Learn Mathematics from START to FINISH
ฝัง
- เผยแพร่เมื่อ 8 ธ.ค. 2020
- This video shows how anyone can start learning mathematics , and progress through the subject in a logical order. There really is no finishing point but this will get you through all of the basic undergraduate mathematics from start to "finish". I also included some graduate topics.
Here are the books that showed up in this video(in order) on amazon.
Discrete Mathematics with Applications by Susanna Epp
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Discrete Mathematical Structures by Kolman, Busby, and Ross
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Mathematical Proofs: A Transition to Advanced Mathematics by Chartrand, Polimeni, and Zhang
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An Introduction to Abstract Mathematics by Bond and Keane
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AGS Pre-Algebra
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Fearon's Pre-Algebra
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College Algebra by Kaufmann
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College Algebra by Blitzer
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A Graphical Approach to Algebra and Trigonometry by Hornsby, Lial, and Rockswold
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Calculus by James Stewart
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Calculus by Michael Spivak
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A First Course in Differential Equations by Zill
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Ordinary Differential Equations with Applications by Andrews
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Elementary Linear Algebra by Howard Anton
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Linear Algebra by Friedgber, Insel, and Spence
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Mathematical Statistics by Wackerly, Mendenhall, and Scheaffer
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A First Course in Probability by Ross
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Fundamentals of Complex Analysis by Saff and Snider
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Complex Variables and Applications by Brown and Churchill
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Analysis 1 and Analysis 2 by Terrance Tao
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Advanced Calculus by Fitzpatrick
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Principles of Mathematical Analysis by Rudin
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Elements ofAnalysis by Ross
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Abstract Algebra by Saracino
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Contemporary Abstract Algebra by Gallian
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Introduction to Topology by Gamelin and Greene
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Applied Combinatorics by Tucker
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Naive Set Theory by Halmos
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Functional Analysis by Kreyszig
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Graph Theory by Gould
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Real Analysis by Royden
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Real and Complex Analysis by Rudin
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Linear Algebra by Lang
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Linear Algebra by Hoffman and Kunze
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Algebra by Artin
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Calculus Made Easy by Thompson
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Geometry by Jurgensen
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Schaum's Linear Algebra
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Linear Algebra by Strang
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(the above links are my amazon affiliate links)
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Udemy Courses Via My Website: mathsorcerer.com
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Math is way more fun when you study yourself, not in school. I feel like school just keeps you in this box and makes maths SO dull
Yes way more fun
Yes, but mathematics at university becomes fun because you research on your own and delve into the foundations of mathematics
@الحياة امل no it not fun
it make me depressed learning that way
@@LinhNguyen-my5my I mean self-learning
I don't know because I find research interesting
Damn true 🔥🔥
"We always want to study what we don't have to study"
Oof, guilty.
I know, always happens!!!!!!!!!!
same 😂😂😂
>history test tomorrow
>hmm, lemme study some math
eso es cierto
So true😂👍
I'm an engineer and i can now see how little I've learnt all through school and college, even thought it always felt a lot. The way we are taught maths, just remembering the formulas not why and what they are, it makes it feel like so much more than it actually is. The feeling of truly understanding a mathematical concept and knowing how and where it is applied is priceless.
I live in a developing country in remote farm country. If these books are available electronically, would it be worth purchasing that format?
So true! In my school, we were taught some formulas here and there, but only to work out the problems on the worksheets. Then, we moved on the next unit in order to pass the exams. Most of the grades in the class were validated with homework (60%) and it was only a completion grade. 😂 So my math skills really never developed, despite me being able to advance to the next grade. I want to just start the journey all over again because I do believe this is a life skill that improves the way you generally think or rationalize. This video really comes in handy for that.
@@kig1358 If electronic textbooks are the only option in your country, then go for it. For me, I find learning using ebooks difficult because I need to flip back and forth between pages, and would prefer hardcopy of a textbook.
@@purplecrayon7281 I would prefer the hard copy, but I don't know if sellers will ship to Ghana, West Africa. I have to ask.
@@kig1358 No go for physical books rather than online because the satisfaction u get after completing a have and seeing all those pages u did is just wonderfull,which will encourage u to study more
I know this feels closed-minded and arrogant, but I’ve actually never thought of using a textbook to read from. I’ve been conditioned so badly to just skip and do the problem sets I forget that there’s actually tons of useful information in these things. Thanks for reigniting a passion to learn!
this has been the BIGGEST realization for me as I started to teach myself stuff after school. textbooks have soooooo much good info *on top of* the exercises (perfect blend of theory & practice)
me too, espacially in School. I just do the problems with out an explenation in how to do them. Idk it feels like cheating not beeeing able to get to the solution on your own. Having to read an explenation on the topic bevor. I dont think thats waht you meant but why not
notably those who're still in school studying merely through youtube or any media except big reading. I don't blame them for such mentality (i myself used to be one of those) due to how poor textbook in schools in general, let alone those in 3rd world countries
You're not the only one!
Bro same
I feel like my hate of Mathematics was rooted in my lack of a solid foundation. I've been thinking about studying it again and this video definitely helps in guiding me down the right path.
Math is a language used to describe the world. If you don't have a lot of experience in the world you won't have anything to apply math to except math itself. When math becomes more practical it can be more interesting to people
@@ka0t1k1 10000 times this! I had to circle back to many of these subjects as I got older. It wasn't until much later that I realized that math all on it's own was interesting and useful as Jacob states. It's a language or a lens for understanding and describing the world. When you start to understand some of the math behind something like orbital transits or logic of how computers operate, it really does become a lot more fascinating. Not that I fully grasp all of this, but at least this time around I want to!
Imo school ruins a lot of things.
Learning is natural and fun, school is often the opposite!
Mathematics^2 = solid foundation
You mean teacher or professor who is unmotivated, poorly paid, socially awkward or plain jerk who went to teach, excuse me heal own psychological issues?
Does anyone else feel they really want to study when they are older as compared to when In school ?
👍👍
It’s because now you have the freedom to choose what to study
@@cameronvincent exactly
@yymenghis64 well is your dad german?
