Designed by Freepik
The Goal
Rebuild my math foundation from the ground up.
The project consists of:
- 2400 math problems from Alcumus (by the Art of Problem Solving)
- 150 problems from Mathematical Thinking and Proof-Writing courses
- 150 problems from Real Analysis
- 150 problems from Theoretical Linear Algebra
- 150 problems from Ordinary Differential Equations with Theory
- A final project
UPDATE: The previous plan consisted of 2700 math problems from Alcumus, 150 problems from StanfordOnline’s Introduction to Mathematical Thinking and 150 problems from Real Analysis.
I changed it because Linear Algebra and Differential Equations courses are very important for my future plans.
Why Am I Doing This?
Back in secondary school, I was really into critical thinking and logic. That curiosity sent me down a rabbit hole where I discovered the axiomatic method in math — you take a small set of axioms, and using logic, you build everything else from scratch.
For me, that was jaw-dropping. Until then, math had always been boring: memorize a formula, use it on a test, repeat. That wasn’t math. This was math (at least the mathematical logic part). I was hooked and wanted to learn more.
Problem was… in secondary school, I never truly learned math — I only studied enough to pass exams. So I tried to relearn all of high school math. Spoiler alert: it didn’t go well. After several failed attempts, I discovered the Art of Problem Solving and their platform Alcumus.
Instead of boring drills, Alcumus offered adaptive, challenging problems that made me think. For the first time, high school math felt creative, challenging, and fun.
I first thought of this project when I started university, but I seriously began it on January 1st, 2025. But a lot had changed in the meantime, I had more math topics under my belt. In my first two years of university, I’ve learned introductory combinatorics, calculus, probability, statistics, matrix algebra, multivariable calculus, and even some elementary number theory. So I wasn’t starting from zero anymore.
Most importantly, I wanted to explore advanced mathematics and get started with research. To rebuild my math skills in a meaningful way, I couldn’t just rely on problem-solving — I needed to step into “real mathematics”, which means I had to combine problem-solving with proof-writing. This project is my way to do both.
Watch the Presentation Video
Progress
I will update this every week
Alcumus
My alcumus profile. You can look me up on AoPS, my username is anordinarylearner
Note: I only consider correctly solved problems.
- Problems solved so far: 1531 / 2700
- Problems attempted: 1749
- Topics mastered: Prealgebra, Algebra, Number Theory
- Remaining topics: Counting & Probability, Geometry, Intermediate Algebra, Precalculus
Mathematical Thinking and Proof-Writing
- Problems solved so far: 0 / 150
Real Analysis
- Problems solved so far: 0 / 150
Theoretical Linear Algebra
- Problems solved so far: 0 / 150
Ordinary Differential Equations with Theory
- Problems solved so far: 0 / 150
Final Project
To be determined