You were my professor for differential equations a couple years back, I am now in my final semester for Electrical Engineering. With out a doubt you were by far my favorite and best professor iv had for my entire degree. Thank you
Hey! I'm an electrical engineering student as well, but this is my first semester. I'm tryna keep up with all the mathematics we've got to study and, yk... You went through the same thing. I just have a question: what would it be a piece of advise you'd give a random guy that's studying your same career? I'd appreciate any answer, mate.
@@tomasvelandia6507 I'm also an EE senior and my best advice would be to join an engineering design project/club or research project as soon as possible so you can get some hands-on experience. This will set you up to get internships, make connections, and it will also help you determine if EE (or engineering in general) is really right for you
@@tomasvelandia6507 Been terrible at math my entire life, graduated with my BSEE last year. Use all the resources you can, write "notes" in your notes on what the relationships are and why you are doing the calculations. I'm going to assume you're in the calc series right now. The hardest part about calculus wasn't even the concepts, it was remembering all the algebraic rules which stopped me from focusing on the calculus. The homework problems 1-5 are always the concept questions! Do not take these lightly, they're simple but they really drive home the point of the entire chapter, the rest is just moving numbers around...it will always start off like an example you have seen in class and once you start thinking it gets hard, there is always some trick to either factor out a number or use some trigonometric substitution due to equivalence (VERY COMMON IN CALC 2 /3 ) then it simplifies back to an example problem. Best of luck
@@tomasvelandia6507I graduated with chemical engineering 4 years ago, I’d say get close with your junior/senior year professors, attend program events to network and teach yourself the section before they do it in class
Not gonna lie, I clicked because I saw a dude capable of overhead pressing 35 kg Nothing wrong with my fellow stickmen, but I'm definitely around for some powerlifting lectures
Yeah because gaining big muscles is easy because all you have to do is the same basic repetitions over or an over and over learning. Math is something that is very difficult to do and may actually be genetically limited or innate @@SouthernFriedPapist
First time i saw computer in 1989, my father told me “if you want be master of computer, you should be very good in mathematics”, and my journey start.
I discovered you due to your Spanish channel, as I'm from Spain. I really appreciate your effort, because I'm a student of the first year of the equivalent to bachelor degree with major in mathematics and minor in statistics and I'm struggling to study on my own on my home. I have discovered that books are a really enjoyable and efficient way of learning, thing I didn't even consider during secondary school. Thank you so much!!!
WUT He has a Spanish channel? Must check ASAP Because yo soy de Argentina y la verdad que estudiar matemáticas en ingles no es tan difícil pero me parece mejor idea hacerlo en español!
This channel is fantastic. If you want to learn by yourself you can. All is shown by the Math Sorcerer. You men and women leave TikTok and learn smart thing. Today you can learn everything with the net.
Nice video! I am reminded of back when I took differential equations. (This was long before the internet.) I forget the text that we used (it wasn't Boyce and DiPrima). Anyway, at one point the author casually mentioned the "well-known gamma function." Well, I did not know it. So I went to library to read up on the well-known gamma function. I must have ransacked a half-dozen books to find the well-known gamma function, but every single one of them did not discuss the well-known gamma function. Instead, without any explanation, each book referred to the well-known gamma function as "the well-known gamma function." I think that was the start of my insanity.
For Gamelin & Greene, basic analysis is a must. Both authors have a background in complex analysis, so there is a heavy emphasis on metric spaces (1/4 of the book).
I struggled with mathematics in high school but I think mainly because I couldn't get my questions answered. Might be a good idea to pick up some of these books. Much thanks for the knowledge.
🎯 Key Takeaways for quick navigation: 00:28 📚 *A comprehensive collection of math books covering various subjects from geometry to algebraic topology is available, with resources organized by subject in the video description.* 03:18 📕 *"Beginning and Intermediate Algebra 5th edition" by Elaine Martin Gay is recommended for those starting with basic mathematics, offering thorough coverage and examples for beginners.* 04:28 📘 *"College Algebra Essentials" is a highly recommended textbook for college algebra courses, featuring comprehensive coverage and suitable for self-study.* 05:34 📗 *"Fundamentals of Trigonometry" by Swokowski is suggested for those focusing solely on trigonometry, offering in-depth coverage of the subject.* 06:59 📙 *"Pre-Calculus Mathematics for Calculus" by Stewart, Redlin, and Watson covers pre-calculus topics extensively, serving as a preparation for calculus courses with modern layout and plenty of exercises.* 09:43 📔 *"Thomas Calculus Early Transcendentals 13th edition" by George B. Thomas Jr. is a standard textbook for calculus courses, featuring comprehensive coverage suitable for calculus 1, 2, and 3.* 11:35 📗 *"How to Prove It: A Structured Approach" by Daniel Velleman is recommended for learning proof writing, providing multiple explanations and suitable for self-study.* 13:57 📙 *"First-Order Mathematical Logic" by Angelo Margaris is a comprehensive book focusing on mathematical logic, suitable for those interested in studying logic extensively.* 15:07 📔 *"Elementary Number Theory" is recommended for math majors interested in number theory, covering fundamental concepts and offering a good entry point into the subject.* 16:32 📘 *"Contemporary Abstract Algebra" by Joseph A. Gallian is widely available and recommended for abstract algebra studies, featuring numerous examples and exercises for self-study.* 18:31 📚 *Introduction to Probability by Feller is recommended for beginners in probability due to its clarity, affordability, and comprehensive coverage.* 20:20 💡 *Graph Theory by Ronald Gould is a challenging subject often encountered in computer science or discrete mathematics courses.* 21:30 💻 *Larson and Edwards' Linear Algebra offers a modern, beginner-friendly approach with ample exercises and answers for self-study.* 23:08 📊 *Statistics by Weiss provides a solid introduction to the concepts of statistics, focusing on computational methods and explanations.