My excellent friend @realityminus3 asked:
Hey mathematics twitter--do any of you know of a good undergraduate textbook for Real Analysis?— RealityMinus3 (@RealityMinus3) December 21, 2020
What would I buy, having read all of the comments and thoughts?
What follows is all of the books mentioned (in alphabetical order by [first] author), and then a lightly edited collation of the replies, including some shared elsewhere.
- Abbott: Understanding Analysis
- Alcock: How to Think About Analysis
- Apostol: Calculus (very expensive)
- Bear: Introduction to Mathematical Analysis
- Bear: A Primer of Lebesgue Integration (advanced)
- Binmore: Mathematical Analysis
- Brannan: A First Course in Mathematical Analysis
- Bressoud: A Radical Approach to Real Analysis
- Bryant: Yet Another Introduction To Analysis - also available on Cambridge core
- Burkill: A First Course in Mathematical Analysis
- Burn: Numbers and Functions
- Clapham: Introduction to Mathematical Analysis
- Cummings: Real Analysis
- Garling: A Course in Mathematical Analysis, Vol I
- Green: Sequences and Series
- Haggarty: Fundamentals of Mathematical Analysis
- Hart: A Guide to Analysis
- Marsden: Elementary Classical Analysis
- Reade: Introduction to Mathematical Analysis
- Ross: Elementary analysis
- Rudin: Principles of Mathematical Analysis (Baby Rudin)
- Spivak: Calculus (advanced)
- Stephenson: Mathematical Methods for Science Students
- Thomson, Bruckner and Bruckner: Elementary Real Analysis (free)
- Whitaker and Watson: A Course of Mathematical Analysis
@BhaiTeraSakhtHa: Walter Rudin.
@tasminS: People will say Baby Rudin, and it is the classic but I think it’s more fun as a third time round text — for learning from I would say Abbott’s Understanding Analysis.
@Moon0nASpoon: +1 for Abbott, that’s what I taught from this summer and I really liked it. Very readable, and big emphasis on learning how to put proofs together, especially in the early chapters.
- @professorBrenda: Highly recommend “Understanding Analysis” by Stephen Abbott. I call it “the book so nice I used it twice” because I learned from the 1st edition while in undergrad, and now I teach my students using the 2nd edition
- @ilsmythe: Abbott is fantastic. I used it to teach an honors section of intro analysis at Rutgers (with the goal that they would be ready for Rudin the next semester) and I thought it worked extremely well.
- @benjamindickman: strongly second this choice. FWIW: if the goal ends up being to go further (I don’t think this will happen…) then i think HS Bear’s book is an accessible undergrad text on Real Analysis II
- @MrMansbridge: Spivak
- @themathdiva: That would be my choice
@soupie66 An amazing book to read before you even start is Lara Alcock’s fantastic book How to think about Analysis (OUP). I wish I had read it before and during my undergraduate course, for it is BRILL!
@Howat_Hazel: have forgotten anything I knew about Analysis but I know Lara Alcock writes excellent books
@ChrisBMaths: Mary Hart’s book, A Guide to Analysis
- @DarrenBrumby: Victor Bryant’s Yet Another Introduction to Analysis
- @MathematicalA: Available on Cambridge core
@soupie66: Whittaker and Watson.
- @Long_tailed_tit: Brannan might be too simple. But written by the
@OpenUniversity and so high clarity of explanation.
- @MathematicalA: Seems to be freely available on the internet
@Mathemacricket: My A Level teacher lent me this book before I started my degree: Fundamentals of Mathematical Analysis by Rod Haggarty.
@isleofmandan: Fundamentals of Mathematical Analysis by Rod Haggarty is quite accessible.
@sumsgenius: The maths dept at uni asked us all to work through Stephenson before we started the degree. It was a long time ago, though.
@JoeHarrisUK: some options from the Cambridge schedules
@matthematician: For accessibility and open-educational-resource availability: Thomson, Bruckner, Bruckner.
@darthkiks: To get a better feel for the motivation behind the theorems, I highly recommend “A radical approach to real analysis” by D. Bressoud
- @TChihMaths: I think I’ll let @LongFormMath plug his own book!
- @LongFormMath: (Cummings: Real Analysis) - It’s like Abbott’s book on steroids!
@profgoat: Now this (Bear: Lebesgue) isn’t a beginner book, but might be an advanced topic book, or a readable refresher for those of us 30 years out of our comps.
@profgoat: Marsden’s book is as old as dirt but I love it.
- @mathdocron: I liked “Elementary Analysis: The Theory of Calculus” by Kenneth Ross.
- @_qnlw: Just used it this year. The content and presentation are okay (some minor things I disagree with). But I am not terribly impressed by the choice and phrasing of the exercises.
I’ll leave the full run-down to Nicholas Jackson:
- @njj4: Hart is a good introductory book that covers sequences, series, continuity, limits, differentiation. Alcock is a very readable introduction that talks about how to think about the subject. Green and Clapham are nice little books. Burkill is a bit old now, and I never found it very readable - it was on the suggested list in my first year (1991) but we used Binmore instead, which was much clearer. Bryant is quite accessible. Burn is readable but strange - the proofs are broken down into guided exercises.
- @sam_holloway: I remember real analysis was the course I struggled to get a good textbook for (back in 1997/8). Bryant I’ve looked at since and it looked like the one that would have helped me!
A selection of other posts
subscribe via RSS