مقاله ای در مورد خود یادگیری فیزیک نوین

Before You Begin

Popular library on Physics

When you're solving problems, working through textibrary, and getting into the nitty-gritty details of each topic, it's so easy to lose the forest for the trees and forget why you even became inspired to study physics in the first place. This is where really, really good (and non-speculative) popular library on physics come in handy: they inspire, they encourage, and they help you keep the big picture in mind.

One big problem is that many popular physics library (especially those written by famous physicists) are incredibly speculative and tend to present an unrealistic view of what the study of physics is all about. When you're learning physics, it's best to avoid these types of speculative library and stick to the ones that talk about the real physics that we know exists (in general, anything by Frank Close or Richard Feynman is a safe bet!).

Here are a handful of my favorite popular physics library, ranked in order of difficulty:

• The First Three Minutes by Steven Weinberg (Level: Easy).An account of the Big Bang by one of the most brilliant physicists of all time.
• The Character of Physical Law by Richard Feynman (Level: Easy). A brilliant, inspiring little book on the laws of nature.
• The Particle Odyssey by Frank Close (Level: Easy). A brilliant popular introduction to particle physics and its history, beautifully illustrated with amazing figures and photographs. (Unfortunately it’s a bit difficult to find online right now, but if you find a copy, you should buy it ASAP!)
• Black Holes and Time Warps by Kip Thorne (Level: Easy/Medium). My absolute favorite popular introduction to general relativity.
• The Theoretical Minimum by Leonard Susskind and George Hrabovsky (Level: Medium). A solid introduction to classical mechanics. Is best understood around level 5 in the undergraduate curriculum.
• The Feynman Lectures on Physics (Boxed Set) and Feynman Lectures on Physics (Kindle Edition) (Level: Medium). Feynman's Lectures are essential readings for everyone interested in physics, and you'll find a copy on the ibraryhelf of every amateur and professional physicist. These lectures are what got me into physics: my astronomy professor told me to read them and see if I liked physics - they changed my life! They are somewhat difficult to understand if you are just getting started, but they will make more and more sense by the time you reach levels 5 and 6 in the undergraduate curriculum.
• Deep Down Things: The Breathtaking Beauty of Particle Physics by Bruce Schumm (Level: Difficult). The very best popular book about particle physics — it clearly explains the most difficult concepts without resorting to speculation. (I had the honor of working with Bruce on a search for supersymmetry at the ATLAS detector.) This book is a great read while you are starting level 7 in the undergraduate curriculum.

Mathematical and Scientific Preliminaries

Before you begin studying physics and working through the topics in the sections below, you need to be familiar with some basic mathematics. A high school education — which should include pre-algebra, algebra 1, geometry, algebra 2, trigonometry, and pre-calculus — is sufficient. If you need a refresher, I recommend either working through the Khan Academy math courses (https://www.khanacademy.org/) or the book Why Math? by R.D. Driver. There's no need to be familiar with calculus before starting, because you’ll learn it as you work through the undergraduate-level courses.

There are no scientific prerequisites for this curriculum. You don’t need to be familiar with biology or chemistry at either the high school or college level in order to understand, although doing some studying on the side can’t hurt. Khan Academy has some great high school science refresher courses that are perfect for this (https://www.khanacademy.org/science).

How to Study

Everyone learns very differently, and knowing your learning style is important: do you learn by reading, by taking notes, by talking, by watching, by doing, or by a combination of some or all of these? For example, I learn by reading and by note-taking, so I read through textibrary very carefully, take copious notes, and summarize each concept in my own words before moving on to something new. Think about this before you begin so that you'll know how to structure your studies.

Regardless of your learning style, you'll still need to solve the physics problems in each textbook. Solving problems is the only way to understand physics. There's no way around it. Even though it can feel tedious at times, there's nothing more rewarding than figuring out a really difficult physics problem and realizing that you figured it all out all by yourself!

One tough thing about learning on your own is that you may not know whether you are solving the problems correctly. Some of the textibrary listed below have answers to selected exercises in the back of the book, but these aren’t always adequate for two reasons: (1) they often only show the solutions to the problems, and not the steps taken to get there; and (2) it’s much better to do all of the exercises rather than just a select few. The good news is that many of the solutions (and step-by-step ways to solve them) can be found online with a simple Google search. If you are going to Google the answers, however, please first try to solve the problems on your own, and try multiple times (you’re not in school trying to get a perfect grade — you’re trying to learn and understand).

