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

Han Zhango
27 Feb 202409:16

TLDRThis video offers a step-by-step guide on how to effectively self-study math, highlighting the importance of understanding definitions, working through examples, filling knowledge gaps, and practicing exercises. The presenter, a math major from Columbia University, shares personal strategies that have helped them master complex mathematical concepts, emphasizing the balance between learning and applying mathematical principles.

Takeaways

  • 📚 Majoring in math involves tackling proofs, theorems, and various fields such as calculus, differential equations, topology, and abstract algebra.
  • 🎓 The speaker, H, is a Columbia University graduate who self-studied math due to reasons like losing attention, skipping lectures, and professors who were too genius to teach effectively.
  • 🔍 H emphasizes that self-studying is a crucial skill in math, acquired after approximately 7,500 hours of study.
  • 📈 The video outlines a step-by-step process for self-studying math, which includes definitions, examples, knowledge gaps, and exercises.
  • 📘 It's recommended to use a textbook with practice questions and thorough explanations, preferably on an iPad for convenience.
  • 📝 Understanding definitions is the first step in learning a math topic; it's more important to know how to use them than what they are.
  • 📑 Examples provided in textbooks are tools to show how to apply definitions, and it's important to work through them to understand the process.
  • 🔍 Filling knowledge gaps involves looking up specific concepts or steps that are unclear, but it's advised to do so sparingly to avoid distractions.
  • 📉 Practice questions are essential for solidifying understanding, with the speaker suggesting doing 10 to 20 questions for each topic.
  • 🔑 Checking answer keys after working on questions is crucial to learning from mistakes and understanding the correct steps.
  • 📝 Memorization of definitions and theorems can be achieved through repetition in practice, but writing them down and testing recall can also be helpful.

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 main components of the math learning framework presented in the video?

    -The four main components are definitions, examples, knowledge gaps, and exercises.

  • Why does the speaker emphasize the importance of self-studying in math?

    -The speaker emphasizes self-studying due to the nature of math where losing attention can lead to confusion, occasional skipping of lectures, and the difficulty in understanding professors who are too genius to teach effectively.

  • What does the speaker suggest as the first step in understanding a math topic?

    -The first step is to understand the topic by reading the definitions, rules, or theorems, which are the foundational concepts in math.

  • 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, such as drinking or watering plants.

  • What is the speaker's approach to dealing with knowledge gaps while studying math?

    -The speaker suggests looking up specific concepts or steps that are not understood, being as specific as possible in the search to avoid being overwhelmed by information.

  • What is the role of exercises in the speaker's math learning framework?

    -Exercises play a crucial role as they help in applying the definitions and theorems to solve problems, which is the core of understanding math.

  • How does the speaker recommend using answer keys while practicing math problems?

    -The speaker recommends checking the answer keys after working on each question to understand the correct steps and learn from any mistakes made.

  • What is the speaker's advice on the allocation of time during a one-hour math study session?

    -The speaker suggests spending 30 minutes on practice questions, 20 minutes on learning and working through examples, and 10 minutes on understanding definitions and filling knowledge gaps.

  • How does the speaker address the issue of memorization in math?

    -The speaker advises that through repeated practice, memorization of definitions and theorems should come naturally, but for extensive memorization, writing them down on a formula sheet and practicing recall is recommended.

  • What is the significance of the sponsored content about Skillshare mentioned in the video?

    -The sponsored content highlights Skillshare as a learning platform offering various courses, including those in math, and provides a one-month free trial for the first 500 people using the speaker's link.

Outlines

00:00

📚 Mastering Self-Study in Mathematics

The speaker introduces their experience majoring in math at Columbia University, with a focus on self-studying due to various reasons such as the nature of math, occasional lecture skipping, and the challenge of understanding some professors. They outline a four-part learning framework consisting of definitions, examples, knowledge gaps, and exercises. The speaker emphasizes the importance of understanding the basics, using examples as tools to apply definitions, and filling knowledge gaps through online resources when necessary. The video aims to guide viewers on how to self-study math effectively, making it a fulfilling, challenging, and fun experience.

05:00

🎓 Embracing Skillshare for Comprehensive Learning

The speaker transitions to discussing the importance of focused learning and the challenges of finding reliable resources. They introduce Skillshare as a sponsor and share their positive experience with a Final Cut Pro editing course, which they still apply today. Skillshare is presented as a platform offering a wide range of classes in creative fields, computer science, programming, and math. The speaker recommends Skillshare for those interested in self-growth and effective study, highlighting the platform's learning paths that guide learners from beginner to advanced levels. They offer a one-month free trial for the first 500 people using their link, emphasizing the value of Skillshare in enhancing learning experiences.

