How To Self-Study Math

Summary

This video offers a structured approach to studying mathematics effectively. It emphasizes gathering quality supplies, choosing a quiet study environment, selecting an engaging math book, and setting a timer for focused sessions. The presenter suggests learning definitions by writing them without looking at the book, working through examples, and tackling exercises to solidify understanding. Reflecting on the study session and considering the value of confusion in the learning process is also highlighted. The video encourages self-study flexibility and the accumulation of a diverse range of math books for comprehensive learning.

Takeaways

• 📚 Gather essential study supplies like high-quality pencils, a pen, a sharpener, a timer, and paper without lines for an effective math study session.
• ✂️ Choose a pencil brand like Ticonderoga for quality and consider a non-electric sharpener for portability.
• 🕒 Use a timer to manage study sessions, with an hour being a recommended duration for focused learning.
• 📖 Select a quiet location to study, such as a secluded room or a library, to minimize distractions.
• 📘 Pick a math book that interests you and is challenging, like 'Calculus by James Stewart', to ensure you're pushed to learn new concepts.
• 🔍 Focus on understanding definitions and concepts by writing them down from memory and working through examples without looking at the book.
• 📝 Practice by doing proofs and solving problems, even if they are not directly shown in the book, to reinforce learning.
• 🤔 Expect moments of confusion while studying math, as they are a natural part of the learning process.
• 📈 Reflect on your study session, consider keeping your work for review, and think about what you've learned and how to improve.
• 🔄 If a book or section is not clear, switch to another book or topic to gain a fresh perspective on the subject.
• 📚 Collect a variety of math books to have different explanations and approaches at your disposal for self-study.

Q & A

What is the main topic of the video?

The main topic of the video is a step-by-step process for effectively studying mathematics.

What type of pencil does the speaker recommend for studying math?

The speaker recommends Ticonderoga pencils for their high quality, which they personally use for studying math.

Is there a specific pen the speaker suggests for those who prefer writing in pen while doing math?

Yes, the speaker suggests a particular pen favored by engineers and physicists, although it is a bit pricey.

What type of sharpener does the speaker prefer and why?

The speaker prefers a sharpener that doesn't use batteries, allowing for portability and use without electricity.

Why is a timer considered an important component for studying math according to the video?

A timer is important for timing study sessions, which the speaker highly recommends as part of the study process.

What kind of paper does the speaker use and why?

The speaker uses paper without lines, inspired by the smartest person they've met, who also used lineless paper, possibly aiding in mathematical thinking.

What is the speaker's advice on choosing a book for studying math?

The speaker advises to pick a book and start reading it, especially if one is indecisive, to facilitate the beginning of the study process.

Which book does the speaker select to demonstrate the study process in the video?

The speaker selects 'Calculus' by James Stewart, specifically the fifth edition, as it is widely used in colleges and universities.

How does the speaker suggest learning definitions in math, such as the hyperbolic functions?

The speaker suggests writing down the definition without looking at the book until you know it well, similar to how they demonstrate with hyperbolic sine and cosine functions.

What is the speaker's approach to working through examples in a math book?

The speaker recommends working through all the examples provided in the book, doing them on your own without looking at the provided solutions first.

How does the speaker deal with exercises in the book that have no examples?

The speaker advises going back to the section and using the information provided to help solve those problems, acknowledging that some problems will be harder and may not be immediately solvable.

What does the speaker suggest as the final step after studying a math section?

The final step is reflection on what was learned during the study session, considering the meaningfulness of the time spent and any points of confusion.

Why does the speaker recommend having multiple math books for self-study?

Having multiple books provides a wider selection of explanations and topics, which can clarify concepts that might be difficult to understand in one book.

What is the speaker's opinion on the amount of content in a single math book?

The speaker believes that a single math book, such as the one by James Stewart, contains more material than what is typically covered in college courses on the subject.