Question

Books on mathematical topics that **REALLY** introduce you to the topic.

Answer 1

Ironically the book this cover is from is one I would actually recommend as a good introduction to graduate algebra. It’s Pierre Grillet’s *Abstract Algebra* and he’s a damn good writer. Plus he knows how to not skip steps and structure things *in order* of understanding.

Sidenote: “Introductory” does not imply undergrad. If something was titled “An Introduction to Class Field Theory” I probably wouldn’t assume that’s for undergraduates.

Answer 2

I reccomended these to someone else on this sub, but Terrence Tao's Analysis I and II. He starts Analysis I from a no-knowledge perspective and builds rigor up from intuition. Great texts.

Answer 3

Munkres' Topology book, Fraleigh's Abstract Algebra book, Pinter's Abstract Algebra book, Curtis' Linear Algebra, Trudeau's Graph Theory, Haberman's PDE, Pressley's Elementary Differential Geometry

are all extremely novice friendly books that still get the key points across.

Answer 4

Abbott's intro to analysis. U can literally just start with no knowledge. Every chapter starts with motivation into problems and theory. In addition, everything is fully contained, so no need to refer to outside sources, except maybe as a help to writing some proofs for exercises.

This is literally my favorite textbook. I hated calc and diff eq textbooks because while they are intuitive and motivation is the topic itself, you are kind of just doing operations without understanding the meaning. Once I hit college math and read this gem, I was blown away.

Another great textbook is the chartrand introductory graph theory. Provides great examples, diagrams, and practice problems that are not only theoretical, but also applied. Graph theory is fun.

Answer 5

*office hours with a geometric group theorist* is a perfect introduction to ggt.

Answer 6

I recently started an internship in statistical analysis and I’ve found *An Introduction to Statistical Learning* to be absolutely indispensable. My LinAlg and Stats classes were great for developing a rigorous understanding of the topics - but as far as an actionable understanding of data analysis, I learned a lot more from this book than from any of my classes. In particular, I don’t think any of my statistics classes gave a proper introduction to working with extremely large datasets.

Answer 7

Visual Group Theory, Nathan Carter. A bright child could read it, lots of pictures, by the end the small finite groups are all old friends, you've developed a powerful intuition, you've covered everything in an undergraduate course, and you know why you can't solve the quintic.

Answer 8

Trudeau’s intro to graph theory.

To be fair he does tell you it requires high school algebra, so there are some prerequisites.

Answer 9

Measure, Integration and Real Analysis by Axler.
It is free and an awesome measure theory book

Answer 10

Would you believe James Gleick's *Chaos*? I read this as a teen and found it fascinating, then did Dynamical Systems at Cambridge as a second year and found I already knew it all. In the course we got all the proofs, but it didn't matter. They were all obvious because I already had the intuitions.