Literate Scientist

When mapping one science domain to another and borrowing terminology even metaphorically one rule to follow is to provide justification. This is very important otherwise people will laugh once they recognize that terminology was just thrown without any explanation or connection. For me this book was very important reading because I also mapped some computer science and engineering technology terminology to the domain of project management. However I provided some sort of justification to my relief.

Fashionable Nonsense: Postmodern Intellectuals’ Abuse of Science

- 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 -

I read this book written by Thomas A. Garrity 4 years ago to fill gaps in my mathematical education. Here I learned the concept of manifolds and differential forms I missed entirely and got the good overview of modern math with informal and semi-formal proofs. This book also persuaded me to read Mac Lane’s “Mathematics, Form and Function”. 

All the Mathematics You Missed: But Need to Know for Graduate School

- Dmitry Vostokov @ LiterateScientist.com -

This book I found and read 4 years ago was written by Edna Ernestine Kramer. At that time I was looking for a lightweight introduction to parts of modern mathematics that I missed during my university education at the end 80s. Remembered my earlier school encounters with Morris Kline’s book “Mathematics: The Loss of Certainty” I wanted an introduction along the historical lines of 20th century and this book was a pleasant discovery. It is more than 700 pages and was printed in small font so it was the long but very enjoyable read. It covers unusually wide range of mathematical disciplines and their historical development from Babylonian era to games, statistical decision and utility theory, functional analysis, topology, homotopy and homology, Grassmann algebras, and many other 20th century developments.

Here is the brief TOC:

1. From Babylonian Beginnings to Digital Computers
2. Mathematical Method and Main Streams Are Launched
3. Mathematical Reasoning from Eudoxus to Lobachevsky
4. Algebra from Hypathia to Hamilton
5. Equations, Human and Inhuman
6. A Universal Language
7. Forefathers of Modern Mathematics and Their Legacy
8. A Calculus for Heaven and Earth
9. Determinism and Its Creators
10. The Elements of Strategy in War and Peace
11. Probabilistic Models, Great Expectations, and Randomized Strategies
12. General Games and Statistical Decision Theory
13. From Dice to Quantum Theory and Quality Control
14. Realm of Random Variables
15. Demons, Energy, Maxwell, and Gibbs
16. Sweet Manuscript of Youth
17. The Unification of Geometry
18. A Special Group and Its Application
19. Geometry for Universe-Builders
20. Post-Relativity Geometry
21. East Meets West in the Higher Arithmetic
22. The Reformation of Analysis
23. Royal Roads to Functional Analysis
24. Infinite Hierarchy
25. Angelic Geometry
26. The Leonardos of Modern Mathematics
27. Twentieth-Century Vistas - Analysis
28. Twentieth-Century Vistas - Algebra
29. Twentieth-Century Vistas - Logic and Foundations
30. Retrospect and Prospect

The Nature and Growth of Modern Mathematics

- Dmitry Vostokov @ LiterateScientist.com -