Become good at Math in 9 mins: How to self-study Math easily

Han Zhango
27 Feb 202409:16

TLDRThis video offers a structured approach to self-studying math, emphasizing the importance of understanding definitions, working through examples, identifying knowledge gaps, and practicing exercises. The speaker, a math major at Columbia University, shares personal strategies that have helped them excel in mathematics, advocating for active learning and the use of resources like Skillshare for further study. The summary encourages viewers to engage with the material, practice regularly, and utilize online resources for a comprehensive learning experience.

Takeaways

  • 📚 Majoring in math involves tackling proofs, theorems, and various math fields like calculus, differential equations, topology, and abstract algebra.
  • 🎓 The speaker, H, is a math and operations research graduate from Columbia University who is mostly self-taught due to reasons like losing attention, skipping lectures, and professors' teaching styles.
  • 🔍 H emphasizes that self-studying is a crucial skill in math, acquired after approximately 7,500 hours of studying.
  • 📝 The speaker outlines a four-part math learning framework: definitions, examples, knowledge gaps, and exercises.
  • 📚 A textbook with practice questions and thorough explanations is recommended for self-study.
  • 🔑 Definitions are foundational and should be understood or memorized, but it's more important to know how to apply them.
  • 📈 Examples are crucial as they show how to use definitions; they are compared to tools that need to be used effectively.
  • 🔍 Filling knowledge gaps involves looking up specific concepts or steps that are not understood, but it's advised to stay focused and avoid online distractions.
  • 📉 The speaker recommends doing 10 to 20 practice questions for each topic to reinforce learning and understanding.
  • 📝 Checking answer keys after working on questions is essential to learn from mistakes and understand the correct steps.
  • 📑 Memorization of definitions or theorems can be achieved through repetition in practice, and using a formula sheet can aid in this process.

Q & A

  • What is the main focus of the video titled 'Become good at Math in 9 mins: How to self-study Math easily'?

    -The video focuses on sharing a step-by-step process for self-studying math effectively, making it fulfilling, challenging, and fun.

  • What are the four parts of the math learning framework mentioned in the video?

    -The four parts of the math learning framework are definitions, examples, knowledge gaps, and exercises.

  • Why does the speaker believe self-studying is an important skill in learning math?

    -The speaker believes self-studying is important due to the nature of math where losing attention can lead to confusion, occasional skipping of lectures, and the fact that some math professors are too genius to teach effectively.

  • What does the speaker suggest for the first part of learning a math topic?

    -The speaker suggests understanding the topic by reading definitions, rules, or theorems and trying to memorize them.

  • How does the speaker use an analogy to explain the importance of examples in learning math?

    -The speaker compares definitions, theorems, or rules to tools, like a cup, which you learn to use in different ways through examples.

  • What is the purpose of working through examples after reading definitions?

    -The purpose is to understand how to apply the definitions in practice, similar to learning how to use a tool in different ways.

  • What does the speaker recommend doing after understanding examples?

    -The speaker recommends doing exercises or practice questions to gain experience and ensure understanding of the examples.

  • Why is it important to check the answer keys after working on practice questions?

    -Checking the answer keys is important to learn from the correct solutions, understand where mistakes were made, and to not waste effort without knowing the right way to solve problems.

  • What is the speaker's advice on how to deal with knowledge gaps while self-studying?

    -The speaker advises looking up specific things that are not understood, being as specific as possible in searches, and avoiding going online too much to prevent distraction.

  • How does the speaker suggest using online resources for self-studying math?

    -The speaker suggests using online resources like Skillshare for learning specific topics, but emphasizes staying focused and not going too deep into unrelated areas during a study session.

  • What is the speaker's recommendation for memorizing definitions or theorems in math?

    -The speaker recommends using repetition through practicing a lot of questions, writing formulas or theorems on a formula sheet for reference, and dedicating time to memorize them without looking at the sheet.

Outlines

00:00

📚 Self-Studying Math: A Step-By-Step Guide

The speaker introduces their experience with self-studying math, emphasizing the importance of understanding definitions, working through examples, and practicing exercises. They highlight the challenges and strategies involved in learning math independently, such as the need to maintain focus and the occasional necessity to skip lectures or seek additional resources. The speaker outlines their learning framework, which includes four main parts: definitions, examples, knowledge gaps, and exercises. They recommend using a textbook with practice questions and thorough explanations, and they provide an example using the chapter on linear equations from a differential equations book. The emphasis is on understanding the core concepts and applying them through practice.

