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CAHSEE Math Exam: Help and Review22 chapters | 255 lessons | 13 flashcard sets

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Lesson Transcript

Instructor:
*Peter Kosek*

Peter has taught Mathematics at the college level and has a master's degree in Mathematics.

Algorithms are everywhere. Computers use them, your friends use them, even you use them. Learn more about what algorithms are, as well as create some algorithms of your own.

An **algorithm** is a finite list of instructions, most often used in solving problems or performing tasks. You may have heard the term used in some fancy context about a genius using an algorithm to do something highly complex, usually in programming. Indeed, you've most likely heard the term used to explain most things related to computer processes. However, what would you say if I was to tell you that there is a very good chance that you, yourself, have followed an algorithm? You may have followed some algorithms hundreds or thousands of times!

Have you ever baked or cooked something? One of the most obvious examples of an algorithm is a recipe. It's a finite list of instructions used to perform a task. For example, if you were to follow the algorithm to create brownies from a box mix, you would follow the three to five step process written on the back of the box.

One of the attributes of an algorithm is that, since it is a list of instructions, there is some step-by-step process that occurs in order. Very often, the order that the steps are given in can make a big difference. Suppose we were to reorder the steps of the recipe on the back of the brownie box and told somebody to put the brownies in the oven for 22 minutes before we told them to preheat the oven. That would be silly! That's why the ordering of the steps is very important.

One of the most common uses for algorithms is in computer science. Computers can't do anything without being told what to do. Algorithms allow us to give computers step-by-step instructions in order to solve a problem or perform a task. For example, let's consider the following algorithm:

*For each odd number from 1 to 9, multiply it by 2 and add 7 to it. Then, write out the results as a list separated by commas.*

How would we start to follow this algorithm? Well, it first says that for each odd number from 1 to 9, multiply it by 2 and add 7 to it. Remember, we need to follow the steps in the order they are given. We first start out with the first odd number, which is 1. Let's multiply it by 2 and then add 7 to get 9. Then, we go to the next odd number, 3. Let's multiply it by 2 and add 7 to get 13. We repeat this process for 5, 7, and 9. Once we finish that, we want to write out the results as a list separated by commas. Therefore, our final output is 9, 13, 17, 21, 25.

Now that we know how to follow an algorithm that's already been written, how could we write our own algorithm to perform a task or solve a problem? For example, if you were given the equation 3*x* + 5 = 17, could you write an algorithm to explain to somebody how to solve for *x*?

In order to do this, think about the necessary steps and the order in which you would have to do them. If you were solving this equation for *x* by yourself, you would probably first subtract 5 from both sides. You would be left with 3*x* = 12. Then, you would divide both sides by 3 to get *x* = 4. Therefore, your algorithm could look something like this:

*First, subtract 5 from both sides. Then, divide both sides by 3.*

Not too bad, right? Algorithms are just a formal way of writing out the step-by-step instructions to give to someone else to perform a task.

One thing worth mentioning is that there can be multiple algorithms that can be written that do the same thing. For example, a different algorithm that could exist to solve for *x* in 3*x* + 5 = 17 could say:

*First, subtract 17 from both sides. Then, add 12 to both sides. Then, multiply both sides by 1/3.*

This is a perfectly acceptable algorithm that performs the same task. The other one might be faster since it had only 2 steps rather than 3, but at the end of the day, it solves the same problem.

Let's take a few moments to review what we've learned. Mainly, we define an **algorithm** as a finite list of instructions used to solve a problem or perform a task. It's not only used by computers or super geniuses who design them and their programs, but is used by pretty much everybody in their day-to-day lives. When making use of an algorithm, it's really important to follow the instructions in the given order to ensure your result is the desired one. Also, remember that multiple algorithms can exist to solve the same problem.

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CAHSEE Math Exam: Help and Review22 chapters | 255 lessons | 13 flashcard sets

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