How can you add infinite numbers and get an integer result? What even does this symbol ∑ mean? Join this series to find out the answers to those questions, along with other fascinating results from the topic of mathematical Series. For me, and others I've talked with, Series is the hardest topic in AP Calculus BC, so if you are planning on taking that course or any Calculus course, this crash course will be helpful in laying the foundations to make your future learning easier. We'll work through mathematical notation and procedures that are frequently used in more advanced math courses, thus helping you prepare for those later studies. Here is the link to the Khan Academy unit: https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:series in case you want a sneak peak before we begin. I'm excited to join you in this series (pun necessary) and see what we can learn together!

As imaginary as complex numbers might initially seem, they are extremely useful in advanced math and engineering courses and are well worth understanding. Join me to gain a solid grasp on complex numbers and to learn how to use them to solve problems and better manipulate trigonometry. We'll be working through the Khan Academy unit here: https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:complex which you are free to look into in advance to see if you are interested in joining the series, or if you just want to get a head start. Not only will we cover the fundamentals in this crash course, but I'll also teach you cool applications and tricks and provide support for any of your questions along the way. I'm excited to join you as you embark on learning the fascinating topic of complex numbers.

What is GIMP? GIMP stands for GNU Image Manipulation Program. It is like Photoshop, but free and open source. In this short series, I'll teach you how to use some of the tools of GIMP (and some aspects of image manipulation in general), and each of us will create a project to present to the group. You'll need to have GIMP installed; download it here: https://www.gimp.org/downloads/ Alternatively, you can use the free and online Photopia: https://www.photopea.com/ which is similar. Note that I will be using GIMP, and it will be best if you can use it as well.

We'll learn about cryptography methods and their weaknesses, forensics and how to hide messages in image files, buffer overflows and how to find vulnerabilities in C code, reverse engineering and how to figure out what a piece of code is supposed to do, and web exploits and things to avoid when making a website. In the process, we'll learn how to work with linux, write python scripts, and use powerful tools. Some programming knowledge would be helpful, but it is not an official prerequisite; if necessary, I can teach some introductory python if you have not had experience with it before. Since the best way to learn this material is through practice with challenges called CTFs (capture the flags), you will need an account for picoCTF.org (just do not use your full real name as your username), which offers challenges and servers that we are allowed to hack. Some of the sessions may involve other software such as ghidra, radare2, or an IDE, but for most of the sessions, a web browser is sufficient. Note that this series is meant to help you be a better programmer and be able to find vulnerabilities in code, whether your own or someone else's; it is not meant for malicious hacking.