* 24:17 🎨 *Fundamentals of Complex Analysis with Applications to Engineering and Science by Saff and Snider is recommended for its depth and quality exercises.* 25:55 🧮 *First Course in Numerical Analysis by Ralston and Rabinowitz is a highly rated, comprehensive resource suitable for self-study.* 26:50 📐 *Geometry: A Comprehensive Course by Pedoe is an advanced text suitable for undergraduate or graduate students seeking a deep understanding of geometry.* 27:44 📖 *Elementary Analysis: The Theory of Calculus by Ross offers a gentle introduction to real analysis with clear explanations and detailed proofs.* 28:55 🌐 *Introduction to Topology by Gamelin and Greene is recommended for its clear explanations and rare inclusion of answers to every problem.* 30:18 🧠 *Algebraic Topology by Munkres is a graduate-level resource requiring a strong mathematical background in topology and proof writing.* 31:29 🔍 *Differential Equations by Nagle, Saff, and Snider is a standard text covering both ordinary and partial differential equations with clear examples and answers.* 32:25 🔄 *Partial Differential Equations by Strauss is recommended for its accessibility and comprehensive coverage, suitable for students with a background in differential equations.* 33:05 📈 *Mathematical Statistics with Applications by Wackerly, Mendenhall, and Scheaffer is a comprehensive resource covering advanced topics in mathematical statistics with calculus prerequisites.* 34:30 🛋️ *Functional Analysis by Kreyszig is considered one of the easiest books on the subject, suitable for students with a strong background in proof writing and advanced calculus.* 35:25 📚 *Algebraic Number Theory by Garling provides a focused study on Galois Theory, recommended as a follow-up to introductory abstract algebra courses.* 36:06 🔢 *Fourier Series by Tolstov is a classic text covering the topic with answers provided for many exercises, suitable for students with an interest in the subject.* 37:18 📚 *The book discussed is "Foundations of Modern Analysis" by Friedman, which offers a blend of modern and classical approaches to differential geometry of surfaces.* 38:02 🎓 *Differential geometry might not be a standard course in math degrees, making books like "Foundations of Modern Analysis" valuable resources for advanced mathematics.* 39:10 💡 *"Introduction to Stochastic Processes" by Sheldon Ross is recommended for studying stochastic processes, offering detailed problem solutions.* 40:17 📖 *"Theory of Rings" by McCoy provides accessible explanations and fundamental properties of rings, suitable for introductory understanding.* 41:26 🧠 *"Methods of the Theory of Functions of Several Complex Variables" by Vladimirov covers specialized topics not commonly taught, making it an intriguing choice for advanced mathematics.* 42:38 🌟 *"Basic Mathematics" by Serge Lang offers a unique approach to various math topics, making it engaging and challenging despite its higher price point.* 44:13 🌌 *Ramanujan used an old-school book like "Theory of Equations" to teach himself mathematics, showcasing the power of determination and self-study in achieving greatness.* Made with HARPA AI
I like "Mathematical Methods for Physicists" by Arfken and Weber. It covers a lot of ground and is good for physicists and engineers. Probably not very good as a first course in most subjects, but it doesn't skip on important proofs and concepts, and as a refresher, it is perfectly adequate.
37:57 What do you mean? Differential Geometry was mandatory in my undergrads degree. It was a little tedious at first but then I understood why things were the way they were and I loved it!
The sorcerer's magnum opus ! A magical math book for every math subject ... Sincere thanks ! The ramanujam book seems to be the one book to rule them all and the one book to bind them ... though it simply just doesn't seem that way (except to someone like ramanujam, perhaps) !
Unrelated to the video, but i'll say it anyway: Watching your older videos vs. watching new ones has really inspired me to go to the gym aswell. I've been going for 2 weeks now and it feels really good. You look awesome by the way, seriously. Keep up the grind my friend, I respect you. Great video as always.
There is valuable content in this video. I had never heard somebody talking with so enthusiasm about math books. Here there is an undergraduated in physics paying attention.
How cool! Keep the videos coming I look forward to them every day and they give me tons of motivation and help me to develop a plan in my self studies!
Since people look at the comments a lot, I guess I'll share two books that I recommend: Introduction to Smooth Manifolds by John M. Lee and An Introduction to Differentiable Manifolds and Riemannian Geometry by Boothby. I recommend both of these simply because they're *actually good introductory differential geometry books,* which are surprisingly uncommon (Math Sorcerer also talked about one in the video). John M. Lee wrote three books about manifolds, and the first one is a book on Topological Manifolds (which works great as a prerequisite to either of these books, I think) :3
Yessss, Kreyszig is so good for functional analysis! There's another edition out there with a brown cover that's ~700 pages, which contains more exercises, too. I'd also shoutout Bartle & Sherbert as another great undergrad Real Analysis text, and Royden & Fitzpatrick on the graduate side.
Another great book: An Invitation to Algebraic Geometry by Smith. Algebraic Geometry has a reputation for being very abstract but this book is really accessible to upper level undergraduate students in case anyone was looking for something like that
Jfc dude, you look like me with my networking book pile. I like you for that, and I have not watched a single video of yours. You and your biceps have earned a subscriber.
I love you including the "lower level" mathematics books bc people have to start somewhere but also i am going to teach my kids math at some point (when they exist) and ive been so far removed from that part of mathematics that having strong resources collected like this rules
My was an engineer, old school with a sliderule and drafting table in his office at home, so I grew up with mathematics and I have read a few of these books and also have several Dover books as well
I actually happened to just recently get Pedoe's Geometry. It's definitely a lot higher level than I had anticipated lol. And what you were saying about Complex Analysis has me excited to take it (hopefully next semester). Sounds like a cool course!
I like your recommendations (and used some of them in undergraduate/graduate study in mathematics). Two books I would add are "Numerical Linear Algebra" by Trefethen and "Partial Differential Equations" by Lawrence Evans. I studied numerical analysis (and completed my dissertation in numerical partial differential equations). For younger students - this is an excellent area to study (alongside material in machine learning).
