Notes by Me

• I started writing notes on group theory. One big complaint I had when I was studying physics was that a lot of the math was often swept under the rug. The physics books were too light on the proofs, and just taught you how to do calculations. The math books were too abstract and tailored to budding mathematicians. So my idea was to write a textbook that proves as much of the math but then goes to examples and applications that theory inclined physics students would enjoy. A lot of the math theory is typed up, but I will need to focus on collecting all the physics examples and problems and typing that up. Maybe I'll find the time to do so eventually. Notes can be found here.

Below are some of the books I am familiar with and my thoughts about them.

Physics Books

• T. Lancaster and S. J. Blundell, "Quantum Field Theory for the Gifted Amateur". Fantastic book on QFT. I thought the book was written very clearly and pedagogically. Out of all the QFT related books I have actually read, I would recommend this one to "get the lay of the land". Many of the standard QFT books are too dense or don't have enough details. Some QFT books just go directly to calculating quantities and the big picture can get lost to a beginner. That said, you will eventually need to read the more advanced QFT books after "Quantum Field Theory for the Gifted Amateur" in order to learn the advanced/modern topics in QFT that aren't covered in this book. I just think that this textbook will make other QFT books very digestable and is a good place to start for someone going into subjects requiring QFT techniques.
• R. Shankar, "Quantum Field Theory And Condensed Matter: An Introduction". Good texbook to read after exposure to quantum field theory techniques from one of the standard QFT books and, preferrably, after learning graduate statistical mechanics. Shankar is an excellent communicator of physics and I think those going into condensed matter theory could pick up a thing or two by reading this textbook. Fun fact: If you go to Shankar's Yale website and click "Errata QFT&CM" on the left menu, you will see my name appear somewhere. (Here is a direct link, downloaded from his webpage on August 16, 2019: Errata - Quantum Field Theory And Condensed Matter: An Introduction by Ramamurti Shankar (2017).)
• A. Zee, "Quantum Field Theory in a Nutshell, 2nd Edition". Humorous and insightful. Anthony Zee has many interesting footnootes and anectodes. I recommend reading it after "Quantum Field Theory for the Gifted Amateur" (QFTGA) as, although it is very insightful, I don't think it is as thorough in details as QFTGA. Zee's book is great because it will deepen your conceptual understanding of QFT. However, you won't become an expert at doing detailed calculations as Zee usually outlines the main idea and the important parts of a calculation but doesn't actually go through it. It's a good read after you learned some QFT and want to review at a conceptual leveling before diving into more detailed/calculational QFT books.
• M. E. Peskin and D. V. Schroeder, "An Introduction To Quantum Field Theory". A standard textbook. Often chosen as the course textbook for the QFT courses at many universities. The focus is primarily on particle physics (some condensed matter systems are mentioned in the renormalization group chapter(s)). The content of the book is must-know for any theorist, but in my opinion the book functions best after learning the "lay of the land" of QFT from a book like "Quantum Field Theory for the Gifted Amateur" (QFTGA). The first 9 chapters are excellently presented and very understandable after reading QFTGA. However, I wasn't a big fan of chapters 10-13, the chapters on renormalization.
• P. Coleman, "Introduction to Many-Body Physics". I really liked the book. This book focuses primarily on condensed matter topics, as opposed to QFT books that focus mainly on particle physics. Piers Coleman often asks "what does this mean"? Many of the exercises involve a part that asks for an interpretation, "physical" explanation, or general comments on the work done, which I found very nice. I found the book very readable as is, but it would be better if some of the typos/inconsistencies were fixed. Here is a list of my suggestions for the book: Errata - Introduction to Many-Body Physics by Piers Coleman (Reprinted 2017). Works extremely well when used together with Atland and Simon's "Condensed Matter Field Theory" book.
• A. Atland and B. Simons, "Condensed Matter Field Theory". Pretty good and modern treatments of quantum field theory topics. As the title suggests, it focuses on using QFT techniques in a condensed matter setting. The topics covered are pretty standard and in the canon of topics known by condensed matter theorists. Not for the complete novice. Prior exposure to quantum field theory techniques is strongly recommended. Works extremely well when used together with Coleman's "Introduction to Many-Body Physics" book.
• P. M. Chaikin and T. C. Lubensky, "Principles of condensed matter physics". Graduate level book. Preferrably read after taking a typical graduate condensed matter physics course (a "solid state physics" type). Includes many nice topics from soft condensed matter physics. Includes some classical field theory, so previous exposure to QFT will make those sections more comprehensible. (Fun fact: I was fortunate and had the opportunity to take a course at Penn that taught from this book...with Tom Lubensky as the instructor! If I remember correctly, it was his last semester teaching before retiring as well. I remember finding the problem sets, which consisted of problems from the textbook, challenging but rewarding. I learned a lot from the class and book.)

