How To Self-Study Math
Summary
TLDRThis 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
📚 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.
🔍 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.
Mindmap
Keywords
💡Study Math
💡Ticonderoga Pencils
💡Sharpener
💡Timer
💡Paper
💡Quiet Location
💡Book Selection
💡Hyperbolic Functions
💡Examples
💡Exercises
💡Reflection
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
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