This is a great resource, and I think it is cool that you included the book that Ramanujan taught himself math with! Thanks for sharing all of this! I would like to point out the obvious. Most mortals are not Ramanujan. He was extraordinary! 😉
Lol I never knew you were a muscle wizard in addition to being a math sorcerer. Used to watch your videos all the time when I was in uni, I guess I gotta start watching your videos again when I start going to the gym
I had to take number theory and graph theory in my undergraduate, but I was also in an Applied Math program. I noticed that you didn't mention anything on mathematical modeling nor dynamical systems. Strogatz is of course the one to go to for the latter. I have a great little Dover book I'd recommend to introduce modelling: An Introduction to Mathematical Modeling - Edward A. Bender. In my graduate studies, I took a course on special functions. I have since lost the book I used and don't remember anything other than 'it had a red cover'!
just bought the Basic Mathematics by Serge Lang. Hope going through this with my daughter will rekindle her love for math. She is bored with the lessons from school and I want to keep her moving along and I want to get back into math too. so hope this will be good for both of us. thanks for the recommendation.
When I took Number Theory, my alma mater required Complex Analysis (which required Intro to Real Analysis) and Abstract Algebra. We had a new faculty member teaching my course. So, he just goes hard into it the first lecture. After some students were asking a bunch of questions. He surveyed the class and found out most of the students only either have taken Intro to Real Analysis or Abstract Algebra before the class and we’re currently taking the other. Only two of the students had taken all three prerequisites. He drastically changed his approach after that. He was an interesting character. I had to get an A in that class to graduate with a high enough math GPA to get departmental honors, which I did. I remember that semester very well despite being 23 years ago. So, much was going on.
Re: Graph theory; for us it was part of the Discrete mathematics course (as you mentioned), which started with combinatorics and difference equations in the first half of the year and then moved onto graph theory for the latter half (second year). I'd love to get back into that fascinating subject. Thanks for the book recommendation, it's a paperback, but VERY reasonable price.
@24:01 Nice Statistics book with problems written in English! I learned calculus by myself with the Larson math book. I couldn't do Statistics because the problems in the book used greek letters, I think it was a Larson book too, I had an issue trying to figure out which letters were variables and which letter were symbols. I got frustrated and stopped
I love sitting here at work yelling “Kenneth Ross!!” quietly as you show the Real Analysis book, currently using the 2nd edition in my Advanced Calc courses, very funny to me. You can find PDFs online if money is an issue for purchasing a physical copy.
I took trig in the 1st semester of 11th grade in 1985. Our book was skinny and focused only on trig. I finally figured out why identities killed me, decades later. Teacher didn't cut it, she didn't teach us to phase the sine to get cosine, to divide to get tangent/cotangent, nor to invert to get cosecant/secant. The intuition of the graphs... Math Sorcerer 💯🧠💪
I'm a grad student in Data Sciene and I always feel like I can never get enough math knowledge(don't have a math bachelors) so thankyou for this so much.
I don’t even know what university you are representing but I loved this and I’m buying most of these when I have enough money but just a few now. Finished gallians abstract algebra a year and a half ago and now haven’t used math for a year so I’m working on writing papers on different topics just for the sake of relearning and this is a great jumpstart
Great recommendations. Some of these helped me a lot. In addition, I'd probably recommend Strang's 'Linear Algebra' for his lucid explanations. For analysis, IMO the best intro was Bryant's 'Yet Another Introduction to Analysis' (it's written at a level that most high school students can understand it).
I did not do well with paying attention in class and maintaing the mental energy to keep up with math from 7th grade onward. I cheated my way through high-school to get by and after coming across this video I'm considering starting over at the beginning/intermediate algebra book. It sounds fun to do without a rigorous schedule and curriculum.
I would like to suggest a book, and honestly I would LOVE to hear the Sorcerer's (hah, just found you on youtube and I love the name, lol) opinion on this particular book... I had this as part of my home "library" year ago, but had to sell all my books at one point due to financial difficulties :x. (sucked because they were my prized posessions - all maths, computer science, physics, logic, etc.) Anyway, I decided to start buying books agian a few years later and this was one of the first ones I got. It helped me at one point when I needed a quick brush-up on algebra and geometry, and I was stunned at how quickly that book got me back up to speed. It's so good , in facct, that I think it could be used by folks who have little to no algebra/geometry/trig going into the book. The book is called "Precalculus Mathematics in a Nutshell" by George Simmons (I just realized the first printing was from 1925! hah). ANyway, I was going to describe and link the book, but when I googled the name this video popped up... The beginning is of the book (the newest? one, which is the one I have) and a guy going over the book and showing it's contents. The latter half of the video is him talking about his own course. I'm not sure what all that is about, but I'm just linking the video for the first part where he takes a look at this book. It really is amazing for such a tiny book (under 150 pages for all 3 subjects!) ruclips.net/video/GF4uPKheG14/видео.html
I always thought the Schuams Guides were an organized attempt to cover the landscape of maths in a series of books What about the Princeton Companion to Mathemetics ? I have purchased several illustrated guides to various fields of maths - helps conceptual grokking
I also recommend the Dover books on mathematics or other sciences. I am most interested in graph theory, so I will probably have a look at the book by Gould.
27:36 This reminds me of a somewhat interesting fact about one of my classes. As an engineering major, I took the class in ordinary differential equations required for all engineers. But they didn't call it that. It was listed in the college catalog, and on my transcript, as "Introductory Analysis"! I wonder how many firms that hire engineers, upon reviewing that, wouldn't know what it meant?
Just bought the algebra one online to start my journey! Kinda cool thinking that I'll get a magic book from the other side of the world to learn spells. I tried finding the elementary algebra one from another of your videos online, but the price from Europe was crazy... Even second hand!
I'm shocked at how no kind of advanced number theory seems to be part of standard curriculum in a lot of places... I've had an analytic number theory, as well as an algebraic number theory class after taking abstract algebra and I can definitely say that algebraic number theory is one of the most beautiful applications of ring theory out there and generally just very enlightening.
Algebraic number theory?? I recommend Ireland and Rosen's _A Classical Introduction to Modern Number Theory_ for an "advanced introduction". Then Marcus' _Number Fields_ for tons of exercises. Cox's _Primes of the form x^2 + ny^2_ is gorgeous. For serious p-adic number theory and class field theory, nothing beats Neukirch's _Algebraic Number Theory_ . I Also really like Andrew Sutherland's notes and problem sets from the MIT Number Theory I course on OCW (everything free and available for download!).
