Artin’s Algebra!

This post has nothing to do with Michael Artin Algebra! Artin of this post is my son, and this is the story of him learning algebra. He is 11 years old now, and I guess one of few students on the planet that still has a positive mentality towards mathematics! We are reading together Gelfand’s’ Algebra, page by page, solving its problems one by one. The section “Letters in algebra” includes the following “Magic trick”. Choose the number you wish. Add 3 to it. Multiply the result by 2. Subtract the chosen  number. Subtract 4. Subtract the chosen number once […]

Structure, Structure, Structure!

Look at this equality: or this one: They are true structurally. In principle, you can just replace one side of the equality with the other side without any extra comment. However, we usually like to describe these in terms of processes. For the first equality, we might say that adding the first two and then the sum to the third is the same as adding the first to the sum of the last two. For the second equality, we might say that from left to right it is multiplying through a set of parentheses, and from right to left, it […]