Best Resources to learn math from zero to Uni from someone who did it

I self-taught myself Math from absolute zero to enter a Top Uni at age 29, I think the right resources made all the difference. These are the resources I found most helpful.

When I was 29, I found out about machine learning and was so fascinated by it. I wanted to learn more after doing a few “applied courses” online.
Then, by some unimaginable luck, I found out that anyone can enter ETH Zurich as long as they pass the entrance exam.
There was just one problem: I couldn’t multiply two-digit numbers without a calculator. I had no formal education post the 6th grade and I never paid attention to math, and I hated it.

I was very embarrassed. But it’s only hard at the very beginning. With the right resources, math becomes fun and beautiful. Your curiosity will grow once a few things “click,” and that momentum changes everything. Math and science changed the way I see and experience the world. Trust me, it’s worth it.

The resources prevent some people from ever experiencing that “click.”
Some textbooks, courses, and platforms excel at some topics and are average at best for others.
Even now I spend 10–15% of my time just scouting materials before I learn anything.
Below is the list I wish I had one day one. From absolute zero to Uni level math, most resources are free.

Notes

• Non-affiliated links. If a “free” link looks sketchy, please tell me and I’ll replace it.

• Khan Academy tip: aim for mastery. It gamifies progress and focuses practice.

• My style is “learn → do lots of exercises → move fast through repetition.”

• A thing I didn’t have back then was ChatGPT, I used to explain concepts to my dog.
  Today I use ChatGPT a lot to fill that gap and challenge my thinking.
  ChatGPT can be a great resource, but ask it to challenge you, criticize and point out the flaws in your understanding. I would not ask it to help with exercises. I think it’s important that we do the work

I hope you’ll find it useful, and stick with it, a little “slope” makes up for a lot of intercept. Consistency is the key. I did 1-3 hours a day, everyday without a single day off.

I have almost 3 million points on KhanAcademy. It’s still one of my proudest achievements. I haven’t used it in years, but I still want to get that black hole badge someday.

My KhanAcademy Badges

The very basics

• Khan Academy (K–8 math): https://www.khanacademy.org/math/k-8-grades
  Go for the mastery challenges, the system just works.

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Arithmetic

I found adding/subtracting hard. Carries (the little numbers you add below the numbers) was just horrible; multiplication/division felt impossible for a really long time.
Then I came Sal, he’s got a way of explaining things and then motivating you to try.
Again, go for the mastery challenges, it’ll force you to be able to do it without tripping up.

• Khan Academy: Arithmetic track

Geometry

Khan’s geometry is great, but some videos are aged and pixelated (I think they have been updating them slowly, you may find this not true anymore). However, the exercises are still fantastic, and he walks you through them often.

• Khan Academy: Basic geometry (lines, angles, shapes, coordinate plane):

• Geometry: An Interactive Journey to Master I absolutely loved this, this one is not free, but it is incredibly intuitive. I once found it for ~$10; not sure they still sell it that way. I think it’s a subscription now.

• Geometry Workbook For Dummies (Mark Ryan): great for extra practice

• CK-12 Website’s Interactive Geometry: if you want to visualize some concepts is a great supplement, I wouldn’t use it or I didn’t find it helpful to study by itself.

Pre-algebra

Prealgebra is a necessary beast to tackle before you get too far into solving for angles and such with geometry. Again, of course, Khan is a great place to start.

• Khan Academy: Pre-algebra. Again, full mastery challenge! Go for it!

• OpenStax: Prealgebra 2e: This book is a great supplement for select topics. The OpenStax book goes quite a bit further. However, because the book is self-contained, you might have to go back and read more chapters if you encounter something you don’t quite understand yet (because Khan Academy hasn’t covered it).

• Eddie Woo (YouTube) if x’s and y’s feel slippery, his videos are filmed in the classroom which give it some extra vibe that can motivate you.

Trigonometry

Contrary to popular belief, trigonometry is actually fun!

Again, KhanAcademy is an excellent resource, but there are a lot of great textbooks out there that I loved, and I loved, like Corral’s Trigonometry and the Openstax Trigonometry. Both are free!

I also found Brilliant.org fun for challenging yourself after learning something, though for learning itself I’ve never quite found it so useful.

