Introduction

---

Greetings and welcome.

As described in this website's about section, this website is a personal "math journal" of sorts, made with the purpose of getting me to study math. I do not reccomend studying math from this website, as I am merely a student that has lost a lot of progress and is trying to catch up, not a math teacher or graduate.

The way I will be focusing on this journal will be as follows- I will add an entry for a topic, complete with a description, why it is used and where, relevant rules and formulas, examples, solving algorithms (if possible), and programming implementations (again, if possible). If I'm feeling particularly inspired, I might add some problems to each entry for solving as well.

I cannot guarantee that I will have a source for everything as some resources might be gated (such as info obtained from my high school math notes), but I'll try to include sources as much as possible.

Entries will generally be submitted in the order that I tackle their associated topics.

Things that have helped me understand math better:

If you're in a similar position to mine, the following list outlines some things that have helped me better understand math.

1. Studying programming

Yes, seriously. While extremely complex and math heavy algorithms undoubtedly require a good comprehension of maths, many (if not most) simple things can be done without knowing complex math (or math at all). Programming trains your ability to think in algorithms, so it is the perfect way to get yourself to take more interest in algorithmic thinking, it's also incredibly useful in your daily life. If gaining knowledge and seeing yourself break your perceived limits excites you (intrinsic motivation), then seeing your code execute well will set a flame within you.
If I receive comments asking for programming resources, I will compile some based on a few categories.

2. Studying logic

Studying logic will help you approach the subject of thought in a new way. Studying even a little bit of it will expand your mind and gradually open it to looking at things in a new perspective.
I reccomend getting a book about logic that has exercises in them. If you just so happen to know latvian, I can suggest books titled "Loģika" by Ivans Vedins. There's a whole series of them, just take the most recent one available to you and dig in.
On a less serious note, if you want to expand your mind a little via a game, I can also suggest playing the original Ace Attorney triology. While some solutions (and characters and plots) are frustrating and, frankly, bullshit, there's also plenty that will teach you to think outside the box.

3. Treating math as a language

Languages are systems of symbols that are used for communicating. We employ verbal systems* in order to communicate with people throughout our daily lives, and symbolic systems* in order to communicate how musicians ought to play songs or how certain values are obtained, how to drive on certain roads, etc. Both of these systems are languages, as they are used to communicate something. Realising this made me shift my perspective away from "what does the creator of this problem want me to do" and into "what is the creator of this problem trying to communicate?"

4. Getting a book with math formulas and definitions

If you can get your hands on one, try to get a book with math formulas in it- the wider the scope the better. I originally got one with the intention of using it as aid in my math studies, however I've found myself using it in daily life, too.

5. Not settling for AI slop

Just don't.

Lessons I've learned

Besides the aforementioned things, there's also some things that I missed earlier that are pretty important to understanding math.

1. Formulas, formulas, formulas

The deeper you go, the more formulas you have to use. This is something that I conveniently missed in middle school- we were just told to use formulas for certain topics and we weren't explained why they matter or why we use them, so my mind didn't make the connection (my disinterest in math at the time certainly didn't help).
If you're in the same boat, here's the reason why so much of math uses formulas- they've been made by predecessors to make solving and expressing complex issues not only fast, but possible. If you're not studying math at a bachelor's or higher degree, you won't be expected to reinvent the wheel wherever you are in life- you just need to think about the ways you can reasonably twist your expressions to fit within formulas to be able to move forward with whatever task you're dealing with.

2. The stalker called exponentiation

Logarithms, exponents or power, a secret third thing I might be forgetting... The basics (in terms of raw knowledge and formulas) of these things are quite brief, yet they're incredibly important to learn as they will stalk you everywhere.

3. Do math problems to learn math

...Doy! A math teacher of mine said that a good rule of thumb is that you can only say you understand a topic if you've solved at least 20 problems.

4. Solve problems regularly

Regular problem solving won't let your "math muscle" deteriorate as easily. One doesn't have to slave away for several hours every day to upkeep one's knowledge, however you shouldn't do one easy problem once every month and call it a day, either.