Note: This is a draft and there are typos. I see them do not worry

This is a reading list for theory things. These contain books I either have read or heard good things about. No guarente on qualifications regarding my opinions on books. I haven’t necessairliy taken the class in some of these references, but that doesn’t mean I haven’t heard people who know these things well mention which resources are good. If you disagree with this list you should let me know.

Physics

The Feynman Lectures are also something to go though if you want. Some people swear by them and some think they are not that rigorous. I personally like them.

My hot take is that if you are young, I wouldn’t even bother with non Calculus based physics. Just accelerate in math and take it. This mostly comes from me believing that intro calculus is not that hard to self tech in about a month (I did this) and then you can just learn physics.

That being said, I don’t want to discourage anyone doing physics just because they don’t know Calculus yet. I think intro mechanics books are fairly understandable without Calculus and I can’t deny you can get fine intuition and a good primer off of Algebra based physics.

Mechanics

The most introductory books in mechanics for someone genuinely interested in physics is Kleppner and Kolenkow as well as Introduction to Classical Mechanics by Morin. I think Morin is a harder but is doable to start at, although if you want a “beginner but still challenging” set physics problems, Morin’s blue book isn’t a bad rec. Kleppner should be doable but hard for someone first learning physics but if even this is too hard you can drop it down to Haliday and Resnick. I was never the biggest fan of Newtonian Mechanics cause I thought it was very arbitrary but in hindsight I wish I studied it more before moving on. Strong intuition with (ordered) Momentum, Energy, Forces, Harmonic Oscilations, Forces, and Circular Motion will help you greatly throughout your Physics journey.

Later in your physics career you come back to Mechanics and take Analytical Mechanics, which introduces newer, higher level ideas than Newtonian Mechanics, notably Lagrangian and Hamiltonian Mechanics. In order to do this, there is the book Analytical Mechanics by John R Taylor, or the one I think I like more but ever so slightly harder which is Goldstein.

Electricity and Magnetism

The most introductory book you hear about in a class is normally Purcell Electricity and Magnetism. I think this book is fine and has decent problems, but I really don’t like the amount he yaps. I have heard strong rebuttals to this opinion though. I would say it is a good reference, and the Special Relativity Chapter (I believe 5) is really good, but I much prefer just going to Griffiths Electricity and Magnetism. I think it is an excellent book. Make sure to be very comfortable in Multivar Calc before you do E&M. I think if you don’t you either

  1. get some mickymouse class where everything reduces to an algebraic or single variable integral or
  2. get lost

Neither of which are good alternatives and both I have experienced. Just make sure to understand Div, Grad, Curl, Stokes Theorem, etc well. In a crunch I think chapter 1 of Griffiths does a fine job at explaining it.

For graduate level E&M there exists the dreaded Jackson E&M as well as the more forgiving Zangwill. I think the exposition in Zangwill might be easier to understand than Jackson.

Waves / Thermo

The class I took used Howard Georgi The Physics of Waves. I have seen two approaches to teaching this subject.

  1. Define simple harmonic motion and then move to the wave equation.
  2. Jump to the wave equation and discuss the implications.

Georgi uses the first one. I think both have tradeoffs but 1 is more comprehensive. I thought the class around the book (Cornell Physics 2218 by Wittich) was good but we didn’t use the book that much (it felt like there was too much in the book for this topic, although others might disagree)

For thermodynamics our class used Schroeder An Introduction to Thermal Physics. The book is fine in exposition but very light in content. I know Enrico Fermi has a short but more comprehensive book people swear by.

I have friends that also think teaching Waves/Schroeder is a useless endeavor. To some extent I agree with this, but I think covering the main ideas on waves again can be good, although this material is very skippable and I am only including it because it’s a staple in the 3 course intro sequence most colleges do.

Quantum Mechanics

The intro book that I like is Griffiths Quantum Mechanics. I think it is a nice book. I have also heard good things about Shankhar especially regarding deriving the Schrodinger Equation and having less bashy problems, but sometimes I think the bash is good practice too.

The main graduate textbook used is Sakuri.

French and Taylor QM is also a common book.

