Serious Games, Clark Abt, University Press of America (1970)

I have given the original publication date by Abt Associates in 1970, and published by Viking in 1971, the current edition was first reprinted in 1987.  I have recently become interested in game-based learning.  This seems to be an area in which the basic vocabulary is just becoming standardized.  The title of the book appears to be the first appearance of the terminology "serious games."  Much of the literature in game-based learning can be traced back to this seminal work.  Well worth reading.

Real Analysis (2005), Real Analysis and Applications (2005) - Frank Morgan, American Mathematical Society

I was introduced to these books when my son David was about to take a class in variational calculus from my friend and colleague, Fred Hickling.  Fred mentioned that Morgan's books were well though out pedagogically.  The calculus of variations is in Real Analysis and Applications and is being used as prelude to Gelfand and Fomin.  If you are a physicist and want to get acquaint yourself with modern mathematical notation - necessary if you want to read Arnol'd's Mathematical Methods of Classical Mechanics for instance - these books are a good choice.  You don't need both as there is a considerable overlap in content, but either would be a good addition to the mathematical library of a physicist.  I still find set theoretic notation repellent, but these books make it easier to review.

Each of the books contain short chapters that summarize information and outline proofs. The chapters in Real Analysis are:

Part I: Real numbers and limits

1. Numbers and logic
2.   Infinity
3.   Sequences
4.   Functions and limits

Part II: Topology

5. Open and closed sets
6.   Continuous functions
7.   Composition of functions
8.   Subsequences
9.  Compactness
10. Existence of maximum
11. Uniform continuity
12. Connected sets and the intermediate value theorem
13. The Cantor set and fractals

Part III: Calculus

14. The derivative and the mean value theorem
15. The Riemann integral
16. The fundamental theorem of calculus
17. Sequences of functions
18. The Lebesgue theory
19. Infinite series ∑an
20. Absolute convergence
21. Power series
22. Fourier series
23. Strings and springs
24. Convergence of Fourier series
25. The exponential function
26. Volumes of n-balls and the gamma function

 Part IV: Metric spaces

27. Metric spaces
28. Analysis on metric spaces
29. Compactness in metric spaces
30. Ascoli's theorem

The chapters in Real Analysis and Applications are:

Part I: Real numbers and limits

1.  Numbers and logic
2.  Infinity
3.  Sequences
4.  Subsequences
5.  Functions and limits
6.  Composition of functions

Part II: Topology

7.  Open and closed sets
8.  Compactness
9.  Existence of maximum
10. Uniform continuity
11. Connected sets and the intermediate value theorem
12.The Cantor set and fractals

Part III: Calculus

13. The derivative and the mean value theorem
14. The Riemann integral
15. The fundamental theorem of calculus
16. Sequences of functions
17.The Lebesgue theory
18. Infinite series
19. Absolute convergence
20. Power series
21. The exponential function
22. Volumes of n-balls and the gamma function

Part IV: Fourier series

23. Fourier series
24. Strings and springs
25. Convergence of Fourier series

Part V: The calculus of variations

26. Euler's equation
27. First integrals and the Brachistochrone problem
28. Geodesics and great circles
29. Variational notation, higher order equations
30, Harmonic functions
31. Minimal surfaces
32. Hamilton's action and Lagrange's equations
33. Optimal economic strategies
34. Utility of consumption
35. Riemannian geometry
36. Noneuclidean geometry
37. General relativity

Both books contain partial solutions to problems.  Real Analysis has 155 numbered pages. Real Analysis and Applications has 197 numbered pages.  Either is worth owning, I have a slight preference for the longer book.

Asymptotic Expansions: Their Derivation and Interpretation, R.B. Dingle (Academic Press, 1973)

I could write a long review of this wonderful book.  But, instead you should read the review by his noted student Professor Sir Michael Berry.  As an added benefit of reading this review you can download a copy of this long out of print book.  If you are a physicist interested in wave propagation, this book is a book that you must have and use.