Practice, practice, practice. Try the Dummies trigonometry workbooks for additional practice.

Algebra

For real algebra, the KhanAcademy Algebra Track and OpenStax’s Algebra Books helped me a lot.
It looks like it’s a long road, but the more you practice, the faster you’ll move. The core concepts remain the same, and I think algebra more than anything is just practice and learning the motions.

I can recommend the Dummies workbook on algebra for more practice.

Note: I didn’t learn the following three topics after Algebra, but you would now absolutely be ready to dip your those in them.

• Khan Academy: Algebra (Algebra 1 → Algebra 2)

• OpenStax: Algebra (as a companion)

• Workbook: Algebra Workbook For Dummies (more reps)

Abstract Algebra

I recommend beginning with Arthur Pinter’s “A Book of Abstract Algebra.” I found it free here, but your local university likely has a physical copy, which I’d recommend.

I tried a lot of books on abstract algebra, and I wouldn’t recommend any others, at least definitely not to start with. It’s not that they aren’t good, but this one is so much better than anything else I’ve found and so accessible.
I had to learn abstract algebra for university, and like most of my classmates, I really struggled with the exercises and concepts.
But Arthur Pinter’s book is so much fun, so enjoyable to read, so intuitive and also quite short (or it felt this way because it’s so fun).

I could grasp important concepts fast, and the exercises made me understand them deeply. Especially proofs that were also important for other subjects later.

Linear Algebra

For this subject, you can not get any better than Pavel Grinfeld’s courses on YouTube. These courses take you from beginner to advanced.

I have rarely felt that a teacher can so intuitively explain complex subjects like Pavel. And it starts with building a foundation that you can always go back to and use when you learn new things in linear algebra.

There are two more books that I can recommend supplementing: First, The No S**t Guide to Linear Algebra is excellent if you just want to get the gist of some important theories and explanations.

Then, the Step-by-step Linear Algebra Book is fantastic. It’s one of those books that teach you theorems by proving them yourself, and there is not too many, but enough practice problems to ingrain important concepts into your understanding.

If I had limited time (Pavel’s Courses are very long), I would just do the Step by Step Linear Algebra Book on it’s own.

• Pavel Grinfeld (YouTube): unmatched intuition, beginner → advanced.

• Supplements:

  • No Bullshit Guide to Linear Algebra (great gist + clarity)

  • Step-by-Step Linear Algebra (learn by proving with enough practice)

• Short on time? Do Step-by-Step Linear Algebra thoroughly.

Number Theory

Like abstract algebra, this was hard at first. I have probably tried 10+ textbooks and lots of YouTube courses.
I found two books that were enough for me to excel at my Uni course in the end.
I think they are both helpful with small nuances, and you don’t need both. I did them both because after “A Friendly Introduction to Number Theory” by Silverman, you just want more.
Burton’s Elementary Number Theory would have likely done the same for me, because I loved it too.

• Silverman, A Friendly Introduction to Number Theory

• Burton, Elementary Number Theory
  Either is enough for a firm foundation.

Precalculus

I actually learned everything at Khan Academy, as I followed the track rigorously and didn’t feel the need to check more resources. I recommend you do the same and start with the precalculus track. You will become acquainted with many topics that will become important later on, which are often overlooked on other sites.

These are topics like complex numbers, series, conic sections (these are funky and I love them, but I never used them directly), and, of course, the notion of a function.

Sal explains these (like most subjects) well.

There are one or two subjects that I felt a little lost on KhanAacademy though. Conic Sections for one.

I found Professor Rob Bob to be a tremendous help, so I highly recommend checking out his YouTube channel. He covers a lot of subjects, and he’s super good and fun.

The Princeton Lifesaver Guide to Calculus is one of my favorite books of all time. Usually, 1 or 2 really hard problems accompany each concept. You get through them, and you can do most of the exercises everywhere else after. It’s more for calculus, but the precalculus sections are just as helpful.

• Khan Academy: Precalculus — covers the stuff many sites skip: complex numbers, series, conic sections, functions.

• Conic sections felt thin for Khan for me; Professor Rob Bob (YouTube) filled the gap nicely.

• The Princeton Lifesaver Guide to Calculus (yes, in a precalc section): my all-time favorite “bridge” book—few but tough examples that level you up fast.