Statistical Mechanics

Not really sure yet…

Solid State Physics

A good introductory book is Oxford Solid State. It contains the basics and has references to other textbooks. Linda Ye’s lecture notes are also good. The bible in the space is definately Ashcroft and Mermin. There are some copies going around with missing info tho so make sure to find one that is good. For a more graduate book there exists __ #TODO. There also exists #TODO

For topological theory I think Bernevig is good and for superconducting is Tinkham (recommended by my nrofessor). I also like topocondmatter online.

Some others recommended by my professor #TODO

  • Im lazy

Quantum Field Theory

A friend who took the class told me to use P&S, Schwartz, and Sredicki. “Schwarz is the weakest of the 3” but also was the most liked out of the 3. You can also look at QFT in a Nutshell by Zee. I think MIT OCW QFT now exists as well. I will fill it out myself in two years 😈.

General Relativity

Sean Carroll’s book seems to be the classic.

Cosmology

Idk lol, the theory seems cool though

Nuclear Physics and Fusion

Never studied, know like one person who has lol

Optics

I like the Uorgeon refrences there are other things to. #TODO

Quantum Info, String Theory

Lots of resources, why r u doing this field lol ggs

Mathematical Physics

This subject is underrated. I have read Kusse (A Cornell) specific book. Some of my classmates did not like it at all, and while there are parts I think are poorly explained, I think he does a good job on content. I know UC Berkeley uses the more common Mathematical Methods in the Physical Sciences by Mary L Boas.

Other Resources

  • David Tongs Notes
  • #TODO

Mathematics

For anything precollegiate I strongly recommend the AOPS sequence of books (Geometrey, Algebra, Trigonometrey, Calculus, etc). In my opinion most pre collegiate math books are such a disgrace / turnoff to the field but these are written by people who are passionate about the subject and I think they do a good job. I think Stuart Calculus is fine for the subject too and is what I would use for learning Multivarabile Calculus if I didn’t want to understand Manifold Theory (but I think doing Multivariable Calculus with manifolds in Hubbard and Hubbard is a much better idea).

Real Analysis

I personally like a combination of starting with Abott and moving to Baby Rudin. For grad/more challenging there is no question, Stein and Shakarchi.

Other books:

  • Ross (questionably easy though)
  • Terry Tao’s book
  • Papa Rudin

Complex Analysis

For introductory books there exists Brown and Churchill as well as Ahlfors. Stein and Sharachi exists for Graduate Complex. A very new graduate level book is A Course in Complex Analysis by Saeed Zakeri like I couldn’t even find that one on the internet last year.

Linear Algebra

I first learned Linear Algebra through Lay. Honestly I think it is a nice introduction to higher level math ideas while being extremely computational (I still go back and look at it when I need to remember how to do some algorithm). That being said I think Gilbert Strangs book might be a better intro for someone serious about mathematics, although both are similar in difficulty / scope. A slightly more difficult book which I quite like is Sheldon Axler’s book. The upper division book I have seen the most is Roman Linear Algebra but I still don’t think its that bad.

Abstract Algebra

The two main books I see are Dummit and Foote and Artin Algebra. I have friends that swear by both. Artin seems to be harder tho.

Topology

Have not read but Munkres is the classic, no question there.

Manifold Theory

I initially learned this topic in Hubbard and Hubbard. I liked this because he is very fundamental with what he talks about, i.e. he doesn’t like talking very abstractly. Afterwards, I think Lee Smooth Manifolds is a good but hard read. For Differential Geo I think Do Carmo is the best. There are a lot of good books on manifold theory.

Others:

  • Calculus on Manifolds by Spivak
  • An Introduction to Manifolds by Tu
  • Topology from the Differentiable Viewpoint by Milnor
  • Advanced Calculus by Loomis and Shlomosternberg

Algebraic Topology

For our class Inna Zakharevich recommended Hatcher + May. Hatcher is a yapper / a bit more the classic, May is extremely dense. We also used Weintraub, which is a more classic book.

Combonatorics

Problems idk

Number Theory

mid

Competition Books

The classics are AOPS Volume 1, 2 intro to problem solving for high school comps. Then for Putnam there is Putnam and Beyond as well as good seminars (CMU, MIT, Cornell is starting one, etc). I will make a future blog post about getting into competitions / how to study theory properly later.

