College Algebra Pre- Calculus Calculus 1,2,3 Differential Equations Probability and stats Discrete I,II Linear Algebra Real Analysis Modern Algebra Geometry Topology Optional( complex analysis, Number theory, Time series,
I would say Topology is a must have! It helped me a lot to understand many fundamental concepts and their connections in between. Stuff like Optimazation or Numerics is cool too (if you are into aplied mathematics)
Would you say I should take Euclidean Geometry before Topology? I didn't have a good background in Euclidean, and I don't have too much space for superfluous classes since I'm double majoring.
@@bottlecap6169 I kind of think euclidean geometry is more of a math history class. You get to cover axiomatic systems and talk about ideas about the 5th postulate. On the other hand, when I took this course we never talked about manifolds or topology. In my opinion, topology is the modern language in which we talk about shapes. There is some distinction between geometry and topology based on some very complicated explanation about whether classification spaces are discrete or continuous. But in general it is important to realize that even the subjects we call geometry like riemannian geometry or smooth manifolds are still based in the language of topology, that is when we discuss geometry we are discussing local aspect of topological spaces. There is no "geometrical space" but there is a formal "topological space". So this is all to say that I think topology is a better use of your time for modern mathematics. You should check out the text by janich on topology. I haven't read it but there is a nice exert at the beginning where it describes topology as a nice language to deal with counterintuitive aspects of shapes. So I highly highly recommend topology instead of that class on euclidean geometry. That euclidean geometry is an old language. Topology is a modern language that will even help you with the old stuff. Topology is the modern language of shapes.
@@bottlecap6169 nope, General Topology can be studied without any pre reqs besides a proofs course. With a proofs course that you've done well, you can do Real Analysis, Complex Analysis, Point Set (General) Topology, and Advanced(Abstract) Linear Algebra, and Abstract Algebra. I say proofs, but I also mean logic etc which most proof books have already.
Thanks for the list! I'm considering going back to school to get a math degree and currently self studying but practically starting over from scratch because it's been so long. Been at it for a year and about to start calc I. Seeing the subjects planned out like this is very motivating.
@@user-wl2rb3rh5c I live in Azerbaijan. Not the country where there is a rule of law. Corruption and there is no free court system. The competition isn't fair, because you just do not need to be talanted to earn money, you need good patron. Companies actually do not need lawyers, they will operate without lawyers well, too. I felt like I have useless job. Besides, dealing with people with lots of personal problems is quite depressive for me :) I gathered money and want to switch my career to applied math and computer science. I loved and love problem solving a lot. It was my biggest mistake in my life to choose law degree despite my school teachers pushing me to get math degree back then when I was 17 years old. My father also is retired math professor who taught in local and foreign universities. When I do math I find peace inside me, it helps me to focus. I just dont want to die as a lawyer. :) I love guitar and math.
All channels like math scorcer are good channels I love channels that actively encourage learning through book recommendations, practice problems, or informative videos of such. You have earned my SUB, I hope to see more amazing videos in future. Would love to see videos doing certain problems if you have time to make such videos like solving specific integrals or teaching basic theorems or stuff.
Great video! Here's my version for the first 3 years of undergrad: sem 1) analysis in R(sequences, derivatives and all that but done properly as a math course, not like calculus), algebra 1 (just the basics about groups, rings etc), topology-1 (up to Van-Kampen theorem). sem 2) Lebesgue measure and integral, linear algebra (Linear algebra done right fits), Algebra-2 (Group Theory). sem 3) ODE-1 (also done as a math course, see V. I Arnold's textbook), Differential Geometry-1 (Just basic stuff about manifolds and all that, probably John Lee's "Intro to smooth manifolds is a suitable chioice, but some chapters could be skipped"), Algebra-3 (Representation theory "Fulton, Harris" sem 4) Differential Geometry-2 (More advanced stuff like bundles, cohomology, see "Dubrovin, Novikov, Fomenko "Modern Geomtery" vol 2,3), ODE-2 (Arnold "Geometry methods in theory of ODE"), Lie Groups and algebras and their representations. 5) Functional analysis-1, PDE (again, done as a math course, probably Simon, Reed "Methods of modern mathematical physics", Algebra-4 (Attiyah, McDonald's book on commutative algebra), complex analysis (again, as a math course with theorems and proofs) 6) Functional analysis-2 (this subject is infinetely big, 1 year is just for the basic introduction), PDE-2, algebraic topology, homological algebra-1. P.S I'm finishing 2 year of undergrad, and how I would like my math courses map would look like, but it didnt, so I have a lot ot catch up on my own.
'Linear Algebra Done Right' goes crazy hard. Was surprised to see you call it a textbook for advanced linear algebra since it requires no linear algebra background (and the first sub-chapter is literally on complex numbers). That explains why it hasn't helped me much in my first year uni linear algebra class lol.
I love this list, although it hurts not see any topology courses🥲 I personally had a much less consistent list of courses, since I picked most of my courses based on how much did the course sound interesting to me, and that way I found the topics that interested me the most, and I think I would recommend this way to every new student, of course after he took the basic courses that are necessary in basically every field in mathematics. Great video!
Point set topology is taught with an analysis course. Analysis is essentially all topology (even starting from epsilon delta proofs; it's just convergence in the standard metric topology on R)
@@ffc1a28c7 yeah we had a segment about metric spaces in our second analysis course. But if you don't take topology you're missing the really juicy parts like the construction of quotient spaces and the fundamental groups:)
I was confused at first with the college algebra 1,2,3 but then you explained it can also be trig and then pre calculus and that made sense. At my college I did that; college algebra, trigonometry, and precalculus.
Love the video and your channel. As an older person (58) learning math as a hobby, I would love to see you match this list with the books you would use in order. The biggest problem I'm having is to choose which books to read with the limited time/money that I have. I'm also a book collector, which compounds the problem. So if you're on a desert island and want to learn math, what's your ideal list, with the caveat of stopping when you're ready for anything at the post-graduate level.
It is a good question… I would say Royden and Fitzpatrick’s Real Analysis for measure theory and other related topics, and Martin Issacs Algebra book for graduate level algebra. I haven’t found my ideal complex analysis book yet but still looking. For functional analysis, definitely the Kreyszig book, and for linear algebra, I would go with Axler.
I'm also learning math as a hobby - brushing up again on my linear algebra, geometry and real analysis so that I can "re-connect" with my favourite subject of differential geometry 🙂
i can speak to recommending probability theory, it's crucial if you're intending to work in a field reliant on applied mathematics. knowing probability theory allows you to conceptualize how to approach problems people often face in these fields
Wanted to revisit this after watching it for the first time when it came out. I just finished Calc 1-3, Diff Eqs and Linear Algebra at community college, and on Monday I start grad school in Statistics. I didn’t follow the path you laid out here, but this was an inspiring video.
