Programming for Mathematicians (Universitext) by D. O’shea (PDF)

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Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Errata: Preface vii, under Acknowledgements it states”A book is like an iceberg. The author is the only part that emerges.Out of sight are those who inspired and helped in other ways. ……..”.This is false when the iceberg is floating upside-down andalmost completely melted.Raymond Seroul “Programming for Mathematicians” (Universitext)is more like “Euclid’s Elements for Cybernauts”.I wish I had known about this book 15 years ago.Now I would be wiser instead of just older.Read the Math.Ignore the Google Translate style of writing.Ignore the quaint old-fashioned Theory of Computer Science.Ignore the sporadic trivial typographical misprints at the most critical cuspcatastrophe points of fundamental mathematical exposition.Just “Read the Math”.Students of C.S.! Start reading this book in college or earlier.Students of Mathematics! Start reading this book in college or earlier.Nerds! Start reading this book well before puberty.Mathematicians! Do NOT read this book. Instead, BUY this book and use itas a template for your own book, about your own sub-sub-discipline.The book explores, explains and exposes most of the elemental discrete algebra,number theory and combinatorics topics, and computer science software designtools, and more, that I was ever privately interested-in, or utilised constructively inprofessional IT projects.Discrete geometry, graph-theory and topology are waiting for (an)other suchhigh-quality book(s). To self-survey, obtain, absorb, enlighten-oneself, and tootherwise autodidact, about any such coherent and closely-coupled constellationsof quasi-abstract mathematical topics, through downstreaming, hardcopy browsing,or ad hoc, judicious, cost-effective and beyond-the-paywall access, can become anightmare to end all nightmares.This subset of The Great Books of Mathematics for Programmers, the recursivefunction Raymond Seroul “Programming for Mathematicians” (Universitext), consistsof a sequential list of top-down design specifications for runnable platform-freepseudocode algorithms, utilising classical algebraic notation, expressions andstructures, which provide remedial pre-requisite fodder for the numeracy-deprivedComputer Science undergraduate, graduate or post-graduate.In 50 years, this is the best mathematics book I have seen, of the hundreds(?) I havetried to read on virtually every aspect of this genre.Every aspect! Only I baulk, and stubbornly try to derive something from first principles,whenever an alleged expository practitioner of the mathematical arts seems to suffer from aninexplicable aversion to describing and explaining “the obvious”( which to the reader it is not ),and instead proceeds to fall-off-a-conceptual-cliff of their own devising.Become a real mathematician. Buy this book.Don’t read George Boole’s Laws of Thought and understand more about probability thanmathematical logic.Don’t read Claude Shannon’s Master’s thesis on Switching Algebra to understand wherecontemporary digital computing came from.Don’t read Edmund Landau’s Foundations of Analysis to understand Peano’s Postulates.Don’t read the archive Abbott Teach Yourself Calculus 1967. It is for 14-year-olds.Don’t try reading Donald Knuth’s Art of Computer Programming vols I, II and III,to understand how we all got to where we are.And don’t even bother with Carr’s Synopsis 1886. It only helped to make a Ramanujan.Just read Raymond Seroul “Programming for Mathematicians” (Universitext).This will lead you to a thousand places you did not know you wanted to be,to learn a thousand things you didn’t know you needed to know.Sidenote: The following is another story for other positive reviews, but I am before its time. So sad. Maybe later.Vector Calculus, Linear Algebra and Differential Forms_ A Unified Approach_ Barbara Burke Hubbard,John H. Hubbard_ 9780136574460_ AmazonApparently too many books I once needed 50+ years ago, passed me by while I did not know where to direct my attention.Now I still have no idea where to look, except by the structured random stumbling search strategy, but quite persistent fora connection-speed-challenged and app-averse old-codger.I always end-up at Amazon. At least they try to show you the Table of Contents, even if no reviews exist.Why cannot we just have “Books that work” and Books that don’t” instead of waiting for crowd democracy to sort them?Now back to Raymond Seroul “Programming for Mathematicians” (Universitext).Starting from the beginning might not be optimal. Hmmm.I can actually do the exercises in chapter 2.Beware. Mathematical thinking is required.I can debug the code in chapter 3.Beware. You have to think like a computer programmer.There is a nice optional red herring in chapter 2.Bertrand’s Postulate. (Which isn’t by the way, butmathematicians’ licence allows them to call it that.).A footnote on page 7 hints that Hardy and Wright Introduction to the Theory of Numbersis the place to go to find a semblence of the Tchebycheff proof.Not quite. After much googling and downstreaming I seem to know more about howHardy, Ramanujan and Erdos, liked to prove it, but not about how Tchebycheff did it.A programmer must be able to semantically parse the mathematics in this book.A mathematician must be able to syntactically analyse the pseudocode in this book.Both must be able to autocorrect the misprints in the book.All the mathematics is relevant for computer science.All the programming is prerequisite for mathematics.A proper book-length review of this book, that can appropriately contextualise it within the hybridisingculture of cybernetico-mathematics or whatever it is supposed-to-be called, is another likely candidatefor lookahead hindsight from the future.Gutenberg technology is good for you. I would recommend holding-on to this book as your life-jacket,while you eye-touch and reality-goggle your way through the syntactically fragmatic pixellated virtualdigital vortex, with or without skateboard-trajectory entry and exit points.Analog is a rock.Digital is a hard place.Love thy technology as thyself. ——————————————————————————-Seroul’s Theory of Computer Science is quite unusual, but manages to impart knowledge by appealingto one’s sense of humor. I thought the PASCAL code snippets were funny, especially the criticism of bador extraneously-featured code, but I have no inclination to read a PASCAL manual or even a BNF chart,or compare implementation differences across platforms.Seroul lays down many best practice guidelines for programmers, and gives examples of code.He then proceeds to violate every one of the best practice guidelines when it comes to writing mathematics.This book seems to be riddled with misprints.Fear not. Solving the riddle and restoring the textual definitions to what they were intended to be,is a wonderful learning experience.You can thereby prove to yourself that you understood the material.Enough …. Or as HAL 9000 would say “My mind is going”.If this review(stepwise-patched free-form source) were input to a proper review compiler,wonder if it could produce formatted output(structured intermediate code)?

⭐Excellent book from an algorithms viewpoint grounded in mathematics principles.

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