
Ask HN: Best way to relearn basic math? - non-entity
I&#x27;m considering going back to school, but upon further thought, the first major roadblock is that I seem to have forgotten most high school math and probably even some easier stuff! I&#x27;m sort of concerned about my ability to relearn 4 years of mathematics in a year or two and was wondering if anyone had and books &#x2F; tips &#x2F; etc. to make it easier
======
jointpdf
First of all, good on you for going back to school—that’s not always an easy
thing to do. What subject are you considering studying?

Khan Academy is definitely the best one-stop-shop for this purpose, as someone
mentioned. The key is to consistently do lots of practice problems over time.
KA is adaptive+gamified, and helps select problems in your “zone of proximal
development” (not too easy, not too hard).

Depending on what you want to get a degree in, you can focus on particular
areas and gloss over others. If CS, then discrete mathematics and logic are
the most important (plus stats/probability/linear algebra for machine learning
and AI). If engineering, then trigonometry/calculus/physics is more important.

Learning also requires motivation, which for me personally requires seeing the
big picture of why the math theory matters and how it was developed. Read the
NYTimes series by Steven Strogatz. I also like “Mathematics for the
Nonmathematician” for an overview of HS-level math that weaves in historical
context (e.g. how Renaissance art or agriculture and mathematics are
intertwined). Watch some YouTube videos on mathy subjects (like Numberphile or
3Blue1Brown or any of the zillions of channels along these lines). I try to do
this as a “learning by osmosis” sort of activity that I fit in to my daily
routine, e.g. when folding laundry or commuting.

Learning is also a social activity, so maybe enroll in a community college
course or find a local study group. I find it’s especially important to have
someone to discuss things with when learning math. I also recommend finding
good public spaces to work in—libraries and coffee shops are timeless math
spaces.

Along those lines—as you’re learning/reading/practicing new concepts, imagine
explaining them to someone else (Feynman method).

Do lots of problems by hand on pen and paper, there is research and eons of
practical experience that shows that doing math is a kinesthetic experience
(that is, there’s literally “muscle memory” for math). Draw pictures and
graphs on paper. Keep all this scratchwork and doodles and stuff in a
notebook.

Learn to process the “I have no idea what’s going on” thoughts and feelings
you get when you’re faced with something new and challenging, or seem to
continually forget things you’ve just (re)learned. That’s par for the course,
you just have to “feel the burn” and keep going. Cheesy but extremely true.

~~~
jointpdf
Oh yeah, and use tools like WolframAlpha to check your work and explore
problems in more depth (like visualizing functions, seeing alternate forms).
Get the app and use the solution explainer thing—essential for e.g. solving
integrals.

It might be worthwhile to learn to solve and verify problems using some sort
of (mathematical) programming language or a CAS. Could be anything, but
something like SageMath comes to mind. Honestly, even Excel is pretty good for
this. Being able to do simple things plot functions, verify work by plugging
in values, simulate random numbers, etc. goes a long way. Developing this
skills becomes even more useful (essential) when you’re at the college level
and beyond.

------
digitalsushi
For reasons that are mundane, I started college at 24 without any math
foundation. I did a full year of remedial mathematics as 0 credit courses, and
by the end of that, I was prepared for pre-calculus, the first course with
credits for an undergraduate degree.

From there, a bevy of other math classes - Differential and Integral Calculus,
Math Proof, Combinatorics and Graph theory, and many half-math, half-something
classes like physics, regular expressions, and everything between.

But all of it was based on the foundation of that year of 0 credit courses. At
the time it seemed like a risky, almost foolish gamble, but in hindsight it
has paid off several times over - by that I mean I have been able to pay off
the entire college tuition, several times - there is zero doubt that it was a
good move, for me, at that time of my life.

I encourage anyone facing the uphill journey of (re)learning math to take a
deep breath, make an itinerary, and sleep on it. And if you decide to start
that journey, don't go alone: Resources exist along the way, like Interstate
rest stops, to help you recharge and get ahead. Remember, that a tutor is also
improving themselves as they teach you, for each time they learn a new way to
explain a concept, they too gain from the experience. It's not a charitable
action to receive extra help learning math.

As you continue, you will possibly feel inclined to pay back and tutor those
following. You too will rediscover the path and improve your math foundation
as you are generous with sharing your perspectives and techniques.

Good luck! It seems like it will take forever, but is over before you know it.

~~~
dhimes
Along these lines, if you are in the US I recommend a local community college.
You'll get a solid foundation, you be on the correct pace, and you'll be
working with people whose primary mission is to teach you. You'll also find
that you're not alone.

