I created this reading guide with the intention of giving people a one stop shop to find a starting point to learn about theoretical topics in stem. When I was younger, at times I found a bottleneck to learning advanced theoretical topics simply knowing about the resources themselves, and having specific knowledgable people introduce them to me has greatly helped me in the past.

Very often do I get asked the question where to find or get started on a specific topic, and I think it is beneficial if I can just write out my opinions here and like to it. I want to emphasize that the things on here are simply my personal opinions about specific topics and can go against others at times. The point isn’t to argue a certain direction against others, but simply give a starting point to those who are interested.

Not all of these recommendations are mine, but they all come from people I trust greatly. If you disagree with this list you should let me know.

Physics

For broad intuition, 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 though never used them much over denser specialized topic books.

I have a hot take here. I think if you are young, I would try and learn Calculus before trying to really emphasize in physics. You can accelerate in math and just take it. I think it is more efficient for development to just do the math first so you are never limited. 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 probably Kleppner and Kolenkow as well as Introduction to Classical Mechanics by Morin. I won’t sugar coat it, Morin is quite a hard book and K&K is challenging too. If you want a “beginner but still challenging” set physics problems, Morin’s blue book isn’t a bad rec either. Kleppner should be doable but hard for someone first learning physics. If even this is too hard you can drop it down to Haliday and Resnick, an easier and very comprehensive one. At times, I think I was never the biggest fan of Newtonian Mechanics because 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 Oscillations, 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 and some ideas in multi body physics, scattering, solving from perturbations, chaos, etc. 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. Both are great.

Electricity and Magnetism

The most introductory book you hear about in a college class is normally Purcell Electricity and Magnetism. I think this book is good and has decent problems, but at times I really don’t like the amount he speaks. 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 Griffith’s Electricity and Magnetism. I think it is an excellent book.

Make sure to be very comfortable in Multivariate Calculus before you do E&M. In many ways, a lot of the intuition in E&M comes from formalizations of vector calculus and although in practice you reduce a lot of the equations down to algebraic or single variable calculus equations, if you aren’t comfortable to some level I think it would be hard to grasp the intuition later physics uses.

I would make sure to generally understand differentiating and integrating either multidimensional spaces or vector fields. Make sure you understand to some capacity: Jacobian, Integrating path integrals, Div/Grad/Curl and intuition they bring, Stokes/Greens Theorem well. In a crunch I think chapter 1 of Griffith’s 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. Jackson has a reputation of being so challenging people take pride in competing it. I think Zangwill is incredibly modern and well written.

Waves / Thermo

The class I took used Howard Georgi: The Physics of Waves. Generally when teaching waves, I have seen two approaches to teaching this subject:

  1. Define the 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 trade-offs but 1 is more comprehensive.

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. I had agreed at times, but I think a well done waves class can solidify many ideas covering the main ideas on waves again can be excellent, this material can is very skippable in the sense that the ideas will all show up later, but formulating intuition from a rigorous class can really help you later. I would emphasize really understanding all the ideas related to different types and generalizations of Oscillators, the formalizations of the wave equations and how it’s done in 3D, dispersion, group/packet velocity, standing waves, and how Fourier analysis can play a really

Quantum Mechanics

All of these are good:

  1. Griffith’s
  2. Shankhar
  3. French and Taylor
  4. Cohen-Tannoudji

I think Griffith’s + Cohen-Tannoudji could be a nice combination. Griffith’s really likes to emphasize the intuition from solving the diffeq, while Shankhar or Cohen likes to formally introduce postulates. Both have value. Griffith’s can have quite bashy problems though, but sometimes I think the bash is good practice too.

The main graduate textbook used is Sakuri. Extremely thorough, well written, quite hard.

Statistical Mechanics

Not really sure yet… Just learn about the partition function I guess.

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 definitely 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. I also like topocondmatter online.

Some others recommended by my professor #TODO

  • TODO: Fill in

Quantum Field Theory

Haven’t taken yet, but 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

Not really sure, the theory seems cool though

Nuclear Physics and Fusion

Never studied, know like one person who even does this stuff these days.

Optics

I like the Uorgeon references there are other some other books too. #TODO

Quantum Info, String Theory

TBD & SUSY

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 pre collegiate I strongly recommend the AOPS sequence of books (Geometry, Algebra, Trigonometry, 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 Multi variable Calculus if I didn’t want to understand Manifold Theory (but I think doing Multi variable 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 has a extremely large amount of text and is a bit more the classic, May is extremely dense which could form a good pair. We also used Weintraub, which is a more classic book.

Combonatorics

To learn this field just do Olympiad problems from some book. At the collegiate level that is like Putnam and Beyond or The Craft of problem solving by Zeitz (highly recommend)

Number Theory

Mid field lwky

Competition Books

Not a comp math kid, but to my understanding 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 doing a theory 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 excellent 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. There are classical ideas like formalizing the systems, controller algorithms (PID, LQR, MPC), state estimators (like Kalman Filtering), and lots of modern results using RL.

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 C++ concurrency in action: practical multithreading or Marc Gregoire - Professional C++.

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.

Doing Algo Competitive Programming problems is an excellent way to learn it as well (you get a lot of intuition but no knowledge on proofs). I think Leetcode is poor compared to USACO or Codeforces. 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 as the most famous ones. 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 I’m not really sure.

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 recommended 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. ML theory 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, I’ll find it at some point #Todo

Quantitative Finance

Green book red book Do Quantguide questions

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