And, finally, a note on learning in a laboratory vs. learning from textibrary. Physics is both an experimental and theoretical science, and while research happens in laboratories and on blackboards and computers, the majority of any physics education does not take place in a laboratory but in lecture classes that teach from textibrary and assign homework problems that are found in textibrary. Yes, there are some laboratory classes (usually at the very introductory levels, and their only purpose is to show that oh, look, Newton’s laws work in the real world after all) and some — some — undergraduates are allowed to participate in research on the side, but physics is taught through textibrary, lectures, and homework problems. Don’t believe me? Take a look at the undergraduate physics curriculum at any university that offers a physics major. Graduate programs in physics are largely the same — both M.A. and PhD programs in physics require two years of core classes — with one key difference: to get a PhD, students need to complete several years of research, a thesis, and — at many programs — take an exam to prove they have mastered the graduate core curriculum. The graduate core curriculum is all textibrary and lectures and homework problems. The textibrary listed in the curriculum I’ve written below are the same textibrary that are used in the top undergraduate and graduate physics programs in the world. Studying them will give you the same education that you would receive at one of these programs — no painfully-annoying-introductory-mechanics-laboratory-class-with-inane-group-projects required.

Undergraduate Physics

Overview

The curriculum of every undergraduate physics program covers the following subjects (along with some electives in various topics), and usually in the following order:

1. Introduction to Mechanics
2. Electrostatics
3. Waves and Vibrations
4. Modern Physics
5. Classical Mechanics
6. Electrodynamics
7. Quantum Mechanics
8. Thermodynamics and Statistical Mechanics
9. Undergraduate Electives

I'm going to cover the details of each of these fields below, including the best textibrary to use and any additional reading you may find helpful in your journey. I'm also going to give some details about the mathematics you'll need to learn alongside each topic.

1. Introduction to Mechanics

What It's All About

An introduction to mechanics course is the first physics class that most people will take in an undergraduate program, and it's the best place to begin independent study of physics as well. This is where you'll start learning how to see the world in mathematical terms. Topics that will be covered: the basics of motion in a straight line, motion in two dimensions, motion in three dimensions, Newton's Laws, work, kinetic energy, potential energy, the conservation of energy, momentum, collisions, rotation and rotational motion, gravitation, and periodic motion.

The Best Textibrary to Use

• University Physics with Modern Physics by Young and Freedman (essential). Work through all of the "Mechanics" chapters (in my edition, these are chapters 1-14).This is the best introductory book I've found, and you can use it when you learn electrostatics and modern physics, too. It does a great job of introducing the relevant mathematics, but you'll need to be learning calculus alongside it. There are plenty of great example problems to work through, and the solutions are easy to find online (though you can also buy a Student Solutions Manual). Please note that you don't need to spend $250 on the new edition — Amazon has lots of copies of the 12th edition, the 13th edition, and the 14th edition that contain the same material.

The Math You'll Need to Learn Alongside It

You'll need to learn calculus while working through University Physics. My favorite introductory calculus book is Thomas' Calculus (you can also use the earlier editions), with Stewart's Calculus (older edition here) coming in as a close second. Work through each chapter, and make sure you can solve problems at the end of each chapter before continuing to the next.

If you are new to calculus and/or find yourself struggling to get accustomed to it, don’t let that stop you. Calculus is really difficult, and it can take a really long time to wrap your head around it. Some things that can help are (1) watching videos like the ones on Khan Academy (https://www.khanacademy.org/), (2) taking Robert Ghrist’s free calculus courses on Coursera, and (3) reading a truly amazing little book called Calculus Made Easy by Silvanus P. Thompson and Martin Gardner that breaks everything down really clearly.

2. Electrostatics

What It's All About

This is where you'll learn about the physics of electricity and magnetism (electromagnetism) in static situations (situations where no motion is involved). Topics covered are: electric charges and electric fields, magnetism and magnetic fields, Gauss's Law, capacitance, resistance and conductance, inductance, current, and how circuits work.

The Best Textibrary to Use

• University Physics with Modern Physics by Young and Freedman (essential). Work through the chapters on "Electromagnetism" (in my edition, these are chapters 21-32). You can find inexpensive copies of the 12th edition, the 13th edition, and the 14th edition that contain the same material.

