Mathematical Analysis and Proof

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1. PyretFeb 2015
   Well, there is no shortage of very good and VERY SIMPLE and rigorous intros to analysis books out today:

   How to Think About Analysis by Lara Alcock.

   Understanding Analysis by Stephen Abbot.

   Mathematical Analysis and Proof by David Stirling.

   Numbers and Functions: Steps into Analysis by Burn.

   Analysis: With an Introduction to Proof by Steven Lay.

   A First Course in Mathematical Analysis by David Brannan.

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2. agentcoopsAug 2025
   I'm biased, but very fond of the open-access introductory textbooks used where I studied. The department was very much pure maths, but the intro classes were accessible to general liberal arts students. I think the texts are relatively unique in that they're very proof oriented, yet with a pedagogical style that doesn't assume the reader is a future graduate student.

   For calculus, three options to see if you like a particular author's style of explanation: http://people.reed.edu/~mayer/math111.html/math111.pdf - the most pedagogical http://people.reed.edu/~mayer/math111.html/math111.pdf - the most beautiful https://people.reed.edu/~jerry/111/calc.pdf - the most technical

   For introduction to mathematical analysis and proof: http://people.reed.edu/~mayer/math112.html/math112.pdf

   For multivariable calculus: https://www.stat.rice.edu/~dobelman/notes_papers/math/calcul... [1]

   For linear algebra, we used the relatively standard Friedberg Insel and Spence [2], but I hear good things about https://hefferon.net/linearalgebra/.

   [1] Link is off university domain, since apparently it was at some point turned into a bit more hardcore textbook oriented towards those going onto graduate studies in mathematics. If curious: https://www.amazon.com/Calculus-Analysis-Euclidean-Undergrad...

   [2] https://www.amazon.com/Linear-Algebra-4th-Stephen-Friedberg/...

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