Math

Math matters more than ever. And I don't consider anyone who isn't good at math "intelligent", and anyone with decent IQ can achieve proficient level of math knowledge. It's always the laziness and unwilligness to learn. One of my personal goals of 2025 is to re-learn math and the book that I chose is No Bullshit Guide to Math and Physics

In general, anyone interested in rekindling and improving their relationship with mathematics should consider this book as an opportunity to repair the broken connection. Math is good stuff; you shouldn’t miss out on it. People who think they absolutely hate math should read Chapter 1 as therapy.

Notes​

1. Math fundamentals​

July 3rd 2025​

Why do we need so many different sets of numbers? The answer is partly historical and partly mathematical. Each set of numbers is associated with more and more advanced mathematical problems.

The only thing you can’t do with the reals is take the square root of a negative number—you need the complex numbers C for that.

Note that multiplication can be defined in terms of repeated addition.

Division is the inverse operation of multiplication.

Often an equation calls for us to multiply things together many times. The act of multiplying a number by itself many times is called exponentiation,

Symbolic manipulation is a powerful tool because it allows us to manage complexity.

As we saw in the section on solving equations, the ability to “undo” functions is a key skill for solving equations.

The function-inverse relationship is reflexive—if you see a function on one side of the above table (pick a side, any side), you’ll find its inverse on the opposite side.

July 4th 2025​

Factoring involves taking out the common part(s) of a complicated expression in order to make the expression more compact.

When dealing with a quadratic function, it is often useful to rewrite the function as a product of two factors.