How to self study pure math - a step-by-step guide
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- čas přidán 5. 06. 2024
- This video has a list of books, videos, and exercises that goes through the undergrad pure mathematics curriculum from start to finish.
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REAL ANALYSIS
Book: “Understanding Analysis” by Stephen Abbott.
Videos: Lectures by Francis Su ( • Real Analysis: Lecture... )
LINEAR ALGEBRA
Book: “Linear Algebra Done Right” by Sheldon Axler
Videos: Sheldon Axler’s Playlist
( • Linear Algebra Done Right )
POINT SET TOPOLOGY
Online Notes with Problems: MAT327 Course Notes (www.math.toronto.edu/ivan/mat3...)
COMPLEX ANALYSIS
Intro Book: “Visual Complex Functions: an Introduction with Phase Portraits” by Elias Wegert
More Technical Book: “Complex Analysis” by Serge Lang
Videos: Wesleyan University Playlist ( • Playlist )
GROUP THEORY
Book: “Topics in Algebra” by Herstein (Chapter 2)
Videos: Lectures by Benedict Gross ( • Abstract Algebra )
GALOIS THEORY
Notes by Tom Leinster: www.maths.ed.ac.uk/~tl/gt/gt.pdf
DIFFERENTIAL GEOMETRY
Book: Introduction to Differentiable Manifolds and Riemannian Geometry by Boothby
ALGEBRAIC TOPOLOGY
Book: Algebraic Topology by Allen Hatcher (available for free on his website: pi.math.cornell.edu/~hatcher/...)
Videos: Lectures by Pierre Albin ( • Algebraic Topology: a ... )
Intro: (0:00)
Linear Algebra: (0:36)
Real Analysis: (2:20)
Point Set Topology: (3:19)
Complex Analysis: (4:09)
Group Theory: (5:46)
Galois Theory: (6:54)
Differential Geometry: (7:23)
Algebraic Topology: (8:44)
Thanks for watching! If you have any resources you'd like to recommend, feel free to comment them down below.
Also, I have a math newsletter where I collate resources to learn topics in math / machine learning and deliver them to your inbox. If you'd like to sign up for the newsletter, fill out this form: forms.gle/Rt1f5StAj3yZtakE6
I used the organic chemistry teacher to get me started in math, because I have a GED to take. I actually like math now
As a person who has to rely on self-study quite often, the thing that grinds my gears is when textbooks are written without a solutions manual. Since solving problems is pretty much the core of mathematics, having the ability to check if you are on the right path or getting a slight push when stuck on a problem is of tremendous help when self-learning and not having an instructor. All of the arguments against having solution manuals don't hold any water in my opinion.
Hopefully, in the future, it will be standard to have solutions to problems at the end of each textbook.
I agree 100%. Personally, I have absolutely no motivation to do the exercises if I have no way of knowing if I did them correctly.
@@marcoskrupiczer6595 eh I don't think that mindset is going to be helpful if you ever want to do research, but I see where you're coming from .
@@kingarth0r dont be pretentious. Research and grad school is about solving previously unsolved problems over the course of months/years. Learning a well known and well studied topic and then doing a few practice problems to solidify your understanding is obviously a completely different endeavor. No one should be wasting their time re-inventing the wheel. step 1 is to stand on the shoulders of giants, and step 2 is see how much higher you can reach. That's why lecturers and universities exist.
@@psd993 beautifully put. I just wanna play the devil's advocate and claim that a solution's manual can be harmful if the learner lacks maturity, say a highschooler for example. Doing exercices is a lot about making mistakes and false starts, discovering one's weak points and lack of understanding and applying old knowledge in new settings. I remember as a kid I'd reach for the solution's manual at the first obstacle and that hurt me. As an adult I know to jump over an exercise and come later letting my subconscious mind do its part. Often times I'd come up with a solution that wasn't the same as author's or I'd revisit parts of the book or course and consolidate my weak understanding of the topic.
