam.com/users/livekKOi0DsjImU
Thanks for being a fan!
∆ Author Jonathan David ∆
i struggle alot with learning math because in my school the books are very bad and skip subjects way too quickyl the books are only workbooks so no explanations and the teacher is always busy
As the science major, your job is to be a problem solver. It sounds like you have a problem you need to solve.
Author Jonathan David
Support your learning journey and help keep this educational channel thriving by leaving a tip - every contribution empowers me to create more valuable content to help you succeed!
Join this channel for $9.99/ month or $24.99/month youtube.com/@authorjond/join
Donate-
Leave a Thanks on TH-cam
Venmo account.venmo.com/u/authorjondt
Cashapp cash.app/$authorjondt
PayPal www.paypal.com/paypalme/authorjond
Patreon www.patreon.com/authorjonathandavid
Check out my custom formula cheat sheets! They are pretty great!
• How to Study payhip.com/b/pWrj3
• Basic Physics payhip.com/b/y58Sr
• Algebra payhip.com/b/r6TmE
• Trigonometry payhip.com/b/LV2y8
• PreCalculus payhip.com/b/lIbKH
• Differential Calculus payhip.com/b/mKsLH
• Integral Calculus payhip.com/b/OvCYE
• Multivariable Calculus payhip.com/b/xHU6Y
• Linear Algebra payhip.com/b/54on7
• Differential Equations payhip.com/b/b6L7k
• Differential Calculus Crash Course payhip.com/b/F437Z
• All Subjects and Crash Course (BONUS Access Code to Download all PDF books) payhip.com/b/aw0b9
Hi Jonathan. I really appreciate the advice that you give. I think young college students should take the time to listen to you :)
Well said!
I'm a Sophomore who took geometry over the summer and have algebra 2 and I'm getting honors algebra 2 next semester. Definitely relate to this.
Good job! Keep up the good work
Hey this was an amazing video - coming from a kid applying to college this fall and wants to double major in math and physics!
Glad you liked it!
i really enjoyed this video. Im a mechanical engineering major getting into calculus. I really like calculus cause it makes me feel like a genius, but i hit a brick wall. I realized that my algebra skills are terrible. Time to go back to Algebra and learn the fundamentals very well. Not in any terrible rush. Do you think I should stress the fundamentals heavily for this field, or just learn what I need and move onto the engineering. I like math but I prefer mechanical
The absolute best way to do this is to take one simple topic, and master it. Then move onto another simple topic and master it. Take it slow at first, and then it will become very easy to master every topic going forward. It’s no different than building any solid foundation.
great vid
Thanks! Glad it help
ya this not knowing alg and trig rlly becomes a problem in calc 3 or physics when u dont understand param equations
Thanks for the words. People need to hear the same from others so it’s real.
Interesting on the YT algorithm. I've actually had the same Idea. I'm starting a CS degree in the fall, instead of jumping directly into Precalculus / Calculus. I decided on taking College Algebra first. Just to make sure I have the fundamentals down first. I've also been self-studying Algebra, Trig, Geometry.
Your plan is pretty much what I recommend to anyone entering stem.
I left college the first time 1 class and a capstone away from a chemistry degree, now I'm in my 30s returning to school for electrical engineering and I started my math self study preparation/review at algebra, despite having passed all the calc classes in the past.
I forget what TH-camr said it, but someone described learning science as building and filling a barrel, each topic is a board on the side of the barrel and water is being dumped into the top. It will fill as high as the lowest board, so as someone just starting, you need to ensure the boards you put on first are tall enough that they don't become the limiting factor later. I hope that metaphor was descriptive enough.
That sounds like a solid plan! Starting with College Algebra before diving into Precalculus or Calculus is a smart move, especially if you want to make sure your fundamentals are rock-solid. Algebra is the foundation for so many concepts you'll encounter later on, and having a strong grasp of it will definitely make the transition to more advanced topics smoother.
It's great that you're also self-studying Algebra, Trig, and Geometry. These subjects are all interconnected, and your self-study will give you a head start as you begin your CS degree. Having a good understanding of these areas will not only help with Calculus but also with many concepts in computer science. It's awesome that you're taking the initiative to build a strong mathematical foundation-it's going to pay off big time!
Thanks for the encouragement! I’m really hoping that starting with College Algebra will help solidify my understanding before tackling more advanced topics. It’s reassuring to know that building a strong foundation now will make things easier down the road.
I’ve been finding the connections between Algebra, Trig, and Geometry pretty fascinating, especially as I start seeing how they all fit together. I’m excited to see how this groundwork will help me with both Calculus and my computer science courses. Thanks again for the support-it’s definitely motivating to keep pushing forward!
@@authorjond What in the chatgpt is going on here
I use it and some videos. But I can take requests.
12:45 - Your instrument mimic comment reminds me of something I heard of called cargo cult programming. Is there any connection?
Which instrument?
