User:IssaRice/Reviews of undergraduate real analysis books: Difference between revisions
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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. | 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?; | 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?; whether it covers any of the history of analysis/traces the history as it goes (there are at least three books like this); | ||
==Tao, Analysis I and II (2006)== | ==Tao, Analysis I and II (2006)== | ||
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==Bartle (he has three books)== | ==Bartle (he has three books)== | ||
oh god, there are so many. | 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? | 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? | ||
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Foundations of analysis by landau; Number Systems and the Foundations of Analysis by mendelson | 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; | 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 [https://math.stackexchange.com/a/188543/35525]; "Foundations of Modern Analysis" by J. Dieudonne; Kosmala, A Friendly Introduction to Analysis; Steven Krantz's Real Analysis And Foundations; "A First Course in Mathematical Analysis" by Burkhill; "Introduction to Real Analysis" by Bartle and Sherbert; "Fundamentals of Mathematical Analysis" by Haggarty; Analysis I by Amann/Escher; Johnsonbaugh and Pfaffenberger's Foundations of Mathematical Analysis; Analysis: With an Introduction to Proof by Steven Lay; Introduction to Analysis by Edward Gaughan; The How and Why of One Variable Calculus by Amol Sasane; Basic Real Analysis by H. Sohrab; A basic course in Real analysis by Ajit Kumar and S. Kumaresan; jacob and evans, A Course in Analysis: Volume I: Introductory Calculus, Analysis of Functions of One Real Variable | ||
Latest revision as of 19:51, 20 September 2021
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?; whether it covers any of the history of analysis/traces the history as it goes (there are at least three books like this);
Tao, Analysis I and II (2006)
Abbott, Understanding Analysis
Rudin, Principles of Mathematical Analysis (Baby Rudin)
Pugh, Real Mathematical Analysis
Spivak, Calculus
Apostol, Mathematical Analysis
Apostol, Calculus I and II
Zorich, Mathematical Analysis I and II
Bloch, The Real Numbers and Real Analysis
Gleason, Introduction to Analysis
Rogers and Boman, How We Got from There to Here
Stein and Shakarchi, Real Analysis
i think this is mostly graduate level material
Folland, Advanced Calculus
Schramm, Introduction to Real Analysis
Bressoud, A Radical Approach to Real Analysis
Taylor, Introduction to Analysis in One Variable and Introduction to Analysis in Several Variables
Lebl, Basic Analysis: Introduction to Real Analysis
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; Steven Krantz's Real Analysis And Foundations; "A First Course in Mathematical Analysis" by Burkhill; "Introduction to Real Analysis" by Bartle and Sherbert; "Fundamentals of Mathematical Analysis" by Haggarty; Analysis I by Amann/Escher; Johnsonbaugh and Pfaffenberger's Foundations of Mathematical Analysis; Analysis: With an Introduction to Proof by Steven Lay; Introduction to Analysis by Edward Gaughan; The How and Why of One Variable Calculus by Amol Sasane; Basic Real Analysis by H. Sohrab; A basic course in Real analysis by Ajit Kumar and S. Kumaresan; jacob and evans, A Course in Analysis: Volume I: Introductory Calculus, Analysis of Functions of One Real Variable