So friends, hello! I really have a great idea about what mathematics is. Mathematics is the symbolic version of how your brain works. Let me explain this, there are four fundamental topics on mathematics. So can think that they are all the same category but not.

Calculus

Differential Calculus: Studies the rates at which quantities change.

Integral Calculus: Concerned with the accumulation of quantities, such as areas under curves and volumes.

Multivariable Calculus: Extends calculus to functions of several variables.

2. Linear Algebra

Matrices: Focuses on the study of matrices and their properties.

Vector Spaces: Deals with the structure of vector spaces and linear transformations between them.

Eigenvalues and Eigenvectors: Concerned with the properties of linear transformations.

3. Discrete Mathematics

Graph Theory: Studies graphs and their properties.

Combinatorics: Concerned with counting, arrangement, and combination of sets.

Number Theory: Deals with the properties and relationships of numbers, particularly integers.

4. Algebra

Abstract Algebra: Studies algebraic structures such as groups, rings, and fields.

Group Theory: Concerned with the study of groups and their properties.

Ring Theory: Focuses on the study of rings, algebraic structures that generalize fields.

4. Geometry

Euclidean Geometry: Studies the properties and relations of points, lines, surfaces, and solids in two and three dimensions.

Differential Geometry: Uses techniques of algebra and calculus for the study of curves and surfaces.

Topology: Concerned with the properties of space that are preserved under continuous transformations.

5. Probability and Statistics

Probability Theory: Studies randomness and the likelihood of different outcomes.

Statistical Theory: Concerned with the collection, analysis, interpretation, and presentation of data.

Applied Statistics: Uses statistical theory to solve real-world problems.

6. Number Theory

Elementary Number Theory: Deals with the properties of integers.

Analytic Number Theory: Uses methods from mathematical analysis to solve number-theoretic problems.

Algebraic Number Theory: Studies the algebraic structures related to algebraic integers.

7. Applied Mathematics

Computational Mathematics: Concerned with mathematical research in areas of science where computing plays a central and essential role.

Mathematical Physics: Applies rigorous mathematical methods to problems in physics.

Operations Research: Deals with the application of advanced analytical methods to help make better decisions.

Okay that’s all the topics, now we are getting the point. So let’s assume that each individual has unique brain and they use different patterns and algorithms to survive and live more. I am suggesting that our brains difference around this 7 topics. For example one person can live like how statistics and probability, and this category is blueprint of how his/her brain work. I really want to give example about myself. So I am now a video game developer and I am currently interested in computer graphics. I hated mathematics in school and collage years, but when I am getting deep understanding level on computer graphics I really needed linear algebra. I found some courses online and check them with hesitation. But surprisingly I am very good at solving matrixes and I understand this ideas very easily. Normally I become bored and quit but not in linear algebra, because my brain is already thinking like that on so many years, I live like that and this is all symbolise of my thought on paper. That’s why I am good at it. But when I go to Calculus I fail and bored because that type of thinking algorithm is not familiar for me. I am saying that these topics are philosophies of life, we just named them mathematic topics and generate some ridiculous biases. So I am really advice you if you reading this notes, go and check these topics, there are tons of courses online, try each of them and select the one which is the most easy for you. If you do that you will understand yourself and your brain more. You will understand how your brain works and advance your thought process with mathematics.

Let’s figure out how to start learning mathematics in 2024. I will show you my method which is almost free and by yourself! But first of all we should fundamentally understand how mathematics occured in first place. So it is known that cave people in 3400 BC used some metrics to count the food they collacted or etc. I want to move forwards to modern mathematics which is around 600 to 300 B.C in Greece. So these people uses mathematics as an exercise of their daily life, for them it was like a thought practice. Not like “I should pass that Calculus 101 with an at least B for my GPA.”

This ancient Greek system had corrupted to 21st century and we lost the main point of the mathematics and the meaning. So the main point is not about engineering, science, economics or any applied mathematic field, of course you can do them but I am suggesting that learning mathematics is a philosophy, which leading learning how to think! For a second, let’s leave this crazy world and think universally, this is very hard I know but you can do it. On the core level, you should learn mathematics whether you are a scientist, artist or an engineer. Mathematics belongs to universe. So I will show you how to learn it.

So thanks to the technology we have crazy machine learning based applications such as ChatGPT, by the way I am not suggesting we sould ignore technology, I am saying that every indivicual needs to learn mathematics because it is seperated philosophy from technology. But technology depends on mathematics. So as you can see on the demonstration, you can find any learning material from the internet an ask ChatGPT(I use premium) where you stuck and step by step you can develop your skills. If this is not enough for you, there is countless of lecture videos on Youtube. I can suggest https://www.youtube.com/@SawFinMath this channel on Youtube. There are full courses which shown in the universities. Crazy right? Anytime, anywhere you can visit that videos and study mathematics.

So if you come to this far, thank you for reading! I wish you a great day! Peace!

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