University of Kwazulu-Natal

Your Approach And Experience Self Studying Mathematics Using Books R

Bonisiwe Shabane
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your approach and experience self studying mathematics using books r

Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Ask questions, find answers and collaborate at work with Stack Overflow for Teams. Ask questions, find answers and collaborate at work with Stack Overflow for Teams. Explore Teams Connect and share knowledge within a single location that is structured and easy to search. Background: I am a university math student with the math skills of a four year old.

I was taught math incorrectly for the past 16 years. I was never taught proofs or given conceptual understanding of math concepts. I was taught to memorize formulas and algorithms instead of understanding concepts. For over six years now, I've been studying mathematics on my own in my spare time - working my way through books, exercises, and online courses. In this post I'll share what books and resources I've worked through and recommend and also tips for anyone who wants to go on a similar adventure. Self-studying mathematics is hard - it's an emotional journey as much as an intellectual one and it's the kind of journey I imagine many people start but then drop off after a few months.

So I also share (at the end) the practices and mindset that have for me allowed this hobby to continue through the inevitable ups and downs of life (raising two young boys, working at... I used to love mathematics. Though I ended up getting an engineering degree and my career is in software development, I had initially wanted to study maths at university. But the reality is, that's a very tough road to take in life - the academic world is, generally speaking, a quite tortuous path with low pay, long hours, and rife with burnout. So I took the more pragmatic path and as the years went by never really found the time to reconnect with math. That was until about six years ago when I came across Robert Ghrist's online course Calculus: Single Variable (at the time I took it, it was just a Coursera course but now it's freely...

Roughly 12 weeks and many filled notebooks later, I had reignited my interest in math and felt energized and excited. Robert, if you read this: thanks for being such an inspiring teacher. Growing up I always loved puzzles and problem solving. I would spend hours working my way through puzzle books, solving riddles, and generally latching on to anything that gives you that little dopamine hit. Tackling math alone takes grit—and the right books can transform confusion into mastery. These eight standouts have earned their place as the best self‑taught math books for driven learners.

Trusted across readers and academic reviews, they’ll help you dissect complex concepts, solve challenging problems, and build true understanding. Whether you're starting with basic algebra, exploring proof-based topics, or prepping for advanced theory, these books rank among the best math books for self-study and best books to learn math—providing structure, clarity, and personal... Pinter’s A Book of Abstract Algebra is widely acknowledged as one of the best self‑taught math books, especially for learners transitioning from procedural math to proof-based thinking. It systematically builds group, ring, and field theory foundations by explaining both the "how" and "why" behind each concept. This ensures it also ranks highly among the best math books for self-study due to its carefully structured problems and approachable commentary. Gallian’s text is one of the best math books for self-study thanks to its engaging delivery and understandable depth.

Designed for motivated learners, it presents modern algebra with clarity, enlivened by historical anecdotes and real-world applications. The exercises range from straightforward to challenging, reinforcing theory and solidifying understanding. This is one of the best self‑taught math books, particularly for advancing into abstraction without feeling overwhelmed. Abbott’s Understanding Analysis is heralded as one of the best self‑taught math books for learners bridging calculus and proof-based real analysis. Packed with intuitive explanations, visualizations, and guided proofs, it demystifies rigorous topics like convergence and continuity. Its conversational style earned praise on r/math as the ideal “friendly analysis book.” That reputation also makes it one of the best books to learn math for anyone seeking conceptual clarity alongside formal rigor.

This vibrant guide is regularly cited among the best math books for self-study, especially for visual or creative learners. By combining manga storytelling with linear algebra concepts—like matrix operations and vector spaces—it makes abstract math accessible and memorable. Readers applaud its intuitive layout and comic-style explanations. It's definitely one of the most engaging best self‑taught math books, using visual narrative to illuminate math fundamentals. I’ve been self-studying math for a while now, and I get way more suggestions for textbooks and courses than I know what to do with. I usually don’t end up trying them out.

This means sometimes I’m missing out on amazing content. What to do about this? My solution is One Textbook A Day (for one week at a time). First, whenever someone recommends a resource, add it to a list. I’ve personally accumulated quite a long list of math-related content. Lots of textbooks, a few lecture playlists, some fiction books.

About 150 in total. Then, randomly read one of the resources each day. I run a python script that outputs one of the entries. I try it out for ~45 minutes. I’m very focused when reading, and I’m not afraid to go on tangents to search up terms I don’t understand. Every time I learn something new.

Most of the material on the list is way beyond my level. However, even when reading something beyond you, you can still learn a lot. It feels like artificially growing a passion for a topic. Mostly what I read doesn’t fit. But other times I end up enjoying it so much that I add it permanently to my schedule. Let me give an example.

I wanted to teach myself differential geometry. While surfing Reddit I found a recommendation for Frederic Schuller’s lectures on the geometric anatomy of theoretical physics. I wanted to listen to them. But you know… just not right now. And that’s normally where most people would leave it. Slowly forgetting.

However because of One Textbook A Day, I ended up listening to his lectures a few weeks later. And it was one of the best and most enjoyable sources I’ve read. I added it to my permanent schedule. And eventually, it became the basis for what is now The Feynman Mafia.

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