This is my hardcore plan for self study undergraduate mathematics before studying physics 1. Openstax Algebra and Trig 2. Openstax Calculus 3. Thomas’s Calculus Early Transcendentals+Solutions 4. Book of proof 5. Real Analysis Jay 6. Algebra and Trig sullivan + Solution 7. Introduction to linear algebra Gilbert 8. Vector Calculus Susan + solution 9. Differential Equations Zill + Solutions 10. Calculus of Variations Elsgolc 11. A First Course In Integral Equations Abdalmajid + Solutions 12. Complex analysis Zill + Solutions 13. A Student's Guide to Vectors and Tensors Fleisch 14. Numerical analysis burden 15. Contemporary Abstract Algebra+Solutions 16. Understanding Topology Ault 17. The Probability Lifesaver 18. Mathematical Methods for Physics and Engineering Riley + Solutions
@@pyrenn no i'm graduated from physics. you dont have to take all this math now. start with algebra and trig first then calculus and then university physics.
I don’t know if you’re still doing this, book after an intro to proofs book (I’m thinking how to prove it, etc), consider doing something like Spivak before doing actual Analysis. You’ll learn a lot & actually get good at proofs. Everything else will be a lot easier
At my current university, they split up the Calculus Sequence into 4 classes rather than 3 classes. Calculus 1 & 2 are the same, but 3 & 4 is pretty much equivalent to your usual Calculus 3 at other colleges. I rarely see this done at other universities outside of a couple community colleges, and other Universities in the region of the US I live in. Also, the general course plan for the Bachelor of Arts and Bachelor of Science has you taking multiple math classes after Calculus 2. It's set up as: -Semester 1: Calculus I -Semester 2: Calculus II -Semester 3: Calculus III Linear Algebra -Semester 4: Calculus IV Differential Equations I After the 4th semester, the degree programs split off in terms of courses, as the BA is less rigorous than the BS in terms of Mathematical Content. But as a BA student I am taking all of the BS courses as I am not a fan of science lol.
What does Calculus IV cover at your university? I know that at most other universities in America, Multivariable Calculus and Vector Calculus are together crammed into Calculus III.
@@lorax121323 It's essentially just multivariable calculus but stretched out into 2 semesters rather than being crammed into just one semester. I go to engineering school, and I think a lot of the reason behind it is to have the Engineering majors grasp the topic of multivariable calculus a little easier than if it was all done in 1 semester. Generally, the Math Curriculum is mainly set up more so for Engineers rather than Mathematicians until you get to your upper-level Mathematics courses like Advanced Calculus, Intro to Topology, or Real Analysis.
I don’t know the country you are in, but where we are probability and statistics are included in the undergraduate degree. So they are not included where you are ?
At my university (years ago), you can take exams prior to starting freshman year for College Algebra and Trigonometry. If you pass, you don't have to enrol for these subjects when the semester starts. You've received credits for them already. We also had Set Theory in college, though no Topology. Set Theory was usually taken along with Linear Algebra and Abstract Algebra (to help lift your overall GPA as Abstract Algebra can be tough - haha). Finally, you cannot call yourself a "true" math undergrad unless you pass Vector Calculus, Abstract Algebra and Differential Equations (ODE, PDE). By this time, close to 60% of your cohort would have dropped out already.😄
@@epicm999 I heard of a group of people who tried to go for an ivy league university math degree as a challenge haha, it could be, though is doing a degree worth it just for it being considered difficult? And is it the only challenge worth taking on and no other?
@@user-wl2rb3rh5c I'm right next to being able to take Vector Calc and am already planning on taking ODE. You do bring up a good point though lol, it's not worth doing a degree for the challenge unless the degree gives you opportunities.
this feels strange coming from a uk background; in first year of my undergrad degree we had mandatory classes on basic real analysis, linear algebra and group theory (among other things like dynamics, probability etc.) for anyone doing a maths degree. Second year had stuff like complex analysis, more linear algebra, topology, ring theory, and lebesgue integration. Third year i got into more galois theory, functional analysis etc. Feels weird to be able to do a full undergrad degree without doing any much serious algebra work beyond linear algebra
Even a lot of Canadian universities are way ahead (we even have stuff like riemannian geometry, full on model theory, category theory, operator theory, representation theory, and lie algebras at the undergrad level at my school). I have no idea how people can justify having a bachelor's in math having not taken more than a dozen math course (and of those, only a handful proof based ones).
This guy has a lot of remedial stuff in here that most STEM math major wouldn’t need. Most high school graduates will have some familiarity with calculus but they generally all need more in college. I think the difference is that math majors and STEM folks take a lot of computational type classes early in since lower level classes are generally the same for math and engineering majors. Also seems like we have a lot more general education in the US and less specialization going into college. Europe and the world at large seems to specialize earlier.
It's very strange, here in Germany (pure mathematics bachelor) we dont have Calculus 1,2,3 in university, everything is prove based and it starts with more advanced courses: 1 semester: Introduction to Real Analysis, Linear Algebra I 2 semester: Real Analysis, Linear Algebra II (which is advanced Linear Algebra) 3 semester: Measure and Integration Theory, Numerical Linear Algebra, Introduction to Probability Theory 4 semester: Introduction to abstract algebra and number theory, Complex Analysis and ODE, Numerical Analysis, Probability Theory 5 semester: Topology, Functional Analysis, Abstract Algebra, PDE 6 semester: 2 of the following: Diff. Geometry, Alg. Topology, Alg. Geometry, Functional Analysis 2, Alg. number theory, advanced PDE, advanced numerical analysis
If you focus on geometry/topology, your master might look like this: 1) Lie groups and algebras, algebraic geometry 2, algebraic topology 2, 2) homotopy theory, representation theory, geometry of schemes 3) homological algebra, representation theory 2, hodge theory 4) your thesis
Understand most people graduate highschool with at most Algebra 1 and a little geometry in the US. From my experience most highschools dont even teach calculus and its normally busses to highschools that do OR dual enrollment in some community college. US school system is ass and a 4 yr degree is about 100k USD so America doesnt like smart people.
It's true that many American schools offer the college algebra/precalculus/calculus sequence as primarily a remedial tool, which takes up space in the first year. However, all top schools in the country are on par with the best European schools; even if the course order is flexible, fundamental undergraduate topics are treated early, such as taking first courses in real analysis/linear algebra/abstract algebra at the freshman level.
@@musashimiyamoto9035 That's bullshit. Most people who intend to major in mathematics out of a US high school have generally finished at least precalc in high school, perhaps even calc 1 and 2.
I’m going to give my IGCSEs in November (if you don’t know, it’s what British curriculum students have to sit for at grade-10) and of course planning ahead and I want to do something in the field of mathematics and your videos make me feel like you are right in front of me talking and giving advices in a very chilled way which I just love about you!! Ty!! Keep going ✨
I am still a sophomore 😅, but I have an opinion I would put a modern algebra course instead of the number theory second course, and I would put a course in topology instead of complex variables second course. I think the core courses for undergraduated students should be in different areas as the student can, and the optional courses should be courses that prepare the student for his master degree.
