Literate Scientist

This is one of the first books I bought more than 5 years ago when I started reading math and physics books after more than 10 year break… I wanted to refresh my math knowledge and especially to learn discrete math that I mostly missed during my Chemistry education. I stumbled upon this book in a bookshop and liked its binding, paper quality and layout inside. I found the book very didactic and now looking back with all knowledge I gained afterwards from other books I would definitely say it is a very good textbook to start learning computer science.

Discrete Mathematics

- Dmitry Vostokov @ LiterateScientist.com -

This is my second Rosen’s book and I started reading on 1st of September, 2008, a year after I read “Life Itself”. Essays were written after the latter book and were intended to clarify it. Therefore if you are about to start reading Rosen’s works it is probably better to read essays first. I’m almost halfway through it and particularly like the discussion about mimesis, its roots and history. This is highly recommended book to read and if you were trained in chemistry, physics and computer science like myself you would find revelations on every page and would never look at modern science with the same eyes again.

Essays on Life Itself

- Dmitry Vostokov @ LiterateScientist.com -

If you ask me now what book I recommend for a broad overview of mathematics I would not hesitate to point to this latest book that I just started reading:

The Princeton Companion to Mathematics (Hardcover)

Although it is 1000 page book with two columns of text it is actually intended to be read from cover to cover! This book is now on top of my math overview recommendations which previously included these books:

• The Road to Reality
• Comprehensive Mathematics for Computer Scientists
• Mathematics: Form and Function
• All the Mathematics You Missed
• The Nature and Growth of Modern Mathematics

- Dmitry Vostokov @ LiterateScientist.com -

I’ve just finished reading this book and despite some bad reviews on Amazon I wasn’t disappointed. The author’s writing style is a bit unusual with some unknown words that you need a dictionary but after a chapter I became used to it and it wasn’t a problem anymore. If you heard about Gödel theorems before but cannot repeat precisely what they are about then this book is for you and you will find detail-free sketch of the proof very clear. I really liked the author’s attack on positivism and postmodernism especially in the light of previously read Fashionable Nonsense. I also liked the conclusion at the end of the book that the life of Gödel was “incomplete” too. The book discusses Vienna Circle and Wittgenstein, relationship between Einstein and Gödel and even some political issues in the Institute for Advanced Study related to Gödel’s life (this is why I included this book under Politics category too). One remark about bad review from the professor who participated in publishing edited works of Kurt Gödel: I can publish works of Aristotle nowadays without much efforts. Will it give me the right to judge other works and proclaim without sound justification that they don’t know philosophy?

Incompleteness: The Proof and Paradox of Kurt Godel (Great Discoveries)

- Dmitry Vostokov @ LiterateScientist.com -

This one I discovered last year and just finished reading. Interesting collection of articles written in the late 70’s and early 80’s about application of mathematics. My favourite were two articles about statistics and two articles about Husserl. The article about Kant biography was nice as well.

Discrete Thoughts

- Dmitry Vostokov @ LiterateScientist.com -

Very good book to learn about mathematical logic, distinction between syntax and semantics, different interpretations of formal languages and how this leads to various different non-classical logics. It will deepen your understanding of mathematics if you studied or encountered only classical propositional and predicate logic and want to learn more about fuzzy logic, for example, among many others. All necessary prerequisites are covered in the first 230 pages of this 500 page book including informal set theory and topology. I read most of this book couple of years ago and want to re-read it soon.

Classical and Nonclassical Logics: An Introduction to the Mathematics of Propositions

- Dmitry Vostokov @ LiterateScientist.com -

Just finished reading it. In summary: Everything is Nothing as their complexity measure is the same. Interesting short and small book to read if you have never heard of computationalism, many world interpretation of quantum mechanics, anthropic principle, self sampling assumption and quantum immortality. Discusses everything briefly and provides bibliography. However I think I should have read David Deutsch’s “The Fabric of Reality” book first which I bought recently and put on my reading list. The number of new concepts introduced was too overwhelming so I consider to read “Theory of Nothing” second time after finishing some other related books. 

Theory of Nothing

- Dmitry Vostokov @ LiterateScientist.com -

If you ask me about the single book to learn about mathematics used in computer science I would recommend without hesitation the following two volumes:

Comprehensive Mathematics for Computer Scientists 1: Sets and Numbers, Graphs and Algebra, Logic and Machines, Linear Geometry

Comprehensive Mathematics for Computer Scientists 2: Calculus and ODEs, Splines, Probability, Fourier and Wavelet Theory, Fractals and Neural Networks, Categories and Lambda Calculus

The breadth of covered mathematics is astonished. Each topic from 43 of them is fit into 10 to 20 pages which is very manageable to read if you need just a review and want to understand major concepts, definitions and theorems. I read the first edition of the first volume when it was published couple of years ago. Now I decided to refresh my knowledge, read the second edition of the first volume and then read the second volume. 

- Dmitry Vostokov @ LiterateScientist.com -