How to Think About Analysis
by Lara Alcock · first published 2014
94% recommend6% neutral
Why HN recommends it
Gentle preparation for real analysis, not a standard textbook. Its first half teaches how to study advanced math, suiting self-learners shaky on proofs who want conceptual insight before Abbott or Rudin.
Summarised by Claude from recommending comments
Analysis is a core subject in most undergraduate mathematics degrees. It is elegant, clever and rewarding to learn, but it is hard. Even the best students find it challenging, and those who are unprepared often find it incomprehensible at first. This book aims to ensure that no student need be unprepared.
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…Mathematics Major - Alcock 3b. Proof writing: How to Prove It - A Structured Approach - Velleman OR Book of Proof (2nd ed) - Hammack (it's free!) 4. Mathematical Analysis: 4a. Good prep for Analysis: How to Think About Analysis - Alcock 4b. Understanding Analysis (2nd ed) - Abbott OR Yet Another Introduction to Analysis - Bryant (has full solutions) OR The How and Why of One Variable Calculus - Sasane OR Mathematical Analysis…
on “Ask HN: How to self-learn math?” ↗…for self-study is Abbott, “Understanding analysis” particularly if you can get the solutions manual, I think the explanations of the proofs are very good. 3) I would also recommend Lara Alcock’s book “How to think about analysis”, which is NOT a textbook, but has a lot of useful information and advice on how to learn analysis. Also, obvious but worth repeating, if you are taking less than one hour per page to get through an…
on “Ask HN: Resources to learn real analysis?” ↗…https://www.amazon.com/Discrete-Mathematics-Applications-Sus... Mathematical Proofs: A Transition to Advanced Mathematics by Chartrand et al: https://www.amazon.com/Mathematical-Proofs-Transition-Advanc... How to Think About Analysis by Lara Alcock: https://www.amazon.com/Think-About-Analysis-Lara-Alcock/dp/0... Learning to Reason: An Introduction to Logic, Sets, and Relations by Nancy Rodgers: https://www.amazon.com/Learning-Reason-Introduction-Logic-Re...…
on “Ask HN: Resources on how to improve abstract thinking skills?” ↗…and funnest would be intro to discrete math or the so called "transition" books. For example, check out [1] Discrete Math by Susanna Epp, [2] Transition to Advanced Math by Gary Chartrand et al, [3] How to Think about Analysis by Lara Alcock, [4] Learning to Reason by Nancy Rodgers [1] https://books.google.com/books?id=PPc_2qUhXrAC&pg=PA1&source... [2] https://www.amazon.com/Mathematical-Proofs-Transition-Advanc... [3] https://books.google.com/books?id=n0tuBAAAQBAJ&pg=PA4&source...…
on “Ask HN: Any resources to learn the fundamentals of critical thinking?” ↗…Proof" by Richard Hammach. It's online free. https://www.people.vcu.edu/~rhammack/BookOfProof/ [4] "Discrete Math" by Susanna Epp https://www.google.com/books/edition/Discrete_Mathematics_wi... [5] "How to Think About Analysis" by Lara Alcock https://www.google.com/books/edition/How_to_Think_about_Anal... [6] "Linear Algebra" by Kuldeep Singh https://www.google.com/books/edition/Linear_Algebra/BJNoAgAA...
on “Ask HN: Looking for a book on algorithms and data structures” ↗…algebra in a while (e.g. Strang or Linear Algebra: Step by Step by Singh). Then: Linear Algebra - Friedberg, et al Linear Algebra Done Right - Axler Linear Algebra - Hoffman & Kunze Real Analysis: How to Think About Analysis - Alcock Understanding Analysis - Abbott Tao's Analysis text Principles of Mathematical Analysis - Rudin Topology: Topology - Munkres Topology A Categorical Approach - Tai-Danae Bradley, Tyler Bryson,…
on “Physics Student Earns PhD at Age 89” ↗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…
on “A Software Engineer’s Adventures in Learning Mathematics” ↗Are you comfortable with proving math statements? If not, How to Think About Analysis by Lara Alcock is an amazing intro to Analysis. http://www.amazon.com/Think-About-Analysis-Lara-Alcock/dp/01...
on “Will Our Understanding of Math Deteriorate Over Time?” ↗"How to Think About Analysis" by Lara Alcock (2014) because the first part (half) of the book is specifically dedicated this aim, "[focusing] explicitly on skills and strategies for learning advanced pure mathematics." (from the…
on “Ask HN: Which books helped you gain mathematical maturity?” ↗…people who could learn analysis perfectly well from friendlier (but not necessarily any less rigorous) sources. Rudin requires a lot of self-motivation. In addition to Abbott which you mentioned, "How to Think About Analysis" (Alcock), good gentle introduction for anyone who tries to dive into an analysis textbook and hits concrete. "Real Mathematical Analysis" (Pugh), good, rigorous approach that doesn't require quite as…
on “The Hacker News Top books of 2023” ↗If you dive into Analysis (the underlying theory behind calculus) this book - "How to Think About Analysis" by Lara Alcock is the book I wish I had when I studied it. Calculus by Spivak is the book I learnt from but it is probably not the easiest, it is very thorough though.
on “Fundamental Theorem of Calculus” ↗…Indian Physics professor and this is written specifically for students to "understand" calculus i.e. it is not a typical textbook. - https://garudalife.in/calculus-the-princess-of-mathematics-v... 4) How to Think about Analysis by Lara Alcock. Provides conceptual insight like the Tarasov book above. Checkout the author's other books too. - https://global.oup.com/academic/product/how-to-think-about-a... I believe we need to…
on “Simplifying and Refactoring Introductory Calculus” ↗…intending to recommend intro analysis book. But now that you mentioned it, for introduction to real analysis, there are even better textbooks out there. For bare-bones hand-holding stuff, there are "How to Think About Analysis" by Lara Alcock and "Real Analysis" by Jay Cummings. The former spends a lot of pages explaining the concepts of convergence and boundlessness and the latter, in addition to what Alcock does, introduces…
on “Free and Open-Source Mathematics Textbooks” ↗…presentational quirk. Again check Amazon for titles. Check libge*n for actual files. The following intro books are so easy anyone and they momma can read these with utmost ease: Discrete Math by Susanna Epp How to Think about Analysis by Lara Alcock Linear Algebra: Step by Step by Kuldeep Singh Real Analysis: A Long-Form Mathematics Textbook by Jay Cummings A Tour Through Graph Theory by Karin Saoub The above mentioned books are…
on “New math book rescues landmark topology proof” ↗…Algebra: Step by Step" by Kuldeep Singh which one needs because Rudin considers Euclidean Spaces proper, not just the reals. Other helpful books include "Yet Another Introduction to Analysis" by Bryant, "How to Think About Analysis" by Lara Alcock, "A First Course in Mathematical Analysis" by Brannan, "Real Analysis: A Long-Form Mathematics Textbook by Jay Cummings" etc. None of these books are perfect. For example, none of them…
on “Ask HN: The book that did it for you in math and/or CS?” ↗