Math Books

• B. O'Neill, "Elementary Differential Geometry, Revised 2nd Edition". Very organized. Focused mainly in R^3 and not as general as an introduction to manifolds textbook. This is best read after finishing the typical lower undergraduate math courses. The chapters are calculational and intuitive. The definitions in more abstract manifold textbooks should appear very well motivated after reading O'Neill's textbook.
• M. P. do Carmo, "Differential Geometry of Curves and Surfaces: Revised and Updated Second Edition". More mathy than O'Neill's book, but also at the undergraduate level. I think it would work great with O'Neill's book as O'Neill's book provides more intuition but do Carmo provides more detailed/in-depth proofs and theorems.
• T. Frankel, "The Geometry of Physics: An Introduction". Geared more towards physicists and engineers rather than mathematicians. Parts of it worked for me and I learned a decent amount from it, but I heard others complain about the presentation. I do think the chapters get sloppier as the chapters go on, but the first 8 chapters are doable.
• L. Tu, "An Introduction to Manifolds (Universitext)". Superb. You can tell Loring Tu spent a lot of time thinking about which material to include and how to present the theorems. It's a perfect math book to read before taking a graduate course on Differentiable Manifolds (or whatever the courses go by nowadays) that might use John Lee's "Introduction to Smooth Manifolds" (700+ pages). Loring Tu's book is a gentler introduction to similar topics and is shorter (~400 pages).
• J. W. Brown and R. V. Churchill, "Complex Variables and Applications". Focuses a lot on applications and calculations, as the book's title would suggest. It does prove a lot of the theorems presented, but it's not as "proofy" as other complex analysis books. Of the complex analysis books I read, I would recommend this to physicists/engineers who want to learn how to calculate and make practical use of complex analysis, putting the harder lemma, theorems, and corollaries for a later time. You learn a lot of techniques from this textbook. The mathematically inclined will want to see more proof-theorem-proof-theorem than found in this book.
• S. D. Fisher, "Complex Variables: Second Edition (Dover Books on Mathematics)". Decent, but not amazing. It is more mathy than Brown and Churchill's book, but I feel like if you know enough math to read the proofs then you know enough math to read some of the more cogent and comprehensive complex analysis books out there, such as Stein and Shakarchi's book.
• E. M. Stein and R. Shakarchi, "Complex Analysis". Simply amazing. Concise, rigorous, and lucid. Suits the mathematically inclined better than the application seekers. Superb undergraduate level complex analysis textbook for math lovers.
• B. Mendelson, "Introduction to Topology: Third Edition (Dover Books on Mathematics)". Very nice. It's amazing what one can cover in approximately 200 pages. Perfect to read over break before taking a topology course, which probably uses the 500+ topology book by J. Munkres. Also perfect for a physicist who wants a general overview of topology, without having to explore all the nooks and crannies of topology that interest the mathematician.
• D. S. Dummit and R. M. Foot, "Abstract Algebra, 3rd Edition". A standard textbook. Often used as the official textbook for graduate abstract algebra courses at many universities. It's definitely good, but probably a little too mathy for a physicist/engineer trying to learn the bare bones of the subject for applications.
• A. Zee, "Group Theory in a Nutshell for Physicists". Humorous, insightful, and contains many interesting footnootes and anectodes (this seems to apply to his books in general). I think this book works very well when supplemented with an undergraduate abstract algebra book oriented towards mathematicians. Zee's book is a little too light on formalism, in my opinion, but it does excel at presenting examples/problems which use group theory that are of interest to physicists.
• G. Chartrand and P. Zhang, "A First Course in Graph Theory". Very lucid and organized. The prerequisites are really just some basic set theory topics and "mathematical maturity" (namely, knowing mathematical induction, how to take contrapositives, and things of that sort). I found the presentation very pedagogical. I thought the material wasn't too basic or too advanced. I also liked that this required no computer science background. My impression was that if one makes it through this book, then he or she should have a very good idea about what graph theory is about and be very well prepared for more advanced study.