Topology is, in my opinion, a must for every math student at the undergrad level. I know some people struggle with it but to be honest, when one grasp the fundamentals of topology most subjects start making a lot more sense, like Complex Analysis, I would even go as far as to say that it should be a prerequisite for taking Complex Analysis. Also, I'm kinda partial to saying that math undergrads should know a little bit of probability theory from both a measure theoretic and a non measure theoretic perspective, not because I particularly enjoy probability but because it gives the students who decide not to and/or are unable to enroll into a master a better shot at getting a good paying job.
Right now im studying maths in my first year in Germany and we have the courses linear algebra 1 and 2 as well as analysis 1 and 2, and cover the themes of the books you mentioned for "Real Analysis" and "adv. lin. alg.". Im courious as to why you cover these themes only in your 3rd/4th year. On the other hand, things like ODE, PDE or number theory are strictly for the 2nd and 3rd years in germany, not for the first years.
I would think those are covered in the differential equations courses. In my ODEs class we did Laplace transforms, and I think the PDEs/Advanced Engineering Math covers Fourier transforms
Interesting. In Finland the first year curriculum consists generally of: Fall: Proofs, Calculus 1 & 2, Linear Algebra 1 (+ compulsory general studies like Finnish, Swedish & English) Spring: Linear Algebra 2 & 3, Advanced Calculus (proof based Calc 1 & 2), Series Spring Electives: Logic 1 & 2, Probability and Statistics, Applied Linear Algebra Knowledge of trigonometry and elementary number theory is assumed.
I picked up Axler's LADR as a freshman into my math major and I strongly agree with 10:40! I fondly remember struggling as much as I could through the first chapters. Holds a special place to me
First of all, if you did every course you listed up to @11:54 at a college you would be there over five years as an undergraduate. I mean College Algebra I-II-III and Calculus I-II-III are sequential, so that completing those sequences is over two years right there.
I would say I wish I saw complex analysis sooner, it is absolutely beautiful and it is really helpful for studying modular forms which is a magical subject
Man… modular forms are something I aspire to understand. I was chemical engineering in undergrad so I got through diff EQ. Right before things get deep. Now I’m self learning and modular forms are a ways away from me now😂
@@Dark_Souls_3 There are something’s you just need to take for granted when learning modular forms (for me it’s been Fourier/harmonic analysis) but in the end they’re just some funky well behaved periodic complex functions. That for some mystical reason are connected to number theory! What are you self learning at the moment if I can ask?
It‘s interesting how different education systems are. Here everything up to and usually including Calc3 is covered in school, university starts with Real Analysis, Linear Algebra and Differential Equations. Which was actually kind of an issue for me because I started my degree 3 years after finishing school so I had to re-learn integration on my own while being asked to prove its underlying ideas in the Analysis class. The additional work was a struggle but I‘m glad I discovered my passion for math and theoretical physics. Better late than never.
I would recommend taking calc 3 if you are a chem major. I ended up dropping it a few weeks in, but think it would of been helpful. Usually just calc 1-2 are required.
@@eshankulkarni2843 It would of been helpful in electricity and magnetism course of physics (2nd semester physics usually) and also in quantum chemistry class (upper elective I took). Both used double and triple integrals, but b/c calc 3 wasn't prereq, we didn't have to solve any on exams. But would of been helpful to know these things to understand better. Again, I would of just preferred I hadn't drop the course. It didn't put me at a disadvantage not having taking it though so I wouldn't worry if you skip it.
For all other business and biology chemistry degrees, math is really useful up to Calc AB-BC levels. After calc 2 (bc) math sort of becomes its own thing, unless you are doing physics. Computer programming is also more math related depending on which branch you go.
Hi I bought the book of how to think about Analysis by lara alcock and I loved it. Thank for the suggestions. I have 22 analysis book including fizpatrick book and bartle but I loved this book more than anything else.. People praise alot about the real analysis book by jay cummings (this is also the Amazon's best selling book), if you don't mind could you do a review on that book as well I want to say this but I love your channel and the way you talk and think are alot similar to math sorcerer( he is also a youtuber)
Thank you for the kind words, I will check out the Cummings book, but will need to read it thoroughly before offering my take. Also, I appreciate the comparison to Math Sorcerer, I like his videos :)
bro my community college had a placement test that if you scored high enough on it would automatically skip you straight to calculus. it was multiple choice and i just guessed for most of the questions bc i was very lost and i scored a 86 just from random educated guesses and now i’m taking this calculus class and i’m failing so hard bc i just don’t remember how to do algebra. i’m literally so fucked dude my parents are going to kill me idk how to tell them i got a 47 on my midterm
Ask yourself why you failed. If you failed because you didn’t study enough, then own up to it and try harder next time. It is possible to come back. I failed a graduate level linear algebra test once, and was able to come back from it through hard work. If you studied your butt off and still failed, then it is not your fault. I would consider taking college algebra again and then retake calculus.
Hi had a great time watching your video, I am intended to learn Differential Geometry on my own, and currently taking a Modern algebra Course and a Course on topology. Can you pin a list adding the geometry path from the functional analysis, please? as I am learning from youtube it is difficult sometimes on which course should I take next for the same
Unfortunately I don’t have much to recommend with geometry at the grad level. I’ve been trying to find great books in geometry. One of my instructors is using a book by Pogorelov however it’s in the neighborhood of calculus 3. He’s says you don’t need much passed calculus 3 to study geometry but I still search.
I have worked differential geometry and smooth manifold theory, and I know you didn't ask me but, it really depends on your foundations. If you have only taken courses like Linear Algebra and Calculus I would recommend you check Do Carmo's "Differential Geometry of Curves and Surfaces", while the approach has been kinda superseded by the study of manifolds, it still a really good book and it gives you some insight into how the ideas of Differential Geometry originated. If you have already taken a course in Topology, Group Theory, and feel comfortable with Calculus and Linear Algebra I would recommend you check either Lee's "Introduction to Smooth Manifolds" or Tu's "An Introduction to Manifolds", they both develop the theory in a very approachable way, with lots of examples. The main difference between manifold theory and (classic) differential geometry is in how they study the same objects, in manifold theory we study local properties that allow us to draw conclusion about the whole object while in differential geometry we study global properties that allow us to study the local properties, there are theorems that guarantee they are both equivalent in most important cases.
@@PenaflorPhi Hi thank you so much for these suggestions, I will start with Tu's "An Introduction to Manifolds" and follow up more. do you have a twitter handle, would like to connect and discuss more if possible :)
This is a great list. I thoroughly enjoyed your video. I can't emphasize enough a strong background on linear algebra and modern algebra, for now my goal is to learn galois theory and class field theory, hopefully sooner than later, but my real objective is to what is the deal with elliptic curves, galois representations and L functions. Any recommendations for this path would be appreciated.
Thank you. My background is in analysis so my algebra recommendations are not the strongest. But some authors I would recommend for studying algebra that I liked were Isaacs, Hunderford, and Conrad.
I'd recommend checking out J.S.Milne's website - he has book-length notes series on topics ranging across field/Galois theory, commutative algebra, algebraic number theory, class field theory, and more. I'm looking to go into number theory, and owe a lot of my foundational knowledge to those texts. Another wonderful book series is Kato's "Fermat's Dream" (Iwanami Tracts in Mathematics). Hopefully these are helpful to you.
