Lesson subsection
Read the explanation, try the on-paper prompts, then explain the idea in your own words. Use AI feedback as a mentor, not a shortcut.
Best flow: read → think on paper → write a short explanation → refine with feedback.
Writing your first proofs feels awkward because you are learning a new language: mathematical English combined with logical structure.
A good way to start:
It's normal if early proofs feel clumsy. Clarity and correctness matter more than style. Style improves automatically with practice.
TL;DR — key idea
Start by restating the goal, listing your assumptions, and connecting them step by step. Focus on correctness and clarity; elegance comes later.
Don’t skip this – writing proofs or explanations on paper is where most of the learning actually happens.
Outline (in bullets) the steps you would take before writing a full proof of a simple statement, like 'the sum of two even integers is even'.
Explain why it is important to write sentences and not just chains of symbols when you are learning to prove things.
Once you’ve sketched some ideas, summarize the main insight in the reflection box on the right.
In 3–6 sentences, explain the core idea of this subsection as if you were teaching a friend who hasn’t seen it. Focus on the logic, not just the final statements.
AI is optional. Use it to spot gaps and sharpen your wording, not to replace your own thinking.