Welcome to my list of recommended texts for selected topics in chemistry, physics and mathematics. I’ve read the majority of the books on this page and has used many of them either in research or for coursework.

So after some thought and a lot of discussion with everyone, I’ve decided to start my own list of good textbooks in chemistry, physics and mathematics, or basically anything that I think might be interesting.

Many people have strong opinions on textbooks but few of these opinions are based on actual experience with reading them. Some people are packrats and will buy books as a proxy for actually reading them. I’ve found reliable recommendations for books hard to come by and so I’ve created this list on my blog mainly for personal reference, but also in the hope of pointing passionate and interested students to the suitable books in suitable topics and for suitable uses.

I have found through my own experience that while many technical books are good as references (i.e. at the advanced level), few are suitable for actual self-study. Texts designed to accompany teaching are oftentimes overly simplistic and gloss over points which established advanced books assume knowledge of. As a graduate student left to his own devices, I find this glaring omission of texts at the intermediate level frustrating and counterproductive.

This list emphasizes books which take both pedagogy and their technical topic seriously, and hopefully will point the way for others like myself who want to know more about a topic beyond the basics, but do not necessarily want to invest several months to digest cryptic books to learn just a few points of interest. There are also the books which are encyclopedic in their completeness and are actually readable enough to make excellent references, which I have included on this list. Finally, this list also documents books which (to my knowledge) are designated classics/”bibles” in the field, and have my frank opinions about them written up if I’ve actually read the books in question.

Being the compilation of a single person, the choice of topics as well as opinions here are necessarily subjective and eclectic. Please send me your comments and recommendations!!

Here are a few topics to get started on.

A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z




Topic: Classical electrodynamics
What it is
A staple of the physical sciences, classical electromagnetism not only describes the behavior of materials under electric and magnetic forces, it is also (for virtually all physics students) the first foray into high-powered mathematics. Many times, doing E&M problems is an exercise more in math technique than actual physics. Depending on the level of rigor, mathematical topics covered will definitely cover multivariable calculus and differential equations, but also (especially at the graduate level) group and representation theory and tensor algebra. You will also encounter all sorts of “named objects”, for example Laguerre polynomials and Bessel function, which are names of solutions to certain differential equations that pop up over and over again in the physical sciences.

Standard textbooks
There are two classic textbooks that I know of:

Introduction to Electrodynamics by David J. Griffiths. Errata available here. Griffiths is an excellent author who takes great pains to explain the physics described by mathematical situations. It appears to be the standard book to use in undergraduate physics courses.
my take: I think the book is nice but it doesn’t strike me as “oh wow!”. In fact, it’s a little bit on the brief side. Maybe I’m just stupid and want things explained to me in pedantic detail.

Classical Electrodynamics by John David Jackson. Errata available here. This is the granddaddy of all graduate elecrodynamics texts, written by a professor originally stationed here in the U of I. This is a great (if concise) reference book but I don’t recommend it for a first-timer. Novice readers will die reading this. You have been warned. People who have actually struggled through graduate electrodynamics have strong opinions about this text. Go draw your own conclusions.
My take: I personally don’t like this book, but I keep it around anyway. Just in case you ever need to look up the relativistic Lagrangian or a spherical Bessel function of the second kind.

The Feynman Lectures on Physics: The Definitive and Extended Edition by Richard Phillips Feynman, Robert B. Leighton and Matthew Sands. Errata available here, although a large number of the known mistakes have been corrected in the 2005 edition linked to in the title. This is the book everyone loves to recommend but few people actually read. If you do, you’ll be blown away by the insight that goes into the presentation of the material. Volume II covers electricity and magnetism.
my take: This book grows on you. I find that the more physics I learn, the more I appreciate the presentation here. I would not recommend this book to learn the topic from, unless if you read it in conjunction with Griffiths’s book above to get a feel for how to actually solve problems.

My picks
I am not an expert, but I kinda like Griffiths’s book. I also like Feynman’s lectures in physics, although the standard disclaimer about this series applies.


Topic: Electrodynamics
What it is
The study of the motion of objects under the influence of electromagnetism. There are classical and quantum versions of the theory.

Topic: Electromagnetism
What it is
The study of electric and magnetic (E&M) phenomena. Depending on the context, you may be interested in either classical E&M theory or quantum electrodynamics in quantum field theory.



Topic: Group Theory
What it is
Group theory is essentially the study of various types of symmetries. The invariance of physical quantities under symmetries has formed an integral part of how physicists and chemists study the properties of matter.

Classic texts

H. Weyl, The theory of groups and quantum mechanics. The classic book explaining why anyone interested in quantum mechanics needs to know group theory. The book is dense and arcane (at one point Weyl uses musical symbols for group elements!) but full of physical, yet rigorous insight.

F. A. Cotton, Chemical applications of group theory. The classic book explaining why anyone interested in chemistry and molecules needs to know group theory. Personally, I don’t like this book because it’s tedious and isn’t very clear in some places what is going on.

M. Tinkham, Group theory and quantum mechanics. This book is popularly used to augment graduate quantum mechanics texts which do a terrible job in explaining the group-theoretic aspects of the addition of angular momentum. It’s actually pretty good for learning how to do things, if not quite why they are done.
My picks

T. Inui, Y. Tanabe and Y. Onodera, Group theory and its applications in physics. Springer series in solid-state sciences vol vol 78. This somewhat obscure book is by far the best book on group theory I’ve ever seen. You can see both the mathematical foundations and loads of physical applications.