To get into L functions and elliptic curves, you'd need a strong background in algebraic number theory for which the book by Stewart and Tall could be a good place to begin. You can also look at the later sections of the book by Ireland and Rosen after going through the first book. For all this, you'd need a good foundation in abstract algebra for which you might look at the books by Artin, and Dummit and Foote. And after all this background, you can look at Silverman's book on elliptic curves. After you've learned these you should also look at objects called modular forms which is (sort of like) the bridge between elliptic curves and L functions. That's how I've learnt the subject (until now). Hope that helps :)
Do you guys not do any Topology, Differential Geometry, Representation Theory or Algebraic Geometry in America? I would consider Topology and Algebraic Geometry a must have for anyone in Algebra or Geometry and Differential Geometry for anyone in Analysis and PDE's.
We certainly do. The content of the video is just one specific recommendation regarding certain courses to take. Many schools (and all competitive ones) in the US study topology as early-on as possible, diff geo in some form, and rep theory/alg geo whenever the algebraic prerequisites are met. There are various courses at as early as the sophomore level across different institutions that introduce all of these aforementioned topics.
I'm currently taking my 1st year as undergrad (double major in math and comsci) These are the predefined curriculum (almost) that our university uses. But it also have applied math subjects every semester like physics and statistics.
I appreciate the video, but as a math student, I'm shocked that you didn't put down at least one topology course. Point-set and algebraic topology are both really important, as well as differential geometry and algebraic geometry. I feel like excluding all of these gives people the wrong impression about what math is.
Is measure theory metric spaces? I notice you didn't stress statistics so much (unless probability covers this) or something like combinatorics (you did mention graph theory). And maybe something like Lie Algebras and Differential Geometry (maybe non-Euclidean geometry covers this). Then there's topology and algebraic geometry which I know little about. Good list though.
Not quite. Metric spaces generalize the notion of distance (think absolute value between points), while measure spaces generalize the notion of length, area, or volume.
Yeah at ASU it’s called “Discreet Math” and it tore me a new one. I’ll never forget, though, there was a homeless guy that was auditing the class and he consistently was getting like 5% better scores than everyone on every exam
@@eshankulkarni2843 the applications of linear algebra in calc 3 go wild, i understood things like the jacobian a lot more tho i suppose if your precalculus course did enough matrices you could get by, calc 2 -> LA -> calc 3 -> ODEs is my favored path
Where is undergraduate level group ring and possible field theory in Abstract Algebra. No undergraduate course can miss it. And a student who studies abstract linear algebra also gets confused with out group ring theory.
Do you have any texts on the algebraic manipulations of sums, multiplications (capital pi), and other stuff that is not too readily taught in any course curriculums. I wish to start tackling MIT-level integrals and more advanced topics in math but need some texts to aid. Any suggestions on texts will be wonderfully appreciated.
In US we say mostly pre-calc not college calculus. In UCLA there is a Pre-calc class and same in UCF and other places. I assume college algebra 1 2 3 stands for Algebra 1 2 and Precalc… The latter makes more sense. As there is usually one more course before Pre calc, that is geometry. High schoolers usually finish Algebra 2 or Pre calc. During highschool, the usual highest mathematics achievement is calculus 2. Calculus 1 and 2 are named AB and BC in high school, which are great introductory to Calculus. Then in college they will take calc 3 4 and other math courses.
Im currently in my first year as an undergrad and am in advanced linear algebra. Out of curiosity, does anyone think it is a bad idea to skip elementary linear algebra and go straight to advanced? My school allows it, I’m just not sure if I’ll need to learn the material a second time.
I’m getting advised for my next semester pretty soon and I’d like to get a bit ahead, would it be a good idea to take calc 3 and elementary diff eq during the same semester?
Have you taken linear algebra yet? calc 3 and linear algebra in the same semester is somewhat doable. I've heard DiffEq is a bit harder so I'd prefer not to take it at the same time as calc 3.
Yes there is. Also you have to remember that in the US we do not specialize at all in high school, not until undergrad. And I was told that in Europe your undergrad is 3 years, vs 4 years in the US.
College Algebra
Pre- Calculus
Calculus 1,2,3
Differential Equations
Probability and stats
Discrete I,II
Linear Algebra
Real Analysis
Modern Algebra
Geometry
Topology
Optional( complex analysis, Number theory, Time series,
As a Math undergrad, this is LITERALLY the best channel on CZcams right now; loving it!!
I would say Topology is a must have! It helped me a lot to understand many fundamental concepts and their connections in between. Stuff like Optimazation or Numerics is cool too (if you are into aplied mathematics)
Would you say I should take Euclidean Geometry before Topology? I didn't have a good background in Euclidean, and I don't have too much space for superfluous classes since I'm double majoring.
@@bottlecap6169 I kind of think euclidean geometry is more of a math history class. You get to cover axiomatic systems and talk about ideas about the 5th postulate. On the other hand, when I took this course we never talked about manifolds or topology.
In my opinion, topology is the modern language in which we talk about shapes. There is some distinction between geometry and topology based on some very complicated explanation about whether classification spaces are discrete or continuous. But in general it is important to realize that even the subjects we call geometry like riemannian geometry or smooth manifolds are still based in the language of topology, that is when we discuss geometry we are discussing local aspect of topological spaces. There is no "geometrical space" but there is a formal "topological space".
So this is all to say that I think topology is a better use of your time for modern mathematics. You should check out the text by janich on topology. I haven't read it but there is a nice exert at the beginning where it describes topology as a nice language to deal with counterintuitive aspects of shapes.
So I highly highly recommend topology instead of that class on euclidean geometry. That euclidean geometry is an old language. Topology is a modern language that will even help you with the old stuff. Topology is the modern language of shapes.
@@fanalysis6734Lmao, we are using janich for linear algebra
A good book doing a bit of both (and more) is Geometry and Topology by Reid
@@bottlecap6169 nope, General Topology can be studied without any pre reqs besides a proofs course. With a proofs course that you've done well, you can do Real Analysis, Complex Analysis, Point Set (General) Topology, and Advanced(Abstract) Linear Algebra, and Abstract Algebra. I say proofs, but I also mean logic etc which most proof books have already.
Keep posting 🙏🏻
Thanks for the list! I'm considering going back to school to get a math degree and currently self studying but practically starting over from scratch because it's been so long. Been at it for a year and about to start calc I. Seeing the subjects planned out like this is very motivating.
I am also planning to take math degree or math related degree at age 36 after 13+ law career :) Math rocks! I love math.
@@eminrzayev7056
Thats awesome! May I ask what made you choose a career change?
@@user-wl2rb3rh5c I live in Azerbaijan. Not the country where there is a rule of law. Corruption and there is no free court system. The competition isn't fair, because you just do not need to be talanted to earn money, you need good patron. Companies actually do not need lawyers, they will operate without lawyers well, too. I felt like I have useless job. Besides, dealing with people with lots of personal problems is quite depressive for me :) I gathered money and want to switch my career to applied math and computer science. I loved and love problem solving a lot. It was my biggest mistake in my life to choose law degree despite my school teachers pushing me to get math degree back then when I was 17 years old. My father also is retired math professor who taught in local and foreign universities. When I do math I find peace inside me, it helps me to focus. I just dont want to die as a lawyer. :) I love guitar and math.