The Math You'll Need To Learn Alongside It

Keep working through the calculus textibrary (Thomas or Stewart) while you work through the basics of electrostatics, but you should finish them by the time you finish the electromagnetism chapters in University Physics. You absolutely must understand the basics of calculus before you move on to the other topics in physics.

3. Waves and Vibrations

What It's All About

The mechanics of vibrations and waves are complex and important enough to demand their own course of study. Mastering this material is essential for learning about quantum mechanics, so don't skip this topic! This is where you will learn about simple harmonic oscillators, damped harmonic oscillators, forced oscillations, coupled oscillators, waves, interference, diffraction, and dispersion.

The Best Textibrary to Use

• Vibrations and Waves by French (essential) and Vibrations and Waves by King (essential). These two library complement each other very well, and contain different problems and solutions.

The Math You'll Need To Learn Alongside It

By this point, you should have finished the introductory calculus library and are ready to move on to more advanced mathematics. You should start working through Zill's Advanced Engineering Mathematics, which is a thoroughintroduction to more advanced topics in mathematics (linear algebra, complex analysis, real analysis, partial differential equations, and ordinary differential equations). The topics in this book are essential — once you master them, you'll have all the math you need to know in order to understand undergraduate physics. You can also buy the (cheaper) 4th and 5th editions.

4. Modern Physics

What It's All About

The fourth physics class that most undergraduates take is usually called "Modern Physics", and it's an introduction to topics in physics that will be taught in greater detail later in the undergraduate physics curriculum. If you plan to study the advanced topics on their own, it's fine to skip this class, but covering these topics now in your independent studies will allow you to grasp the advanced topics that you hear so much about and that probably got you into physics in the first place. This is where you'll learn the basics of thermodynamics, relativity, quantum mechanics, atomic physics, nuclear physics, particle physics, and cosmology.

The Best Textibrary to Use

• University Physics with Modern Physics by Young and Freedman (essential). Work through the "Thermodynamics" section (chapters 17-20 in my edition of the book), and the "Modern Physics" section (chapters 37-44). You can find inexpensive copies of the 12th edition, the 13th edition, and the 14th edition that contain the same material.

The Math You'll Need To Learn Alongside It

Continue working through Zill's Advanced Engineering Mathematics. Once you have mastered all of the topics in this book, you'll have all the math you need to know in order to understand undergraduate physics.

5. Classical Mechanics

What It's All About

This is where you’ll really learn classical mechanics, which you were introduced to in the very first course (Introduction to Mechanics). You'll study the topics in much greater depth, and learn how to use different mathematical formalisms of classical mechanics (the Lagrangian formalism and the Hamiltonian formalism) to solve problems in mechanics.

The Best Textibrary to Use

• Taylor's Classical Mechanics (essential). This is a fantastic introduction to classical mechanics.
• Morin's Introduction to Classical Mechanics with Problems and Solutions (supplement). Morin's book is a good supplement to Taylor's, and contains some great problems to work through.
• Problems and Solutions in Introductory Mechanics by Morin (supplement). Even more great problems (with solutions) to work through, and contains some great problem-solving strategies.

The Math You'll Need To Learn Alongside It

If you haven't finished working through Zill by now, you should master the topics in it by the time you finish studying classical mechanics.

6. Electrodynamics

What It's All About

Earlier, you learned about electrostatics: the study of static (non-moving) electricity and magnetism. By now, you know the mathematics to understand electrodynamics, which encompasses everything about classical electricity and magnetism. You'll cover electrostatics again, then learn about Laplace's equation, multipole expansions, polarization, dielectrics, the Lorentz Force Law, the Biot-Savart Law, magnetic vector potential, electromotive force, electromagnetic induction, Maxwell's equations, electromagnetic waves and radiation, and special relativity.

The Best Textibrary to Use

• Griffith's Introduction to Electrodynamics (essential). This is the book on undergraduate electrodynamics and one of the very best physics textibrary ever written. Make sure you work through every single problem in the book.
• Div, Grad, Curl and All That by Schey (supplement). This is a short textbook on vector calculus that is very helpful when trying to work with vectors in electrodynamics.
• A Student's Guide to Maxwell's Equations by Fleisch (supplement). Maxwell's equations are essential in understanding electrodynamics, and this book is the best supplement on the topic.