Finally a math instructor who is physically muscular and intellectual at the same time in real life. Not the media Hollywood caricature of nerdy tutors, students and instructors who are lanky and physically weak and introverted! Hollywood and the entertainment media missed their stereotypical mark once more. Thank you for showing us the mathematics material on here and thank you for your channel
Well, actually every one should learn maths just like any other language, everyone has its own pace - it never meant that someone is dumb, but just needs more explanation. That's why I found you fast as light and slow as ant. ❤❤❤ Thankyou so much for being on earth, you are a blessed soul with special instinct, you bought Maths - back to my life. ❤❤❤
I was really excited about the "computer exercises" in abstract contemporary algebra, thinking they were programming exercises, but was disappointed to find that they are exercises where you play around with inputs for some pre-built software. Would love some recommendations for math books where the reader does the programming.
You are, without a doubt, engaged in your true passion. But could you do it without the tank-tops? A bit too much the "mad scientist" look for me. Keep up the good work! :)
Personally I'm a creative type, I create something in my head then set out to acquire specific subjects and skills to prove oe disprove it, I used have mindset of a good mathematician is one who learns all math regardless of interest, I soon came to realise that is not the case, a good mathematician has a mission mindset
I'm trying to go through How To Prove It atm, and the difficulty and abstraction REALLY ramp up like crazy in section 4.3. It's actually insane. Some problems I can't even understand what they mean/what they're asking. Others I can but they're extremely convoluted and intricate.
We're using math methods by Boas for our math "boot camp" physics class. You should check it out: it re-introduces series, complex numbers, linear algebra...etc. Anything that a physics major would need. Its free online.
I am a student who loves mathematics very much and I am trying to find my passion. Since I love mathematics, I want to ask you a question so that I can benefit... Is there a complete series of books and mathematics where there is an explanation and history of the theories and how they were discovered, etc.
"Fun" fact: in my high school book the part where you deal with the unitary circle is called goniometry, while trig is defined as goniometry applied to triangles
Really love this vid! Im sitting here watching it while taking notes on which books to get. On proof writing books, I would also recomend a book called A Book of Proof by Richard Hammack. Math Sorcerer recconened it in different vid, said it was free so i got it, studied it and really loved it! You can get a free pdf print out of this book online. Thats what I did at work.
For intro to Abstract Algebra Galian is great, but in my humble opinion the best introduction to the subject is Aluffi’s Algebra Notes from the underground. It is really gentle, and increases the level of nuance of the presentation as the material is developed. There are other two factors that make it my first recommendation: 1) it’s a rings first textbook. (Commutative) Rings are more familiar and easier to grasp than groups for people who haven’t been previously exposef to the subject. 2) it is the only undergraduate textbook in my recent memory that covers modules
idk about yall but the only reason i regret buying munkress instead of this topology book is because the font is the cmu serif latex font and my book is written in times new roman
You were my professor for differential equations a couple years back, I am now in my final semester for Electrical Engineering. With out a doubt you were by far my favorite and best professor iv had for my entire degree. Thank you
Hey! I'm an electrical engineering student as well, but this is my first semester. I'm tryna keep up with all the mathematics we've got to study and, yk... You went through the same thing. I just have a question: what would it be a piece of advise you'd give a random guy that's studying your same career?
I'd appreciate any answer, mate.
@@tomasvelandia6507 I'm also an EE senior and my best advice would be to join an engineering design project/club or research project as soon as possible so you can get some hands-on experience. This will set you up to get internships, make connections, and it will also help you determine if EE (or engineering in general) is really right for you
@@tomasvelandia6507 Been terrible at math my entire life, graduated with my BSEE last year. Use all the resources you can, write "notes" in your notes on what the relationships are and why you are doing the calculations. I'm going to assume you're in the calc series right now. The hardest part about calculus wasn't even the concepts, it was remembering all the algebraic rules which stopped me from focusing on the calculus. The homework problems 1-5 are always the concept questions! Do not take these lightly, they're simple but they really drive home the point of the entire chapter, the rest is just moving numbers around...it will always start off like an example you have seen in class and once you start thinking it gets hard, there is always some trick to either factor out a number or use some trigonometric substitution due to equivalence (VERY COMMON IN CALC 2 /3 ) then it simplifies back to an example problem. Best of luck
@@tomasvelandia6507I graduated with chemical engineering 4 years ago, I’d say get close with your junior/senior year professors, attend program events to network and teach yourself the section before they do it in class
@@tomasvelandia6507 work your ass off in your signals and systems class. Signals are used in a lot of (pretty much all) courses later in your degree
0:00 [Intro]
3:07 Beginning & Intermediate Algebra
4:23 College Algebra
5:20 Trigonometry
6:43 Precalculus
9:32 Calculus
11:31 Proof Writing
13:51 Logic
15:06 Number Theory
16:24 Abstract Algebra
18:39 Probability
20:09 Graph Theory
21:16 Linear Algebra
22:50 Statistics
24:05 Complex Analysis
25:49 Numerical Analysis
26:41 Geometry
27:29 Real Analysis
28:54 Topology
30:30 Algebraic Topology
31:13 Differential Equations
32:11 Partial Differential Equations
32:56 Mathematical Statistics
34:19 Functional Analysis
35:17 Galois Theory
36:00 Fourier Series
36:54 Differential Geometry
38:06 Real Analysis (Graduate)
39:04 Stochastic Processes
40:12 Ring Theory
41:21 Functions of Several Complex Variables
42:30 Basic Mathematics
44:01 Miscellaneous
46:12 [Outro]
Thanks you so much, i was going to do the same comment
What a hero. I was really hoping somebody posted a list like this cause I'm only interested in a couple of subjects :D
Good afternoon, pls can you tell me which one(beginner friendly) will do for MST224 :Mathematical methods
For pnc, log sets relation f(x)?
I am missing algebraic geometry.
It's really nice to see a jacked dude teaching math. It always seems like all the geniuses I see out there don't exercise. Bravo Math Sorcerer!