I don't recommend self-study, simply because if that was for you then you
probably wouldn't have asked the question. It may turn out after a couple of
classes jump-starting you that you then want to self-study: fine, you can make
that decision then (we'll even give you advice lol). But don't start there.

Source: I used to teach in a community college, and saw a lot of students just
like you.

------
ll350
suggestion for you. "Maths - A Student Survival Guide" by Jenny Olive:
[https://www.amazon.com/Maths-Students-Survival-Self-Help-
Eng...](https://www.amazon.com/Maths-Students-Survival-Self-Help-Eng..). She
basically starts out with the simplest algebra (fractions) and gradually works
up to topics in 1st semester Calculus. And she starts each chapter with a
short quiz to test yourself and skip ahead if already know the material. This
book is great for what you are describing, if I'm understanding you. I picked
it up when I was preparing to return to college after being away for many
years. I supplemented it with another book I highly recommend: "Mastering
Technical Mathematics" by Stan Gibilisco and Norman Crowhurst:
[https://www.amazon.com/Mastering-Technical-Mathematics-
Third...](https://www.amazon.com/Mastering-Technical-Mathematics-Third..). I
found that Jenny Olive's book was well designed and preferred it's style to
any math textbook I have ever used. Even so occasionally I would get bored
while working thru it. That is when I flip thru the Stan Gibilisco's book,
which was full of interesting looking problems and examples. When I would try
to solve one of them, it would become apparent that I still need to work on
the fundamental concepts that were prerequisites for solving the problem. Thus
I would return to Jenny Olive's book right where I left off, re-energized by
the desire to master those fundamentals that she covers so well

~~~
logari
An intelligent comment. Good one.

------
aawalton
Khan Academy
([https://www.khanacademy.org/math](https://www.khanacademy.org/math)) is
excellent. I recommend working through the exercises as far as you can and
then re-learning concepts grade by grade. I go through this process every few
years just to stay fluent.

------
sn9
Before you do anything, you should take Coursera's _Learning How to Learn_ to
make sure you have efficient study habits.

Khan Academy is probably your best bet. Paul's Online Math Notes, PatrickJMT,
and BetterExplained can be useful supplements.

If you want to "bring a nuke to a knife fight", you could work your way
through all of the Art of Problem Solving books [0]. They go much deeper than
a standard curriculum so your foundation would be extremely strong (especially
if you use Anki to schedule your review of problems/definitions you've
understood and solved). Completing it would mean there's unlikely to be any
math book that's outside of your reach. This is complete overkill, though.

[0]
[https://artofproblemsolving.com/store](https://artofproblemsolving.com/store)

------
tonyedgecombe
K.A. Stroud is good, lots of how to do maths, very practical:

[https://www.amazon.co.uk/Foundation-Mathematics-K-
Stroud/dp/...](https://www.amazon.co.uk/Foundation-Mathematics-K-
Stroud/dp/0230579078)

[https://www.amazon.co.uk/Engineering-Mathematics-K-
Stroud/dp...](https://www.amazon.co.uk/Engineering-Mathematics-K-
Stroud/dp/1137031204)

------
Buttons840
This is a good site:
[http://tutorial.math.lamar.edu/](http://tutorial.math.lamar.edu/)

Also, if you have interest in a specific subject, exploit your own interest
and start with what you're interested in. Don't force yourself to relearn from
the beginning just for the sake of starting from the beginning.

Also, your goal will be one or more of: pass a math class, learn to solve real
world problems with math, and/or learn math for fun. All of these are possible
even if you have some gaps in your knowledge.

------
logari
I have read all the comments as of this typing. Some good, others okay. Ish.
While there is no doubt that Khan Academy is really good, it depends on good
for WHOM?

You don't sound like a typical KA learner, from what I see from your post, so
a more accurate answer would be to ask you: how motivated are you to re-learn
math?

If you are 110% motivated, I think you will have to first read Morris Kline's
"why the professor cannot teach" which is an attack on the way math is taught
starting from late 50's, especially in the U.S or the West.

After that, you will know what to do next. Depending on your future choices,
you could start with building a strong algebra foundation before going to
other branches.

To do that, you could read Polya's "how to solve it" as a general motivator,
but as your main book, college algebra by Bittinger (or was it Bettinger) is
the best that I know so far.

Make sure it is the pre 90's edition.

------
hackermailman
Find out the book your school is using for first year, it's likely Stewart's
'Early Transcendentals' Calculus or possibly Gilbert Strangs book (my online
school used it for Math 101)
[https://ocw.mit.edu/resources/res-18-001-calculus-online-
tex...](https://ocw.mit.edu/resources/res-18-001-calculus-online-textbook-
spring-2005/textbook/) with the bonus of Strang's book being Calculus is
explained in the first chapter and the entire rest of the book is just
exercises and applications.

Go through all the exercises, looking up the things you don't remember in the
rest of the resources mentioned here already. Maybe your school offers some
kind of advanced placement and by doing this you can also skip a semester of
single variable calculus saving yourself tuition costs.

------
tsumnia
As others have said, Khan Academy is great. I used it to prep for the GRE
