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.

Outlines

00:00

📚 Preparing for Effective Math Study

This paragraph introduces the video's purpose, which is to demonstrate a step-by-step process for studying mathematics effectively. The speaker emphasizes the importance of gathering the right supplies, such as high-quality pencils (Ticonderoga pencils are recommended), a good pen for those who prefer it, a sharpener, and a timer for session management. The choice of paper without lines is highlighted, inspired by a highly intelligent individual the speaker knows. The paragraph concludes with advice on finding a quiet study location, suggesting places like secluded rooms, college, or public libraries for an optimal study environment.

05:01

🔍 Diving Deep into Math Self-Study Techniques

The second paragraph focuses on the self-study process for math, starting with selecting a book, in this case, 'Calculus' by James Stewart. The speaker advises picking a section that is both interesting and challenging to promote learning. The importance of understanding definitions, such as hyperbolic functions, by writing them down from memory is stressed. The paragraph continues with the recommendation to work through examples and proofs without looking at the book's solutions to solidify understanding. It also touches on the necessity of attempting exercises, especially those without provided examples in the book, to test comprehension. The speaker concludes with the suggestion to reflect on the study session, consider keeping the work for review, and acknowledges the normalcy of confusion during the learning process. The paragraph ends with encouragement to continue self-study with different books to gain varied perspectives and deepen mathematical understanding.

Keywords

💡Study Math

Studying math refers to the process of learning and understanding mathematical concepts, principles, and problems. In the video's theme, it is about following a structured approach to effectively learn mathematics. The script emphasizes the importance of a step-by-step process, which includes gathering supplies, choosing a quiet location, and selecting appropriate study materials.

💡Ticonderoga Pencils

Ticonderoga Pencils are a brand known for their high-quality graphite and durable construction, making them a preferred choice for writing and drawing. In the context of the video, they are recommended as a good quality pencil for studying math, suggesting that the right tools can enhance the learning experience.

💡Sharpener

A sharpener is a tool used to sharpen the tips of pencils, which is essential for maintaining clear and precise writing. The video mentions a battery-free sharpener, emphasizing portability and the convenience of sharpening pencils without electricity, which is useful for studying in various environments.

💡Timer

A timer is a device used to measure and track the duration of an activity. In the video, a timer is recommended for timing study sessions, which helps in managing study time effectively and ensuring focused periods of learning.

💡Paper

Paper is a material used for writing, drawing, and printing. The video specifically mentions the use of unlined paper for math, which is believed to contribute to better mathematical thinking. The script suggests that using unlined paper, as preferred by a highly intelligent individual, can influence one's approach to math.

💡Quiet Location

A quiet location is a place with minimal noise and distractions, ideal for concentration and productivity. The video emphasizes finding a quiet spot for studying math to enhance focus and efficiency in learning.

💡Book Selection

Book selection refers to the process of choosing a book for study or reference. The video provides advice on picking a math book, suggesting that one should choose a book that is interesting yet challenging to promote learning and growth.

💡Hyperbolic Functions

Hyperbolic functions are mathematical functions that have a similar form to the trigonometric functions but are defined in terms of exponential functions. In the script, the definition and understanding of hyperbolic functions like sinh(x) and cosh(x) are used as an example of learning a new concept in the chosen book.

💡Examples

Examples in a math context are worked-out problems that illustrate how to apply concepts and solve problems. The video script encourages working through examples in the book to practice and reinforce understanding of the material.

💡Exercises

Exercises are problems or tasks given at the end of a section in a math book, designed to test understanding and application of the concepts learned. The video mentions doing as many exercises as possible, including those without provided examples, to deepen comprehension.

💡Reflection

Reflection in the context of studying refers to the process of reviewing and contemplating what was learned during a study session. The video concludes with the importance of reflecting on the study session to assess the meaningfulness of the time spent and to identify areas for further study.

Highlights

Introduction of a step-by-step process for studying math effectively.

Recommendation to gather quality supplies such as Ticonderoga pencils, a good pen, a sharpener, a timer, and unlined paper.