Not gonna lie, I clicked because I saw a dude capable of overhead pressing 35 kg
Nothing wrong with my fellow stickmen, but I'm definitely around for some powerlifting lectures
Yeah because gaining big muscles is easy because all you have to do is the same basic repetitions over or an over and over learning. Math is something that is very difficult to do and may actually be genetically limited or innate @@SouthernFriedPapist
a true genius is a master of the mind and also the body.
It's either physical health or a nice hair cut. You don't get both.
@@lv1543just making shit up
Look at those guns! 🧠 & 💪🏽 are essential!
I noticed those too😉
Math is essential for working out!
Brains and gains
@@marytredinnick3366Must be from carrying all those math books.
He's gonna cut his hair one day and grow a beard while eating math textbooks for breakfast! ❤😂🔥🫡 epic
First time i saw computer in 1989, my father told me “if you want be master of computer, you should be very good in mathematics”, and my journey start.
16:20 i love how you can see a single line and it blows your mind
I discovered you due to your Spanish channel, as I'm from Spain. I really appreciate your effort, because I'm a student of the first year of the equivalent to bachelor degree with major in mathematics and minor in statistics and I'm struggling to study on my own on my home. I have discovered that books are a really enjoyable and efficient way of learning, thing I didn't even consider during secondary school. Thank you so much!!!
WUT He has a Spanish channel? Must check ASAP Because yo soy de Argentina y la verdad que estudiar matemáticas en ingles no es tan difícil pero me parece mejor idea hacerlo en español!
Same here man
@@dethskullcrusher How ya doin mate
He has a spanish channel! Would you please provide me with the link?
Never underestimate a man who has three or more books on abstract algebra.👍💪
I've 29 books, especially on abstract algebra.J Gallian is good enough,But my favourite one is T.W Hungerford.
@@knowledge_hunter2005 Doing PhD on Algebra or a book collector? I believe 2-3 generic picks suffices, most of the rest is reading papers.
@@kartikpandey8739probably a collector, but can you blame them?😤
Got any math books that are fiction?
@@bryanbryan2968Alice in Wonderland
This channel is fantastic. If you want to learn by yourself you can. All is shown by the Math Sorcerer. You men and women leave TikTok and learn smart thing. Today you can learn everything with the net.
Nice video!
I am reminded of back when I took differential equations. (This was long before the internet.) I forget the text that we used (it wasn't Boyce and DiPrima). Anyway, at one point the author casually mentioned the "well-known gamma function." Well, I did not know it. So I went to library to read up on the well-known gamma function. I must have ransacked a half-dozen books to find the well-known gamma function, but every single one of them did not discuss the well-known gamma function. Instead, without any explanation, each book referred to the well-known gamma function as "the well-known gamma function."
I think that was the start of my insanity.
? Projective geometry? Abstract algebra? Numerical analysis? Special functions? Tensor and vector analysis? Lie groups and Lie algebras? Formal ordinary differential equations? Functional analysis? Calculus of variations? Stochastic processes?
For Gamelin & Greene, basic analysis is a must. Both authors have a background in complex analysis, so there is a heavy emphasis on metric spaces (1/4 of the book).
I struggled with mathematics in high school but I think mainly because I couldn't get my questions answered. Might be a good idea to pick up some of these books. Much thanks for the knowledge.
My friend vance passed calculus 1 thanks to your lectures! he appreciates you so much!🎉🎉🎉
This guy somehow manages to look like Einstein, Jeff Bezos and Vin Diesel at the same time
🎯 Key Takeaways for quick navigation:
00:28 📚 *A comprehensive collection of math books covering various subjects from geometry to algebraic topology is available, with resources organized by subject in the video description.*
03:18 📕 *"Beginning and Intermediate Algebra 5th edition" by Elaine Martin Gay is recommended for those starting with basic mathematics, offering thorough coverage and examples for beginners.*
04:28 📘 *"College Algebra Essentials" is a highly recommended textbook for college algebra courses, featuring comprehensive coverage and suitable for self-study.*
05:34 📗 *"Fundamentals of Trigonometry" by Swokowski is suggested for those focusing solely on trigonometry, offering in-depth coverage of the subject.*
06:59 📙 *"Pre-Calculus Mathematics for Calculus" by Stewart, Redlin, and Watson covers pre-calculus topics extensively, serving as a preparation for calculus courses with modern layout and plenty of exercises.*
09:43 📔 *"Thomas Calculus Early Transcendentals 13th edition" by George B. Thomas Jr. is a standard textbook for calculus courses, featuring comprehensive coverage suitable for calculus 1, 2, and 3.*
11:35 📗 *"How to Prove It: A Structured Approach" by Daniel Velleman is recommended for learning proof writing, providing multiple explanations and suitable for self-study.*
13:57 📙 *"First-Order Mathematical Logic" by Angelo Margaris is a comprehensive book focusing on mathematical logic, suitable for those interested in studying logic extensively.*
15:07 📔 *"Elementary Number Theory" is recommended for math majors interested in number theory, covering fundamental concepts and offering a good entry point into the subject.*
16:32 📘 *"Contemporary Abstract Algebra" by Joseph A. Gallian is widely available and recommended for abstract algebra studies, featuring numerous examples and exercises for self-study.*
18:31 📚 *Introduction to Probability by Feller is recommended for beginners in probability due to its clarity, affordability, and comprehensive coverage.*
20:20 💡 *Graph Theory by Ronald Gould is a challenging subject often encountered in computer science or discrete mathematics courses.*
21:30 💻 *Larson and Edwards' Linear Algebra offers a modern, beginner-friendly approach with ample exercises and answers for self-study.*
23:08 📊 *Statistics by Weiss provides a solid introduction to the concepts of statistics, focusing on computational methods and explanations.*
24:17 🎨 *Fundamentals of Complex Analysis with Applications to Engineering and Science by Saff and Snider is recommended for its depth and quality exercises.*
25:55 🧮 *First Course in Numerical Analysis by Ralston and Rabinowitz is a highly rated, comprehensive resource suitable for self-study.*
26:50 📐 *Geometry: A Comprehensive Course by Pedoe is an advanced text suitable for undergraduate or graduate students seeking a deep understanding of geometry.*
