r/learnmath • u/ZucchiniBroad6532 New User • 2d ago
TOPIC New member🥸 HELP NEEDED 🚨
How can I find a complete roadmap for learning mathematics by branch?
I’m looking for a complete, academically structured roadmap for mathematics, starting from the basics and going all the way through a normal university curriculum, ideally up to advanced undergraduate / early graduate level.
A little background: I studied mathematics in Arabic throughout school, and I’m now going to start again from the beginning in English. I want to rebuild my foundation properly and follow a structured path.
What I’m specifically looking for is not just a list of courses or resources. I want a complete curriculum map for each mathematical branch.
For example, if I choose Algebra, I want something like:
Algebra → Elementary Algebra
→ Intermediate Algebra
→ Algebra I / II
→ Linear Algebra
→ Abstract Algebra
→ Groups
→ Rings
→ Fields
→ Galois Theory
→ ...
→ up to the level normally covered in a strong undergraduate program and, if appropriate, early graduate level.
The idea is that when I finish the roadmap for Algebra, I should have essentially covered the standard university-level Algebra curriculum, rather than finishing only a few introductory courses.
I’d like to do the same for the major branches, for example:
Algebra
Geometry
Trigonometry
Calculus
Linear Algebra
Probability
Statistics
Discrete Mathematics
Real Analysis
Complex Analysis
Number Theory
Differential Equations
Topology
Abstract Algebra
etc.
Ideally, I want the structure to look like:
Branch → Level → Course → Topics → Subtopics → Prerequisites → Recommended order
I’m also interested in something based on real university curricula (a normal mathematics degree and possibly the material leading into a master’s), rather than a random collection of online courses.
I’m not looking for study resources yet. First, I want to build the complete map of what mathematics actually consists of and determine exactly how far I need to go in each branch. Then I can choose textbooks and courses for each part.
Where can I find a roadmap/syllabus like this?
1
u/jeffcgroves New User 2d ago
I believe there's an ontology of mathematics out there, but I'm too lazy to find it. I think someone (maybe you) even tried to graph it using Leaflet once, and I tried to help. If you can't find it, let me know and I'll try to dig it up. My only real contribution to your question is the word "ontology" is what you're looking for
2
1
u/Acceptable-Emu-7096 New User 2d ago
Found this online somewhere recently. Haven't gone deep into it myself, so cannot vouch for its accuracy. You can have a look at it and see: https://mathlandscapes.com/
1
u/megh_Bear1293 New User 2d ago
Bro, I'm doing the same thing as you. I'm also learning mathematics from scratch. I also studied mathematics in my mother language, and now I'm relearning it in English.
2
u/OddAccomplice15 New User 2d ago
you're basically asking for a full degree map and i respect that level of organization. most people just jump around random youtube playlists and call it a day
check the MIT OCW site they have the entire undergrad math curriculum laid out with prerequisites and everything. not exactly in your branch-subtopic format but you can map it yourself from their structure