Become good at Math in 9 mins: How to self-study Math easily
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
- ๐ Majoring in math involves tackling proofs, theorems, and various fields such as calculus, differential equations, topology, and abstract algebra.
- ๐ 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.
- ๐ H emphasizes that self-studying is a crucial skill in math, acquired after approximately 7,500 hours of study.
- ๐ The video outlines a step-by-step process for self-studying math, which includes definitions, examples, knowledge gaps, and exercises.
- ๐ It's recommended to use a textbook with practice questions and thorough explanations, preferably on an iPad for convenience.
- ๐ 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.
- ๐ Examples provided in textbooks are tools to show how to apply definitions, and it's important to work through them to understand the process.
- ๐ Filling knowledge gaps involves looking up specific concepts or steps that are unclear, but it's advised to do so sparingly to avoid distractions.
- ๐ Practice questions are essential for solidifying understanding, with the speaker suggesting doing 10 to 20 questions for each topic.
- ๐ Checking answer keys after working on questions is crucial to learning from mistakes and understanding the correct steps.
- ๐ 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
๐ 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.
๐ 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
๐กSelf-study
๐กDefinitions
๐กExamples
๐กKnowledge Gap
๐กExercises
๐กTheorems
๐กProofs
๐กOperations Research
๐กLinear Equations
๐กSkillshare
๐กMemorization
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.