ITT we fix this image.
>almost no algebra
>no combinatorics
>no set theory or logic
>no geometry
>no numerical analysis
>only a little topology
It's basically a syllabus fast track for analysis.
Let's make an actual syllabus for someone to go from Khan Academy to having the knowledge of an Undergrad in General Math from MiT all without having to set foot in a higher learning institution.
This is the path to an undergrad in general math from MIT. Beyond an introduction, topics in algebra and modern geometry are too advanced for undergraduates on the standard track. What is posted here is consistent with what an undergraduate math education would look like. At MIT, algebra is required, but once again it is merely an introduction, and the rest of what you listed are electives or seminars.
What if this 'updated' version included course numbers for MIT open courseware, since that school is being used as an example?
>>7647454
OCW is lacking in a lot, if not most of it's courses. The amount of good MIT OCW programs I can count one hand.
>>7647411
Nobody is going to take all those classes in one year, especially not an MIT undergrad. They're too busy committing suicide after finding out that they paid too much for a university that doesn't care about them.
>>7647411
Differential Geometry:
"Differential Geometry: Curves - Surfaces - Manifolds" by Wolfgang Kühnel
--- I have personally read this book and it is an excellent introduction to the topic. It covers a lot of information in only ~400 pages. Everything from the basics like properties of curves in R^2 to much more advanced topics like Riemannian Geometry. Also includes an overview of GR at the end.
Algebra:
"A Book of Abstract Algebra" by Charles C Pinter
-- Have not personally read it but it gets great reviews and I am pretty sure a lot of people on /sci/ are familiar with it.
Algebraic Topology:
"Algebraic Topology" by Allen Hatcher
-- I have not personally read this book but it is a universally loved book on the topic.
-- There is also a youtube video lecture series to go along with it. I have watched these and enjoyed them.
https://www.youtube.com/playlist?list=PLpW0M9zJ2RQ6Q_nu6nl30Mpx918tFn7Fo
Algebraic Geometry (For Physicists):
"An Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces " by Martin Schlichenmaier
--- I have read this book and can personally recommend it. However it is the only book on Algebraic Geometry I am familiar with and while it only focuses on pure math, the topics it focuses the most on are those important in String Theory.
>>7647638
That Pinter book skims the surface of algebra, really it isn't too great, if it wasn't a dover book for the price it wouldn't be very good.
>>7647855
Well Artin is another pretty well liked one. And I have read that one and it goes very in depth.
>>7647868
>>7647887
Artin is nice but very linear algebraic. Good if you've done a lot of linear algebra, but every example is of a matrix group. It also misses lots of stuff you should see in a proper treatment of algebra. I think it's worth reading, but not your first algebra book.
D+F is not as well written, but it has everything and a ton of exercises. It's really great for your first time through if you can already write a good proof. If you can't, Gallian will hold your hand a lot better than Artin or D+F.
I really think OP's track is dumb though. Get good at calculus, learn some epsilons and deltas, convergence theorems, integration theory. You don't need 3 whole years of analysis.
I think you should get a Gallian level of algebra, as well as number theory, combinatorics, set theory and logic by the end of your sophomore year, around the time you should have finished calc three and maybe analysis.
>>7647638
Dummit and Foote is the standard algebra text. Exercises out the ass.
I have Pinter's book as well right in front of me.
>>7647906
I don't see why Axler would be off the textbook list. I recently wanted to nail my linear algebra down and that book did it for me.
In terms of timing, I don't think it matters when you hit a topic as long as it makes sense in sequence and you hit it well.
>>7647411
Is there something like this for electrical engineering? I want to take next year and get a good grasp on the maths again before going back to uni.
>>7647411
http://4chan-science.wikia.com/wiki/Math_Textbook_Recommendations
>>7647411
One major fix is to make it even more clear that 'STEP ONE' is volume one of Stewart's calculus (the book price list appears to contradict it by saying "Stewarts (1-3)". Another thing is to not call them fucking chapters, you could not fucking do all of limits in one day.
