Studying Is the suggestion for self-learning mathematics from books wrong?

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Self-learning mathematics from books can be challenging, particularly for individuals without prior knowledge or experience in subjects like calculus. The discussion highlights that when learners encounter difficulties, they lack immediate support, as books cannot provide interactive assistance. This raises the question of the necessity of teachers, who offer personalized explanations and guidance. While self-teaching is feasible, formal instruction is often more effective for establishing a strong foundation in STEM subjects. It provides structured feedback, helps identify knowledge gaps, and offers credentials that are recognized by others, enhancing the overall learning experience.
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Why some people suggest self learn math from books, is the suggestion for self-learning mathematics from books wrong?
For example, I think that men how never get in contact with calculus(plus have gaps in prior knowledge), will have really hard time to self learn topic with only books. When you stuck in one part in book, who will ask for help? Book can't talk

If we can just self learn from books, why we have teachers?
I think teacher or any person who will explain the material to you(in person or video lecture) is better option than self learn from book.

What do you think about it?
 
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I think you have the right idea.

While self-teaching is certainly possible, to really establish a solid foundation in just about any STEM topic, it tends to be far more efficient to go through formal instruction from experts. As a learner this gives you formal, standardized, external feedback on your knowledge base and your skill set. It helps you to identify gaps in understanding. It gives you the opportunity to seek assistance when you encounter problems. And when you're done, you have a credential that others will recognize.
 
Given the current funding situation, you should contact potential departments or research groups before you apply and pay any application fees. Many programs are not taking new graduate students at all this cycle because of funding uncertainty, unless a specific advisor can show they already have money to support you for five years. This is what I’ve heard directly from 20–30 programs. Do not waste money applying blindly.

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