You always want what you can't have~
Arithmetic = basic calculation.
Prealgebra = basic application.
Geometry = space calculation.
Algebra = 2d calculation.
Trigonometry = triangle calculation.
Calculus = approximation.
Probability = prediction.
Numerical Analysis = last resort calculation.
The books in videos is that in chronological sequence for study? Or creator just show all the subjects that must learn in mathematics?? I dont understand..
I was always “bad” in mathematics, This year I started learning on my own, I’m in my 30s. This really helped me. Thank you!
How is it going?
What will you do if your not a graduate from math ??
Been a year, how far are we?
@@mohammedriyazansari4462 , why you need to be a graduate if someone wants to learn Mathematics?
Im 30 as well and im about to start my own self learning journey
Mathematics was always slightly more interesting when i wasnt studying for school
Yup!
Absolutely
interestingly, I was always great in mathematics, but I don't have the patience for my math classes, mainly because I live in Brazil and here the private education system is horrible and the public is even worse.
@@user-so8zo5tv5v I agree, the Brazilian educational system is a failure
Sooooo agree with YOU 👍
Math textbooks really be having some of the most out of context covers
😂😂😂😂 trees
LOL THAT SO TRUE. I have a random landscape of snowy terrain on the cover of my math handbook in the last year of high school
Lmfaoo, bro you gotta check out some Accounting books then😂😂 we got birds, buildings, beaches, some paper with a pen on it, and HANDS
@@frankmondo9198 it has truest because it’s applying some examples in real life w discrete mathematics, I guess they’re trying to convey math is everywhere
@@ShawnFX bro my accounting text book got a frog on it 😭😭
Thanks so much for these books. I suffered brain damage years ago in high school and my math knowledge was lost. I'm working to get back to where I was and beyond. I gave up because I would have to build up from literally the beginning. Yet, with these, I know I'll get there! Learning the right way!
Stay strong man
Bro you should document your journey on learning math again ,I am sure a lot of people would be interested
You'll surely reach the heights buddy. Stay strong
I studied math for a while at university, but quickly learned that learning just for the sake of it just isn't my thing. As a mathematician, you really need this special kind of mindset, not caring if what you are doing is actually useful or not. It might be some day, but not necessarily today or even within your lifespan. That's why people like me end up in computer science and electrical engineering 😝
hehehehe
Seriously i m 21 year old and want to restart my schooling in proper way , seriously i want to study math , science and every other subjects from beginning . Subjects are interesting but school makes them only mark oriented. I wish life give me second chance.
Good luck❤️
Same here. I'm an English major but I always hated that I hated mathematics. I want to learn it from the very beginning again, I think it'll help me with thinking more logically, etc.
aw i feel you. i'm a ninth grader and i've skipped all of online classes and cheated on tests this year. now, we're going to have school in person so i want to study everything or i'll fail. and i wish you goodluck. and since you're 21 i bet everyone will be easy for you
*everything. sorry typo
happy to help :) contact me:)
There's free knowledge everywhere... All you have to do is be hungry enough to consume..😁
👍
Wow it won’t be free if you consider your time and efforts as costs.
By Ranchhod Das chanchad(movie 3 idiots)
Stay hungry stay foolish
True 👍
When I was in school I loved math but my depression at the time was too severe and caused me to lack focus. Now that I’m older I’ve gained a new refreshed appreciation for math/STEM as a whole. I wish there were a way where I could teach myself online in an organized manner and receive college credits or certifications without going to college.
Hope you've continued your journey :) congratulations on getting out of that dark place. You can always take a Udemy course or follow some online groups.
CLEP exams can give you college credit for passing exams and the free site modern states has a bunch of courses that will prepare you for each exam and gives a free voucher for the CLEP.
I had a similar experience.
Epp was a professor at my university, started there a year or two after she retired. Her book on Discrete Math is fantastic
Isaac Newton: Invents an entire branch of mathematics during the plague
Me: Eats an entire bag of chips in one sitting during a plague
Haahahaha
Lol ur profile pic has some hair thingy
According to BBC documentary, Newton loved live in solitary instead of congregating with another scientist. In solitary he lived around 12 years alone in home. Furthermore, he didn't respect those who were not good in mathematics especially Robert Hooks.
Newton on Chips.
Arguably a better way to spend your time
The biggest lie I’ve heard and believed for so long was the idea that some people are born to do math and some can’t, believing in this makes you stop trying because its as if it is entirely determined and out of your control. Going back to the basics and really starting from the beginning will help, I never had the right foundation so I struggled whenever the questions would change. There’s no such thing as a “math person”, you can learn anything you want.
Absolutely true! I hear that a lot as a math teacher so I usually try to relate it to any other learnable skill: it just takes time and practice to master.
@@WestExplainsBest when I really wanted to start back with the basics in highschool but didn’t know how I went up to my teacher to ask for help n didn’t understand after he tried explaining so he figured I was just messing about so he ignored me n told me to leave since he was helping other students who were better/more serious abt math. Knowing that even the teacher didn’t think I had a chance kinda shot down any confidence I had to try to learn math again
True. However, some people are smarter than others and grasp things easier
@@randomstix3351 That's why teachers are such an essential part of the learning and why every interaction I have is so important. The best thing teachers can do is work to establish meaningful connections with their students, i.e. care about them as humans, and usually the bad interactions like the one you described can be minimized.
@@ivanr4300 True. As with every other skills, some people have a natural inclination to master it more quickly. The goal should be to elevate everyone's math abilities regardless of how they compare to one another.
Calculate Made Easy is a game changer. Definitely a relaxed read, but incredibly helpful to build intuition.
i just love the way this man talks about maths, with such a passion and energic
Dumb me thought he would teach me entire maths in 18 mins👁👄👁
Haha
I thought he will talk about NCERT ! 🥲
Its not only You🙂
@@avii23 🤣🤣
Same hahahh
I am 53 years old and I have decided to start studying again. I had no foundation growing up and lots people trying to and holding me down. Now I have gotten rid of the dead weight, I am going to start over from the beginning and do it right and for myself. I am going to try this method and ideas. The whole concept of teaching yourself is appealing to me. 😁😁😁
Right on sir!!!