after being of college for 5 years. I took my answering very seriously, so I
would only move forward if I got 5 questions in a row correct. If I continued
to answer wrong, review the session.

If you have the time, community colleges are also a worthwhile approach (if
you have one). Their entire purpose is to help strengthen the community. Many
are taught as distance courses or even night courses because they recognize
that the people that need this education probably can't afford to attend
during traditional school hours. Finally, it adds a small level of
accountability to your education. You paid money for the class, there is a
specified time and grading rubric for class which forces you to continue while
something like KA or other MOOCs have very high attrition rates.

------
bitlax
You don't say what you're going back to school for or what you plan on taking
when you get there, so my answer might be a bit different with that
information. But even if you didn't pay all that much attention the first
time, it won't take you a year or two to brush up on high school math. You
should be fine with a month of nights and weekends with a problem book. You'll
probably want to get something like a Precalculus Problem Solver or Schaum's
Outline and just do all of the exercises, or look for a textbook with full
solutions. Give each problem a good try, don't beat yourself up if you don't
come up with the answer, but make sure you understand the solution. You could
probably ask on the forums on the Art of Problem Solving if you're really
stumped. Good luck!

------
frankbreetz
I would recommend Khan academy, but I don't think the resource is that
important.

What is important is consistency, if you grow by 1% every day for a year will
be 37X where you started(1.01^365 =37). So do a little every single day and
you will be fine. I find this to be better than to do something every week. It
is easier to get in rhythm if you do it every day, you can find fifteen
minutes every day, on your way to and from work, during lunch, heck you can
even do it while you're in the bathroom. I always tell myself the Bruce Lee
quote “Long-term consistency trumps short-term intensity.” Take your time and
be consistent.

------
varunpramanik
I’m going through a similar process. Over the years, I had fits and starts
trying to relearn what I had forgotten and clarify what I didn’t intuitively
get. With the usual caveats about different people having different learning
paths, I didn’t find the knowledge stuck with me if I tried picking a broad
math topic (ex: “statistics”, which encompasses a lot) and trying to re-learn
everything about it.

Over the last few months, I realized a different approach that had been most
effective for me. If I picked a specific thing I found challenging to do or
wanted to develop as a skill, I could work backward from there to probe
through ever more fundamental concepts where I had a gap in knowledge until I
hit something I didn’t need explained to me. Having gone through that backward
journey, the path forward now was more clear and obvious. It helped as well
that I was motivated to dig deeper because increasing my knowledge within this
narrow context had an immediate practical utility for me.

If you would like to take this approach, you need to start somewhere specific.
For example, I had a generic goal to learn how I could deploy machine learning
in an actually valuable way. After many failed attempts to meet that goal
satisfactorily, I decided to pop open MindNode, write TensorFlow 2.0 in the
main node, pull up the TF 2.0 Alpha documentation, and start reading from the
top. For each thing I didn’t immediately understand (ex: eager execution,
input layer shape), I created a node. For each node, I began Googling and
reading pretty much everything on the first page of results. If I encountered
something within the explanations I didn’t get, that became a new child node.
Among the many things I explored, I realized a grain that stuck in my mind was
“but why do the rules for matrix multiplication feel so arbitrary”. Exploring
that question led me to 3Blue1Brown’s linear algebra playlist on YouTube. I
can’t begin to describe how it felt when those videos helped me “get” matrix
multiplication. With that fundamental bit of math starting to make sense, the
more complex concepts are becoming clearer too.

In a nutshell, the approach I’m taking is to start with something specific
that’s personally meaningful, and then dig in to it to find out what exactly
isn’t clear to me. I hope it helps to think about this approach as an option.

------
moviuro
FWIW, when entering my CPGE [0] in France, our math teacher asked we forget
everything about math except: natural numbers (0, 1, etc.), addition and
multiplication. Everything needed to be scraped and "taught correctly", and it
took only 2 years to get back up to speed (the entire program for the school
year is available (in French):
[https://prepas.org/ups.php?entree=programmes](https://prepas.org/ups.php?entree=programmes)).

Math is incredibly simple to build from scratch (as in: doesn't require a ton
of knowledge) [1]. How long it takes for it to "click" though is another
matter: I've had a very hard time with calculus and basic logic in first year,
and thoroughly failed my second year.

I don't have a book to recommend though (everything was taught in class, no
textbook); though I remember vaguely some books that others here do recommend.

[0]
[https://en.wikipedia.org/wiki/Classe_pr%C3%A9paratoire_aux_g...](https://en.wikipedia.org/wiki/Classe_pr%C3%A9paratoire_aux_grandes_%C3%A9coles)

[1] [https://en.wikipedia.org/wiki/Axiom](https://en.wikipedia.org/wiki/Axiom)

------
davismwfl
I totally get it. My daughter took algebra last year (she is going into high