Irresistible Integrals - George Boros and Victor Moll, Cambridge 2004

This is a good companion to Interesting Integrals by Paul Nahin that I reviewed earlier this year.  If you are only going to buy one of them, the book by Nahin is the better option.  However, if you like to calculate integrals or just want to improve your skills you are going to want to own both.  Both books are ideal for building the skills you should have, but don't if your calculus class focused on using calculators.

If you like evaluating integrals you are in good company - G.H. Hardy couldn't resist a challenging integral.  If the books discussed in this post are too advanced for you, Hardy's Pure Mathematics is a good, rigorous introduction to calculus - it is much smaller than modern calculus textbooks, but you will learn more from it than you would from most modern calculus books.

From Eros to Gaia - Freeman Dyson (Pantheon 1992)

A brief not to mention that there was an earlier collection of non-technical papers from Freeman Dyson.  The section in this one are Stories, Things, Institution, Politics, Books, and People.  For me the higlight articles are Carbon Dioxide in the Atmosphere and the Biosphere, To Teach or Not to Teach, and Death of a Project.  If you like Birds and Frogs you will like this and vice-versa.

The Life and legacy of G.I. Taylor - George Batchelor (1996)

Published by Cambridge University Press in 1996 - the story of the long and productive life of Geoffrey Ingram Taylor.  One of the greatest minds of the twentieth century - he was an active and productive researcher for more than 60 years.  apart from Taylor series, if you come across some mathematics or a physical principle with the name Taylor on it, GI is probably the Taylor in question. Taylor was the grandson of George Boole.  On testament to his talent is that Taylor was able to accurately measure the yield of the early atomic tests by dropping some scraps of paper and observing them.  Likely the authority on blast waves in the late 1940s.  His contributions range from gravity waves in the atmosphere, to turbulence, to electrohydrodynamics.  Read the book to learn about this highly original mind - and then, if you are able to understand them, read his collected papers (in 4 volumes) - many of his ideas are still waiting to be followed up.

Night of the New Moon - Laurens van der Post (1970)

Published by the Hogarth Press in 1970 and clearly not a book on mathematics or science.  I read this soon after it was published so I would have been 14 or 15.  The book influences the way that I think down to the present day.  Laurens van der Post is a renowned author who wrote many books on Africa (and I have read them all as I am an explorer at heart.)  In this book the author details how he was a guest on an un-named talk show.  The earlier guest was a survivor of Hiroshima and he detailed what a tragedy it had been for Japan.  van der Post agrees that it was a tragedy, but as a POW for three-and-a-half years in Java, the use of the atom bomb was his salvation.  He and his fellow prisoners were at a low ebb and would not have lasted much longer.  You should read it - it was also sold as The Prisoner and the Bomb.  The book was written after the TV appearance - he talked of his experiences rather than his planned talk about Africa.

It continues to influence me because it taught me to find out all sides to a story before coming to a conclusion.  I won't retell the story, but I will note that it is the probable source for many stories of prisoner of war camp stories that appeared after it was written.  It is not the source for Bridge over the River Kwai - that was a 1952 book by Pierre Boule and was a work of fiction.  Looking at some of the shared elements, it seems reasonable that Boule talked to van der Post or some of his contemporaries.

Dreams of Earth and Sky - Freeman Dyson (2015)

Freeman Dyson's other new book.  This one is a collection of his columns and reviews for the New York Review of Books. The book contains 21 separate columns on everything from Feynmann to Biotech to global warming.  Dyson has an interesting take on global warming.  Again, a great overview of the way a public intellectual should contribute.  I read this one from beginning to end too, but most will probably want to jump around.  I reread Dyson's books with some regularity.

