Literate Scientist

This is a book I bought a few years ago and started reading immediately but put aside and only this summer read it fully from cover to cover. In order to appreciate its content you need some degree of mathematical and computer science maturity. For example, if you have never heard of his theorems and only read Incompleteness: The Proof and Paradox of Kurt Godel or similar popular book then you would have difficulty going through the book and it would appear boring. It is not an entertaining or bedside reading. This is why I put it aside on the first reading although I knew about this theorem since I read “Mathematics: The Loss of Certainty” more than 25 years ago being a schoolboy (in Russian translation). Just before writing this review I ordered “There’s Something About Godel: The Complete Guide to the Incompleteness Theorem” and the latter looks like less heavy reading judged from excerpts from its publisher website. Putting all these reminiscences aside I really enjoyed second reading of “Godel’s Theorem”. It really clarified some points from ¬B->¬A or PA & ¬Con(PA) perspectives and made me curious about fixpoints. I even borrowed the latter term and introduced them for crash dump analysis and debugging: “a dereference fixpoint”. I also liked chapters 4 and 6 about using Godel’s theorems outside mathematics and clarifying misconceptions in Rucker’s and Penrose’s books. However, after a few months I cannot recall anything definite what I read from that book although I felt good that I understood everything while reading so perhaps the book requires the 3rd reading for me I’m going to give it another try after “There’s Something About Godel” and update this review.

Godel’s Theorem: An Incomplete Guide to Its Use and Abuse

- Dmitry Vostokov @ LiterateScientist.com -

The CRC Encyclopedia of Mathematics, Third Edition - 3 Volume Set

I spotted this book on Amazon US and was thrilled to have the new edition in 3 volumes for easy handling when reading. I also have the previous edition that is even featured on my own book cover (the picture of my previous library book arrangement, the book is highlighted in white rectangle in the lower right corner):

This is a unique volume that sits between The Princeton Companion to Mathematics (that I’m also reading now) and Encyclopedic Dictionary of Mathematics: The Mathematical Society of Japan (that I also own). In fact after reading 3 volumes from cover to cover I can start with 2 volumes of EDM. There is also Springer Encyclopaedia of Mathematics in 11 volumes with various additional supplement volumes that I plan to own as well and it looks to me on the same level as EDM.

After searching for the best price I ordered a copy from Amazon DE and after my purchase in just a few days the price was up by 50%! I can only explain this that more people tried to purchase after I used twitter to announce this encyclopedia (there were 5 copies available on Amazon DE and in just 2 days only 1 left) or there was a mistake in price.

3 volumes arrived and I immediately started reading them, a few pages from each volume every day using mod 3 reading technique, for example, Wed - Vol I, Thu - Vol II, Fri - Vol III, Mon - Vol I, an so on. I prefer paper books for bulk reading instead of electronic version (in this case corresponding website) although if I’m interested in a specific article or a keyword I go to Wolfram MathWorld website to get the latest update and citations. These paperback volumes are just for day-to-day scheduled reading to get ideas and general mathematical education. This is why I don’t need an Index. For example, just after reading the first pages I got the idea of cubic (qubic) memory representation.

I usually put reviews on Amazon after I finish a book from cover to cover but in this case the review would be waiting for at least a year so I write it now based on my first impressions. After some time I plan to update it.

- Dmitry Vostokov @ LiterateScientist.com -

I read this book from cover to cover while flying on a plane from Dublin to St. Petersburg and back. That was so wonderful reading experience - I couldn’t put the book down during those flights. I recall that I visited the Department of Mathematics a few times when I studied Chemistry in Moscow State University although at that time I knew next to nothing about Russian mathematicians. The book touched me so deeply that I bought the main work of Florensky: The Pillar and Ground of the Truth, the history of Russian philosophy and several books explaining Orthodox Church. This is the best mathematics history book I have ever read, my feelings perhaps comparable to those that I experienced when I finished reading Mathematics: The Loss of Certainty by Morris Kline but that was more than 20 years ago.

Naming Infinity: A True Story of Religious Mysticism and Mathematical Creativity

- Dmitry Vostokov @ LiterateScientist.com -

I’m in love with QFT. I noticed this planned monumental 6-volume work some time ago but I bought this book from Amazon UK (I give the link to Amazon US here) after reading Quantum Field Theory Demystified and looking for more thorough ab initio treatment of QFT. Upon its arrival I immersed myself into it and in my opinion the first volume is like The Road to Reality but more mathematically oriented with proofs, numerous examples, historical notes, generous citations and references.