0:08 did you just suck up straight air?
Snorted it
Super interesting video! I've taught myself Calc 1, 2 and now on Calc 3. I plan to learn the math that comes after that i.e. Diff EQs, Linear Algebra, etc.
From what I understand Algebra will show up in almost all the further math courses and is needed to tackle advanced topics, is there a book you would recommend for someone to really solidify their understanding of Algebra?
Every course beyond algebra is just applied algebra. And a lot of the stuff in algebra was derived from further applications of algebra lol. Sullivan algebra and trigonometry book is good. Pretty much any algebra book but I like their flow is very straightforward.
@@authorjond Thanks for taking the time to reply! and hope to see more videos coming out of your channel :)
They’ll never end!
So true man great video
Appreciate it
I`ve had many of these similar thoughts...I as well started with physics and switched to math. I definitely agree with arrogance aspect, when I go to social gatherings I`ve learned not to bring up my research and other things I do. As for pure math and applications, I believe some of the most advanced mathematical physics is tending towards utilizing a lot of ideas from Langlands program. Math to me is beautiful but becoming more of a hobby and prefer to work with my hands. Modeling systems, software, finance, etc. is just very boring to me and i`ve dabbled in a bit of it all. You should consider making a series out of this relative topic I enjoyed it quite a bit!
It’s a journey!
If you enjoy my podcast, they will be at this channel going forward. Please subscribe. www.youtube.com/@authorjondpodcast
Sometime around the 8 minute mark you say something like: I’m not an applied mathematician because I wasn’t trained as one, I was trained to teach people the foundations of math so they can go and be applied mathematicians. But don’t you think you should know how to do applied math a little? Love the video !❤
Thanks for the comment! Here is today's replies- th-cam.com/video/_NdEh1eM4tk/w-d-xo.html
Have a great semester!
∆ Author Jonathan David ∆
So, I haven't been in school for 11 years and I'm finally quitting my job to go after my dream degree in physics. I feel I need a restart/refresh on math(starting Algebra again in college instead of jumping into pre-cal). I've had a couple friends who tells me precal covers algebra and to just dive in. Should I dive in, or stick my toes in the water starting fresh?
Thanks for the comment! Here is my reply- th-cam.com/video/Uh471yPtdoA/w-d-xo.html
∆ Author Jonathan David ∆
Please support this channel by ordering an "Ultimate Cheat Sheet for Math and Physics" payhip.com/b/aw0b9 [NOTE- I do live Q&A sessions every night about 8:00 PM Central (US Chicago Time).]
Order by the subject for $9 per subject
• How to Study Guide payhip.com/b/pWrj3
• Basic Physics payhip.com/b/y58Sr
• College Algebra Cheat Sheet payhip.com/b/r6TmE
• Trigonometry Cheat Sheet payhip.com/b/LV2y8
• Precalculus payhip.com/b/lIbKH
• Differential Calculus or Calculus 1 Cheat Sheet payhip.com/b/mKsLH
• Integral Calculus or Calculus 2 Cheat Sheet (includes sequence and series) payhip.com/b/OvCYE
• Vector Calculus, Several or Multivariable Cheat Sheet or Calc 3 payhip.com/b/xHU6Y
• Linear Algebra Cheat Sheet payhip.com/b/54on7
• Differential Equations Cheat Sheet payhip.com/b/b6L7k
Request a Custom Solution authorjonathandavid.com
Donate via Venmo account.venmo.com/u/authorjondt
Donate via Patreon patreon.com/authorjonathandavid
Donate via Cashapp cash.app/$authorjondt
Donate via PayPal paypal.com/paypalme/authorjond
@authorjond sorry to bother. Video says it was removed by author.
Yeah, yeah. I deleted the live stuff. It was messing with the algorithm behind-the-scenes. Everything’s gonna be pre-recorded now except for my life book signing.
i needed this as a high school student lol
Appreciate it! Thanks for checking out my channel! @authorjond
Dope I'm 30 trying get my math up to become an pre engineering student
Just make sure you have a super solid foundation of algebra. Spend more time in college algebra than anything else, and the rest of the courses will be a breeze. If you google a college algebra or you can find a PDF for a college algebra trigonometry or pre-calculus PDF by Michael Sullivan that’s a great book to study. You can master everything in that book, the rest of math will be a walk in the park. The rest of math is applied algebra.
2:45 That's not really true... :/
I started learning calculus when I was maybe around the age of 15 or 16? Because I was really curious as to how the sine function was calculated. They just told me "this is a sine function" and I was like "but how though?" That's a difficult starting point for learning calculus I think, but nonetheless I still became super infatuated with the subject and I still learned it all the same. As long as you get excited every time you discover mathematics you haven't learned yet, you can learn a difficult subject even without knowing prior subjects very well. What you do whenever you find a reference to something you don't know, is you just go look it up, and then learn whatever that is. And then if there's something in that tutorial you don't know, you go look up that concept until you're familiar.