Topic: Mathematical Methods
What it is
Mathematical methods is actually a canon of mathematical topics that graduate students in physics and chemistry are supposed to know in order to do real work. Rather than dump a big list of Things To Know here, I’ve arranged them in a table according to rough categories of mathematical fields as well as an approximate hierarchy of things to learn in sequence.

Calculus Integration and differentiation in one variable Multivariable calculus Ordinary differential equations Partial differential equations Integral equations and Asymptotic Series
Analysis Real analysis (esp. series expansions) Complex analysis Integral transforms (Hilbert, Fourier, etc.) Functional analysis and distributions Stochastic differential equations
Vector spaces Linear algebra Tensor algebra Differential geometry and manifolds Topology
Abstract Algebra Groups and representations
Statistics Probability and combinatorics Random variables, hypothesis testing, sampling theory Regression analysis, least-squares curve fitting Maximum entropy and Bayesian inference Random sampling: Markov chains and Monte Carlo
Numerical methods Numerical algorithms Difference equations Error analyses of algorithms Experimental design and principal factor analysis

Standard texts
Morse and Feshbach

Hilbert and Courant

Reed and Simon

My picks
Advanced Mathematical Methods for Scientists and Engineers: Asymptotic Methods and Perturbation Theory by Carl M. Bender and Stephen A. Orszag.

Mathematical Methods of Physics and Engineering by Riley, Hobson and Bence.
This book actually steps you through the concepts with loads of illustrative examples. Great for self-study or getting the point quickly without poring through theorems and tedious derivations.




Topic: Path Integrals
What it is
Path integrals are an example of high-powered math that rarely shows up in undergraduate curricula but then suddenly explode all over the place in graduate chemistry or physics courses. One can think of it loosely as a generalization of many-variable integration to describe a continuous infinity of integration variables. This technique is also known as functional integration.

Standard texts
Quantum Mechanics and Path Integrals by Richard Phillips Feynman and Alfred R. Hibbs. The unofficial errata website sums it all up: “This famous book is full of extraordinary insight and excruciating errors.” Unfortunately for budding students of this important mathematical tool, you’d be hard-pressed to find a copy of this book for anything less than $300 nowadays, and the library copy is probably sitting around on some faculty member’s shelf (or perpetually on reserve).

Despite the title, this is really a book trying to approach the mathematics of path integrals from the physicists’ intuitive (i.e. hand-waving) approach of doing things, a.k.a. “we know what we’re doing, let the mathematicians handle the gory details”. Feynman discovered and developed the application of the technique in his graduate dissertation, until one day legend has it (see the preface of Kleinert’s book) that Feynman realized that he couldn’t solve the quantum mechanical problem of the hydrogen atom using path integrals.

Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets by Hagen Kleinert. Errata available here. Postscript files of many chapters of the book may be available here. Spot mistakes and Professor Kleinert may feel inclined to email you the missing chapters that aren’t available for download. The third edition of this book (all 2 kg of it) solidifies its reputation for being the bible of path integration. The fields of application are incredibly diverse, and I personally find it fascinating that the same mathematics is ubiquitous in theoretical physics, computational chemistry, and high finance. This is the book you will want to read after chowing down Feynman’s book above and feeling a bit queasy about the mathematical niceties of the functional measure and topological defects in Hilbert space.
my take: If you want rigor, style and lots of applications, you’ll find them here.

My picks
Techniques and Applications of Path Integration by Lawrence S. Schulman. Errata not available online. This is the cleanest exposition of path integrals that I have found anywhere. If you’ve been subsisting on ramen noodles after purchasing Feynman and Hibbs, you will be very pleased to know that the third edition is now printed by Dover Books and therefore won’t cost you your other arm and leg. Highly recommended for newbies. Start here!


Topic: Quantum Dynamics
What it is
Quantum dynamics is the study of atomic nuclei as it behaves under the time-dependent Schrödinger equation. This topic uses quite a bit of path integrals.

Standard textbooks
I don’t think there is a universally agreed one, although I could be wrong.

My picks
Classical and Quantum Dynamics : From Classical Paths to Path Integrals by Walter Dittrich and Martin Reuter. Errata not available. Clear and well written, an excellent introduction to time-dependent semiclassical theory and covers esoteric topics such as the use of Maslov indices and their topological origins.

Topic: Quantum Mechanics
My picks
Introductory Quantum Mechanics by Richard Liboff. This is one of the few-and-far-between examples of a book you can self-study from. One eventually grows out of it and finds its style somewhat pedantic and with missing patches here and there, but it excels at familiarizing you with the standard mathematical techniques and concepts, and actually applying such knowledge to real applications.

Principles of Quantum Mechanics by Ramamurti Shankar. Once you feel sick of Liboff, it’s a good time to switch over to Shankar. It’s much more rigorous but also more involved. A great reference piece.




Topic: Thermodynamics
What it is
The bane of all engineering and physical science students, and one of the most poorly taught topics all around.

My picks


Thermodynamics and an Introduction to Thermostatistics by Herbert B. Callen.
A great followup to Reif’s introductory book. Everything you wanted to know about Maxwell relations, Pfaffians and Legendre transformations in a readable, clear style.