7. Quantum Mechanics

What It's All About

By this point, you're ready to really dive into the fundamentals of quantum mechanics and its applications — one of the most beautiful, interesting, and thought-provoking topics in all of physics. You'll learn to see the world in a completely new way. You'll learn about the wave function, the Schrodinger equation, perturbation theory, the variational principle, the WKB Approximation, the adiabatic approximation, and scattering.

The Best Textibrary to Use

• Griffith's Introduction to Quantum Mechanics (essential). This is, without a doubt, the book on undergraduate quantum mechanics, written by the same Griffiths who wrote the Introduction to Electrodynamics. It's written in the same concise and beautiful style, and every single problem is worth solving.

8. Thermodynamics and Statistical Mechanics

What It's All About

Thermodynamics is the field of physics concerned with kinetics (dynamics) related to heat and energy, while statistical mechanics is all about the microscopic principles that underlie the Laws of Thermodynamics. This is where you'll learn about the laws of thermodynamics, entropy, the canonical ensemble, Maxwell distributions, Planck's distribution, Fermi-Dirac statistics, Bose-Einstein statistics, and phase transitions.

By the time you've finished this topic, you'll have mastered all of the fundamentals of undergraduate physics!

The Best Textibrary to Use

• Schroeder’s An Introduction to Thermal Physics (essential). A very thorough and comprehensive introduction to thermodynamics and statistical mechanics; contains very clear and straightforward explanations and examples.
• Introductory Statistical Mechanics by Bowley and Sanchez (supplement). A good second text to have on hand to reference.

9. Undergraduate Electives

What They’re All About

Now that you understand all of the fundamentals of undergraduate physics, you have a solid foundation and can study more advanced and specialized topics, including (but not limited to) astronomy, astrophysics, biophysics, cosmology, electronics, optics, particle physics, and string theory.

The Best Textibrary to Use

• Astronomy: The Cosmic Perspective. A wonderful introduction to astronomy, accessible to anyone who is just beginning to study physics.
• Astrophysics: An Introduction to Modern Astrophysics by Carroll and Ostlie. A comprehensive introduction to modern astrophysics.
• Biophysics: Biophysics: An Introduction by Glaser. A solid introduction to the principles of biophysics.
• Cosmology: Ryden's Introduction to Cosmology. My absolute favorite introductory cosmology book.
• Electronics: Basic Electronics for Scientists and Engineers by Eggleston. Accessible to anyone who has worked through the basics of electrodynamics.
• Optics. Optics by Hecht. The classic (and truly amazing) optics textbook.
• Particle Physics: Griffith's Introduction to Elementary Particles. Written by the same Griffith who gave us the Introduction to Electrodynamics and Introduction to Quantum Mechanics, this book is the perfect introduction to the fundamentals of particle physics and is a joy to work through.
• String Theory. A First Course in String Theory by Zwiebach. The essential introduction to string theory.

Graduate Physics

Overview

Graduate-level physics requires mastery of every topic within the undergraduate physicscurriculum above as a prerequisite.

The graduate physics core is comprised of:

1. Mathematical Methods in Physics
2. Electrodynamics
3. Quantum Mechanics
4. Statistical Mechanics
5. General Relativity
6. Quantum Field Theory
7. Graduate Electives

I'll cover each of these in the sections below. (Note: many graduate students are required to take a course in classical mechanics as part of the graduate core, but if you've mastered the material in undergraduate classical mechanics there is no need for this).

1. Mathematical Methods in Physics

What It's All About

Studying electrodynamics, quantum mechanics, and stat mech in more depth at the graduate level requires a greater level of mathematical rigor. To prepare, you'll need to learn the following in greater detail: Fourier analysis, tensors, ODEs, PDEs, real analysis, complex analysis, algebra, and group theory (to name a few).

The Best Textibrary To Use

• Mathematical Methods for Physicists by Arfken, Weber, and Harris (essential). This book covers the essentials of everything you'll need to know for the mathematical rigor demanded by the graduate core.
• Tolstov's Fourier Series (supplement). The best book on Fourier Analysis ever written. Complements the main text very well.
• Complex Variables by Fisher (supplement). Amazing overview of complex analysis. Can be used along with Needham's Visual Complex Analysis to supplement the main text.
• Zee's Group Theory in a Nutshell for Physicists (supplement). A brilliant introduction to group theory for physicists.