school), and I had to relearn things I haven't had to do in a long time, and
more so learn the way in which it was being taught. I use math quite a bit
(and some is quite complex), but there are parts of Algebra that you just
don't use commonly. Also, at least in the U.S. they teach Algebra (math in
general) far different than how I learned it growing up and in college.

So to help her we went took Khan Academy lessons together and that way I could
understand what it was they were going for and could help her understand if
she had questions. I highly recommend them, really was super helpful and lets
you move through stuff you know and slow down where you need to practice some.
There are also a lot of places online you can download worksheets to do
practice, which in the end is all you probably need to do to see where you
are.

Another resource you can try is go to your local community college and see if
they will let you audit a couple of the math courses. Or see if you can sit in
on some of the adult learning math classes, usually those are geared to
working people trying to get their GED or HS diploma but at least where I am
they are usually super helpful to people who just need a refresher on math or
english etc. I was helping a friends machine shop get more organized and
improve their working situation and we sent a lot of the CNC operators to the
adult learning classes for a very small fee ($50 or so) to get some help on
math etc. So worth it, and what they all appreciated was there was no
judgement of young 18-20 year old kids (that can be intimidating for some
people) like there could have been in regular remedial math classes in
college.

You'll do good, it comes back to you for the most part and you will crank
through it faster then you initially think. Good luck!!

------
hluska
I went back to University in my late twenties after six years away. While I
worked in the tech industry as a developer, I hadn’t done any actual math
since University calculus nearly nine years before.

My first semester back, I had a calculus course. It was an absolute nightmare.
I knew that if I had taken the class fresh out of high school, I would have
dominated it. But, I didn’t. I fucked up and dropped out. Now, I was
completely fucked...

But, I passed that class, went on and finished a degree. I got through that
class with a few strategies:

1.) I told my professor the truth. When I went to speak to him, I was prepared
for him to tell me that I just wasn’t qualified. To my surprise, when I told
him how long I had been away from school, he wasn’t actually surprised. He
told me that because of the work I did, I likely had the capacity to pass the
class, I’d just need to work a little harder to “re-remember” that I knew it.
He suggested two strategies. I had made some friends in the class, so he gave
us permission to hand in one copy of the weekly assignments as a group. The
second strategy was to go and investigate the tutoring opportunities my
University made available to mature students.

2.) My university had several opportunities for mature students. They had
regular math labs where people like me could go in, ask the most incredibly
stupid questions and get really good answers. One particular graduate student
helped me way more than I deserve and even took me to the bookstore to find a
good introductory Calculus text.

3.) Working in the group was really amazing. First, I learned to trust myself.
A large percentage of the time, I was actually doing things correctly. But, my
time away convinced me that I couldn’t trust my instincts. Having two friends
to say “you dumb fuck, you’re doing that right” helped so much. Second and
most importantly, that first semester back was a huge shock and I wanted to
drop out many times. Being part of a group where I had to meet up with two
people twice a week kept me in school.

4.) “Re-remember” become a personal mantra. Writing that ‘word’ still hurts,
but holy shit, was that ever an important concept for my ego.

------
lumberjack
Many unis offer a prereqs class just for people like you and for others who
might have had inadequate secondary schooling. You might want to check out
whether your prospective college/university does this.

------
DanBC
For very basic math have a look at past-papers and marking schemes for the uk
"Functional skills" maths.

[https://qualifications.pearson.com/en/qualifications/edexcel...](https://qualifications.pearson.com/en/qualifications/edexcel-
functional-skills/Maths.coursematerials.html#filterQuery=category:Pearson-
UK:Category%2FExam-materials)

------
hoursxminutes
I'm in a similar position, so I have blown the dust off my Nintendo DS and
bought Brain training for 50p at a local shop. You can get the Math focused
version "Math training" too.

The games track your progress well and adapt to your skill level. It is away
from your connected devices so reduces your chance of getting distracted. Also
it's a beautifully designed game.

------
Dowwie
Take a look at the math portion of the test prep material for the GMAT or
other examinations. These materials include answers and solutions to
questions. There are also online communities explaining concepts to each other
in more detail. GMAT covers number properties, fractions, decimals and
percents, basic geometry, and algebra. It's a very good refresher.

------
codingdave
I concur with everyone who says Khan Academy - their UX will let you speed
through the stuff you already remember well enough, so you won't waste too
much time on the basics, and it will help you focus in on the gaps where you
have forgotten the material.

------
j88439h84
Israel Gelfand, "Algebra", is a really good book on basic math.