You can go learn algebra as you need to when it comes to calculus, you don't need to be a master at it.
edit: Maybe you'll argue that I don't really know calculus intimately, because I learned it that way. I mean, every technique and theorem, I know the proof to. If you ask me, "What's the proof for chain rule?" I could take you step by step. I know the proof for integration by parts, or the fundamental theorem of calculus. Is that still surface level?? I'm not trying to brag or anything btw. I definitely agree that calculus is not impressive, higher level algebra and analysis is impressive. Calculus is just a simplified and boxed up condensation of those two subjects. I'm just bringing this up because I feel arguments concerning personal experience and evidence would be the most valid arguments to make here.
I think, personally, if you want to learn calculus before algebra, go for it man. That goes for any subject. Just try it regardless of how advanced it is. Don't go in with expectations, don't judge yourself or others for not understanding the subject immediately. Just learn the subject because you personally want to, and don't worry about anything. You're spending your time wisely educating yourself.
I always say, "Nothing said is true."
You certainly can. Without going into extraordinary detail, depending on which advanced subject you choose, it may turn out to be a rabbit hole. There might be so much foundational knowledge you would need to know before you could even begin to understand or start operating confidently in that subject.
I agree that it's sort of a gray area. His thing was music, my thing is weight lifting. You might not be able to lift 200 lbs initially. You would keep adjusting the weight until it's a weight you can bear, but it's also challenging for you. Then you attempt to lift a heavier weight again once you become more comfortable with the weight setting you chose.
I was the arrogant guy. I got through calc 1 in high school and got a 4 on my AP exam. Skipped to Calc 2, then I did Calc 2, Calc 3, linear algebra, differential equations 1, and statistics by the end of the first semester of my sophomore year. Would I say that I knew these subjects well? Not really. I was doing a bunch of classes around them too (about 18 credit hours a semester + I was an undergraduate research assistant.) I just rehearsed enough that I could pass. I was also a computer science major, so I was trying to jump ahead in my CS course work. I think I was on junior level classes really early and was set to graduate a semester earlier.
I jumped into a machine learning course in which they would prove out a bunch of the basic machine learning concepts, and I would see integrals everywhere and gradients. But I wasn't ready for that. I played the music, but I didn't understand the music. I think you understand math best when you're forced to prove something is true as opposed to going through the motions. My math really leveled up when I took proofs and proof intensive courses. Had I took fewer classes and dedicated more time to honing my math, I probably wouldn't have struggled in machine learning.
Anyway, my take on this is, if you choose an advanced subject (for which you may be unprepared,) don't make it your entire focus. Focus on your core mostly but also in the background building up your knowledge around the target field. It'll bite you in the ass eventually otherwise. Also, at some point, you begin to think a lot of what you learned was unimpressive/uninteresting. Oh huh, groups, rings, polynomial rings, fields... pretty trivial honestly.. You might know and understand these things, but they're a mere fraction of the things you would need to know to make a real contribution to anything in mathematics.
Infinity is the longest rabbit hole
Each day I respond to comments live as it is easier to do than writing text that gets misunderstood and leads to anger. You can join or view here th-cam.com/users/liveeXBAvqGlkHY?feature=share
Great video🖤
Glad you enjoyed
Thank you
You're welcome
This is semi-decent advice if you are not actually that interested in math. If you are only looking at the applications of math, sure you want a really good foundation of basic subjects like high school algebra and trigonometry so that you can do quick calculations and understand applications. However, if you are actually interested in pure mathematics there is no reason to stay in algebra for an extended period of time, if you understand the basic concepts you can move on.
You said in your video "algebra is way more complicated than calculus" which is... odd. I would not like to really compare the "complicatedness" of any given math subject because you can basically go as deep as you like. I am a number theorist and thus work with a lot of algebra (specifically galois theory) and my coworker and close friend works in analysis; I would never tell him that his field is "less complicated" than mine because every field of math is complicated, you can just go as deep or as shallow as you want. Your argument is that what you learn in an elementary algebra course is just the applications of deeper algebra which is true, but the same applies for introductory calculus: you are just learning the results of real analysis.
I think foundations are important but don't be afraid to move on. When I was an undergraduate I skipped my school's intro to proofs class and multivariable calculus to jump straight into undergraduate real analysis and never looked back. I would absolutely recommend others to do the same if they feel they truly love mathematics and are ready for that leap.
I always say “anything said is not true.”
Great video you got a new sub
Wutang ain’t nothing to F with!
Do you tutor?
I only accept about five students each semester. Usually for vector calculus, linear, algebra, or differential equations.
Awesome title fr
You already know
I haven’t watched the full video yet but i’s just like to say, as one of those people you’re referring to, it’s not just about looking intelligent, it’s also because i don’t want to interact with people
Sad, i should tend to that, but yeah
Totally can relate.
@@authorjondthank you!
Awesome! Have a great semester!