2. Graduate Electrodynamics

What It's All About

Graduate-level electrodynamics covers the same topics as undergraduate electrodynamics but with greater mathematical rigor.

The Best Textibrary To Use

• Classical Electrodynamics by Jackson (essential). This is the bible of classical electrodynamics, and everyone who works through either loves it or hates it (I loved it). If you can master everything in this book and work through a decent selection of the problems, you'll have mastered electrodynamics.

3. Graduate Quantum Mechanics

What It's All About

Graduate quantum mechanics is far more advanced than what you learned at the undergraduate level. Here you'll learn, in great depth, all there is to know about quantum mechanics, including quantum dynamics (the Schrodinger equation, the Heisenberg picture, propagators, and Feynman path integrals), angular momentum, symmetries and conservation laws of the quantum world, perturbation theory, scattering theory, relativistic quantum mechanics, decoherence, and interpretations of quantum mechanics (the Copenhagen vs. Many-Worlds interpretations).

The Best Textibrary To Use

• Sakurai's Modern Quantum Mechanics (essential). This is my favorite textbook on quantum mechanics, and the one I used to learn quantum mechanics for the very first time. It's a wonderful, elegant, simple book with clear and understandable problems. Try to work through all of the problems — if you do, you'll understand quantum mechanics very well.
• Quantum Mechanics and Path Integrals by Feynman (essential). Sakurai's coverage of Feynman's Path Integral formalism of quantum mechanics doesn't do it justice. Working through this text (written by Feynman himself) is not only useful, but incredibly fun.
• The Principles of Quantum Mechanics by Dirac (supplement). Dirac was one of the founding fathers of quantum mechanics and quantum field theory. This book is important historically, and also will open your eyes to the need for quantum field theory.
• Principles of Quantum Mechanics by Shankar (supplement). A great supplement to Sakurai for more information about each topic. A bit too dense to serve as a primary text, it works best as an addition or reference.
• Decoherence and the Appearance of a Classical World in Quantum Theory (supplement). This book is very dense and you may not understand all of it even after working through Sakurai, but understanding decoherence is essential to understanding how the classical world arises from the quantum.
• The Everett Interpretation of Quantum Mechanics: Collected Works 1955-1980 (supplement). Very few library have been written on interpretations of quantum mechanics, and reading through this volume helps to understand the limitations of our interpretations as well as the complexities and details of Everett's Many-Worlds interpretation.

4. Graduate Statistical Mechanics

What It's All About

Now that you have a more solid mathematical background and understand all of the fundamentals of quantum mechanics, it's time to approach graduate-level statistical mechanics. You'll revisit the Laws of Thermodynamics, and then pick up from where you left off in undergraduate statistical mechanics.

The Best Textibrary To Use

• Statistical Mechanics by Pathria and Beale (essential). This book is, admittedly, a bit frustrating, but it's worth suffering through because if you make it all the way to the end and work through the majority of the problems, you'll know stat mech like the back of your hand.
• Huang's Statistical Mechanics (supplementary). This is a great book to supplement the main text — is a good bridge between undergraduate stat mech and Pathria.

5. General Relativity

What It's All About

By now you'll have a very deep understanding of Einstein's special theory of relativity, but, as you may have noticed, general relativity (GR) — the theory of gravitation — hasn't yet been mentioned. That's because GR is a mathematically demanding topic — not only do you need to know all of the math you've learned so far,  but you'll need to learn differential geometry in order to make sense of how gravity works. Here, you'll revisit special relativity and the intricacies of spacetime, then learn the basics of differential geometry, how to deal with curvature, the essentials of gravitation, how black holes work, and the basics of cosmology.

The Best Textibrary To Use

• Spacetime and Geometry by Carroll (essential). This is the book on general relativity, and Carroll does a phenomenal job of introducing the essentials of differential geometry and general relativity.
• Einstein Gravity in a Nutshell by Zee (supplement). A great, accessible overview.
• Wald's General Relativity (supplement). Wald's book is a very abstract, high-level overview of general relativity, and makes a great supplement to Carroll's book. Go to Carroll for the overview, look it up in Wald for the high-level abstractions, and then look in the apple book for the dirty details.
• Gravitation by Misner, Thorne, and Wheeler (supplement). Also known as the "apple book" thanks to the apple gracing its cover, this book goes into the nitty-gritty details of general relativity in ways that no other book does.
• Weinberg's Gravitation and Cosmology (supplement). Weinberg is one of those rare physicists who has not only been at the forefront of every major field in physics, but has written about each of them as well. His library tend to be inaccessible to beginners, however, and this book is no exception. It does make a good supplementary reading, but I'd advise reading it after you've worked through the rest.
• Differential Geometry of Curves and Surfaces by Manfredo P. do Carmo (supplement). The classic differential geometry textbook; may be useful to help you wrap your head around differential geometry.

