Mapping My Math Journey: From Wide Surfaces to Goal-Oriented Lines

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I’m currently balancing two different approaches to studying mathematics. One is a comprehensive undergraduate calculus textbook, and the other is a Japanese book focused on a specific mathematical model.

The calculus textbook is thorough and covers a wide range of topics. While the content is relatively accessible, the sheer volume of it is massive, so I’ve only made it through about 20%. The other book is around 200 pages, and I’m about 40% through it.

Today, I want to talk about this second book. The mathematical level is similar to the textbook, and the “standard route” would be to finish the calculus text first. However, that would be an incredibly long journey. Instead, my current goal is to learn the minimum mathematics necessary—specifically Fourier analysis and differential equations—to grasp the model.

If the calculus textbook is about studying math as a “broad surface,” this book feels like following a “straight line” toward a specific goal. Through this targeted approach, I can really feel firsthand just how practical and useful mathematics can be.

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