Mindmap

Keywords

💡Self-study

Self-study refers to the process of learning a subject independently without direct guidance from a teacher. In the context of the video, the speaker emphasizes the importance of self-studying math due to its nature and the speaker's personal experiences with lectures. The video outlines a step-by-step process for self-studying math, which includes understanding definitions, working through examples, identifying knowledge gaps, and practicing exercises.

💡Definitions

Definitions in math are the established rules, theorems, or principles that serve as the foundation for understanding more complex concepts. The video script mentions that the first step in self-studying math is to understand the definitions of the topic being studied, such as the definition of a linear equation. Definitions are crucial as they set the stage for applying mathematical concepts in examples and exercises.

💡Examples

Examples in the context of the video are the practical applications of definitions that demonstrate how to use them to solve problems. The speaker uses the analogy of a tool to explain the importance of examples, stating that just as one learns to use a cup for different purposes, one must learn to apply definitions through examples. The script illustrates this by showing how to solve a linear equation using the method described in an example.

💡Knowledge Gap

A knowledge gap refers to the areas where a learner lacks understanding or needs to acquire more information. The video script suggests filling knowledge gaps by looking up concepts that are not understood while working through definitions or examples. The speaker advises being specific in searches to find relevant information and emphasizes the importance of not getting distracted by electronic devices during study sessions.

💡Exercises

Exercises are the practice problems that learners work through to apply and reinforce their understanding of definitions and examples. The video recommends doing 10 to 20 questions for each topic and emphasizes the importance of checking the answer keys to learn from mistakes and understand the correct steps. Exercises are a key component of the self-study process as they help to solidify the concepts learned.

💡Theorems

Theorems in mathematics are statements that have been proven and are used to establish other results. The script mentions that majoring in math involves tackling thousands of theorems. Theorems are integral to the process of understanding and proving mathematical concepts, and they are often the subject of study and application in self-study.

💡Proofs

Proofs are the demonstrations of the truth of a theorem or proposition in mathematics. The video script alludes to the extensive work with proofs that comes with majoring in math. Proofs are essential for validating mathematical statements and are a critical part of the learning process in the field of mathematics.

💡Operations Research

Operations Research is a discipline that deals with the application of advanced analytical methods to help make better decisions. The speaker mentions studying math and operations research at Columbia University. It is a field that often intersects with mathematics, utilizing mathematical models and algorithms to analyze and solve complex problems.

💡Linear Equations

Linear Equations are algebraic equations in which each term is either a constant or the product of a constant and a single variable. The video uses the chapter on linear equations in a differential equations book as an example to demonstrate the self-study process. Linear equations are fundamental to many areas of mathematics and are used to illustrate the process of understanding definitions and solving problems.

💡Skillshare

Skillshare is an online learning community that offers thousands of classes in various creative and technical fields. The video features Skillshare as a sponsor and highlights the platform's offerings in film, illustration, design, and programming, among others. The speaker recommends Skillshare for those interested in self-growth and learning new skills.

💡Memorization

Memorization is the process of committing information to memory. In the context of the video, the speaker suggests that through extensive practice, definitions and theorems become memorized due to repetition. The video also recommends using a formula sheet for formulas or theorems that need to be memorized, and setting aside dedicated time to recall them without looking.

Highlights

Majoring in math involves tackling proofs, theorems, and navigating through various math fields.

The speaker is self-taught in math, having studied at Columbia University.

Three reasons for self-studying math: losing attention, skipping lectures, and professors being too genius to teach.

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

The step-by-step process for self-studying math includes definitions, examples, knowledge gaps, and exercises.

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

Understanding math topics starts with definitions or theorems that mathematicians have discovered or proved.

Definitions are like tools that need to be understood and memorized for their application.

Examples in math textbooks demonstrate how to apply definitions to solve problems.

After understanding examples, practice similar questions to gain experience and ensure comprehension.

Filling knowledge gaps involves looking up specific concepts or steps that are not understood.

It's important to stay focused and avoid online distractions while studying.

Skillshare is recommended as a learning platform with various classes for self-growth.

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

Checking answer keys after working on questions is essential for learning from mistakes.

Memorization of definitions or theorems comes with repetition through practice.

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

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