It’s nice to learn when you don’t have tests at the end of the day
aye aye sir...grind on it 💪
me too
Good luck man! You can do it.
I come back to this video whenever I need to be motivated to study. I'm not sure why, but being able to see the road from where I am to where I want to be is very exciting.
I absolutely love the way he talks about Math: beautiful, amazing, interesting. Those words are not familiar to us students who are taught math as a very dull and boring subject. From the bottom of my heart, thank you❤
Math was always the most difficult subject for me in HS, but at the same time it felt more fulfilling when I actually understood it.
Interesting this strategies and learning tips is absolutely indispensable for everyone wishing to explore maths again and forever. Thanks dude
Castro... Nice.
😂😂😂
😂
😂😂
Timestamps
00:00 - *Intro*
00:31 - Discrete Mathematics
02:32 - Mathematical Proofs
03:36 - Pre-Algebra
04:15 - College Algebra
04:58 - Algebra & Trigonometry
06:01 - Calculus
07:46 - Differential Equations
08:30 - Linear Algebra
09:29 - Mathematicsl Statistics
10:11 - Complex Analysis
10:46 - Mathematical Analysis
11:54 - Abstract Algebra
12:25 - Topology
12:42 - Combinatorics
13:04 - Naive Set Theory
13:26 - Functional Analysis
13:43 - Graph Theory
13:59 - Real Analysis
14:44 - Linear Algebra
15:35 - Calculus
16:09 - Geometry
16:27 - Linear Algebra
16:58 - *Outro*
Thank you for this😊.
👍.
Really nice
Thank u 👍😄
Find it weird that Geometry is right at the end when it's one of the first things you learn
I’ve been looking for this video for 10 years now. I’m a resident doctor specialising in obstetrics and gynaecology but math has always been the love of my life
In my mid 40s. And I've been re-learning math as well. I moved countries (three different languages) when I was young, and as a result I have tons of holes in my math education. So I started over again in my mid 40s, now that I have time and the means to do it. I think the advantage this time for me is the fact that I can really dig into areas I enjoy. And with some life experience behind me I think it helps me compared to when I was young learning this stuff with no frame of reference. Anyway thanks for putting this together, I ordered bunch of books using your links. Hope it supports this great channel!
The thing is: math is a language. You should be teached about how to be fluent in it, being able to improvise and to make equations like you write an idea or essay with words. In school/university they only teach you empirically like, put this number here this other here and calculate.
Any resources that teach like this?
@@christucker7425 i an also searching
@@christucker7425 same
@@christucker7425 It is already within your mind via imagination.
@@boyinalabcoatboyinalabcoat393 for more basic math AoPS is wonderful
Discrete math, logic, and boolean algebra are really handy for understanding elementary computer science. Even if you don't study computer science, having some familiarity with the math goes a long way in understanding how a computer works.
So discrete math is a beginner type ?
@@alphawavesready6639 it’s been nearly 20 years since I received my degree. I don’t remember discrete structures requiring heavy algebra and being discrete you don’t use calculus. The closest thing you will encounter are infinite sums. You will be working with set theory which requires a different mode of thinking.
So to sum up while not necessarily beginner math, I don’t see a lot of obstacles that would cause you to give up.
Is it computer science from math field ?
@@adipurnomo5683 yes. It’s more theory and math heavy than a management of IT systems degree. I remember having to do linear algebra and discrete structures specifically as well as statistics and probability which involved calculus.
@@ericbarlow6772 welp, so it is true that compsci is going to be math heavy.
For reference purposes, i keep coming back to this video again and again. This video has truly helped me. Thanks a lot.
Wow, this video is an absolute game-changer! I've scoured the entire Internet and even consulted professors at university to find a comprehensive guide on learning math from the ground up, and I'm thrilled to say, THIS is it! 🙌 Thank you for finally providing the exact path to follow. Your clarity and structure make the journey seem so much more manageable. Grateful to have stumbled upon this gem. Time to dive into the world of math with confidence! 🚀 #MathematicsJourney #GratefulLearner
Tip for high school students: Don't ignore topics in your textbooks just because they are not included in the syllabus. At least go through them
👍
Yeah.
Tip for high schoolers--invent more time in the day so this is feasible
Noop i say learn it all because you need to, well... apart from Geometry and Trig but schools make you learn it lol, but Math easily snowballs and every bit is helpful to understand the harder stuff and that will be the stuff giving you a FAR better understanding of anything even schools throw at you. While learning Math i've been learning it properly and i learn everything except what i don't need and learning everything helps me see the connections and patterns between all the numbers no matter how you use them in a Concept and that helps me more cleverly and easily solve any question thrown my way.
You make it sound like this is just a high school thing.
I regret not focusing more on math
I'm 23 and I feel so left behind
It's never too late I guess
Oh yeah it's never too late, you have soooooooooo much time. I didn't even start until I was 24!! You got this❤️
@@johnathanjohnson7483 thanks, I just realized math is basically all graphs. Everything about math can relate to graphs.
@@ultracrepidarian1456 no that’s not true.
M 28 and have a Masters in Biochemistry and guess who's revisiting undergrad Mathematics?? Meeeeee😂😂😂✌
I'm 33. I started my maths journey last year. Never ever too late.
It is so enjoyable to see you showing these beautiful mathematical books!
I hated math while going through high school but absolutely loved calculus and really liked taking a group theory class. Upper education of math is so different than what they teach you previously.
Is that true I like maths but I keep failing again and again I'm in my 12th grade😢
@tgbraava You probably have a shaky foundation of the basics if you keep failing at 12th grade. This happens commonly if you're a kid for a myriad of reasons, don't worry much as long as you resolve to fix it. Good luck man
8 years ago I tested as having grade 7 math skills. After grade 12 math, I went on to take college algebra. Since then I've been studying chemistry with the goal of getting into a biotechnical program.
Never give up, and don't let people discourage you. I spent years believing the teachers who said I was wasting their time. I'm 37 and a single parent. It's never too late.
never too late!