05:00

🔍 Filling Knowledge Gaps and Effective Practice

This paragraph delves into the process of addressing knowledge gaps during self-study by using online resources when necessary. The speaker shares their experience with Skillshare, a learning platform that offers a wide range of courses, and they recommend it for those interested in self-improvement and learning new skills. The speaker then discusses the importance of doing practice questions or exercises, suggesting a ratio of 30 minutes for practice, 20 minutes for examples, and 10 minutes for definitions in a one-hour study session. They stress the value of checking answer keys to understand the correct steps and learn from mistakes. The paragraph concludes with advice on memorization, suggesting the use of a formula sheet for definitions or theorems that need to be remembered and the practice of writing them down without looking.

Mindmap

Keywords

💡Self-study

Self-study refers to the process of learning independently without the direct guidance of a teacher or instructor. In the context of the video, self-study is emphasized as a crucial skill for mastering math. The speaker shares their personal experience of being largely self-taught, highlighting the importance of self-study in understanding complex mathematical concepts and solving problems on one's own.

💡Mathematical Proofs

Mathematical proofs are rigorous demonstrations that certain statements are true within a particular mathematical theory. The video mentions tackling hundreds of proofs, indicating the depth and breadth of mathematical study. Proofs are fundamental to the discipline, as they validate theorems and establish the reliability of mathematical knowledge.

💡Theorems

A theorem is a statement that has been proven based on previously established statements, such as other theorems or axioms. The script refers to 'thousands of theorems' to illustrate the extensive body of established knowledge in mathematics that students are expected to learn and apply in their studies.

💡Definitions

Definitions in mathematics are precise statements that explain the meaning of a concept or term. The video emphasizes understanding definitions as the first step in learning a new math topic, as they provide the foundational understanding necessary to grasp more complex ideas and solve problems.

💡Examples

Examples in the mathematical context are specific cases worked out to illustrate how to apply definitions, rules, or theorems. The script describes examples as tools that show the application of definitions, much like how a cup can be used for different purposes, thus helping to solidify understanding.

💡Knowledge Gap

A knowledge gap refers to the difference between what one knows and what one needs to know to understand a concept fully. The video suggests filling knowledge gaps by looking up information when encountering confusion, which is an essential part of the self-study process in bridging understanding.

💡Exercises

Exercises are problems or tasks designed to test and reinforce learning. The script recommends doing 10 to 20 questions per topic to practice applying the learned concepts, emphasizing the importance of exercises in solidifying mathematical skills.

💡Answer Keys

Answer keys provide the correct solutions to exercises, allowing students to check their work and understand where they may have gone wrong. The video mentions the importance of checking answer keys to learn from mistakes and ensure that practice is effective.

💡Memorization

Memorization is the process of committing information to memory. In the context of math, it often involves remembering formulas and theorems. The video suggests that through repeated practice, memorization of definitions and theorems becomes more natural and effective.

💡Formula Sheet

A formula sheet is a document that lists important formulas and theorems for reference. The video recommends creating a formula sheet to aid in memorization and as a reference while practicing problems, which can be particularly helpful when there are many concepts to remember.

💡Skillshare

Skillshare is an online learning community that offers thousands of classes on various topics, including creative disciplines, computer science, programming, and math. The video features Skillshare as a sponsor and highlights its value for those interested in self-improvement and learning new skills.

Highlights

Majoring in math involves tackling proofs, theorems, and various math fields like calculus, differential equations, topology, and abstract algebra.

The speaker is self-taught in math due to the nature of math, occasional lecture skipping, and professors who are too genius to teach.

Self-studying math is considered the most important skill the speaker learned after 7,500 hours of studying.

The math learning framework consists of four parts: definitions, examples, knowledge gaps, and exercises.

A textbook with practice questions and thorough explanations is recommended for self-study.

Understanding the topic's definition is the first step in self-studying math.

Definitions, theorems, and rules are tools that need to be understood and applied.

Examples in math are crucial to demonstrate the application of definitions.

Working through examples helps solidify understanding and prepares for exercises.

Filling knowledge gaps involves looking up specific concepts or steps that are unclear.

It's important to be specific when searching for information to avoid information overload.

Skillshare is highlighted as a platform for learning various skills, including math.

Skillshare offers a one-month free trial for the first 500 users through the provided link.

Doing practice questions is essential for understanding and applying math concepts.

Checking answer keys after working on questions is crucial for learning the correct methods.

Memorization of definitions and theorems comes with repetition and practice.

Writing formulas or theorems on a sheet can aid in memorization during practice.

The speaker encourages viewers to try the self-study method and share their experiences.

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