6. Quantum Field Theory

What It's All About

Quantum Field Theory (QFT) is the heart of all modern high-energy physics: the Standard Model of particle physics is a QFT. The whole idea behind QFT is that we are doing quantum mechanics on classical fields, and it works remarkably well. Along with GR, QFT will be the most challenging part of your physics education, but perhaps the most rewarding (I know it was extraordinarily rewarding for me!). It may take many, many years to master. You'll learn about how to quantize fields, Feynman diagrams, quantum electrodynamics (QED), renormalization, non-Abelian gauge theories, quantum chromodynamics (QCD), the Higgs mechanism, the Glashow-Weinberg-Salam theory of electroweak interactions, the symmetries of particle physics, and spontaneous symmetry breaking.

The Best Textibrary To Use

• Zee's Quantum Field Theory in a Nutshell (essential). This is my favorite physics book of all time, and the most beautiful introduction to QFT ever written. You'll walk away understanding the basics of QFT and with a deep understanding of the fundamental nature of the universe.
• An Introduction to Quantum Field Theory by Peskin and Schroeder (essential). This is the bible of QFT, but its far too terse and encyclopedic to work through on its own and must be studied alongside Zee. Covers everything you could possibly want to know about QFT. Try to work through the problems, but be aware that mastery of QFT will take a very, very long time.
• Weinberg's The Quantum Theory of Fields, Volume 1 (supplement). Another great volume by Weinberg, who was one of the most important physicists in the history of particle physics. This book should be used only as a supplement, and preferably not read until Zee and Peskin and Schroeder have been completed. It's not a book to learn from, but one to gain additional understanding of QFT through after you've mastered all of the basics.
• Lie Algebras in Particle Physics by Georgi (supplement). This dives into the details of Lie Algebras in QFT.

7. Graduate Electives

What They’re All About

The graduate curriculum can be split into several categories: (i) the core courses, (ii) specialized coursework and graduate electives, and (iii) research. Graduate students typically take the core courses first, which focus on the same topics covered in undergraduate courses but in much greater depth and with far more mathematical rigor. Students then choose more specialized courses and electives depending on their area of research in physics, including (but not limited to) condensed matter physics, cosmology, electronics, optics, particle physics, quantum computing, solid-state physics, and string theory.

The Best Textibrary to Use

• Condensed Matter Physics: Lubensky’s Principles of Condensed Matter Physics. A modern, comprehensive textbook. Fairly advanced, and is easier to understand after completing the graduate core and working through something like Ashcroft and Mermin.
• Cosmology: Mark Trodden and Sean Carroll’s TASI Lectures: Introduction to Cosmology. Supplement with Steven Weinberg’s Cosmology.
• Electronics: The Art of Electronics by Horowitz and Hill. The best electronics textbook there is, period.
• Optics: Optics by Hecht. The classic optics textbook.
• Particle Physics: Quarks and Leptons by Halzen and Martin. Wonderful overview that’s fun to read and work through. Supplement this with Modern Particle Physics by Mark Thomson, which is up-to-date on contemporary discoveries like the Higgs.
• Quantum Computing:Quantum Computation and Quantum Information by Michael A. Nielsen and Isaac L. Chuang. Also known as “Mike and Ike,” this is the standard introduction to quantum information and computation.
• Solid-State Physics: Solid-State Physics by Ashcroft and Mermin. The classic introductory solid-state textbook. Supplement with Introduction to Solid State Physics by Kittel.
• String Theory: String Theory: Volume 1, An Introduction to the Bosonic String and String Theory: Volume 2, Superstring Theory and Beyond, by the late Joe Polchinski; and String Theory and M-Theory: A Modern Introduction. I found it really enjoyable to pair Polchinski’s library with Becker Becker Schwarz when I was learning string theory — they complement each other well.