The importance of choosing a quiet location for studying to enhance productivity.

Suggestion to pick a math book and start reading without overthinking the choice.

Emphasis on selecting a book section that is interesting yet challenging to promote learning.

Advising to set a timer for focused study sessions, recommending one hour as a good duration.

The method of writing down definitions without looking at the book to ensure understanding.

Working through all examples in the book to practice and reinforce learning.

Encouragement to attempt exercises without examples in the book to test understanding.

The value of reflection on the study session to assess the meaningfulness of the time spent.

Suggestion to keep or discard study materials based on personal preference.

The idea that moments of confusion during math study should motivate further study.

The benefit of self-study in allowing flexibility to choose what and how to study.

Highlighting the vast amount of content in math books, often exceeding college course material.

Recommendation to acquire multiple math books for a comprehensive understanding of topics.

The uniqueness of different math books in covering various topics and explaining concepts differently.

Conclusion summarizing the importance of effective study methods and the value of self-study in learning math.

Transcripts

in this video i'm going to show you how

to actually study math i'm going to give

you a step-by-step process that you can

follow so you can sit down and actually

learn some mathematics and it really

doesn't take that long if you follow

these steps you'll be able to study

smart and make effective use of your

time step one is to gather your supplies

so for the purposes of this video i'm

going to show you the things that i've

been using whenever i do math this is a

really good choice for a pencil these

are ticonderoga pencils and they're

really good quality so currently this is

the pencil i use and it's pretty awesome

i'll leave a link in the description by

the way to all the supplies i use in

case you want to check them out if

you're one of those people who likes to

do mathematics and pen then this is an

incredible one i've known a lot of

people who are engineers and physicists

and they tend to use pen

and they tend to produce a lot of really

correct mathematics personally i prefer

pencils but if you're a pen person this

one's pretty incredible although it is a

little bit pricey of course everyone

needs a sharpener and i like having one

that's pretty good this one doesn't use

batteries so i can take it with me so if

i decide to do math outside i can take

it outside and it doesn't require any

electricity or anything like that one of

the most important components is of

course a timer so you can use this to

time your sessions which i highly

recommend this is a really simple one

that works great and it uses one double

a battery of course you can't do math

unless you have something to write on

and this is paper notice this paper

doesn't have lines the reason i use

paper with no lines is because the

smartest person i ever met used paper

with no lines and i thought maybe that's

making him better at math so i started

using paper with no lines and ever since

then i have been hooked so you've

gathered your supplies you have either a

pen or a pencil a timer

a sharpener and some paper that you're

comfortable with and it doesn't have to

be these i would just recommend using

what you prefer if you prefer a

mechanical pencil get that remember you

want to be as comfortable as possible

when you're working on math the next

thing you want to do is pick a quiet

location you can see here the room that

i'm actually in is very very small and

very secluded and it is extremely quiet

so

try to find the quietest spot you can so

you can sit down and be productive if

you can't find a quiet location to study

then try to find a place where you can

go that is a little bit more quiet

consider college libraries or even

public libraries those are usually

pretty good places to go study the next

step is a really fun step and it's

picking a book and this is a step that

you might get stuck on my advice is just

pick a book and go with it if you can't

make a decision just grab one of your

math books and start reading it now i've

got a lot of books here as you can see

we've got some calculus advanced

calculus vector analysis combinatorics

more calculus differential equations

linear algebra more differential

equations real analysis number theory

some abstract algebra some

multi-variable calculus some real

analysis some topology a little bit more

calculus and some trig so all kinds of

choices and for the purposes of this

video i'm actually going to pick one of

these books and i'm going to show you

how to study because this is such a

popular book and it is so widely

available and it is so widely used by

colleges and universities all over the

world i've chosen this one this one is

calculus by james stewart and it is the

fifth edition this is a super thick book

that people use to take calculus one two

and three in colleges in the u.s and in

canada once you have the book you have

to decide what section you want to read

my advice is to pick something that you

want to read so something that is

interesting to you but at the same time

you want to pick something that is going