Birds and Frogs Selected Papers, 1990-2014 - Freeman J. Dyson

Freeman Dyson has long been my favorite physicist.  He is also my favorite polymath and one of the all-time best science writers.  This just published (2015) collection of papers includes talks about science, memoirs, articles on politics and history, and some technical papers.  Included is the famous paper which introduces the classification of mathematicians into frogs and birds.  Indeed Dyson was described as the Frog Prince of Physics in Salon in 1999.  Include is an homage to George Green - and there is a technical article on partitions and the grand partition function - so Green Functions and partition functions in the same work - those who know me that this alone would likely cause me to add the book to my collection!  This isn't a book that you would sit down and read from cover to cover (at least after the first time.)  This is a great chance to read a variety of works by one of the greatest problem solvers who has ever lived. - Dyson is not a Nobel Prize winner, but if he wasn't going to get one for his seminal work in quantum field theory, he should have won for his work in adaptive optics.  The paper on the origins of life should be read by every scientist - if you like it you should read Dyson's book Origins of Life, the second edition of which appeared in 1999.  I'll write a review of this book at some point in the future.

So, in summary, a worthy addition to anyone's personal library - and a must read if you want to see what a first-rate public scientist does.

No Highway - Nevil Shute (Norway)

This book was first published in 1948.  Why am I reviewing it here?  It was used as a metaphor by Michael Marder of the UTeach Institute - in this book the failure of a transatlantic plane due to metal fatigue is investigated.  A plane called a Reindeer fails catastrophically due to metal fatigue.  The crash - there is actually only one, is ascribed to pilot error.  The whole affair was oddly prescient as this is very similar to the actual events surrounding the de Havilland Comet which was the first commercial airliner.  Michael Marder suggests that people are doing the same thing in their analysis of education - we are blaming teachers when there are obvious systemic problems.   You can find an early version of Marder's thesis here.

Nevil Shute's novel reads well - I'm sure that I have read it before - I probably read all his novels as a teenager.  Michael Marder described him as the Michael Crichton of his era.  To my mind Shute's books have held up better than Crichton's - both had many of their books made into movies.  This book, and many others are available for the Kindle.  If you happen to be in Canada, it's even simpler as many of his works have entered the public domain and they can be found on the Canadian version of Project Gutenburg.  I could tell you more about the book - but I'm not going to, just read it you will most likely enjoy it.

If you want to learn more about Nevil Shute Norway, you can find lots of informational this site.  Review and plot synopses for his books can be found here.

Exploring Quantum Physics through Hands-on projects, David and Shanni Prutch. (Wiley, 2012)

A unique book - instead of concentrating on theoretical quantum mechanics, this book details experiments that you can perform to observe quantum phenomena.  The range of experiments is wide - everything from Young's double slit experiment to quantum entanglement and quantum cryptography.  The book explains how to do the experiments and how to find and build the instrumentation that you need.  Every physics students should be aware of this work.  You can get a flavor of the text by visiting the author's website.  If you like to build things and tinker with equipment, this is a website that you will bookmark.

Inside Interesting Integrals - Paul J. Nahin (Springer, 2015)

If you want to improve your integration skills this is the book for you.  The perfect book if you are stuck at home on a snow day and you like to make calculations (I am, and I do.)  My only quibble with this book is that the author uses MATLAB to check his results.  I prefer books that teach students to determine whether the answers make sense.  I suppose that most people use numerical routines to check results these days - but keep in mind that they don't always get the right answer.  Personally, I'd prefer to use Python or R to check the results - I prefer that students know what algorithms are being used.  All in all,   a worthwhile book.

Doing Bayesian Data Analysis - John K. Krushke (Academic Press, 2015)

I have been interested in Bayesian methods for many years - this book makes the calculations accessible to almost anyone.  The current version of the book is the second editions, it was published in 2015.  For an overview, I suggest visiting the author's webpage.  Simply the book explains how to implement Bayesian methods.  As well as providing an overview of Bayesian methods, the book provides and introduction to the appropriate software tools: R, JAGS, and Stan.

An Introduction to the Theory of Infinite Series - T.J.I'A. Bromwich

If you own only one book on infinite series, this is the book to own.  My copy is a second edition, first printed in 1928 by MacMillan - my copy is from 1949.  It has been reprinted by MacMillan and others since.  It's an easy read if you are familiar with Hardy's Pure Mathematics or other books at a similar level.  Coverage includes sequence, real, and complex series, power series and gamma functions.  The book contains an illuminating discussion of uniform convergence.  If you use series in your work as a mathematician or a physicist, this book should be on your bookshelf.