@@kingarth0r the difference is that when you are a researcher your work goes through a peer review process where your results receive feedback and criticism from other researchers. The results of research are never discussed individually.
As someone who is depressed, this is the most joyful video I have watched in a long time. Thank you for posting this.
... what
I don't mean to offend you, but this is not a wholesome video or something... It's a math learning guide, how does that cheer you up
Lmfao
Bot
math gives this feeling of certitude and determinism that equations embodies, learning a new concept and solving a problem also has a unique feeling to it, totally understand it.
@@Sciencedoneright welcome to aesthetics. In case you haven't noticed, it's quite subjective.
Should keep me busy for the next 5 years
I would have liked to see this video like 25 years ago. All this material free online. What a wonderful time is today. I want to thank you in the name of humanity.
That’s true
This makes me very happy. I studied comp sci at uni but have been trying to learn some higher math on my own lately. The specific resource recommendations are extremely valuable to me. I consider this a Christmas gift!
same boat. i need a lot of math in my research that my CS degree simply didn't prepare me for. These kind of resources are amazing!
Plz help those students who can't go to school in this corona pendamic one click for them
i am pursuing an undergrad cs degree. what sort of math should i be learning myself that my degree wont have in its syllabus?
@@ashwinjain5566 Depends on the program and ur research area. What I find most useful is Advanced Linear Algebra, Differential Geometry, Topology, Tensor Calculus, Advanced Probablity Theory with a bit of Measure theory, Continuous + Convex Optimization
man, i want the same for this year.
I appreciate how you didn't overload us with resources but gave it straight forward. Much much more appreciated than the channels that throw tons of books or resources.
As a theoretical physics graduate student, I can strongly recommend the textbook "Differential Geometry, Gauge theories, and Gravity" by Gockeler and Schucker to understand differential geometry with just a physics undergraduate background, where the book introduces but also applies this subject to numerous areas of modern physics - I really recommend it!
Also, if you're a physics student and don't really know where to start, I would strongly recommend "Modern Mathematical Physics" By Szekeres which basically introduces from the ground up and assuming no prerequisite all the parts of maths you need to do physics at an advanced level. Hope it helps :)
Nakahara's _Geometry, Topology, and Physics_ is an excellent text as well. What it lacks in readability, it more than compensates for in completeness and rigor, explaining everything from vector spaces to cohomology to differential forms. Wholeheartedly recommend it as a referrence text for the physicist or physics-adjacent mathematician.
perfect timing
Are you also graduated from MIT,and perhaps your name is gordon?
I just finished fourth year quantum. I was confused by the linear algebra book that didn't talk about determinants.
Wow thank you! Excited to start Szekeres
I'm extremely overjoyed to have found this video. I've been wanting to self-study pure maths (with some physics as a little treat) for a year or two now, and am currently strengthening my foundational understanding of the basics, but was bumbling through the undergrad stuff with the help of the MIT courses and Stack Overflow. I'm incredibly grateful that you included videos alongside the textbooks, since I tend to learn better with a combination of both (but mostly the former). This video is like finding an oasis in the midst of a desert, thank you so much!
This video is left as an exercise for the reader.
Please don't take this video verbatim. It follows the British system, and it's not very accurate. In most countries a math degree is 4 years, not 3. There are much better books than the ones nentioned in the video, which include also solution manuals, such as Spivak's, Fraleigh's, etc. (i don't see why one shouldn't use determinants!). The video ommitted basic pure math courses, such as Number Theory. An Abstract Algebra course is a must, and it would include both Group Theory and Galois Theory mentioned above, plus more (rings, fields, etc). Some of the courses he mentioned are not necessary for a basic pure math degree. Such as Algebraic Topology. Finally, a course in History of Math is always important so one can see all these topics in perspective.
I disagree that history of maths is important if you want to understand pure mathematics. But you are right that a general abstract algebra course is missing here. Rings and fields (and to a lesser degree, modules) are so important to understand. Also number theory lacks a mention which I find an odd choice.