to push you a little bit you want to

study something that you really haven't

seen before or something that you feel

uncomfortable with you want to push

yourself into that uncomfortable place

so that learning actually takes place

after all the whole point is to actually

learn something now it's time to set the

timer i like to set it for one hour i

feel like one hour is a good amount of

time to study most subjects and then you

just get started so you start reading

the book you notice that it gives you

the definition of the hyperbolic

functions so the first thing you want to

do is make sure you know that definition

so how do you do that well the best way

to do that is to actually write down the

definition and you want to be able to

write it down without looking at the

book for example the hyperbolic sine of

x or sinch x

is going to be half the difference of e

to the x

and e to the negative x so you take e to

the x you subtract e to the negative x

and you divide by two

the hyperbolic cosine is going to be the

average of e to the x and e to the

negative x so you take e to the x you

add e to the negative x and you divide

by two and for the rest of them if you

noticed in the formulas they're very

similar to the trig functions so you can

go on from there and fill in the rest of

the formulas for your hyperbolic

functions if you find yourself having to

look at the book you want to start over

and do everything without looking at the

book until you know the definition's

cold as you continue reading the text

you want to work through all of the

examples for example here you notice

they give you the hyperbolic identities

and they have a proof of one of them so

maybe prove the one they do but do it on

your own without looking at their

solution and maybe do a couple more just

for practice then you continue reading

the text and doing all of the examples

that you can not everything will make

sense and that's normal and you want to

just work through it and try to

understand as much as you can from the

examples that are given in the book once

you get to the exercises you should feel

pretty good about yourself because you

made it through the entire section at

this point you should start doing as

many problems as you can in a book like

this you'll have answers to most of the

odd numbered problems which really helps

one thing you will notice in most math

books is when you get to the problems at

the end of a section you're going to

find problems for which there are no

examples in the book so you wonder how

am i supposed to figure those out well

that's when you have to go back to the

section and try to find

information that you can use to help you

solve those problems if you still can't

figure them out it's okay books like

this have tons of problems and some of

them are harder than others and if

you're wondering why the author didn't

include examples of every single type in

the book it's because then the book

would be insanely huge so they have to

pick and choose what content they

present in the book so now you're done

studying you should feel good about

yourself you got a lot done and this is

the last step it's to reflect reflect on

what you did reflect on how meaningful

your time was you just took an hour of

your life and you learned a lot of

mathematics if you like you can keep

your work you can buy a hole puncher and

put it in a binder you can stack it up

in a big stack or you can throw it away

whatever you like as the day proceeds

you're going to find yourself thinking

about some of the math you did maybe

there was some points that you found

confusing and you might feel a little

bit confused and i really think that's

normal when you study math and when you

read a math book you're not going to

understand everything you're going to

have moments of confusion and those

moments of confusion should motivate you

to study more next time one of the great

things about self-study is you can study

whatever you want so the next time you

have a study session you can study

something completely different if you

didn't like the book that you were using

you can get a different book math books

are so cheap you can get books at really

good prices and the really good thing

with math books is they contain so much

information for example

this book here has enough material to

teach you calculus 1 calculus 2 and

calculus 3. in fact if you went to

college and you took all three courses

calc 1 calc 2 calc 3 you probably

wouldn't even cover all the material in

this book in fact i pretty much

guarantee it there's just so much

content in a book like this if you're

wondering which book to get my advice

would be to get as many books as

possible a lot of times you'll pick up a

book and read a certain section from

that book

and it won't be very good and then you

pick up another book and it's a little

bit more clear for example here we have

two differential equations books but

they're very very different this is the

one by edwards and penny and this is the

one by zil and they do have some

similarities but this one covers a lot

of topics that this one doesn't so by

having a wide selection of books that's

really going to help your self-study

journey hopefully this video has given

you some ideas on how to have better

study sessions and learn math on your

own i hope this video has been helpful

good luck and take care