Hey mate just wanna check up, how are you doing now?
I am also 37, totally screwed up at school at 12 and didn't open a textbook ever since. Did many odd jobs in my teens and twenties.
Became a business owner at 27, but decided that I wanted to know theoretical physics, computer and data science.
But I have two kids and a wife to take care for. So I am setting aside enough money to be able to study for a few years. Now I am done creating a roadmap to learn all that is needed to learn what I want.
It truly is never too late to study.
Good luck to everyone!
Good luck!!
@@TheMathSorcerer Thanks!
And to all kids in here. Better do your best in school now, because when you are an adult it is certainly more difficult. But it's never impossible!
Learn Mathematics from START to GIVING UP.
Rofl
When the book is good, you won't lol
For real lol 😂
That was me when I finished Calc 2 🪦
th-cam.com/video/EMHtNNP6s0A/w-d-xo.html specially for you
recently, I picked up a book about geometry in the fourth dimension, but then I realized that I didn't understand anything outside the thought experiments! That sent me down a rabbit hole trying to figure out what I don't know, but now I'm re-realizing how cool math as a whole is! This is a great roadmap that I will come back to reference :)
Thank you so much! I’ve been out of college for awhile and want to conquer this hill, during college I couldn’t focus completely due to other distractions. I promised myself I’d tackle it again later in life
As a high school math teacher with limited higher level math skills and a penchant for purchasing lots of old math books I sincerely appreciate this video.
Awesome👍
I check out vintage math books at Open Library where you can digitally burrow them and read online. Membership at Open Library is *FREE* and borrowing of ebooks is free too. If I like what I see there, I may order copies and buy them.
Thanks teach.
@@pinklady7184 I also use www.pdfdrive.com
I got TONS of maths textbooks and physics textbooks, chemistry, mechanical engineering, aerospace, all subjects in scienc, science history, programming, computer science, like everything is there to download for free. And it’s totally legal! The books on there have a free license use and published for free. The ones that have copyright infringement get removed! So no guilty feelings by downloading those textbooks.
I got like 30 Gb of textbooks on my cloud storages. Like 1000 textbooks already and I keep hoarding and hoarding.
Sometimes I also get the hard copy edition if I really like the book. I personally love a real book more because you can actually feel it in your hands. But the hard copy textbooks are expensive and I am always on the look out for cheap deals on marketplaces. I love buying maths and science books.
I got so many maths books, I need 10 lifetimes to go through all of them! LOL
@@pinklady7184 Thank you for the recommendation!
Fianally a mathematician humble enough to give book recommendations instead of trying to explain something in yotuube just to show how much he/she knows. You need to be really humble to do this kind of videos. Most of the mathematicians I know feel like the smarty pants kid of the class.
You're focused on the wrong thing. This is one problem people have when it comes to learning. If you want to learn math, things like that should stop mattering to you... How does the teacher treat people? Is he/she being nice? Why are some mathematicians so cocky? These questions will distract from actually putting in the work to understand. Mindset is key.
@@seank8054 The amount of likes my comment has says something about the crappy attitude of most mathematicians and math teachers. Not all but most. Their toxic attitude affects learning for everybody. Many people seem to agree with me.
@@Galbex21 they have a lack of social skills
@@rainypath96 It's the issue of the technician vs the teacher. It's two wholly different skillsets that you have to develop. I've met some people with phenomenal technical skills in their field, yet they fall flat when training and coaching people. I've also met people who were above-average to good in their technical skillset, but were awesome teachers and trainers. Interesting thing that happens though; the great trainers tend to learn more about the subject as they teach it and they get better at it themselves. They may never become the very best in their field, but you'll often find they've trained and coached the people who are.
We're all stupid to some extent, whether lacking emotional intelligence or some other important facet of life!
Dude! I have been looking for something like this for FOREVER! I fell in love with math while studying Biophysics at UC Berkeley in the 80's. I went on to medical school and have been practicing emergency medicine now fo over 30 years. I'm planning to retire soon and I wanted to do more math to stimulate the little gray cells...thank you!
Ed Saff was my professor last semester in differential equations at Vanderbilt. Although I didn’t take Complex Variables, he also wrote a book on differential equations that we used that I also think is really good. It was kind of weird having a professor who wrote the book that we were using for his class.
1.descreate math
2.abstract math
3.algebra
4.trigonometry
5.calculus
6.differential equations
7.linear algebra
8.statistic and probability
9.complex analysis and variable
10.elementary analysis
11.abstract algebra
12.topology and combinatorics and set theory and functional analysis
13.graph theory
14.real analysis
15.geometry
16. database theory
17. cellular automata
18. tensors and AI, image recognition etc
19. game theory
20. cryptography and data compression
... I learned a little bit of everything, because a general understanding of a lot of these is needed to do freelance computer programming...
Ya I forgot to include that👍
12 needs to be broken up
why geometry is on the 15th position ? it must be first!
@@meteor8076 geom is hard man…
I live how you kinda treat them as books ,that you can read for fun, rather than as textbooks.
For sure !!!
GUYS I HAVE A DOUBT HE RECOMMENDED 2 BOOKS FOR CALCULUS AND ALGEBRA (4 IN TOTAL)
SHOULD I DO ALL 4 OR ONLY 2 (1 FROM ALGEBRA AND 1 FROM CALC ) PLEASE GIVE REPLY FAST
@@JourneytoBetterSelf get 2
I have seen a few textbook prefaces or study guides that warn against reading a math or physics textbook as if it were a novel. But, that doesn’t mean you can’t read it as a bedtime book. It’s just that you might not get a lot out of it if you aren’t actively reading and trying the exercises.
@@ru7935 ty :)
Btw u mena 2 total right
I watched this video when it was first posted long time back and I keep coming back to it. This video will be relevant for a few more decades.
Despite how many times I study the topics on our curriculum, I still feel like I'm missing something. This is exactly what I need, thank you very much!
I was never particularly strong in math, until in 7th grade when I started self studying Algebra 1. I took a CBE and jumped 2 years ahead in math. Self studying is the best advice I could give anyone.