Thank you for the video. I wish CZcams had a "love" button. Please don't remove the previous version of this video from the channel. It was so informative and helpful. Just add "2020" or something in the title. I love that video too! Like this comment if you want that video back.
I think he already removed the previous version (people in the comments were insufferable, I think that s why). I m really glad he made a new version though
@@everlastingideas8625 what was in the previous version???
The one-sentence-descriptions of these subjects are just pure gold.
Great video! As someone who got an undergraduate degree in math, many of the resources here are excellent resources that I made good use of. I look forward to checking out the others to fill in the gaps on some of my weaker subjects.
Where did u graduate & what r u doing currently?
Malayali aanalle. Naatil evideya?
As some one in an engineering major we study just as much math and its PAINFUL!!
@@dontreadmyusername6787 you're not studying as much maths as a maths undergrad
@@sandraaiden8587 maybe but there's a lot of math in electrical engineering
this is my favorite math channel by far, your voice is soothing and your explanations are always easy to follow.
DUDE you are an incredible content creator! Not only finding all the resources that best help newbies into classic maths, but also providing insight into their way of teaching!
Thank you for bringing all this together, true hero! Your voice is wonderfully relaxing too!
As someone who's doing a degree in mechanical engineering but has a very strong passion for pure math I very much appreciate this video, as well as yours and everyone else's free and amazing videos on many different math topics all across youtube.
Keep up the great quality!
lol why didn't you go into math? engineering is like the antonym of math
@@mastershooter64 You'll maybe encounter some day people with more than one interest. It's my case, too, I'm a student in microengineering and I have a strong passion in pure math
@@mastershooter64 it was hard to find a good and affordable university, I didn't have faith in my math knowledge enough to enroll into a pure math class, my passion for physics is not any lesser, and last but not least, it is significantly easier to find an enjoyable and well payed job with an engineering degree from everything that I've seen.
I would say engineering is an offshoot of mathematics or it is essentially mathematics with a different name. Many famous equations/relations in Mec.Eng are derived by mathematicians instead of engineers themselves. For example Prandtl , Blasius, Navier ,Stokes etc.
@@hussainsallar3355 Not to mention that at that time those people were really not one or the other but both, mathematicians and engineers, and sometimes also worked in other fields as well. Scientists in general (including many mathematicians and engineers), were really just called "Natural Philosophers" until the middle to end of the 19th century.
That is actually one of the things that really attracts me to maths, it is not only very interesting on its own, but it is also a quite universally powerful instrument for the study of any other science. That is why I intend to pursue a masters in Applied Mathematics after I finish my bachelors in mechanical engineering.
Hey. I just want to say you've really inspired me to get back into self studying mathematics. I had done a lot of self study in the past, when I had much less mathematical maturity, and got discouraged, in part because I kept skipping prerequisites and the like. Thank you for this and other videos.
This video is pure gold. Thank you so much for putting this resource together!
This video collects lots of useful online resources and recommended textbooks. The content is clear and well-structured and I appreciate your work to illuminate a way to learn pure mathematics!
wow this is exactly what I was looking for just now, can't believe it was uploaded today! thanks for this!
Calculus by Michael Spivak (Third or Fourth edition) is unexpectedly a really good introduction to not just real analysis, but also some number theory and a little abstract algebra at the end of the textbook. It doesn't require any prerequisites, as stated by the author (I think). It also justifies most theorems that are brought up, has proofs for them, and most importantly, an ungodly amount of examples (like 60 per chapter, making up most of the book).
For everyone else please don't use Spivak as first calculus book, I beg you
@@Miguel_Noether why? :)
@@maiiaskrypnyk5234 It's very challenging. Even Caltech only uses Apostol.
@@Miguel_Noether I have without realising what analysis was, no wonder it was so goddamn difficult. I just wanted to learn basic differentiation and integration, but ended up learning how to prove some statements from real analysis.