27:44 📖 *Elementary Analysis: The Theory of Calculus by Ross offers a gentle introduction to real analysis with clear explanations and detailed proofs.*
28:55 🌐 *Introduction to Topology by Gamelin and Greene is recommended for its clear explanations and rare inclusion of answers to every problem.*
30:18 🧠 *Algebraic Topology by Munkres is a graduate-level resource requiring a strong mathematical background in topology and proof writing.*
31:29 🔍 *Differential Equations by Nagle, Saff, and Snider is a standard text covering both ordinary and partial differential equations with clear examples and answers.*
32:25 🔄 *Partial Differential Equations by Strauss is recommended for its accessibility and comprehensive coverage, suitable for students with a background in differential equations.*
33:05 📈 *Mathematical Statistics with Applications by Wackerly, Mendenhall, and Scheaffer is a comprehensive resource covering advanced topics in mathematical statistics with calculus prerequisites.*
34:30 🛋️ *Functional Analysis by Kreyszig is considered one of the easiest books on the subject, suitable for students with a strong background in proof writing and advanced calculus.*
35:25 📚 *Algebraic Number Theory by Garling provides a focused study on Galois Theory, recommended as a follow-up to introductory abstract algebra courses.*
36:06 🔢 *Fourier Series by Tolstov is a classic text covering the topic with answers provided for many exercises, suitable for students with an interest in the subject.*
37:18 📚 *The book discussed is "Foundations of Modern Analysis" by Friedman, which offers a blend of modern and classical approaches to differential geometry of surfaces.*
38:02 🎓 *Differential geometry might not be a standard course in math degrees, making books like "Foundations of Modern Analysis" valuable resources for advanced mathematics.*
39:10 💡 *"Introduction to Stochastic Processes" by Sheldon Ross is recommended for studying stochastic processes, offering detailed problem solutions.*
40:17 📖 *"Theory of Rings" by McCoy provides accessible explanations and fundamental properties of rings, suitable for introductory understanding.*
41:26 🧠 *"Methods of the Theory of Functions of Several Complex Variables" by Vladimirov covers specialized topics not commonly taught, making it an intriguing choice for advanced mathematics.*
42:38 🌟 *"Basic Mathematics" by Serge Lang offers a unique approach to various math topics, making it engaging and challenging despite its higher price point.*
44:13 🌌 *Ramanujan used an old-school book like "Theory of Equations" to teach himself mathematics, showcasing the power of determination and self-study in achieving greatness.*
Made with HARPA AI
I like "Mathematical Methods for Physicists" by Arfken and Weber. It covers a lot of ground and is good for physicists and engineers. Probably not very good as a first course in most subjects, but it doesn't skip on important proofs and concepts, and as a refresher, it is perfectly adequate.
37:57 What do you mean? Differential Geometry was mandatory in my undergrads degree.
It was a little tedious at first but then I understood why things were the way they were and I loved it!
The sorcerer's magnum opus !
A magical math book for every math subject ...
Sincere thanks !
The ramanujam book seems to be the one book to rule them all and the one book to bind them ... though it simply just doesn't seem that way (except to someone like ramanujam, perhaps) !
Loving these new videos! Keep it coming, thanks for the good content! 🇮🇹
Unrelated to the video, but i'll say it anyway: Watching your older videos vs. watching new ones has really inspired me to go to the gym aswell. I've been going for 2 weeks now and it feels really good. You look awesome by the way, seriously. Keep up the grind my friend, I respect you.
Great video as always.
There is valuable content in this video. I had never heard somebody talking with so enthusiasm about math books. Here there is an undergraduated in physics paying attention.
How cool! Keep the videos coming I look forward to them every day and they give me tons of motivation and help me to develop a plan in my self studies!
Since people look at the comments a lot, I guess I'll share two books that I recommend: Introduction to Smooth Manifolds by John M. Lee and An Introduction to Differentiable Manifolds and Riemannian Geometry by Boothby.
I recommend both of these simply because they're *actually good introductory differential geometry books,* which are surprisingly uncommon (Math Sorcerer also talked about one in the video). John M. Lee wrote three books about manifolds, and the first one is a book on Topological Manifolds (which works great as a prerequisite to either of these books, I think)
:3
Perfect timing, I was about to email you last night about this very topic! Also sick gains on the arms!
Mathbro flexing the developed delts in thumbnail. Haven’t seen the video yet but keep up the gains mathbro
Wow. Thank you!!! I will recommend these books to my children.
Yessss, Kreyszig is so good for functional analysis! There's another edition out there with a brown cover that's ~700 pages, which contains more exercises, too. I'd also shoutout Bartle & Sherbert as another great undergrad Real Analysis text, and Royden & Fitzpatrick on the graduate side.
Another great book: An Invitation to Algebraic Geometry by Smith. Algebraic Geometry has a reputation for being very abstract but this book is really accessible to upper level undergraduate students in case anyone was looking for something like that
Jfc dude, you look like me with my networking book pile.
I like you for that, and I have not watched a single video of yours.
You and your biceps have earned a subscriber.
I love you including the "lower level" mathematics books bc people have to start somewhere but also i am going to teach my kids math at some point (when they exist) and ive been so far removed from that part of mathematics that having strong resources collected like this rules
My was an engineer, old school with a sliderule and drafting table in his office at home, so I grew up with mathematics and I have read a few of these books and also have several Dover books as well
I actually happened to just recently get Pedoe's Geometry. It's definitely a lot higher level than I had anticipated lol.
And what you were saying about Complex Analysis has me excited to take it (hopefully next semester). Sounds like a cool course!
That author has an unfortunate name
@@mehmetofantalia 😂😂
I like your recommendations (and used some of them in undergraduate/graduate study in mathematics). Two books I would add are "Numerical Linear Algebra" by Trefethen and "Partial Differential Equations" by Lawrence Evans. I studied numerical analysis (and completed my dissertation in numerical partial differential equations). For younger students - this is an excellent area to study (alongside material in machine learning).