If only I knew that 7 years ago.
Cbe?
@@jorayx credit by exam. you take the test and get higher than a 80, it will count as an entire year of math.
Agree, algebra makes a lot easier if you learn it by yourself
Love love love
Book List mentioned in this video
Discrete Math books:
Discrete Mathematics with Application 2nd edition by Susanna S. Epp
Discrete Mathematical Structures by Kolman | Busby | Ross
Proof writing books:
Mathematical Proofs A Transition to Advanced Mathematics by Gary Chartrand, Albert D. Polimeni, and Ping Zhung
An Introduction to Abstract Mathematics by Robert J. Bond and William J. Keane
Pre-Algebra:
AGS Pre-Algebra
The Pacemaker Curriculum Pre-Algebra
College Algebra:
College Algebra 3rd edition Jerome E. Kaufmann
Blitzer College Algebra
A Graphical Approach to Algebra & Trigonometry by Hornby, Lial and Rockwold
Geometry by Jurgensen Brown King
Calculus:
Calculus by James Stewart
Calculus 3rd edition by Michael Spivak
Differential Equations:
A first Course in Differential Equations with Modeling Applications 10th edition by Dennis G. Zill
Ordinary Differential Equations With Applications by Larry C. Andrews
Linear Algebra:
Elementary Linear Algebra 3rd edition by Howard Anton
Linear Algebra 4th edition by Stephen H. Friedberg, Arnold J. Insel, and Lawrence E. Spence
Linear Algebra by Serge Lang
Linear Algebra by Kenneth Hoffman and Ray Kunze
Finite-Dimensional Vector Spaces 2nd edition by Paul R.Halmos
Linear Algebra 3rd edition by Schaum's Outlines
Linear Algebra and Its Application 2nd edition by Gilbert Strang
Statistics:
Mathematical Statistics with Applications 6th edition Dennis D. Wacherly, Wilia Mendenhall III, and Richard L. Scheaffer
A First Course in Probability by Sheldon Ross
Complex Variables/Complex Analysis:
Fundamentals of Complex Analysis with Applications to Engineering and Science 3rd edition by E. B. Saff and A. D. Snider
Complex Variables and Applications 7th edition James Ward Brown and Ruel V. Churchill
Real Analysis:
Analysis I 2nd edition by Terence Tan
Analysis II by Terence Tan
Advanced Calculus A Course in Mathematical Analysis by Patrick M. Fitzpatrick
Principles of Mathematical Analysis by Walter Rudin
Elementary Analysis: The Theory of Calculus
Abstract Algebra:
Abstract Algebra A First Course by Dan Saracino
Contemporary Abstract Algebra 3rd edition by Joseph A. Gallian
Introduction to Topology 2nd edition by Theodore W. Gamelin and Robert Everist Greene
Applied Combinatorics by Alan Tucker
Naïve Set Theory by Paul R. Halmos
Introductory Functional Analysis with Applications by Kreyszic
Graph Theory Ronal Gould
Real Analysis 2nd edition by H. L. Royden
Real and Complex Analysis by Rudin
Algebra by Michael Artin
Calculus Made Easy by Silvanus P. Thompson F.R.S. and Martin Gardner
awesome!
Very underrated comment!
thank you sir !!
Thank you
are they in order, saw the video a while ago but don't remember, also thank you
Thank you bro it is a lot more fun when you don’t have a teacher in front of you and desire the subject.
I’m here 2 yrs late but very appreciative of the book list, as well as the reinforcement that each book does not have to be mastered. I’ve decided to relearn math from the beginning. I stopped with calculus in hs. I really enjoyed it and was able to tutor many of my classmates. However now I’m seeing now abysmal my California public school education was, and math especially. Through youtube I’m seeing so much explanation and enthusiasm, whereas my education was “memorize this, it just ‘is’, and do a hundred repetitions of solving the equation by tomorrow”. I’m not sure there was actual teaching going on at any point!
Math can be very fun when you're not under pressure to perform well on exams under burdening time limits
Very true! I have had exceptionally bright students who simply needed a while to process each problem. Still brilliant students though!
People are getting intimidated by the number and length of the books, but even just a few of the ones at the start would give a non math major a huge boost.
Here’s hoping, just got the 1st book
Except if you want to abolish government and then God
@@vladkuprienko7162 You take basket weaving for that.
@@vladkuprienko7162 that's a tad bit too far from what I'm signing up for here
@@vladkuprienko7162 Fool
Thank you for the layout and guidance, much appreciated. I am starting a self-teaching journey into Mathemetics, and this was helpful.
this is so helpful. I've always wanted to become good at maths because when I understood our classes, it was actually quite fun. But sometimes it was difficult for me to fully understand the material because of the quick pace of the syllabus so I found myself struggling. I don't have math classes anymore but I genuinely want to start at least learning/reviewing my high school math topics.
The Math Sorcerer:- Math is Easy. Anyone can learn math.
Me:- Algebruh
Lol
Algebra is one of the easiest to learn mate.. Its just not taught that way.
self education is the most important thing you learn after you study in college high school or any institutional jailhouse. dont get me wrong college high school is good it builds your character- i don't think it's a waste of time but there are things you cannot do and things you don't do and the schooling doubles that effect so better to take schooling and just make it work and take it positively otherwise you will loathe it in the end when it should be a good exp even when it was bad or worse. make it positive.
Algebruh? It's importand for understand the amazing math universe. Hahaha but it's difficult for me too.
Aklei tension
This is why it’s very important to read, read, read. We are taught to hate math. But it’s fun and you feel great once you’re able to solve the math problems. Great video!
You were taught to hate math?
@@I_would_like_to_buy_an_E Math cannot be understood for most people without strong determination .
@@I_would_like_to_buy_an_E Can you learn? Should we try and help you understand?
@@I_would_like_to_buy_an_E That's great. Are you interested in hard sciences?
@@I_would_like_to_buy_an_E I went to college for hard sciences, but I was a computer nerd for all my life.