@@Miguel_Noether I came looking for copper, but instead found gold lol
Thank you so much for making a self study guide video again. I started down following the advice from your original, but then it disappeared... now it's back and updated :)
When I was in college, I wanted to take more math beyond Calc III and Linear Algebra, but I didn't have the time or funding to do it. Beyond being interesting, I found it helpful with writing music and thinking about writing in different ways. I'm glad you smart professionals provide these resources for us.
Thanks so much for this hard work for others! It's very confusing to explore the world of pure math by self-study, and your channel is very helpful.
Thank you so much! After highschool i choose to take on a psychology career even if I've really loved maths, always promising myself to self-study it but everytime getting lost, this video is a treasure
So happy to see all these resources being shared.
Who else when watching this video: FINALLY.
Amazing video. I've used quite a few of those myself and I've also found a couple of new things that will come in handy this semester. Thanks
I will also put my brick in this wall. I studied mathematics a couple of years a go and I really loved all the mathematics books from Schaum's Outlines series. They have books on Group Theory, Linear and Abstract Algebra, Real and Complex Calculus and many more etc. Usually those books first present the theory and provide examples. Then you have solved problems where you see how a given problem can be tackled and finally the problems for the reader to solve (with answers at the back). I remember a lot of the content was aligned to my university courses and I could learn a lot from them. Plus they're very good for studying on your own without a teacher/mentor/professor. They are basically so good that now (a few years after graduation) I'm still collecting them since I want them in my personal library for future reference or just to have them just in case (they are really hard to come by in Poland). And one tip in advance. Look for the older versions of the books or first/second editions in some cases. The reason is because slowly some good parts or even entire sections are being cut out. I don't really understand the reason behind this but anyway - you have my opinion right here. Stays safe Comrades!
Your mommy
I'm very grateful for reposting these ideas. I had purchased the Understanding Analysis by Abbott book but your original video had gone offline before it arrived! My course in calculus 2 is finished and I'm looking forward to self-study on pure math in '22.
You put this video up again. Thank you so much!!!
Thank you so much. I'm a data scientist who has been trying to teach myself pure math for several years. I'm working on Linear Algebra Done Right now and wanted to jump to abstract algebra after I finished.
Thanks a lot bro. It is quite rare to find good "manuals" and useful advice for self study. And it takes a lot of time to get into a book and trying to understand the concept the book works and how the author tried to deliver his knowledge. Thanks a lot for this list. Especially for the Playlist!
This is beautiful. Thanks for all the references to dig deeper.
wow this is great thank you so much! I really know where to start right now! I just stopped university because stress was consuming me.. now I can just live my life and still learn some mathematics thank you so much!
So I'm not hugely up on my Pure Mathematics as I moved toward the Applied end of the subject after graduating, but those interested in the Singularity Theory part of Differential Geometry (stuff like Cusps, Swallow Tails, and Envelopes), I would recommend "Curves and Singularities" by Bruce & Giblin. It has lots of nice pictures!
Thank you so much for taking the time to present and share this subject matter.
This video is extremely informative, it spent me a morning to follow every topics one by one! Good job, man!😀
Awesome content. Please cover self study for other fields of mathematics eventually. Thanks for this.
I agree we need more visualizations. Just seeing the checkerboard for complex functions lead me to realize you can use similar checkerboards to illustrate Stokes’s theorem.
OH MY GOD YOU'RE BACK!!!! i didn't see your last 2 uploads until now!!
I've been looking for a video like this for years now!
I thought this was going to be more about how to focus when doing math, how to understand concepts and solve problems and so on, but still a nice collection of resources!
I am amazed at how I cannot understand anything from any of your videos. Guess I just have to study more.
This is amazing! Im planing to study all my math courses again next year and this is exactly what i need it. Thanks!!!!
This is a great video and resource. Thank you for posting!
Such a great video! I've just finished my MSc in Statistics but I'm now looking to spend time self-studying the pure maths modules I had to miss to focus on stats... So this video couldn't come at a better time!
From which University did you get your M. Sc?