Other references

Links to things I like: Evan Chen Napkin OTIS Stuff Euler Circle Books

Engineering, CS, and Misc

In general, I think being a theory bot in engineering or industry cs is a horrible way to go about things. I feel like I see a lot of kids come out of university having done nothing but the school system knowing only theoretical ideas in engineering to walk into the real world with zero intuition but high “qualifications” only to be a terrible engineer (blog post coming soon). I highly recommend spending most of your time just doing projects to learn real applied skills, but even in the applied sciences theory is still enormously important. For those of you who are the opposite (someone who only does projects all day), I advise you to also learn some theoretical and problem solving ideas in Math, Physics, Theoretical CS, etc. I think a lot of the interesting problems in engineering require understanding of these ideas, and if you are good at making projects, don’t let a snobby theory kid intimidate you into thinking you can’t understand it.

That being said there are still things that you should learn and so here is it.

Circuits

For circuits I think that Practical Electronics for Inventors by Scherz and Monk is a good reference table.

Computer Architecture

For VLSI our class uses CMOS VLSI design: a circuits and systems perspective by Weste. For computer architecture you can look at the ECE2300 or ECE4750 online material from Cornell (I believe its public). The books for ECE4750 by the syllabus are: Hennessy and Patterson “Computer Architecture: A Quantitative Approach” and Harris and Harris Digital Design and Computer Architecture. I heard good things about Patterson’s book from Anne Bracy. Regarding GPU design a distinguished NVIDIA Architect once told me that “the only way to understand how a modern GPU works is to be employed at NVIDIA and read the internal docs, otherwise this will give you an idea on how they worked in the 80’s”. Modern CPU design could be similar, I wouldn’t know. FPGA dev should be ok I think.

Nanofab

I am not really sure yet. The class I took at Cornell used Plumber but the book was so bad it made me want to drop the class. I would not read that book, it has zero structure.

Control Theory

Not sure a good reference on this topic, but def theory topic to study

Systems Programming

I think reading a book on systems programming is a horrible way to get good at it, but if you want formalization I recommend #TODO. I think there are ideas in parallel programming you should read theory on but I don’t know of any resources right now.

Algorithmic CS

This is one of the only things in CS I think you should formally study. I recommend Algorithms by Robert Sedgewick. Klienberg and Tardos have a book called Algorithm Design that is used at Cornell.

For competitive programming you really only need the usaco.guide. It extremely well made.

The Art of Computer Programming by Donald Knuth is held in extremely high regard.

Compilers

Two were recommended to me once. There is the Dragon book and one other I am forgetting. I think it might be Engineering a Compiler by Keith D. Cooper and Linda Torczon or Advanced Compiler Design and Implementation by Steven S. Muchnick.

Programming Languages

You should study it formally, I don’t do this field but a friend recommended Types and Programming Languages by Benjamin C. Pierce and Static Programming Analysis

Distributed Computing

You might be cooked on this one as I think almost everything is in papers, you can read some here though: #TODO

Machine Learning

I have bad references for ML. A friend recomended Probabilistic Machine Learning: Introductory Topics and Probabilistic Machine Learning: Advanced Topics by Murphy.

For Reinforcement learning you can read. Reinforcement Learning: An Introduction by Sutton and Barto. Wen Sun at Cornell has a fairly good book along side a course. This field moves extremely fast though, section made in June 2025.

Recommended to me by friends in Deep Learning:

Most of this stuff seems to not be in books yet

Organic Chemistry

Structure and Reactivity: An Introduction to Organic Chemistry by Brian P Coppola was recommended to me by the best Biophysics people I know, but it is almost impossible to get for free (ask a local library to buy it)

Quantum Chemistry

Fairly comprehensive list written down somewhere, ill find it at some point #Todo

Quantitative Finance

Green book red book Quant guide

Thanks to

  • Francis Fung for sending me many of these resources over our conversations
  • Friends that have continually mentioned the right resources to look at
  • Reviewers:
    • Me
    • Haadi Khan
    • Ethan Uppal
    • Eddie Zhang