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Welcome back.

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This lecture is going to go over all the mathematical operators available in Lua as well as the math

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library.

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You should already know the basics of math such as adding, subtracting, dividing, multiplying and

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exponentiating numbers.

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Here you can see all of the different operators responsible for those actions, such as adding, subtracting,

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dividing, multiplying, exponentiating.

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And then we also know about the modulus operator, which calculates how many times a number can fit

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into another number and returns the remainder.

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So for example.

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If I were to divide seven by three using the modulus operator, we know that we can fit three into seven

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two times, and the remainder left over would be the value of one.

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Same thing if we did six modules two.

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We know that two can fit into six three times.

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And because there's not going to be any remainder, the leftover is zero.

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And that's what's returned by our modulus operator.

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We also have these other operators here that are specific to luoyue.

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And the one that we saw previously was this one where we can add a number to itself.

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So if we had a variable that stored the value of one instead of doing, let's say a is equal to a plus

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one, we can just do a plus equal one, and that achieves the same effect.

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We can also do the same thing with subtracting a number by itself.

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We can do the same thing with division, multiplication, exponents, and even the modulus operator.

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Let's go ahead and take a look at these mathematical operators in action.

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I'm going to create a variable called a and just store the value of two.

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And then what I'm going to do is put a bunch of print statements here.

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And I'm just going to print something like a plus one.

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And then I'm going to print out a minus one.

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We can print out a divided by two.

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We can print out a multiplied by two.

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We can print out, let's say, a to the power of four, and then we can print out a modulus to.

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What do you think's going to print out?

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Well, let's find out if we hit run.

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As you can see, a plus one is equal to three.

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A minus one is equal to one.

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A divided by two is equal to one.

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A times two is equal to four, a to the power of four is 16, and then two fits into two one times,

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so there's no remainder left over, which means we return or print out the value of zero here.

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Now, just like regular mathematics, the interpreter follows the order of operations, which is usually

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referred to as Pemdas or Bodmas, which either stands for parentheses, exponents, multiplication,

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division, and then addition or subtraction, and bodmas stands for brackets, orders, Division, multiplication,

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addition and subtraction.

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Both of these acronyms mean the same thing.

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So the first things that get operated on are the things that are inside of parentheses, and then the

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next are anything that have exponents.

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And then after those is going to be multiplication and division.

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And then finally the last ones that get operated on are addition and subtraction.

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To demonstrate the order of operations.

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What I'm going to do is print into the console.

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We're going to take a and we're going to wrap our a value inside of parentheses.

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Inside of these parentheses I want to add the value of let's say three.

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And then I want to raise this to the power of two.

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And then afterwards we can subtract this by, let's say, nine divided by three.

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Now if the interpreter follows the order of operations, then the value that should get printed into

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the console should be the value of 22.

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So we can go ahead and hit run.

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And there we go.

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We get the value of 22 as we expect, proving that the interpreter follows the order of operations.

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Now, the last thing I want to talk about here is going to be the math library.

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And this gives us access to a bunch of functions that aren't implemented as operators, such as getting

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the absolute value of a number, the square root of a number, and many other trigonometric functions.

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Now, I'm not going to be your math professor today, so I'm not going to go into much depth about all

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of these mathematical functions, as that would take way too long and you probably won't remember any

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of it.

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However, the math library also has some functions that give us, for example, the smallest number

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that is greater than or equal to a number we specify, which is useful for floats.

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We have other functions to get the largest number that is smaller than or equal to a number we specify.

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We can use some other functions which are called math.max.

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Which will return the largest number out of the numbers we pass to the function.

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We also have math.min, which will return the smallest number out of the numbers we pass to the function,

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and there's a whole bunch of other ones.

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So we go ahead and index the math library by typing out math.

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As you can see, there's just a whole bunch of different mathematical functions, trigonometric functions,

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and just a bunch of stuff that would take way too long to learn about.

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But they're all here inside of the math library for us to use.

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Specifically here, I want to focus on the math dot random function that we took a look at earlier,

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and this function returns by default a pseudo random number between 0 and 1.

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When we do not specify a range or pass a range to the function, they're called pseudo random numbers,

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because numbers generated by a computer are never truly random, and this is because computers are awful

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at generating random numbers.

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Now we can also specify a seed for the random function, which means that the number that gets returned

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by this function is based on the seed.

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A seed will always return the same number, just like how a seed in a video game like Minecraft will

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always return the same world.

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To demonstrate this, I'm going to create a for loop that loops five times.

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So we can do for I is equal to one.

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And we want to loop five times.

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And what we want to do is we want to set the math dot random seed equal to the current index.

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And then we want to print out what gets returned by our math dot random function.

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Now, since this math notrillionandom function is going to return a value based on the seed, every

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single time we execute this loop, we should expect the same number to get printed out through each

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iteration of this loop.

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So with a random seed of one, any time we execute this math dot random function, as long as it has

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a seed of one, it's always going to return the same number.

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So if we run our game here.

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As you can see, we get five different numbers based on those seeds from 1 to 5.

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And then if we go ahead and stop the game and then run our game again.

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As you can see, we get the exact same numbers printed out in the console, and we can keep stopping

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the game and rerunning the game over and over again, because these will always print the same numbers

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out.

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And that's because those numbers are based on the seed that we pass here.

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If we do not want to specify a seed, then we can just go ahead and delete this.

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And our Math.random function will continue to generate random numbers inside of the console.

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So if we hit run.

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As you can see, we get a bunch of random numbers between 0 and 1, and then if we hit stop and then

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run the test again.

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Here we get a complete different set of random numbers.

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And one last time, if we hit stop and run again.

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We get another set of random numbers.

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All righty.

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That is all from me for this lecture.

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I hope you enjoyed and I will see you in the next one.

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Happy scripting.