Calculus

We’re finally ready for calculus!

With this subject, I would start with two books: The Princeton Lifesaver Guide (see above in Precalculus) and Calculus Made Easy by Thompson (I think “official” free version here).

If you only want one, I would just recommend doing the Princeton Guide from the very beginning until the end and try to do all of the examples. Regardless of the fact that is doesn’t have actual exercises, though, it helped me pass the ETH Entrance exam together with all the exercises on KhanAcademy (though I didn’t watch any videos there, I found Calculus to be the only subject that is ordered confusingly on Khan, they have rearranged the videos and they are not in order anymore, I wouldn’t recommend it, at least to me, it was just confusing and frustrating).

People often recommend 3Blue1Brown.
If you have zero knowledge like I did. I’d recommend against it. It’s too hard to understand without any of the basics.
After you know some concepts, it helps, but it’s definitely not for someone teaching themselves from zero it requires some foundation and then it may give you visual insights and build intuition with concepts you have previously struggled with, but importantly thought about in depth before!

If you would like to have some examples but don’t desire a rigorous understanding, I can recommend YouTube channels PatrickJMT and Krista King. They are excellent for worked examples, but they explain little of anything.

For a couple of extra topics like volume integrals and the like, I can also recommend Professor Rob Bob again for some understanding. He goes more in-depth and explains reasoning better than PatrickJMT and Krista King. But his videos are also much longer.

Finally, if you have had fun and you want more, the best calculus book for me (now that I have actually also studied analysis) is Spivak’s Calculus. It blends formal theory with fun practical stuff.

I loved it a lot, the exercises are great, and it helps you build an understanding with proofs and skills with practice.

• If you pick just one book: The Princeton Lifesaver Guide to Calculus. Read from start to finish and do all the examples. Paired with Khan exercises, it got me through the ETH entrance exam.

• Also excellent: Calculus Made Easy (Thompson) — friendly and fast.

• 3Blue1Brown? Great, but not for day-zero learners, imho. Watch after you have the basics to deepen intuition.

• Worked-example channels: PatrickJMT, Krista King (good mechanics, lighter on reasoning).

• More depth on select topics (e.g., volume integrals): Professor Rob Bob again.

• When you want rigor + joy: Spivak’s Calculus — proofs + practice, beautifully done.

A Bonus:

Morris Kline’s Calculus: an intuitive physical approach is nice in connecting the dots with physics.
I also had to learn other subjects for the entrance exam and after all the above, doing Physics with Calculus somehow made a lot more click.
Usually, people would recommend Giancoli (the Uni version for calculus) and OpenStax. I did them in full too.
But, for understanding calculus was Ohanian for me. The topics and exercises really made me understand integration, surfaces, volumes, etc. in particular.

I have done a lot more since and still love math, in particular probability and statistics, and if you like I can share lists like these on those subjects too.

Probability and Statistics

Tsitsklis MIT Open Courseware Course is amazing. He has a beautiful way of explaining things, the videos are short but do not lack depth.
I would recommend this and

https://www.probabilitycourse.com/

by Hossein Pishro-Nik which is the free online version of the Book. I’ve completed it a few times and I enjoy it each time. The exercises are so much fun. The physical copy of this book is one of my most valuable possessions.

For more statistics, Probability & Statistics for Engineers and Scientists by Walpole, Myers and Ye, as well as the book by Sheldon with the same name.

Blitzstein and Hwang have a book that covers the same topics and I think you can interchange, it builds great intuition for counting and probability in general. The free harvard course has videos and exercises as well as a link to the free book.

How to use this list

1. Start at your level (no shame in arithmetic).

2. Pick one primary resource + one practice source.

3. Go for mastery challenges; track progress; repeat problems you miss.

4. When stuck: switch mediums (video ↔︎ text), then return.

5. Keep a tiny “rules.md” of your own: what to try when you’re stuck, how long before you switch, etc.

6. Accept that the first week is the hardest. It gets fun.

I’ve done a lot more since and still love math—especially probability and statistics. If you want a follow-up guide for those, reply and I’ll share the list. This is a work in progress, and that’s the point.

Cheers,

Oli

P.S. If any “free” link here isn’t official, ping me and I’ll replace it.