>almost no algebra
What? It does linear algebra and abstract algebra, with a suggestion to move onto ring/fields.
>no combinatorics
I'll grant you that.
>no set theory or logic
Surely that'd be in the proofs book of 'STEP TWO'?
>no geometry
Again, it's in the additional courses part, and you're gonna want the foundation that the main guide gives you for when you move onto shit like topology.
>no numerical analysis
In the additional courses and I wouldn't want to do numerical analysis without some of the stuff in the main guide... heck, my uni has 'core algebra' and calculus listed as prerequisites for a numerical analysis course.
Heck... comparing it with my uni, maths students have mandatory algebra, intro stats, intro applied, real analysis, complex analysis and linear algebra.
>>7648474
>>7647411
Oh, and also make it more appropriate for students from different backgrounds, for example - a student who's passed college in the UK could happily skip Stewarts... or I think so anyway, I'm pretty sure Spivak everything Stewart does and the only things I remember learning from Stewarts were limits and local linear approximations. You only really need Stewart for practising simple computation.
>>7647411
>>7648474
I think lecture notes with problem sets are superior to books.
I think reading a book from cover to cover and taking the time to understand every fucking proof is a waste of time.
With lecture notes you get a feel of achievement quicker.
So in my opinion you should make a list of good lecture notes and problem sets
>>7648482
You've clearly missed the point of the fucking image.
I do agree that this image only goes into any depth for those hoping to build up to Rudin. I'll put together a similar guide for the budding algebraic geometer when I get a little while.
>>7649257
1. git good at algebra
2. Eisenbud
3. Hartshorne
4. Hartshorne
5. Learn French
6. EGA
>>7649274
Can anyone confirm that french have good introduction level mathematic literature
>>7648482
>you get a feel of achievement quicker
top kek, might as well watch popsci vids if feeling good is your goal
>>7647948
http://4chan-science.wikia.com/wiki/Electrical_and_Electronics_Engineering
>>7649082
>I am arguing that lecture notes and problem sets are superior to plain books.
What is the difference between lecture notes with problem sets and a book with exercises?
>>7649274
french confirmed for being no1 language for modern algebra
>>7649308
>Soit X un schéma...
It's pretty. That and the French basically invented the modern field.
>>7649291
bkristof (dot) free (dot) fr
This is the webpage of a first year prep class teacher who makes amazing lecture notes (each chapter has a corresponding problem set).
In my opinion, it's much better for a beginner than any book.
The first year covers basic set theory, number theory (prime factorization, Bezout's theorem), calculus (real and complex numbers, series, limits, continuity, differentiability, asymptotic analysis, series, integration of piecewise continuous functions on a segment, 1st and 2nd order linear ODE), linear algebra (linear systems, vector spaces, dimension, matrices, inner-product spaces, orthogonal group, 3d geometry), a tiny bit of abstract algebra (basic facts about groups, rings, fields and some stuff about polynomials and rational fractions) and discrete probability
>>7649291
For algebraic geometry, EGA and SGA are good.
Not the best desu.
>>7649297
My hero
Thanks man
OP list is something an autist would list. The picture you posted is correct. Those are the basics. What you posted, OP is elective or graduate school topics. MIT doesn't require most of their maths student to take those classes, unless you want it as an elective.
>>7649304
They come to the point quicker
After all it's all about applying the stuff, fuck the proofs m8
>>7648474
So what does the pic mean by 1-3? Stewart has his main Calculus, along with countless others and it seems easy to get confused.
Whenever I look at Stewart's books, it seems impossible to get a whole chapter done in a day while actually learning anything. Am I just missing something?
>>7650269
I believe it means buy all 3 volumes of calculus and use it for revision, but STEP ONE is only the first volume.
>>7649484
Hey these look great for practicing my French. Thanks
>>7649484
>MPSI C du lycée Chaptal
Still can't believe they rejected my application there ;_;
>>7653004
I feel the same for Durham uni in the UK.
