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Books used in undergrad math at colleges outside the United States.

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At my university in India:
Freshman year: Thomas Calculus and Gilbert Strang Linear Algebra
Sophomore year: Dummit-Foote Abstract Algebra, Halmos set theory, Hoffman and Kunze, Carothers/Rudin for Real Analysis

After that for respective electives, books like Munkres, Ahlfors, Spivak etc
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We started learning Calculus (Analysis) with Zorich's Mathematical Analysis I. It was a bit overwhelming for us 19 year olds.
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In Finland, we barely use textbooks in bachelor's level university mathematics. It's a mix of lecture slides, handwritten lecture notes and typed lecture notes. Books may be named as reference works but you wouldn't primarily study using them.
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At University of Toronto in the math specialist program we've used the following books (I can't speak for the any fourth year courses yet). The specialist program is a program that's tougher than a major, though, and is essentially a substitute for a double major.

First year:

- *Calculus* by Spivak
- *How to Prove It: A Structured Approach* by Velleman
- *Linear Algebra Done Right* by Axler

Second year:

- *Calculus on Manifolds* by Spivak
- *Differential Equations, Dynamical Systems, and an Introduction to Chaos* by Hirsch, Smale, and Devaney
- *Elementary Number Theory* by Jones and Jones
- *Elementary Differential Geometry* by Pressley
- *Topology* by Munkres

Third year:

- *Abstract Algebra* by Dummit and Foote
- *An Introduction to Manifolds* by Tu
- *Complex Analysis* by Alfhorz
- *Partial Differential Equations: An Introduction* by Strauss
- *Real Mathematical Analysis* by Pugh

Edit: after looking at the past syllabi, fourth year textbooks include the following, though it seems a lot of them only have instructor notes rather than textbooks.

- *An Introduction to K-Theory for C^*-Algebras* by Rordan, Larden, and Lausten
- *Analysis Now* by Pedersen
- *Differential Topology* by Guelliman and Pollack
- *Multiplicative Number Theory* by Davenport
- *Real Analysis: Modern Techniques and their Applications* by Folland
- *Riemannian Geometry* by Do Carmo
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I’m sure Ian Stewart’s Calc textbooks are used everywhere - I used them in Canada and they were great. I frequently refer to them when tutoring high school students in Calc, because their nelson books are trash.
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In australia doing a physics degree:

SEM1: Calc 2 from the US, plus introductory lin alg.

Apostol Calculus volume 1, Stewart Calculus, Lang first course in calculus. Mainly used for practice problems as the teaching was done by lecturer.
Little bit of strang linear algebra

SEM 2: intro to multivariable, plus more linear algebra.

Strang Linear Algebra, Axler linear algebra, lang linear algebra. Apostol Calculus volume 2. Stewart again.

SEM 3: rigorous multivariable calculus

Apostol Calculus volume 2. Advanced engineering mathematics by Zill.

SEM 4: Rigorous linear algebra 2 course.

Axler, Strang, Lang, Rorres. All linear algebra.
Lang Undergraduate Algebra (group theory and rings/polynomials)

SEM 5: Complex Analysis.

Lang Complex Analysis, Zill Advanced Engineering Mathematics, Visual Complex analysis,

SEM 6: no math units.

One of my physics units uses Tensor Calculus for physics by Neuenschwander

SEM 7: Diff Geo and some topology.

Boothby intro to differentiable manifolds and riemannian geometry.
Modern Differential Geometry for physicists, Isham.
Spacetime and geometry, Sean Carroll.

SEM 8: Functional Analysis and Group Theory in physics.

Group theory in a nutshell for physicists, A Zee.
Pinter, A book of abstract algebra.
Not sure yet for functional analysis. Probably mostly just lecture notes
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In French preparatory classes (first two years post-HS for most people pursuing maths) most students don't use books all that much and rely on their teacher's notes. The popular texts are focused on supplementary material for competitive exams (such as the ENS).
Some of the most well-known ones are :
- Xavier Gourdon's Analyse and Algèbre
- Francinou, Gianella, Nicolas' Oraux X-ENS (problem books for oral exams)
- Roger Godement's Cours d'algèbre, Analyse (a bit old fashioned now. One particularity is that he goes off on anti-war rants so that's fun)
- Arnaudies, Fraysse's Cours de mathématiques (also old fashioned)
There are also a LOT of commercial so called "tout-en-uns" ("everything-in-one-volume") that cover all the basic material for competitive exams. (I have no titles to give you because they're basically all interchangeable)

At the next level (in a typical math French curriculum, to prepare for the agrégation - which includes some math studied at the graduate level in the US, since most people pass the agrégation five years after hs) the books used get more thematical.
Some well known international ones are Rudin's Real and complex analysis (Baby Rudin is mostly unheard of though because the content in it is already covered by books meant for preparatory classes), Hardy-Wright, Lang, Artin, Brezis, Hirsch-Lecombe.
Some books I haven't seen used outside of France are Daniel Perrin's Algèbre, Zuilly and Quéffelec's Éléments d'analyse, Michèle Audin's Géométrie.

There's also Bourbaki but I don't think anyone reads these except the mathematicians writing them tbh
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Some lecture notes provided by the lectureres are really good. I am not posting any links because those would be in German.
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In Korea - it varies a lot by school. I went to a relatively prestigious school.

Calc (1/2) : We learn calculus in high school (if you are stem major). We use a Korean textbook (which assumes that you know basic calc at the level of AP Calc BC). Honor calculus course covers bit more, like cauchy sequences and construction of real numbers. Btw I think US schools have 3 calc course. We have 2, calculus and vector calculus.

LinAlg : Depending on one's taste, one can choose among classes using Korean textbook (heavy in algebra, covers dual space and stuff), Friedberg (standard) and Strang (application oriented)

Intro to analysis : Korean textbook which is basically baby rudin but in Korean and less compact

Topology : Munkres or Kahn. My class used Kahn. Topology II uses Hatcher

Algebra : Fraleigh or Hungerford

Complex analysis : Depends on who gets to teach. Either Gamelin or Stein

Real analysis : We have two courses, one for upper undergrads and one for beginning graduates. Folland / Papa rudin. Both occasionally uses Korean textbook which is like...less-compact papa rudin.

Basically for major subjects, we use either mainstream popular textbooks or their Korean counterparts. This is mostly unique to my school since there were some professors who thought writing good textbooks in Korean might help students. About half of those books seems to be survived and are being used.
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in Brazil we use loads of books published by the Sociedade Brasileira de Matemática

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