User:IssaRice/Reviews of undergraduate real analysis books

i'll slowly be filling this out.

the given years are for the first edition of the book, which gives a quick view of how old the material in the book is likely to be. but for the review, i am usually using the latest edition of the book.

for each book say: year of first edition; sequential vs continuous functions approach; whether real system is constructed (and if so how); R vs R^n; whether it treats general metric spaces; good pictures or not; level of mathematical maturity required (e.g. is it suitable for someone who hasn't done proofs at all? does it assume you're very good at going through math books already?); level of suitability for self-study; does it have solutions?;

Stein and Shakarchi, Real Analysis

i think this is mostly graduate level material

Taylor, Introduction to Analysis in One Variable and Introduction to Analysis in Several Variables

[1] [2]

Bartle (he has three books)

oh god, there are so many. you start out thinking "how hard could it be to catalog and review all the undergrad level real analysis books?" and it really does turn out that there are SO MANY.

other books to add: Royden? Strichartz's The Way of Analysis? Kolmogorov & Fomin's Introduction to Real Analysis? Lang's Real and Functional Analysis? Ross's Elementary Analysis. Lang's Undergraduate Analysis. Hardy's A Course of Pure Mathematics?

lara alcock, jay cummings, the guide to rudin's book, The Real Analysis Lifesaver by Raffi Grinberg

Foundations of analysis by landau; Number Systems and the Foundations of Analysis by mendelson

Bryant's Yet Another Introduction to Analysis; A Problem Text in Advanced Calculus by John Erdman; Mathematical Analysis by S. C. Malik and Savita Aror; Fundamental Ideas of Analysis by Reed; calculus book by salas/etgen/hille; Elements of Real Analysis by denlinger; Introduction to Real Analysis by SK Mapa; Hoffman's Analysis in Euclidean Space; Hoffman's Elementary Classical Analysis; 'A First Course in Mathematical Analysis' by David Alexandar Brannan; Trench; Elementary Real Analysis by Brian S. Thomson, Judith B. Bruckner, Andrew M. Bruckner; Mathematical Analysis I by Elias Zakon; Alan Sultan's 'A Primer on Real Analysis'; Introduction to Analysis by Mattuck; Introduction to Analysis by Maxwell Rosenlicht; Courant and John's 'An introduction to Calculus and Analysis', volumes I and II; An Introduction to Classical Real Analysis by Karl Stromberg; "Guide to Analysis" by Hart & Towers; Steven R. Lay's book "Analysis - With an Introduction to Proof"; Real analysis by Frank Morgan; Methods of Real Analysis: Goldberg; Mathematical Analysis: A Straightforward Approach by K.G. Binmore; Sherbert's Introduction to real analysis; Thomas Bruckner's Elementary real analysis; Andrew M. Gleason's Fundamentals of Abstract Analysis; Introductory Real Analysis by Frank Dangello and Michael Seyfried; An Introduction to Analysis by G. G. Bilodeau, P. R. Thie and G. E. Keough; Advanced Calculus by Watson Fulks; Advanced Calculus by R. Creighton Buck; Analysis by Its History by Ernst Hairer and Gerhard Wanner; D.E. Weisbart, has a book "An Introduction To Real Analysis"; vaughan jones's lecture notes [3]; "Foundations of Modern Analysis" by J. Dieudonne; Kosmala, A Friendly Introduction to Analysis;