I ended up working in computer science for the last 20 years. Mostly in the network admin/security admin stuff, But I also have experience in development. I program almost daily.
Self learning is something I try to do every day.
thank you for a great video, I plan to study mathematics by myself (autodidact/self-study). the goal is want to see how far my understanding can stand with mathematics because when I was in school I used to hate math. Math is super hard, but until one day a mathematics teacher chose me to be part of math olympiad (even though I didn't get into the next step, I was still glad and proud of myself!).
In the other hand, I would like to show that every kids deserve their freedom in thought about finding a fun way in study math. :)
Mathematics was my favourite subject in school and it will always be ❤️
Mathematics is mother of all sciences.
What is the use of this maths in real life ,,,,accept + - %÷×
@@piyushacharya1313you have to get very good at observing, and you can find all sorts of fascinating ways of describing how things are.
That is like asking what is the practical use of having a specialised vocabulary.
With a specialised vocabulary, you can write very specific and meaningful things with thought and hard work,
The same goes for maths, when describing abstract patterns that happen in the world :)
@@piyushacharya1313permutations and combinations, probability and many other topics can be applied in real life
Video starts with "Start to Finish" and I'm expecting addition and subtraction.... and he says we will "Start with learning to write proofs"
Haha
😂😂😂
I thought the same thing
Me too
@@TheMathSorcerer I think the crowd has spoken... We want our how to learn math "Start to Finish" elementary to high school edition!
What confused me about math was always the 'how' of why things work, not the 'why' of how things work. I wanted to know how a formula worked more than what it does.
do proofs
@jshowa o that's cool. what does hard mean? landing on the moon hard or learning to draw hard? because right now I'm in the process of spending hundreds of hours learning to program front end web development
@jshowa o Oh, I knew that. I only very recently started studying web development.
@jshowa o and it's not something every school teaches well
If math isn't proof that we're in a simulation, I don't know what is.
You, sir, are a gentleman and a scholar. No seriously, thank you for this. It's hard even for the most motivated self-learner to find the drive and motivation without some kind of structure. I've been looking for something like this for a long time.
Thank you so much for suggesting discrete math first (i got the first book with the applications). This is what has been missing for my mind to fully absorb mathematics. I got pretty much one of each type of book in this video. I watch this video multiple times because I'm so thankful of your suggestions. I thoroughly enjoy discrete math... math in general, but this one made it all make sense. I wish i studied it years ago
00:00 - Intro
00:31 - Discrete Mathematics
02:32 - Mathematical Proofs
03:36 - Pre-Algebra
04:15 - College Algebra
04:58 - Algebra & Trigonometry
06:01 - Calculus
07:46 - Differential Equations
08:30 - Linear Algebra
09:29 - Mathematicsl Statistics
10:11 - Complex Analysis
10:46 - Mathematical Analysis
11:54 - Abstract Algebra
12:25 - Topology
12:42 - Combinatorics
13:04 - Naive Set Theory
13:26 - Functional Analysis
13:43 - Graph Theory
13:59 - Real Analysis
14:44 - Linear Algebra
15:35 - Calculus
16:09 - Geometry
16:27 - Linear Algebra
16:58 - Outro
Good
You may suck at the game but you’re a Saint 🙏
I had trouble with Outro.
Thank you!!!
Can I download them online?
These types of videos are what everyone needs, but nobody knows what they need. Thanks!
I hated math at school but now at university studying for IT I realize how useful it is, regretting I didn't do it by myself back then. Hope I'll get my hands on all of this in a very short time. Thank you
I devloped severe anxiety because of school and especially math
It was so difficult for me to comprehend It all
I wasn't able to understand concepts and math is like building blocks if you don't have a base you've got absolutely nothing but I love math I truly do I find it extremely beautiful
I want to learn and rid of the pain that has stuck with me from memories of not being able to answer in class and being humiliated
Thank you
Can you imagine learning Mathematics from the start to an advanced level where you are now able to Apply Mathematical knowledge/concepts.. to Business, and become wealthy from doing so.
I've imagined what you described and sometimes it makes you depressed knowing how much more potential so many people could have had if we focused more on locally creating or pursuing independent curricula such as schools specifically specializing in mathematical/STEM training without being bogged down by the red tape of one-size fits all strict standards of 10+ years in general education. Try proposing you're awesome idea to some traditional liberal arts purists ,whom unfortunately run the national gamut, as they get on their intellectual high horse over "well rounded" knowledge because saying the word or suggesting "specialization" or "vocational" in affiliation with a math curriculum would have them think you're an idiot.
Wished humans would lived 1000s of years. Then I would had finished these books slowly slowly taking my time. And not only these but physics and chemistry also
But the funny thing is ... you only need a few years to finish all of these! Because you're no longer stuck on a 4hours of math per week (if that) aka school schedule! You can do 4 hours everyday and you'll be done with all of this and then some in maybe a few years, maybe less ^^
Nerd
@@shoaibakther1453 loser
Yep. Lots of books to read but so little time.
@@kalsieru I do 3 - 4 hrs maths everyday. That's not the point. It's not just maths I wish to learn. I want to learn all of subjects. All knowledge of mankind. But the time I have got in my life is just not enough to do so. There are other things in life too u know except for studies.
There are 3 ways of doing math. Discrete Math is used for exact answers. Calculus and Rounding for approximate answers. Probability for guess numbers. But really calculus can get exact answers because the size of universe are as minuscule
as numbers.
Wow. Absolute wow. Been looking for a list of books from start to finish to learn math. I have a BMath and want ti teach my kids. Thanks!
I've always struggled with Mathematics in school from Elementary all the way to College. This is the subject which I devoted most of my time to, staying up late and then waking up in the early hours of the morning in order to finish my homework. I feel that this is the one subject in school where it is absolutely essential to have a patient and devoted teacher who will guide you through it instead of only focusing on the students who excel at it.
That's a shame that there are very few of them. And by the way, few students who actually go for advice (after putting on the effort of learning) with the teachers - most of the time, the indifference goes both ways and it becomes a vicious circle.