A minor nitpick: the study of differentiable manifolds without a distinguished 2-form (such as a metric or symplectic form) is generally referred to as differential topology, while the inclusion of such a form "elevates" the subject to geometry. So, the point where you say differential geometry ends is actually where differential geometry begins.
This is not true. Certainly not where I'm from. Differential topology is simply the study of the topology of differentiable manifolds. There is tonnes that you can call geometry without a metric or a symplectic structure. My own research for one
Perhaps a better way to think of it is that differential topology is the study of global properties of smooth manifolds while differential geometry is more about the local properties. As always there is some overlap.
@@Aetheraev I'll admit that the distinction given here isn't always exactly correct, and I hoped that my use of "generally" would cover me for situations where it fails. However, at least as far as I've seen, calculus on differentiable manifolds isn't considered geometry, which is the subject of the first six chapters of Boothby referenced in the video and by my comment.
In the end, I think it comes down to semantics and it's not truly important where exactly the lines are drawn; the main purpose of my original comment was simply to correct the statement, "This part marks the end of the differential geometry portion of this book," as the Riemannian geometry that follows really has the *most* right of any material in the text to be called differential geometry.
This is one of the best videos I've ever seen, thanks a lot
A marvellous video. Thank you for providing this information.
I really like Munkres’ “Topology” as an undergrad text for point/set topology.
Man,
I got those books thanks to you, and I can say that the real analysis one is really well done!
Actually, every problem that mathematic books have (not defining important things, not explaining the history of a concept, refusing to give simple example, etc.) isn't in this book so far in my reading
did you find them on the internet for free?
update : all of them except one are on the internet for free
@@salwaadlouni1855 Library Genesis btw
I’m so glad you put the Frances Su lectures in the description. I’ve watched countless Real Analysis lectures and video tutorials on a personal journey to be good at math. Frances Su explains the subject incredibly well. He does some serious hand-holding, which is exactly what that course seems to require. It’s so well done.
Do you watch the Math Sorcerer?
this is incredibly useful, thanks for making it!
I like how learning pure math basically makes you a better electronics engineer. Thanks for providing such insightful list.
Im in first year of electronics engineery and i just can feel how many holes there are in my pure math education, so im trying to improve in order to be a better engineer tomorrow day, pluss its a cool hobbie...!
Pure math gives you a comprehensive background about the origins of mathematical models and tools used in engineering: Its formulation and its scope (sometimes in engineering we ignore this information, resulting in a wrong interpretation and bad application of some math concepts)
I find "Elementary Linear Algebra" by Howard Anton to be a great book with plenty of illustrations and problems to solve. I used it much more than the book we used in class and it builds up the topic from scratch.
This is the most helpful video for self learners I've seen, thank you
Wow, the video I never knew I needed. Thank you so much
Socratica's short course of abstarct algebra was pretty amazing
Thank you so much! I'm a med student who loves math (crazy, I know). I've always regretted missing the opportunity to learn pure math at uni level. I'm excited to use these resources!!
You’re in the wrong course
@alfredhitchcock45 what do you mean?
@@rijakhalid9011 you should have taken bs math or engineering
@@alfredhitchcock45 too late lol I'm already in 4th year of med school
thanks for this excellent breakdown, it's something I have been looking for. I'll be watching a lot of these recommended videos
Awesome Video!!!!
I studied trigonometry from a T-shirt of my gf
So I noticed the topics for the undergraduate curriculum in this newer version of the video changed slightly but either way it makes me want to bring up a somewhat list of things you would see as an undergraduate in university.
First off, not everyone does calculus and differential equations in high school (generally speaking most don't): so if you're going to university, expect those. The topics of Linear Algebra, Real Analysis, and Abstract Algebra are generally the common core of every undergraduate math degree; however, most people will do more things like complex analysis and topology. A lot of American universities will have a class dedicated to learning how to write proofs and learning basic set theory and number theory. Group Theory and Galois Theory aren't usually taught on their own as courses but are rather a large chunk of a first and second semester abstract algebra course respectively. Not everyone does differential geometry or algebraic topology when they're an undergrad but a lot do. Other undergraduate courses include: Probability, Number Theory, Euclidean Geometry, Partial Differential Equations, and basically anything that says "intro to [branch of math]" is either an advanced undergraduate course or a graduate course.