@@eminrzayev7056
That's really cool bro! I wish you best of luck with you studies!🙂
@@user-wl2rb3rh5c Thanks a lot.
All channels like math scorcer are good channels I love channels that actively encourage learning through book recommendations, practice problems, or informative videos of such. You have earned my SUB, I hope to see more amazing videos in future. Would love to see videos doing certain problems if you have time to make such videos like solving specific integrals or teaching basic theorems or stuff.
Great video! Here's my version for the first 3 years of undergrad: sem 1) analysis in R(sequences, derivatives and all that but done properly as a math course, not like calculus), algebra 1 (just the basics about groups, rings etc), topology-1 (up to Van-Kampen theorem). sem 2) Lebesgue measure and integral, linear algebra (Linear algebra done right fits), Algebra-2 (Group Theory). sem 3) ODE-1 (also done as a math course, see V. I Arnold's textbook), Differential Geometry-1 (Just basic stuff about manifolds and all that, probably John Lee's "Intro to smooth manifolds is a suitable chioice, but some chapters could be skipped"), Algebra-3 (Representation theory "Fulton, Harris" sem 4) Differential Geometry-2 (More advanced stuff like bundles, cohomology, see "Dubrovin, Novikov, Fomenko "Modern Geomtery" vol 2,3), ODE-2 (Arnold "Geometry methods in theory of ODE"), Lie Groups and algebras and their representations. 5) Functional analysis-1, PDE (again, done as a math course, probably Simon, Reed "Methods of modern mathematical physics", Algebra-4 (Attiyah, McDonald's book on commutative algebra), complex analysis (again, as a math course with theorems and proofs) 6) Functional analysis-2 (this subject is infinetely big, 1 year is just for the basic introduction), PDE-2, algebraic topology, homological algebra-1. P.S I'm finishing 2 year of undergrad, and how I would like my math courses map would look like, but it didnt, so I have a lot ot catch up on my own.
'Linear Algebra Done Right' goes crazy hard. Was surprised to see you call it a textbook for advanced linear algebra since it requires no linear algebra background (and the first sub-chapter is literally on complex numbers). That explains why it hasn't helped me much in my first year uni linear algebra class lol.
It's proof heavy though. Very few computational questions like the ones you'll find in an introductory course.
I love this list, although it hurts not see any topology courses🥲
I personally had a much less consistent list of courses, since I picked most of my courses based on how much did the course sound interesting to me, and that way I found the topics that interested me the most, and I think I would recommend this way to every new student, of course after he took the basic courses that are necessary in basically every field in mathematics.
Great video!
Point set topology is taught with an analysis course. Analysis is essentially all topology (even starting from epsilon delta proofs; it's just convergence in the standard metric topology on R)
@@ffc1a28c7 yeah we had a segment about metric spaces in our second analysis course. But if you don't take topology you're missing the really juicy parts like the construction of quotient spaces and the fundamental groups:)
@@shabbos_goy4876 fair point.
I was confused at first with the college algebra 1,2,3 but then you explained it can also be trig and then pre calculus and that made sense. At my college I did that; college algebra, trigonometry, and precalculus.
Love the video and your channel. As an older person (58) learning math as a hobby, I would love to see you match this list with the books you would use in order. The biggest problem I'm having is to choose which books to read with the limited time/money that I have. I'm also a book collector, which compounds the problem. So if you're on a desert island and want to learn math, what's your ideal list, with the caveat of stopping when you're ready for anything at the post-graduate level.
It is a good question… I would say Royden and Fitzpatrick’s Real Analysis for measure theory and other related topics, and Martin Issacs Algebra book for graduate level algebra. I haven’t found my ideal complex analysis book yet but still looking. For functional analysis, definitely the Kreyszig book, and for linear algebra, I would go with Axler.
@@PhDVlog777 Thank you.
I'm also learning math as a hobby - brushing up again on my linear algebra, geometry and real analysis so that I can "re-connect" with my favourite subject of differential geometry 🙂
Same here, older man learning math as a hobby😀
i can speak to recommending probability theory, it's crucial if you're intending to work in a field reliant on applied mathematics. knowing probability theory allows you to conceptualize how to approach problems people often face in these fields
Wanted to revisit this after watching it for the first time when it came out. I just finished Calc 1-3, Diff Eqs and Linear Algebra at community college, and on Monday I start grad school in Statistics. I didn’t follow the path you laid out here, but this was an inspiring video.
This is my hardcore plan for self study undergraduate mathematics before studying physics
1. Openstax Algebra and Trig
2. Openstax Calculus
3. Thomas’s Calculus Early Transcendentals+Solutions
4. Book of proof
5. Real Analysis Jay
6. Algebra and Trig sullivan + Solution
7. Introduction to linear algebra Gilbert
8. Vector Calculus Susan + solution
9. Differential Equations Zill + Solutions
10. Calculus of Variations Elsgolc
11. A First Course In Integral Equations Abdalmajid + Solutions
12. Complex analysis Zill + Solutions
13. A Student's Guide to Vectors and Tensors Fleisch
14. Numerical analysis burden
15. Contemporary Abstract Algebra+Solutions
16. Understanding Topology Ault
17. The Probability Lifesaver
18. Mathematical Methods for Physics and Engineering Riley + Solutions
I'm also considering to study physics, are you in highschool too?
@@pyrenn no i'm graduated from physics. you dont have to take all this math now. start with algebra and trig first then calculus and then university physics.
@@Ahmed99AK I see, alright. Thank you!
@@pyrenn you're welcome
I don’t know if you’re still doing this, book after an intro to proofs book (I’m thinking how to prove it, etc), consider doing something like Spivak before doing actual Analysis. You’ll learn a lot & actually get good at proofs. Everything else will be a lot easier
At my current university, they split up the Calculus Sequence into 4 classes rather than 3 classes. Calculus 1 & 2 are the same, but 3 & 4 is pretty much equivalent to your usual Calculus 3 at other colleges. I rarely see this done at other universities outside of a couple community colleges, and other Universities in the region of the US I live in. Also, the general course plan for the Bachelor of Arts and Bachelor of Science has you taking multiple math classes after Calculus 2. It's set up as:
-Semester 1:
Calculus I
-Semester 2:
Calculus II
-Semester 3:
Calculus III
Linear Algebra
-Semester 4:
Calculus IV
Differential Equations I
After the 4th semester, the degree programs split off in terms of courses, as the BA is less rigorous than the BS in terms of Mathematical Content. But as a BA student I am taking all of the BS courses as I am not a fan of science lol.
This is literally the exact same sequence as me lol.
@@oscarbraun6825 👀👀👀👀
What does Calculus IV cover at your university? I know that at most other universities in America, Multivariable Calculus and Vector Calculus are together crammed into Calculus III.