This is a great resource, and I think it is cool that you included the book that Ramanujan taught himself math with! Thanks for sharing all of this! I would like to point out the obvious. Most mortals are not Ramanujan. He was extraordinary! 😉
I hope this stays up forever so I can keep coming back to this list. This is so cool for someone rediscovering mathematics.
Thanks for the road map!
Lol I never knew you were a muscle wizard in addition to being a math sorcerer. Used to watch your videos all the time when I was in uni, I guess I gotta start watching your videos again when I start going to the gym
Finally !!! Another video about math books !! ❤
I had to take number theory and graph theory in my undergraduate, but I was also in an Applied Math program. I noticed that you didn't mention anything on mathematical modeling nor dynamical systems. Strogatz is of course the one to go to for the latter. I have a great little Dover book I'd recommend to introduce modelling: An Introduction to Mathematical Modeling - Edward A. Bender.
In my graduate studies, I took a course on special functions. I have since lost the book I used and don't remember anything other than 'it had a red cover'!
I already took all of these classes before I went to medical school. But, I subscribed because you are HUGE! Damn. I gotta get back to the gym.
just bought the Basic Mathematics by Serge Lang. Hope going through this with my daughter will rekindle her love for math. She is bored with the lessons from school and I want to keep her moving along and I want to get back into math too. so hope this will be good for both of us. thanks for the recommendation.
I think it's great when mathematicians have good muscles, good job man. I think professors hate that, because they refuse to lift weights.
When I took Number Theory, my alma mater required Complex Analysis (which required Intro to Real Analysis) and Abstract Algebra. We had a new faculty member teaching my course. So, he just goes hard into it the first lecture. After some students were asking a bunch of questions. He surveyed the class and found out most of the students only either have taken Intro to Real Analysis or Abstract Algebra before the class and we’re currently taking the other. Only two of the students had taken all three prerequisites. He drastically changed his approach after that. He was an interesting character. I had to get an A in that class to graduate with a high enough math GPA to get departmental honors, which I did. I remember that semester very well despite being 23 years ago. So, much was going on.
I need to bookmark this video, it such a great overview of maths books!
Re: Graph theory; for us it was part of the Discrete mathematics course (as you mentioned), which started with combinatorics and difference equations in the first half of the year and then moved onto graph theory for the latter half (second year). I'd love to get back into that fascinating subject. Thanks for the book recommendation, it's a paperback, but VERY reasonable price.
THE book on graph theory is Richard Diestel. It’s not a debate.
@24:01 Nice Statistics book with problems written in English! I learned calculus by myself with the Larson math book. I couldn't do Statistics because the problems in the book used greek letters, I think it was a Larson book too, I had an issue trying to figure out which letters were variables and which letter were symbols. I got frustrated and stopped
I love sitting here at work yelling “Kenneth Ross!!” quietly as you show the Real Analysis book, currently using the 2nd edition in my Advanced Calc courses, very funny to me. You can find PDFs online if money is an issue for purchasing a physical copy.
Very, very, very helpful video. It was very interesting to look at the books you recommend. Now I wish I had them all in my library.
I took trig in the 1st semester of 11th grade in 1985. Our book was skinny and focused only on trig. I finally figured out why identities killed me, decades later. Teacher didn't cut it, she didn't teach us to phase the sine to get cosine, to divide to get tangent/cotangent, nor to invert to get cosecant/secant. The intuition of the graphs...
Math Sorcerer 💯🧠💪
I'm a grad student in Data Sciene and I always feel like I can never get enough math knowledge(don't have a math bachelors) so thankyou for this so much.
I like to imagine math sorcerer llifting all his books for workout and reading some of them at the same time. Absolute chad
That’s the same calculus book we used for my engineering calculus course during undergrad! I actually thought it was a solid book
nice!!!
@@TheMathSorcererSir, where can I send you email?
I don’t even know what university you are representing but I loved this and I’m buying most of these when I have enough money but just a few now. Finished gallians abstract algebra a year and a half ago and now haven’t used math for a year so I’m working on writing papers on different topics just for the sake of relearning and this is a great jumpstart
Great recommendations. Some of these helped me a lot.
In addition, I'd probably recommend Strang's 'Linear Algebra' for his lucid explanations. For analysis, IMO the best intro was Bryant's 'Yet Another Introduction to Analysis' (it's written at a level that most high school students can understand it).
Both excellent books!!!!!!
The geometry book isn't Regular Polytopes by H. S. M. Coxeter? It's the geometry bible!
I did not do well with paying attention in class and maintaing the mental energy to keep up with math from 7th grade onward. I cheated my way through high-school to get by and after coming across this video I'm considering starting over at the beginning/intermediate algebra book. It sounds fun to do without a rigorous schedule and curriculum.
Great list of books! will definitely be getting these for myself! Thank you Prof!
I would like to suggest a book, and honestly I would LOVE to hear the Sorcerer's (hah, just found you on youtube and I love the name, lol) opinion on this particular book... I had this as part of my home "library" year ago, but had to sell all my books at one point due to financial difficulties :x. (sucked because they were my prized posessions - all maths, computer science, physics, logic, etc.) Anyway, I decided to start buying books agian a few years later and this was one of the first ones I got. It helped me at one point when I needed a quick brush-up on algebra and geometry, and I was stunned at how quickly that book got me back up to speed. It's so good , in facct, that I think it could be used by folks who have little to no algebra/geometry/trig going into the book.
The book is called "Precalculus Mathematics in a Nutshell" by George Simmons (I just realized the first printing was from 1925! hah). ANyway, I was going to describe and link the book, but when I googled the name this video popped up... The beginning is of the book (the newest? one, which is the one I have) and a guy going over the book and showing it's contents. The latter half of the video is him talking about his own course. I'm not sure what all that is about, but I'm just linking the video for the first part where he takes a look at this book. It really is amazing for such a tiny book (under 150 pages for all 3 subjects!)
ruclips.net/video/GF4uPKheG14/видео.html
I used to go up t9 Barnea amd Novles and read the Dover math books when I was younger.