@@hebermoreno7963
All it takes is for a teacher to crush a student's self esteem once or twice and they'll never bother trying again. School made failure a big deal, if I got a bad grade I was mocked by teachers and other students, I had to fear how my family would react and I had to fear my scores not being high enough when finishing the year. It grinds you down and makes you hate trying anymore because you associate learning with inevitable failure and stress.
Failure is a part of learning, it's the act of putting your plans into practice and seeing with your own eyes where and how your method doesn't work which naturally makes you come up with better conclusions. School destroys that, a lot of people grow up thinking that they should never try anything ever because if they're not good at the start, they'll never be good ever.
@@snark567 sadly, I agree with you and can relate to that nonsense competition inside the classrooms from my own story (mainly in junior high school). Nobody teaches you that you have to (and in general will) run out of lots of erasers before actually digging math, and that mistakes and frustration are essential in the process of learning. But here we are, learning it again as adults, with nobody watching.
I’ve realised that my math teacher was focusing more on the equation, not the reason, not the purpose of using it, how to use it and apply it in real life, the beauty of mathematics, like, we were just taught how to solve it, not why to do it and how this and that in things
@@I_would_like_to_buy_an_E wow bro im sure he didnt realize that
Life lesson: every subject is more fascinating and interesting once you leave school and learn yourself. School was the biggest waste of 16 years it was made dull and boring. Science I hated now I have a high understanding of chemistry and physics due to feynman and degrasse tyson.
Homeschooling>the rest
Degrasse Tyson is the main G
And due to walter white too
Its mostly because how they are taught. Luckily got a chemistry teacher who was very much fascinated with the subject itself, he taught us very well, he was a researcher, although it was no requirement for a teacher to be one, I think that's one of the reason he was really good at explaining things about the subject. He would go into the details (that he isn't required to) to explain the intricate details just so that to that it starts making sense.
I liked his teaching because he did not make it plain and boring, and just blabbered theory but he used to provide context, and connect all the things with the real world.
So I think it depends lot on the teacher's qualification, personal interest in the subject, charisma, to be able to engage students in a subject.
And is rightly said by Dr. Walter Lewin- "those teachers who make physics boring are criminals", and I think It applies to all the subjects there are to teach in this world. Either you teach it with great interest and develop students' interest in the subject or you don't teach it at all, because that only creates burden, and wrong opinions are formed about the subject even the subject doesn't deserve it the teacher does.
Aah. Feels good to let it all out now. 😌 Sorry if anyone might be offended but that's just how I feel.
Eh, Im sorry while I like those authors I dont think you can say you know physics and chemistry at a "high level" without college.
Thanks for the tips! I hope I re-learn math and use it in my daily life. I wanted to pursue an MBA but the pre-MBA subjects where mostly math subjects so I got cold feet haha! Where I came from, emphasis was put on the "speed" of solving mathematical problems and less on the how and why we arrived at the answer. Maybe I'm just a slow learner but I will give it one more try.
I’m from Morocco, most (all) of the Maths we studied in school was in Arabic and we didn’t have really this distinction between each maths branch, like we don’t call each branch by its name, we refer to every thing as “maths” and this had put a little bit of difficulty on me trying to learn Maths in English without knowing each branch is about, for this I decided to learn from the start, like really from the start so I can have finally this distinction in my mind
Kano kaytkayaw 3lina 😂😂😂😂
I remember not being a fan of mathematics back in high school (my performance was above average though). Fast forward to university doing my economics degree and I absolutely fell in love with it during my third year to the point where I wished I majored in math instead. I finally saw the beauty that math had _as a language_ and I felt cheated by the school system. It was only after I'd started learning it by myself without any forced study and dry tutoring that I fully appreciated the place that mathematics had in the universe
You said it. I never thought of it before as language learning like when I studied French. But that is what it is and how it should be taught.
Wait till you learn art
Hey! I'm an econ major too and want to re-learn all of math, right from high school math. Any books you recommend to cover everything i should know in math up until year 4 of an econ undergrad degree?
@@leannemartis7180 honestly if you just follow the books recommended in the video you'll have everything you need to know.
How’d you do study math from the beginning?
Idk why I read "Learning Mathematics From Start to Spanish"
Lol
That's how math is to the most of us lol
That's what my eyes saw too. I was like wtf! Lol.
Lol
not Finnish? :'D
Thanks for creating this comprehensive list of 40 books, would have hoped for more in Geometry but thats okay. This is almost a lifetime of learning to master.
I hope to come back to this video in the future with success, because I'm doing maths on my own now, and it just gave me hope
As Mark Twain once said - dont let school interfere with your education. Back in high school here in Eastern Europe (and even earlier in primary) I used to hate math. With the onslaught of time however and the age, I started realizing that not only you cannot live without it but also the type of teaching which we got and the environment which I was in harmed and impacted my way of perceiving math. Hence why consider getting back to the roots. Such videos help a lot, thanks!
👍
Ya either order is fine
The same happened to me. I'm just now attempting to make up for the wasted time.
Any progress since?
Exactly same!
I was pretty bad at maths and school just made me do it for the sake of passing exams. I didn't see the relation of maths with the world back then at all. Just graduated from CS last year with average score and now I see maths being pretty useful, and secondly, since I have a job and see where exactly something is applied I got a pretty good point to define using maths.
And just like he showed in the video, the books are insanely good, I started off with Susanne Epp and it is a mesmerizing book, I've still yet to complete it but I can already understand a lot of math topics on the web and elsewhere.
I'm a behavioral neuroscientist wanting to transition to computational neuroscience. I did calculus in high school 20 years ago, now I cannot solve for x to save my life. Today I have received my copy of Epp's Discreet Mathematics. The journey begins. :)
Good 👍
4 months how's proofs going?
Slower than I would have liked; more fun than I ever imagined.
@@breakthelegacy awesome, I wish you luck!
Hello nice to see your videos. I am really excited to see that someone exactly like me !
Unfortunately due to family reasons I became an engineer, but my love to math during my school days was immense.... even I collected Bourbaki books... regards. From India.
Thanks for this Math Sorcerer! Really helpful for undergraduate math students!