@@lorax121323 It's essentially just multivariable calculus but stretched out into 2 semesters rather than being crammed into just one semester. I go to engineering school, and I think a lot of the reason behind it is to have the Engineering majors grasp the topic of multivariable calculus a little easier than if it was all done in 1 semester.
Generally, the Math Curriculum is mainly set up more so for Engineers rather than Mathematicians until you get to your upper-level Mathematics courses like Advanced Calculus, Intro to Topology, or Real Analysis.
*multivariable & vector calculus
I think Probability and Statistics should also be included in the undergraduate degree
I don’t know the country you are in, but where we are probability and statistics are included in the undergraduate degree. So they are not included where you are ?
@@yehahlearn how to read
At my university (years ago), you can take exams prior to starting freshman year for College Algebra and Trigonometry. If you pass, you don't have to enrol for these subjects when the semester starts. You've received credits for them already.
We also had Set Theory in college, though no Topology. Set Theory was usually taken along with Linear Algebra and Abstract Algebra (to help lift your overall GPA as Abstract Algebra can be tough - haha).
Finally, you cannot call yourself a "true" math undergrad unless you pass Vector Calculus, Abstract Algebra and Differential Equations (ODE, PDE). By this time, close to 60% of your cohort would have dropped out already.😄
Is that a challenge?
@@epicm999
I heard of a group of people who tried to go for an ivy league university math degree as a challenge haha, it could be, though is doing a degree worth it just for it being considered difficult? And is it the only challenge worth taking on and no other?
@@user-wl2rb3rh5c I'm right next to being able to take Vector Calc and am already planning on taking ODE. You do bring up a good point though lol, it's not worth doing a degree for the challenge unless the degree gives you opportunities.
@@epicm999
Agreed, and that's awesome! Goodluck on your studies friend ^^
@@user-wl2rb3rh5c Thank you! I wish you thr best in your endeavors.
this feels strange coming from a uk background; in first year of my undergrad degree we had mandatory classes on basic real analysis, linear algebra and group theory (among other things like dynamics, probability etc.) for anyone doing a maths degree.
Second year had stuff like complex analysis, more linear algebra, topology, ring theory, and lebesgue integration. Third year i got into more galois theory, functional analysis etc.
Feels weird to be able to do a full undergrad degree without doing any much serious algebra work beyond linear algebra
Yeah, European universities are light years ahead of the US. Guess they've had more time to settle into a system
Even a lot of Canadian universities are way ahead (we even have stuff like riemannian geometry, full on model theory, category theory, operator theory, representation theory, and lie algebras at the undergrad level at my school). I have no idea how people can justify having a bachelor's in math having not taken more than a dozen math course (and of those, only a handful proof based ones).
This guy has a lot of remedial stuff in here that most STEM math major wouldn’t need. Most high school graduates will have some familiarity with calculus but they generally all need more in college. I think the difference is that math majors and STEM folks take a lot of computational type classes early in since lower level classes are generally the same for math and engineering majors. Also seems like we have a lot more general education in the US and less specialization going into college. Europe and the world at large seems to specialize earlier.
It's very strange, here in Germany (pure mathematics bachelor) we dont have Calculus 1,2,3 in university, everything is prove based and it starts with more advanced courses:
1 semester: Introduction to Real Analysis, Linear Algebra I
2 semester: Real Analysis, Linear Algebra II (which is advanced Linear Algebra)
3 semester: Measure and Integration Theory, Numerical Linear Algebra, Introduction to Probability Theory
4 semester: Introduction to abstract algebra and number theory, Complex Analysis and ODE, Numerical Analysis, Probability Theory
5 semester: Topology, Functional Analysis, Abstract Algebra, PDE
6 semester: 2 of the following:
Diff. Geometry, Alg. Topology, Alg. Geometry, Functional Analysis 2, Alg. number theory, advanced PDE, advanced numerical analysis
If you focus on geometry/topology, your master might look like this:
1) Lie groups and algebras, algebraic geometry 2, algebraic topology 2,
2) homotopy theory, representation theory, geometry of schemes
3) homological algebra, representation theory 2, hodge theory
4) your thesis
Understand most people graduate highschool with at most Algebra 1 and a little geometry in the US. From my experience most highschools dont even teach calculus and its normally busses to highschools that do OR dual enrollment in some community college. US school system is ass and a 4 yr degree is about 100k USD so America doesnt like smart people.
It's true that many American schools offer the college algebra/precalculus/calculus sequence as primarily a remedial tool, which takes up space in the first year. However, all top schools in the country are on par with the best European schools; even if the course order is flexible, fundamental undergraduate topics are treated early, such as taking first courses in real analysis/linear algebra/abstract algebra at the freshman level.
That's similar to what we have in Australian National University.
@@musashimiyamoto9035 That's bullshit. Most people who intend to major in mathematics out of a US high school have generally finished at least precalc in high school, perhaps even calc 1 and 2.
Amazing flow, but you haven't mentioned topology at all
I’m going to give my IGCSEs in November (if you don’t know, it’s what British curriculum students have to sit for at grade-10) and of course planning ahead and I want to do something in the field of mathematics and your videos make me feel like you are right in front of me talking and giving advices in a very chilled way which I just love about you!! Ty!! Keep going ✨
I love how calm you are.
Thank you! I am planning to study mathematics in college and this gives me a great perspective!
Exactly what I've been looking for! Thanks for the upload 👍🏻
Great! I will make sure to apply this in 5 years from now! :D
I would say that intro to point-set topology helps a lot with intro to analysis as you see everything generalized
Interesante, gracias por las recomendaciones.
I am still a sophomore 😅, but I have an opinion
I would put a modern algebra course instead of the number theory second course, and I would put a course in topology instead of complex variables second course.
I think the core courses for undergraduated students should be in different areas as the student can, and the optional courses should be courses that prepare the student for his master degree.
Topology is, in my opinion, a must for every math student at the undergrad level. I know some people struggle with it but to be honest, when one grasp the fundamentals of topology most subjects start making a lot more sense, like Complex Analysis, I would even go as far as to say that it should be a prerequisite for taking Complex Analysis.
Also, I'm kinda partial to saying that math undergrads should know a little bit of probability theory from both a measure theoretic and a non measure theoretic perspective, not because I particularly enjoy probability but because it gives the students who decide not to and/or are unable to enroll into a master a better shot at getting a good paying job.
I would also include stochastic processes
As a guy who has a degree in math, this was a great video! The only class I'm suprised you didn't mention is Topology! Love your channel!
Right now im studying maths in my first year in Germany and we have the courses linear algebra 1 and 2 as well as analysis 1 and 2, and cover the themes of the books you mentioned for "Real Analysis" and "adv. lin. alg.". Im courious as to why you cover these themes only in your 3rd/4th year. On the other hand, things like ODE, PDE or number theory are strictly for the 2nd and 3rd years in germany, not for the first years.
Transformation methods, which cover Fourier and Laplace transformations could also enter this list somewhere.
