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What are obscure textbooks that you have liked or think has good quality?

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Duistermaat and Kolk's multidimensional real analysis. Perhaps the theory portion isn't the greatest, but that selection of exercises is. Half the book consists of just problem statements from all kinds of different domains, like physics, the Riemann zeta function, complex analysis, differential geometry. Even browsing through the different problems is amazing.

Bloch's the real numbers and real analysis. This is an introductory real analysis text, but what makes it stand out is its careful focus on foundations. It starts by giving the Peano axioms, and rigorously constructing Z, Q and R in a way no other book does (although Tao kind of gives the idea, but imo doesn't work it out much). The book then continues by rigorously going over the properties of the real numbers, including a proof that decimal expansions of the real numbers exist and are "unique".  Then it continues to usual analysis topics, but even there there is a focus towards the foundations, for example he proves that the intermediate value theorem is equivalent to completeness of the real numbers, and there are many other neat bits like this.

Carothers, real analysis. I just really love how this book does real analysis. He assumes you are familiar with real analysis on R and a tiny bit of linear algebra (vector spaces and linear maps, nothing more). Then he goes on doing metric spaces, function space and measure theory on R. There are a ton of problems which really help a lot in internalizing the theory.

Freitag & Busam's complex analysis. Here are two books on complex analysis that I really like. Great collection of problems (most of which are solved in the back or with hints!), and nice theoretical development.

Anderson & Feil, abstract algebra. Not too different from a standard AA text, but does rings first and only then groups. I always felt this to be better since for example quotient rings are more intuitive to grasp than quotient groups.

Brannan's geometry: Does geometry from the point of view of Klein: covers affine and projective geometry (and motivates it), and hyperbolic, elliptic and inversive geometry and relates them to eachother using the language of group theory. The problem selection isn't the greatest though.

Any book by Keith Kendig, especially his book on plane algebraic curve. He throws rigor out of the window so it's not meant as a standard textbook, but he does offer a damn lot of intuition and nice pictures!  


Cox, O'shea and Little's "ideals, varieties and algorithms" is in my opinion the best introduction to algebraic geometry. There is a heavy focus towards algorithms (for example Grobner bases) though. But he really gives intuition to why we should care about algebraic geometry and why some questions arise naturally.   


Silverman's "Friendly introduction to number theory". Like all of Silverman's books this is a gem.

Not sure if it's obscure, but I really like Simon's comprehensive course in analysis, and Harthorne's "Euclid and beyond" too.
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The way Lebesgue theory is taught in Jones’ *Lebesgue Integration On Euclidean Space* is fantastic! The first chapter actually deals with a full intuitive construction of the lebesgue measure starting with intervals in R^n, then building through the with polygons, open sets, compact sets, then finally arbitrary measurable sets and the properties of the Lebesgue measure are slowly developed along th way. Then the second chapter demonstrates the invariance of the Lebesgue measure. Finally after all this build up you get to start with Lebesgue integration. I really love this exposure to the subject and the exercises are phenomenal and so enlightening!
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Werner Ballmans' *Lectures on Kahler manifolds* is one of the best references I've come across for basic complex geometry.
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I am really fond of Azriel Levy's Basic set theory. If you are at a certain level of mathematical maturity I feel like its the perfect book to have a feel around the basics of set theory.

For my tastes there is a little bit of a gap between "set theory for undegraduates" (Jechs introduction to set theory, Goldrei's book) and "real set theory" (Kunen, Jech), where the first one doesnt care too much that all of the proofs should (theoretically) have an equivalent deduction in ZFC and the second one is comfortable and careful enough with the material to just believe that everything has an underlying ZFC statement. As a consequence I never felt that I have solid ground under me when reading either, and Levy's book fits neatly into that gap between pre-rigor and post-rigor.
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Not sure if it’s obscure, but I don’t often see people recommending Leary’s “A Friendly Introduction to Mathematical Logic” when people ask for logic book recs.

I think it’s a really good book that can help you get into the field if you have even some mild math maturity (some undergrad algebra/analysis)
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It’s not necessarily obscure for the people in the field, but I think Spectral Methods in MatLab by Trefethen is a gem.
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Poor - Differential Geometric Structures
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- Piskunov's Calculus
- An Introduction to Abstract Algebra (Rings, Groups and Fields) by Todd Feil
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Klaus Janich - Vector Analysis (Intro smooth manifolds text)

Hawkins - Ergodic Dynamics

Baldi - Stochastic Calculus

Kesavan - Functional Analysis

Rogers and Williams - Martingales, Markov Processes and Diffusions
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I like Valenza's Linear Algebra: An Introduction To Abstract Mathematics.

It's the first mathematics textbook I ever read, before I'd even started undergrad, and it kicked my ass, but in a good way.

It's basic linear algebra, but introduces it via group theory and categorical notions. There is one example of a matrix multiplication in the book (he claims it would be against the spirit of the book to do any more). He introduces products and direct sum via the universal property, dual space as an example of contravariant functors, etc. All this meant I had some vague idea what a functor was before I had even learned what a Riemann integral was.

More accessible than it sounds. It's the book that inspired me to do a maths degree.

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