Honestly this was really helpful. I used to be the “smart kid” that kinda burned out in middle and high school. I kinda learned how to bullshit my way through math because I didn’t think I’d major in stem. Then I fell in love with geology and realized how screwed I was needing to not only know math but get into engineering physics classes. I am just barely getting through trig realizing I don’t think I know much of math at all and don’t know where to start because I have a very bad foundation. So thank you! I’ll definitely try to do some self teaching so I can go into this feeling confident!
Yeah, I was so good at every subject in elementary school, I didn't have to do a single piece of homework or study and could ace every test in every subject. Then it got hard and I had no idea to how learn.
@@jaredf6205 yeah i was very good in maths in till my 10th grade. Now as online classes started, all my interest has gone. I didn't study in my 11th grade. Now i am weak in maths
@@jaredf6205 guess I’m not the only one lmaoo
I litteraly could've learned mathematics well if it wasn't for school! I get that some people like school and that's great , but it's not for everyone! I find myself learning many new things and enjoying it outside of the school system! I feel like school didn't do anything for me that benefits in my life today ! Altough i wouldn't say it was a waste of time
School is a place for ordinary people to get a certificate to prove that they have learned certain staff, so that they can get a job or enter graduate studies.
I want to create a daily program for self studying math for this summer and was surfing through my explorer and suddenly your post came up, Just in the right moment! Thanks a lot
This is what I’ve been wanting thank you!
I'm impressed with your level of highly specialized knowledge. As a middle and high school math teacher, it amazes me just how little of the surface we in fact cover of mathematics. Glad there are people like you to teach people beyond their secondary education.
@GRAPHENE IS IN THE MASKS, SWABS and PCR TESTS!!! alright schizo
This is the kind of content I pay my internet bill for
Lol
I graduated with a Bachelors and Masters in Engineering and I still find myself just randomly going over Stewart's 5th Edition Calculus book, loved that book.
This is what I have been looking for, ty. Grew up moving around a lot, changing schools every 1 to 2 years, so I have a lot of gabs in my mah skills. I'm planning on going into mechanical engineering.
I grew up failing at math. Still can’t do it. Yet I click on this video when TH-cam randomly recommends it to me
Hehe it's a step in the right direction!!
Dude! I thought you wanted to share a redemption story
@@mohammadreza5038 haha!! I wish I had one but it just never happened. Math was my one and only Achilles heel. (Still is, unfortunately)
@@rooowtwx This is your chance!
Waiting for a redemption story in a few years.
Lol same. I have never passed math quizz and exam in my entire life.
I'm 21 restarting learning math and it seems like a huge amount of work. I'm re-going-through Stewart's calculus and Spivaks calculus but solving every problem takes over 15-30 hours per chapter.
For what reason? Curiosity ? Or are you looking to get a career using mathematics?
@@robbartlett4426 both ig you could say
It gets crazy long. I remember having 2 days between class, but the assigned homework would take me 40 hours of pencil-to-paper time (I'm a bit slower so it took me longer, other students took 30 hours). Those are times I never want to relive. I would have to all-nighter Sunday through Friday, then sleep Friday and Saturday and start again.
@@zants_ for Stewart's I found the opposite. Sections start having sub 50 questions a lot more. And the difficulty isn't hard.
I haven't done much of Spivaks yet but dang each chapter definitely takes awhile. I did HEAR that it gets easier but apparently that comes down to getting used to the level of difficulty. From my experience with Spivak so far it ain't a joke.
Which book are you referring to, I can definitely believe it taking that long for Spivak. For Stewart's there are long chapters but not too many of them.
I think that's about right when you are self-taught and are learning to LEARN. Wheras school is learning to get a good grade - it's not the same and never allows real opportunity for the lesson to be absorbed and mastered.
I've always hated math and did badly in school like most people, but ever since I started to learn programming, I implicitly began liking the logic and (without knowing) made connections to math. Fast forward a couple of years and I had to take math in college to obtain a diploma for my course, and I actually liked it, despite how hard it was for me (we're talking about going from 8th grade math to differential calculus, set theory and some algebra in a semester...).
Now I've been out of it for a while and working as a software engineer, but due to my interests in math I decided to pick it back up, this time starting with the first book on Discrete Math, and I can't help but notice patterns to programming here, like "that works like a for loop", or "that's polymorphism!".
Self studying this stuff and not being forced to learn it just to pass exams feels really good, hopefully I'll be able to study enough to go to uni either next year or in 2 years for Computer Science and Engineering, which is an area I'm really passionate about (kinda late at 28 years old, but hey... what can you do!).
Thanks Wizard, I feel like this is what I was missing as a software engineer and can't help but want to fill in the gaps, now it's only up to me to make it happen!
Thank you so much for this video. I didn't get a solid foundation for Math at school. A lot of the Math that I didn't understand during high school makes a lot of sense to me now when I do self studies. I was confused where to start. This video is so valuable.
You're very welcome!
@@TheMathSorcerer thanks a lot sir,my foundation in mathematics was vey poor,eventhough i have opted for biology,still i am going to self each mathematics and remove my greatest fears
Self-taught things are more likely to be understandable for me personally
My Maths teachers made me hate Maths, they would just hand us formulas and theories without telling us its significance or why it works.
i used to hate math but since I had and still have a great math teacher i’m actually fascinated by it, and it led me to watching this video. math also helps me so much in physics and stuff, its crazy how I got to look at physics a different way once i finished calculus. I can’t wait to study more math next year in college and by myself
Physics made me look at math differently aha I was acing my physics but failing at math. Make it make sense...
Last time I went to college was 2014- 2015. At that point, the last time I was in a math course was when I graduated high school in 2010.
The teacher of the course I needed to take was russian and I barely understood her. I was so overwhelmed. I literally dropped out and haven't gone back to school since because my fear of being in school and taking these hard courses like maths and sciences and not being able to perform and absorb the information without dampening my GPA.
So I decided, why don't I just teach myself all of the hardest subjects and take as long as possible and don't go back to school until I've already learned it.
This channel has been a Godsend.