I would think those are covered in the differential equations courses. In my ODEs class we did Laplace transforms, and I think the PDEs/Advanced Engineering Math covers Fourier transforms
Pretty sure that is covered in DiffEq classes
Thank you for the recommendations, this is very helpful
Interesting. In Finland the first year curriculum consists generally of:
Fall: Proofs, Calculus 1 & 2, Linear Algebra 1 (+ compulsory general studies like Finnish, Swedish & English)
Spring: Linear Algebra 2 & 3, Advanced Calculus (proof based Calc 1 & 2), Series
Spring Electives: Logic 1 & 2, Probability and Statistics, Applied Linear Algebra
Knowledge of trigonometry and elementary number theory is assumed.
Great video, thanks so much Vince!!
I picked up Axler's LADR as a freshman into my math major and I strongly agree with 10:40! I fondly remember struggling as much as I could through the first chapters. Holds a special place to me
First of all, if you did every course you listed up to @11:54 at a college you would be there over five years as an undergraduate. I mean College Algebra I-II-III and Calculus I-II-III are sequential, so that completing those sequences is over two years right there.
Most people do the "College Algebra" sequence in high school, so start with Calc I in college first semester. Also, summer classes exist.
Really good videos! I don’t see math content quite like this 🎉
I would say I wish I saw complex analysis sooner, it is absolutely beautiful and it is really helpful for studying modular forms which is a magical subject
Man… modular forms are something I aspire to understand. I was chemical engineering in undergrad so I got through diff EQ. Right before things get deep. Now I’m self learning and modular forms are a ways away from me now😂
@@Dark_Souls_3 There are something’s you just need to take for granted when learning modular forms (for me it’s been Fourier/harmonic analysis) but in the end they’re just some funky well behaved periodic complex functions. That for some mystical reason are connected to number theory! What are you self learning at the moment if I can ask?
I would say linear algebra before calculus in order to understand derivatives and integrals in 1d / higher dimensional function is a must.
It‘s interesting how different education systems are.
Here everything up to and usually including Calc3 is covered in school, university starts with Real Analysis, Linear Algebra and Differential Equations.
Which was actually kind of an issue for me because I started my degree 3 years after finishing school so I had to re-learn integration on my own while being asked to prove its underlying ideas in the Analysis class. The additional work was a struggle but I‘m glad I discovered my passion for math and theoretical physics. Better late than never.
Mine was a little different, we did linear algebra in high school as well. University started with discrete math, analysis, abstract algebra, etc.
I would recommend taking calc 3 if you are a chem major. I ended up dropping it a few weeks in, but think it would of been helpful. Usually just calc 1-2 are required.
How would calc 3 have been helpful for a chem degree?
@@eshankulkarni2843 It would of been helpful in electricity and magnetism course of physics (2nd semester physics usually) and also in quantum chemistry class (upper elective I took). Both used double and triple integrals, but b/c calc 3 wasn't prereq, we didn't have to solve any on exams. But would of been helpful to know these things to understand better. Again, I would of just preferred I hadn't drop the course. It didn't put me at a disadvantage not having taking it though so I wouldn't worry if you skip it.
When I acknowledge that I have a real analysis class in my freshman year in university, I knew I'm in big trouble...
For all other business and biology chemistry degrees, math is really useful up to Calc AB-BC levels. After calc 2 (bc) math sort of becomes its own thing, unless you are doing physics.
Computer programming is also more math related depending on which branch you go.
Math is also a mapping of Philosophy, The Quadrivium, and Language, as Math is an Art, not merely a Science.
Absolutely! One needs a strong algebra background to undergo Calculus.
Don't forget point set topology in undergrad and algebraic topology in grad school.
These videos are great this channel is going to be huge
Hi I bought the book of how to think about Analysis by lara alcock and I loved it. Thank for the suggestions. I have 22 analysis book including fizpatrick book and bartle but I loved this book more than anything else.. People praise alot about the real analysis book by jay cummings (this is also the Amazon's best selling book), if you don't mind could you do a review on that book as well
I want to say this but I love your channel and the way you talk and think are alot similar to math sorcerer( he is also a youtuber)
Thank you for the kind words, I will check out the Cummings book, but will need to read it thoroughly before offering my take. Also, I appreciate the comparison to Math Sorcerer, I like his videos :)
Thanks for the awesome information!
bro my community college had a placement test that if you scored high enough on it would automatically skip you straight to calculus. it was multiple choice and i just guessed for most of the questions bc i was very lost and i scored a 86 just from random educated guesses and now i’m taking this calculus class and i’m failing so hard bc i just don’t remember how to do algebra. i’m literally so fucked dude my parents are going to kill me idk how to tell them i got a 47 on my midterm
Ask yourself why you failed. If you failed because you didn’t study enough, then own up to it and try harder next time. It is possible to come back. I failed a graduate level linear algebra test once, and was able to come back from it through hard work.
If you studied your butt off and still failed, then it is not your fault. I would consider taking college algebra again and then retake calculus.
Hi had a great time watching your video, I am intended to learn Differential Geometry on my own, and currently taking a Modern algebra Course and a Course on topology.
Can you pin a list adding the geometry path from the functional analysis, please? as I am learning from youtube it is difficult sometimes on which course should I take next for the same
Unfortunately I don’t have much to recommend with geometry at the grad level. I’ve been trying to find great books in geometry. One of my instructors is using a book by Pogorelov however it’s in the neighborhood of calculus 3. He’s says you don’t need much passed calculus 3 to study geometry but I still search.
@@PhDVlog777 yah I got it. thanks for replying
I have worked differential geometry and smooth manifold theory, and I know you didn't ask me but, it really depends on your foundations. If you have only taken courses like Linear Algebra and Calculus I would recommend you check Do Carmo's "Differential Geometry of Curves and Surfaces", while the approach has been kinda superseded by the study of manifolds, it still a really good book and it gives you some insight into how the ideas of Differential Geometry originated.
If you have already taken a course in Topology, Group Theory, and feel comfortable with Calculus and Linear Algebra I would recommend you check either Lee's "Introduction to Smooth Manifolds" or Tu's "An Introduction to Manifolds", they both develop the theory in a very approachable way, with lots of examples.
The main difference between manifold theory and (classic) differential geometry is in how they study the same objects, in manifold theory we study local properties that allow us to draw conclusion about the whole object while in differential geometry we study global properties that allow us to study the local properties, there are theorems that guarantee they are both equivalent in most important cases.
@@PenaflorPhi Hi thank you so much for these suggestions, I will start with Tu's "An Introduction to Manifolds" and follow up more. do you have a twitter handle, would like to connect and discuss more if possible :)
Topology is missing from the list, a must do, fun of a different kind
I’m an undergrad going into comp sci, but I have a growing love for math
I’m a pure math undergrad and I’m currently in Real Analysis 1, it’s quite challenging.
0 is the supremum of the real numbers I will not elaborate
@@justrandomthings8158 using p-adic metric but instead ||p^k*r||=-p^k?
To do anything practical with machine learning, linear algebra is essential.
