The Science of Life Lecture Series

So, there has been a debate going around social media as of late.  It deals with the order of operations, and the fact that the vast majority of people seem to forget that each step of the order of operations ends with the phrase "from left to right".  That phrase is irrelevant most of the time, but when it's not irreverent, it's crucial. Damn you PEMDAS! So what is 9!/8!(3^2)?  Is it 81 or 1?  Or is it something else entirely?  Now I am going to tread lightly here so as to not enrage too many hearts. Before I answer this question, it would be a good idea to review the algebraic order of operations , or PEMDAS: Perform all operations inside parentheses using the remainder of the order of operations as your guide to the order.  Any parentheses within parentheses are to be performed from the inside out and from left to right. Perform any and all exponent from left to right. Perform all multiplication and division from left to right. Per...

In this third section of Chapter 1 , I will cover the basics of equation solving.  I've already touched on this in Physics , and will get to in in Chemistry; this is vital for all of math and science, including Economics. Equivalent Forms One of the most vital statements in Algebra is that two equations which have the same solutions are equations.  In all future endeavors, both science and in math, we look to solve for the variable that is unknown, and the final form of that equation doesn't look anything like the initial equation, but is in an equivalent form, so has all of the same solutions as the initial equations.  For any real numbers a, b, c, and d, $a+c=b+c$ is equivalent to $a=b$ and $a=b$ is equivalent to $a \times d=b \times d$.  What we can do from here is say that $a+c=b+c$ is equivalent to $a \times d=b \times d$. Like Terms In any equation, a "term" is any constant, variable, product of any number of constants and/or variables, or the qu...

In this first section from Chapter 1 , I'll cover some basics of Algebra, including basic terminology. Basic Terms: When a letter is used for a stand-in for a value which can take up any range of numbers, we call it a variable.  When a letter is used to represent a specific number (typically when we don't know what it is, but there can only be one), it is said to be a constant. Our Constants An example of this is the gross pay; the pay on your pay check before taxes is given by P G =H×W, where H is the hours worked and the W is your hourly wage.  Since hourly wage doesn't change from week to week, it is considered to be constant.  If you work part time, than your hours in any given week is considered a variable, because they do tend to change. An algebraic expression consists of a combination of constants, variables, and operation signs.  For example, H×W from the pay equation above is considered an expression.  When an equals sign is placed ...