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The Goal
Cultivate a rigorous foundation in mathematics and formal proof-writing, elevating the analytical skills required for research.
The project consists of:
- 2400 math problems from Alcumus (Art of Problem Solving) to develop problem solving and conceptual understanding.
- 150 problems from Stanford Online's Introduction to Mathematical Thinking to strengthen formal reasoning skills.
- 150 proofs from elementary mathematical topics.
- 300 problems from Real Analysis for mastering the theoretical underpinnings of calculus.
- A final research-oriented project.
Curriculum 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.
The curriculum was revised to increase proof-writing practice.
The Motivation
Back in secondary school, I became interested in critical thinking and logic, which led me to the axiomatic side of mathematics: starting from a few assumptions and building everything through reasoning. That completely changed how I saw math.
Before that, math had mostly been about memorizing formulas and applying them on exams. Discovering proof-based reasoning showed me a deeper and more meaningful side of the subject, and I wanted to pursue it seriously.
The problem was that my early training had gaps. I had learned enough to pass exams, but not enough to reason rigorously or write proofs. After several unstructured attempts to “relearn everything,” I found the Art of Problem Solving and its Alcumus platform, which emphasized challenging problems and careful thinking.
Through that approach, math became creative and demanding rather than mechanical.
I first considered this project when I started university, but committed to it seriously on January 1st, 2025. It is designed to develop the rigor and mathematical maturity required for research-level work.
Watch the Presentation Video
Progress
Updated Weekly
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: 1539 / 2400
- Problems attempted: 1757
- Topics mastered: Prealgebra, Algebra, Number Theory
- Remaining topics: Counting & Probability, Geometry, Intermediate Algebra, Precalculus
Stanford Online’s Introduction to Mathematical Thinking
Pk0001, CC0, via Wikimedia Commons
- Problems solved so far: 28 / 150
View the course assignments and my solutions:
- Assignment 1:
- Assignment 2:
- Assignment 3:
Proofs from Elementary Mathematical Topics
Kilom691, CC BY-SA 3.0, via Wikimedia Commons
- Problems solved so far: 0 / 150
Real Analysis
Oleg Alexandrov, Public domain, via Wikimedia Commons
- Problems solved so far: 0 / 300
Final Project
To be determined