I 100% can attest to this. I go to Florida State University and that's exactly how it's set up here.
Yeah differential equations is pretty uncommon in most high schools. I went to a well-funded public school, and having AP single-variable calc was honestly a privilege. I'm now in a well-funded liberal arts college, and you're on-point with the classes usually completed for the major. This video seems to assume more a magnet-school type of math education and a large university or a quite advanced undergraduate curriculum.
alg top is hardly an undergrad subject
@@TomMS In Canada, there's an intermediary between high school and university. Most students with a stem focus use that period to take Calculus and Diff Eq, which is probably the cause of the disconnect.
@@wontpower Interesting. Didn't know that!
Highly recommend the real analysis. Took a semester of real analysis and the book's been a huge help
Wow, this was an Excellent video! Great summary and thanks for all these resources 💯👏
I'm following you right now! 😁
This video is a nice christmas gift to us, the viewers... Thank you for sharing this with the world; I've been engaged with the channel since "The derivative isn't what you think it is" and this channel truly has a unique style. Your way of explaining topics make them feel approachable and nice.
¡Merry christmas, cardinal of the natural numbers!
Thank you so much!
This video is incredibly valuable! Can't thank you enough!
Fantastic video! I'm glad I subscribed to your channel
MIT ocw aggregates a lot of resources and problem sets, with lecture notes and practice exams for essentially all of undergrad and grad school. Probably one of the most comprehensive resources in existence.
Nice video. As a second year math PhD myself now, I feel like math is basically just self studying🤣
This video is perfect and everything I hoped for, thank you!
amazing video , will follow this video.
I've watched all of your videos thus far and I just have one request for you: PRODUCE MORE! :D
I really like your style and neck for explaining things. PLplspls, you are great!
Great work compiling all of this together! I do think there are some issues with order and what material is presented.
First (and most glaringly) a genuine abstract algebra treatment is not given. Groups are certainly important, but rings are equally if not significantly more important. While modules are typically covered in a graduate course, they certainly can be discussed (at least free modules or modules over PIDs) in an undergrad class. Galois Theory is almost certainly graduate level material, and you need a good amount of field theory to even begin discussing it seriously. My first Algebra book was Aluffi's "Algebra Chapter 0" but that's quite fast and uses a lot of category theory, Artin's Algebra book would be a good undergrad level book to work through.
I also think that point-set topology need not be a standalone class. Basic point-set topology should be covered in Real Analysis (open/closed sets, compactness, closure, limit points, etc.) , and advanced point-set topology should be introduced on an as-needed basis in an algebraic and/or differential topology class. If one were to do Real Analysis through Spivak (which I recommend) then this would happen organically.
Overall though I think you did a great job. The book recommendations were on point and the rough order was solid.
completely agree
Thank you for this. Finishing Abstract Algebra right now and then have Abstract Calculus right after.
thank you so so much for putting together this superb list of resources. i switched majors from engineering to urban planning, but I don't want to just give up on pure math because of that, this video came up on my recommendations at the best time haha
as a physics student I really recommend the Wu Ki Tung's book for group theory. It's pretty easy to follow, with you a lot of emphasis in examples and uses in physics.
For GROUP THEORY category, my main go to book is "Contemporary Abstract Algebra" by Joseph Gallian.
Current shoutout after 12 hours with it (yay Christmas) is "All the Math you missed (but need to know for graduate school)" by Thomas Garrity so far has been a fun book.
I totally agree. Gallians book is perfect as a low entry point into the subject. So many easy to understand and intuitive examples given, along with actual applications of group theory.
Abstract Algebra by Gregory T Lee is also really good. It's a bit more difficult, and is drier. But is also far more concise and more rigorous.