I feel like Galois theory is missing
more vids!! these are great watches
Galois Theory and Representation Theory were great classes for me in undergrad.
This is a great list. I thoroughly enjoyed your video. I can't emphasize enough a strong background on linear algebra and modern algebra, for now my goal is to learn galois theory and class field theory, hopefully sooner than later, but my real objective is to what is the deal with elliptic curves, galois representations and L functions. Any recommendations for this path would be appreciated.
Thank you. My background is in analysis so my algebra recommendations are not the strongest. But some authors I would recommend for studying algebra that I liked were Isaacs, Hunderford, and Conrad.
I'd recommend checking out J.S.Milne's website - he has book-length notes series on topics ranging across field/Galois theory, commutative algebra, algebraic number theory, class field theory, and more. I'm looking to go into number theory, and owe a lot of my foundational knowledge to those texts. Another wonderful book series is Kato's "Fermat's Dream" (Iwanami Tracts in Mathematics). Hopefully these are helpful to you.
To get into L functions and elliptic curves, you'd need a strong background in algebraic number theory for which the book by Stewart and Tall could be a good place to begin. You can also look at the later sections of the book by Ireland and Rosen after going through the first book. For all this, you'd need a good foundation in abstract algebra for which you might look at the books by Artin, and Dummit and Foote. And after all this background, you can look at Silverman's book on elliptic curves. After you've learned these you should also look at objects called modular forms which is (sort of like) the bridge between elliptic curves and L functions. That's how I've learnt the subject (until now). Hope that helps :)
Which pen is that?
Pentel EnerGel 07
lol pen is
Wow, it's mostly my UG classes as I took them. I don't think I see "Logic" in there.
Do you guys not do any Topology, Differential Geometry, Representation Theory or Algebraic Geometry in America?
I would consider Topology and Algebraic Geometry a must have for anyone in Algebra or Geometry and Differential Geometry for anyone in Analysis and PDE's.
We certainly do. The content of the video is just one specific recommendation regarding certain courses to take. Many schools (and all competitive ones) in the US study topology as early-on as possible, diff geo in some form, and rep theory/alg geo whenever the algebraic prerequisites are met. There are various courses at as early as the sophomore level across different institutions that introduce all of these aforementioned topics.
hey man, cool videos. hope to see more
Thanks for this video.
I found Kreyzig quite good for mathematical methods/differential equations and complex analysis. Something about it that clicked with me.
A high schooler who wants to do math this is great
i love your videos
Can you add book recommendations for each subject. That might be very useful if I want to self study. Thanks
I'm currently taking my 1st year as undergrad (double major in math and comsci)
These are the predefined curriculum (almost) that our university uses. But it also have applied math subjects every semester like physics and statistics.
can you take photos of you demonstrations works and up to drive and share with us please, thanks
Great video mate👍🏻
4:32 parrot 🦜
bruh I'm taking abstract algebra and adv linear algebra sophomore year and I'm boutta fail finals ;( Axler is beating my ass
I appreciate the video, but as a math student, I'm shocked that you didn't put down at least one topology course. Point-set and algebraic topology are both really important, as well as differential geometry and algebraic geometry. I feel like excluding all of these gives people the wrong impression about what math is.
Point set topology is foundational to analysis. You can't do analysis without it, so I assume it'd be covered under that.
Bro really hates Topology. Otherwise, great list i really enjoy your videos°
I like math , I study autodidact with your books thanks
i was a biochemistry major and they us go up to calculus III. looking back at it, i wonder why
What about Topology, Chaos Theory, Lie Algebra and Differential Geometry? (All postgraduate)
Is measure theory metric spaces? I notice you didn't stress statistics so much (unless probability covers this) or something like combinatorics (you did mention graph theory). And maybe something like Lie Algebras and Differential Geometry (maybe non-Euclidean geometry covers this). Then there's topology and algebraic geometry which I know little about. Good list though.
Not quite. Metric spaces generalize the notion of distance (think absolute value between points), while measure spaces generalize the notion of length, area, or volume.
Yeah at ASU it’s called “Discreet Math” and it tore me a new one. I’ll never forget, though, there was a homeless guy that was auditing the class and he consistently was getting like 5% better scores than everyone on every exam
Discreet math tore you new one? And in top of that you got bested by a homeless guy? Wow that is tough 😅
pro tip take LA before calc 3
why? I took calc 3 last semester and I'm taking LA right now, I found it was better to take calc 3 immediately after calc 2
@@eshankulkarni2843 the applications of linear algebra in calc 3 go wild, i understood things like the jacobian a lot more tho i suppose if your precalculus course did enough matrices you could get by, calc 2 -> LA -> calc 3 -> ODEs is my favored path
Topology???
Where is undergraduate level group ring and possible field theory in Abstract Algebra. No undergraduate course can miss it. And a student who studies abstract linear algebra also gets confused with out group ring theory.
Do you have any texts on the algebraic manipulations of sums, multiplications (capital pi), and other stuff that is not too readily taught in any course curriculums. I wish to start tackling MIT-level integrals and more advanced topics in math but need some texts to aid. Any suggestions on texts will be wonderfully appreciated.
I'm cs undergrad student and we did Introduction to Abstract Algebra course
what a great site!!!
In US we say mostly pre-calc not college calculus.
In UCLA there is a Pre-calc class and same in UCF and other places.
I assume college algebra 1 2 3 stands for Algebra 1 2 and Precalc…
The latter makes more sense. As there is usually one more course before Pre calc, that is geometry.
High schoolers usually finish Algebra 2 or Pre calc.
During highschool, the usual highest mathematics achievement is calculus 2.
Calculus 1 and 2 are named AB and BC in high school, which are great introductory to Calculus. Then in college they will take calc 3 4 and other math courses.
Yes I agree with this. I recently finished high school and the highest math achievement for myself and some classmates is Calc 3 and Linear Algebra.
Please bless us Oh Graduated One
Lmao
You forgot to add remedial algebra 1
which state are you from? you have a distinct accent
What kind of pen are you using in this vid?
good
Combinatorics?
Topology is also very important especially for those interested in Analysis at the graduate level.
Im currently in my first year as an undergrad and am in advanced linear algebra. Out of curiosity, does anyone think it is a bad idea to skip elementary linear algebra and go straight to advanced? My school allows it, I’m just not sure if I’ll need to learn the material a second time.
Do it. If you want to do math, the best way to get good at it is to do difficult stuff.
I’m getting advised for my next semester pretty soon and I’d like to get a bit ahead, would it be a good idea to take calc 3 and elementary diff eq during the same semester?
Have you taken linear algebra yet? calc 3 and linear algebra in the same semester is somewhat doable. I've heard DiffEq is a bit harder so I'd prefer not to take it at the same time as calc 3.
The disrespect tor topology
How does a bachelor in the US sum to a the first year of undergrad in europe... There must be some difference in what each course corresponds to...
Yes there is. Also you have to remember that in the US we do not specialize at all in high school, not until undergrad. And I was told that in Europe your undergrad is 3 years, vs 4 years in the US.
Why you do not put topology?
Gracias