# Section2Proof Portfolio

ΒΆMathematical discovery happens in phases. Most new discoveries begin as a **conjecture**, a mathematician's educated "hunch" about what might be true. Then comes the hard part: the **exploration**, the scrawled calculations on scraps of paper, the hours spent blankly staring at a whiteboard, and the time spent reading about other related results that might be helpful. Only after the evidence is strong enough and the "right" argument emerges comes **formalization**, where the argument is carefully organized in a logical progression from beginning to end, any potential missing links identified and filled, and all references and citations appropriately made. Finally comes the **presentation** where the formal argument is communicated in a way that's appropriate for the audience who is to read it.

Conjecture, explore, formalize, present: This is how mathematicians work. While you're learning abstract algebra this semester, I not only want you to come into new knowledge and skills about the ideas of mathematics; I also want you to have an authentic experience of this process as a nascent mathematician yourself. Your **Proof Portfolio** is the setting for that experience, where you'll have the opportunity to focus on this process with a particular eye toward its final steps: formalizing and presenting your arguments.