Importantly, both these books are easy to get. Unlike a lot of the older (and more expensive!) textbooks that are often recommended for Abstract Algebra and/or group theory.
@@maxbesley1412 "All the Math you missed" is a blessing. Thanks for the recommendation!
I have studied both MARLOW ANDERSON and JOSEPH GALLIAN for abstract algebra. Even Though Gallian contains more content than Anderson, but I like the way anderson introduces the concepts. If you have studied number theory or just want to study number theory along abstract algebra, I think anderson will make a lot of sense than gallian. Anderson introduces concepts by ring first approach which for a beginner makes more sense than a group first approach.
@@ABHISHEKSINGH-nv1se Will add the anderson book to my birthday wishlist this year.
@@ABHISHEKSINGH-nv1se what's title
One of the best video on youtube for Maths major.
Fantastic video! So much information in such a short space.
How dare you omit our glorious Rudin, hallowed be his name!?
In all seriousness great video and resources.
surprised Dummit and Foote (Abstract Algebra) was not mentioned at all in this video. Extremely useful resource for Group theory, Galois theory, and much more.
Probably the best undergraduate book for abstract algebra.
What a great idea for a video. Thank you!
I love when they include numerous examples. When I was learning math, the teacher always showed us the easy examples, but would give us the challenging ones. Like, I get it, but you can't just show us how to do A, B, and get C, but tell us to do our own problems that require us to get from A to E.
A few comments from an erstwhile math student . . .
+1 on Topics in Algebra by Herstein. A lovely book: rigorous proofs and accessible explanations.
+1 on Algebraic Topology by Hatcher. Excellent examples and illustrations.
- 1 on Intro to Differentiable Manifolds by Boothby. It's hit or miss. The pace is uneven, the exposition often too spare. It tries to cover too much in its modest length: differentiable manifolds, Riemmanian geometry, group actions, Lie groups, Lie algebras -- without giving each topic full, proper treatment. Try Lee instead (see below).
NB:
For differential geometry, Lee's Intro to Smooth Manifolds is a solid, modern supplement/replacement to Boothby, or suitable for self-study (perhaps if you're comfortably reading at graduate-level).
For topology, Munkres' Topology book is a solid bet.
For group theory, Abstract Algebra by Dummit and Foote has good breadth and depth and covers everything Herstein's does. A good starter book in group theory is Fraleigh's First Course in Abstract Algebra; suitable for self-study.
man thanks for uploading it again 😭😭😭😭 i was tryna find this video everywhere on your channel 😭😭😭😭
Thanks for making this list
Thank you for making such content.. You might don’t how helpful it can be for someone like myself..Big Cheer to you bruh
Finally the video came back
But better
Thnks
Bro thanks
Math is beautiful and a great way to look into the wonders of the universe! Bravo!
This is very helpful and informative. Thank you for posting this!
Excellent books suggestions. Some I've enjoyed and some I've never seen. Also, the Wesleyan complex analysis lectures are on Coursera, so can be watched with quizzes and exercises there.
Richard E Bouchard's lecture courses on CZcams are well worth a watch too. Group theory, Galois theory, complex analysis and algebraic topology are there, along with number theory and other areas.
Currently working through Borcherd's series on Group Theory. Highly recommend.
Could you please share the link of Wesleyan complex analysis as I didn't get them
@@subikshakannan8570 It is in the description.
Do you guys recommend studying some of the mathematical concepts listed in the video concurrently or individually?
@@Phoenix-he1mm I would learn them in this order: linear algebra-->real analysis-->complex analysis-->group theory-->point-set topology-->Galois Theory-->algebraic topology-->differential geometry
I recommend Tao’s & Zorich’s book for real analysis
Also Smale’s book on differential equation is a great start to dynamical system
woah, i dont have any words to explain. thank you so much. not for the book, but the path you showed. Here at university we are reading just to pass the subject, but deep down we can have fun doing math problems. I miss when i was young and loved to do maths.
Taking graduate algebraic topology next semester thank you SO MUCH for the point set website