~~~
adrift
I don't get why people mention this title so often, for a beginner it's
confusing at best especially the first few chapters.

------
bootsz
I highly recommend Khan Academy:
[https://www.khanacademy.org/](https://www.khanacademy.org/)

------
rramadass
I suggest the following approach;

Start with some school textbooks for grades 8-12 i.e. Secondary Education.
This is more for a refresher course in the absolute basics.

The above can be supplemented with the following books to develop intuition;

1) Who is Fourier - [https://www.amazon.com/Who-Fourier-Mathematical-
Adventure-2n...](https://www.amazon.com/Who-Fourier-Mathematical-
Adventure-2nd/dp/0964350432/ref=sr_1_1?keywords=who+is+fourier&qid=1563268572&s=books&sr=1-1)

2) Functions and Graphs - [https://www.amazon.com/Functions-Graphs-Dover-
Books-Mathemat...](https://www.amazon.com/Functions-Graphs-Dover-Books-
Mathematics/dp/0486425649/ref=sr_1_1?keywords=Functions+and+graphs&qid=1563268628&s=books&sr=1-1)

After this is when you enter undergraduate studies and you have to fight the
dragon of "Modern Maths" which is more abstract and conceptual. In addition to
standard textbooks; i suggest the following;

1) Concepts of Modern Mathematics - [https://www.amazon.com/Concepts-Modern-
Mathematics-Dover-Boo...](https://www.amazon.com/Concepts-Modern-Mathematics-
Dover-
Books/dp/0486284247/ref=sr_1_1?crid=3RJG1Q2661MUE&keywords=concepts+of+modern+mathematics&qid=1563269004&s=books&sprefix=concepts+of+modern+ma%2Cstripbooks-
intl-ship%2C376&sr=1-1)

2) Mathematics: Its Content, Methods and Meaning -
[https://www.amazon.com/Concepts-Modern-Mathematics-Dover-
Boo...](https://www.amazon.com/Concepts-Modern-Mathematics-Dover-
Books/dp/0486284247/ref=sr_1_1?crid=3RJG1Q2661MUE&keywords=concepts+of+modern+mathematics&qid=1563269004&s=books&sprefix=concepts+of+modern+ma%2Cstripbooks-
intl-ship%2C376&sr=1-1)

3) Mathematical Techniques (i am linking this so you can see the reviews but
get the latest edition) - [https://www.amazon.com/Mathematical-Techniques-
Dominic-Jorda...](https://www.amazon.com/Mathematical-Techniques-Dominic-
Jordan/dp/0199249725/ref=sr_1_4?qid=1563269267&refinements=p_27%3ADominic+Jordan&s=books&sr=1-4&text=Dominic+Jordan)

Finally, if you would like to learn about all the new-fangled mathematics your
best bets are;

a) The Princeton Companion to Mathematics - [https://www.amazon.com/Princeton-
Companion-Mathematics-Timot...](https://www.amazon.com/Princeton-Companion-
Mathematics-Timothy-
Gowers/dp/0691118809/ref=sr_1_1?qid=1563270182&refinements=p_27%3ATimothy+Gowers&s=books&sr=1-1&text=Timothy+Gowers)

b) The Princeton Companion to Applied Mathematics -
[https://www.amazon.com/Princeton-Companion-Applied-
Mathemati...](https://www.amazon.com/Princeton-Companion-Applied-
Mathematics/dp/0691150397/ref=sr_1_2?crid=2NDD0046R25BJ&keywords=the+princeton+companion+to+mathematics&qid=1563270163&s=books&sprefix=the+princeton%2Caps%2C367&sr=1-2)

One important piece of advice that i have is to become comfortable with the
Symbols, Notation and Formalism used in Mathematics. Most students are
intimidated by the Formalism (which is nothing more than a precise form of
shorthand to express abstract concepts) and give up on studying Mathematics
altogether. This is a shame since it is merely the Form and not the Function
of Mathematics.

------
rdlecler1
A Mathematicians Delight by WW Sawyer