I'm not interested in math but I'm just glad this guy popped up on my feed. He clearly just wants to share knowlege.
I once had this math professor who was super jacked that you remind me of
I always thought the Schuams Guides were an organized attempt to cover the landscape of maths in a series of books
What about the Princeton Companion to Mathemetics ?
I have purchased several illustrated guides to various fields of maths - helps conceptual grokking
I’m working my way through the first book you reviewed and I was able to snag the 9 DVD set of instructional videos that accompanies it.
I also recommend the Dover books on mathematics or other sciences. I am most interested in graph theory, so I will probably have a look at the book by Gould.
This is exactly what I needed , thank you master 😊
27:36 This reminds me of a somewhat interesting fact about one of my classes. As an engineering major, I took the class in ordinary differential equations required for all engineers. But they didn't call it that. It was listed in the college catalog, and on my transcript, as "Introductory Analysis"! I wonder how many firms that hire engineers, upon reviewing that, wouldn't know what it meant?
Professor Sorcerer, thank you for an outstanding video/lecture on One Math Book for every Math Subject.
Good video! really interesting for any anyone who wants to gain some understanding in entry to mid level mathematics. Thx!
Just bought the algebra one online to start my journey!
Kinda cool thinking that I'll get a magic book from the other side of the world to learn spells.
I tried finding the elementary algebra one from another of your videos online, but the price from Europe was crazy... Even second hand!
I'm shocked at how no kind of advanced number theory seems to be part of standard curriculum in a lot of places... I've had an analytic number theory, as well as an algebraic number theory class after taking abstract algebra and I can definitely say that algebraic number theory is one of the most beautiful applications of ring theory out there and generally just very enlightening.
Algebraic number theory?? I recommend Ireland and Rosen's _A Classical Introduction to Modern Number Theory_ for an "advanced introduction". Then Marcus' _Number Fields_ for tons of exercises. Cox's _Primes of the form x^2 + ny^2_ is gorgeous. For serious p-adic number theory and class field theory, nothing beats Neukirch's _Algebraic Number Theory_ . I Also really like Andrew Sutherland's notes and problem sets from the MIT Number Theory I course on OCW (everything free and available for download!).
Brother, the best book for beginners in group theory ...... P. S. ALEXANDROFF an Introduction to the THEORY of GROUPS
I love these longer videos!
Finally a math instructor who is physically muscular and intellectual at the same time in real life. Not the media Hollywood caricature of nerdy tutors, students and instructors who are lanky and physically weak and introverted! Hollywood and the entertainment media missed their stereotypical mark once more. Thank you for showing us the mathematics material on here and thank you for your channel
Im glad this video showed up. I really want to learn math and I have a mental block with learning math maybe
Well, actually every one should learn maths just like any other language, everyone has its own pace - it never meant that someone is dumb, but just needs more explanation. That's why I found you fast as light and slow as ant.
❤❤❤ Thankyou so much for being on earth, you are a blessed soul with special instinct, you bought Maths - back to my life. ❤❤❤
I was really excited about the "computer exercises" in abstract contemporary algebra, thinking they were programming exercises, but was disappointed to find that they are exercises where you play around with inputs for some pre-built software. Would love some recommendations for math books where the reader does the programming.
You are, without a doubt, engaged in your true passion. But could you do it without the tank-tops? A bit too much the "mad scientist" look for me. Keep up the good work! :)
Personally I'm a creative type, I create something in my head then set out to acquire specific subjects and skills to prove oe disprove it, I used have mindset of a good mathematician is one who learns all math regardless of interest, I soon came to realise that is not the case, a good mathematician has a mission mindset
I'm trying to go through How To Prove It atm, and the difficulty and abstraction REALLY ramp up like crazy in section 4.3. It's actually insane. Some problems I can't even understand what they mean/what they're asking. Others I can but they're extremely convoluted and intricate.
We're using math methods by Boas for our math "boot camp" physics class. You should check it out: it re-introduces series, complex numbers, linear algebra...etc. Anything that a physics major would need. Its free online.
Sir,I am form India your book colection is
Very nice book colection for maths
We appreciate your insights. Keep working hard.
“With effort, great things can be accomplished.” I love that. 💪
thank you for your effort in keeping up this channel
This is an awesome resource! Thankyou!
You have amazing determination, keep up the good work 👍
bro is telling us to do math and flexing both at the same time, perfect way to get an people into math honestly
What drives you to offer free content for the world?
We are indebted.
I am a student who loves mathematics very much and I am trying to find my passion. Since I love mathematics, I want to ask you a question so that I can benefit... Is there a complete series of books and mathematics where there is an explanation and history of the theories and how they were discovered, etc.
"Fun" fact: in my high school book the part where you deal with the unitary circle is called goniometry, while trig is defined as goniometry applied to triangles
Really love this vid! Im sitting here watching it while taking notes on which books to get. On proof writing books, I would also recomend a book called A Book of Proof by Richard Hammack. Math Sorcerer recconened it in different vid, said it was free so i got it, studied it and really loved it! You can get a free pdf print out of this book online. Thats what I did at work.
My professor used Freund's Mathematical Statistics for a one year course in Probability and Statistics. He covered the whole book.
I love your video so much!!! thanks for the advice.
For intro to Abstract Algebra Galian is great, but in my humble opinion the best introduction to the subject is Aluffi’s Algebra Notes from the underground. It is really gentle, and increases the level of nuance of the presentation as the material is developed. There are other two factors that make it my first recommendation:
1) it’s a rings first textbook. (Commutative) Rings are more familiar and easier to grasp than groups for people who haven’t been previously exposef to the subject.
2) it is the only undergraduate textbook in my recent memory that covers modules
I know this has nothing to do with the topic, just wanted to say : You are in great shape!
idk about yall but the only reason i regret buying munkress instead of this topology book is because the font is the cmu serif latex font and my book is written in times new roman
Thank you, buffed Kirk Hammett!
I guess I finally see some basis for base chemistry. What kinds of geometries? I can’t pick just one book for that!
Not gonna lie i'd love to see those weird math books you speak of when you are talking about vladimirov's book. Great video as always sorcerer.