Quantum Field Theory I: Basics in Mathematics and Physics: A Bridge between Mathematicians and Physicists (v. 1)

- Dmitry Vostokov @ LiterateScientist.com -

I read this book in a few days briefly glancing at problem solutions because my aim was to review QM I studied long time ago. Highly recommended for a quick review. I noticed some misprints in derivations even during quick read but all explanations (physical semantics) are very clear. Now I venture into mathematics and physics of Quantum Field Theory Demystified that I hope to finish in a few days too. Here detailed mathematics (especially derivations) of QFT is almost unfamiliar to me so I expect to learn something new here and my future book review will reflect this reading and learning experience.

Quantum Mechanics Demystified

- Dmitry Vostokov @ LiterateScientist.com -

As soon as I finished Linear Algebra Demystified I started reading this book and read it in a week. This book is about general relativity, only a few pages cover special one. Lots of equation derivations which I mostly skipped while approaching the end of the book. The algebraic treatment of tensors is refreshing after The Road to Reality which uses mostly graphical notation devised by Roger Penrose. I finally understood what Christoffel symbols are for and the distinction of holonomic and nonholonomic coordinate bases. I would say that this book is very heavy on the syntax of physics and has less discussion of physical semantics. I’ve started reading Quantum Mechanics Demystified and then I plan to start with Quantum Field Theory Demystified. After that I approach a bit more semantics by reading A Unified Grand Tour of Theoretical Physics by Ian Lawrie.

Relativity Demystified

- Dmitry Vostokov @ LiterateScientist.com -

It is interesting to compare core school subjects in 70-80s USSR with those in UK and Ireland. I certainly missed any religious education and many art-isms. Physical education (games) was also different except football and climbing a rope. So I bought this book in a local bookshop a few months ago to align my basic school education and finished reading yesterday while waiting in a queue in Irish visa office near Dublin O’Connell Bridge:

Homework for Grown-ups: Everything You Learnt at School…and Promptly Forgot

It was also useful for me to learn some English words from basic biology, classics and geography.

- Dmitry Vostokov @ LiterateScientist.com -

I bought a dozen Demystified books a few years ago to teach myself several subjects I missed from my education or to quickly refresh my knowledge. One of them was:

Linear Algebra Demystified

I read it quickly yesterday and it really refreshed my knowledge and cleared some confusion aroused from reading more advanced applied mathematics books. My next reading sequence is Relativity Demystified, Quantum Mechanics Demystified and Quantum Field Theory Demystified.

- Dmitry Vostokov @ LiterateScientist.com -

This is a book that I noticed in a bookshop 6 years ago. I was curious by its title and front cover because at school I was interested in foundations of mathematics and abstract algebra ideas. I bought this book and from it I first heard of and learnt about category theory.

Conceptual Mathematics: A First Introduction to Categories

Very accessible and highly recommended as the first introduction but it requires probably the second reading if you are not used to mathematical abstractions. Fortunately there is the second edition coming after almost 15 years that seems have extra 50 pages added and I’m looking forward to reading it too.

Conceptual Mathematics: A First Introduction to Categories (Second Edition)

- Dmitry Vostokov @ LiterateScientist.com -

This book I bought a few years ago but only started reading 4 months ago and just finished:

Understanding the Infinite

I must say that it was not a light read and it requires certain mathematical maturity beyond undergraduate courses. The first part deals with Cantor and Zermelo set theories and axioms. It is very dry sometimes and chapters are long which was not good for me because I was only reading 10 - 12 pages per week while commuting. In many places the author assumes that a reader already knows a lot about logic and set theory, for example, at the end, he devotes a page or two about Putman modal logic and uses freely its quantifiers without explaining them. Some glossary at the end would have greatly benefited this book. What I found clarifying is the fact that there are two foundations of set theory: the notions of logical and combinatorial collections. For the latter the Axiom of Choice is self-evident and is no longer controversial. The second part starting from chapter VI is more philosophical and concerns with epistemology and ontology of the infinite. At least at the beginning it clarifies the difference between potential and actual infinity. In the middle we see the use of schemas to avoid quantifiers. At the end of the book the author discusses the theory of indefinite large and small, its extrapolations to infinite and provides examples from mathematical analysis. The main theme of the book, as I understand it, is that our intuition about infinity arises from intuitive understanding of indefinitely large sets, their hierarchies and extrapolations.

- Dmitry Vostokov @ LiterateScientist.com -