Some math resources!

"Structures are the weapons of the mathematician" - Nicolas Bourbaki

I detest mathematicians, who denote \(\mathbb{Z}_p\) as the set of integers modulo a prime \(p\)!. Let me fix this notation, \(\mathbb{Z}_p\) denotes the set of \(p\)-adic integers, \(\mathbb{Q}_p\) denotes the set of \(p\)-adic numbers, \(\mathbb{Z}/p\mathbb{Z}\) denotes the set of integers modulo a prime \(p\) and \(\mathbb{F}_p\) denotes a finite field with order \(p\).

  1. Texnique (a competitive latex typesetting game)
  2. Dexter Chua (My go-to website for referencing Cambridge notes)
  3. Dover Books (Really adavanced affordable math books)
  4. COMS (Holy grail for searching conferences)
  5. Mathmeetings.org (Something after COMS)
  6. Commalg.org (The website for the commutative algebra community)
  7. The Fields Institute for Mathematical Sciences (Research institute affiliated with University of Toronto)
  8. Keith Conrad (Really good intuitive expository notes on specific algebraic topics, also visit Brian Conrad's webpage!)
  9. Zena Project (On up-to-date information about proof formalization in Lean)
  10. Álvaro Lozano-Robledo (Lectures on elliptic curves and galois reprsentations, with youtube channel and math blog)
  11. Andrew Lin (Good reference for courses from MIT and Stanford)
  12. Clay Mathematics Institute (Good resources written by top mathematicians, which are fun to read!)
  13. Evan chen (Popular for the "Napkin" math guide)
  14. J.S. Milne (Amazing textbooks and questions, if you are an algbera-kind of person)
  15. An Invitation to Enumeration (If you love combinatorics and want to learn it in and out)
  16. Open Math (Wanna learn linear algbera, here you go!)
  17. Noam Elkies (One of the best blog for algorithmic number theory)
  18. Terry Tao (Best mathematics blog)
  19. Quiver (hack for creating commutative diagrams in latex)
  20. Number theory web (All-in-one resource on number theory)
  21. researchseminars.org (List of all AMS seminars)
  22. LMFDB (Expert database on L-functions and modular forms)
  23. Quanta magazine (best resource to know what is happening within the research community)
  24. Applied Cryptography Group (good resource for cryptography and number theory)
  25. William stein (Founder of sage math software)
  26. Avi Wigderson (Wrote an amazing book on theoretical computer science called "math and computation")
  27. MSP (publishes journals in all major area of mathematics)
  28. NLab (good to know little bit about every area of mathematics)
  29. encyclopedia of mathematics (The wikipedia for math)
  30. Planet Math (Mini-version of a wikipedia on math!)
  31. Silverman (Author of best books on Elliptic curves and Algbera)
  32. AOPS (who doesn't know about this, lol!)
  33. QRM (if you are interested in quantitative risk management)
  34. CEMC (good place if you want to refine your high-school math and olympiad skills)
  35. MATH 600 (resource to learn latex from A-Z)
  36. Open Text and Libre Text (Can find good explanations and examples for calculus and algebra courses)

Here are some really good and useful resources for a mathematician, who wants to enter the industry!

  1. Quant Guide (Leetcode for a quant wannabe)
  2. Quant Questions (Best for a quant interview prep)
  3. kaggle (Leetcode for a ML and Data Science follower)
  4. Leetcode and Neetcode (The OG one!)
  5. Parity-Zetamac (Online game to practice options strategies pricing)

Here, are some \(\LaTeX\) style templates that I use for different purposes, lindrew.sty for taking lecture notes and kafkanotes.sty for taking notes while reading research papers.

I get this question asked quite often, "when should I buy a physical mathematics book?" My answer is when the book is extremely cheap comparitively to other math books in the market or an online pdf is not available for free. Kind of obvious tho!

Modern number theorists (especially, Prof. Kevin Buzzard) would love to formalize the extraordinary proof of Fermat's Last Theorem in Lean. But doing this would require us to formalize crazy amount of theories and algebraic structures. First, we need to define the obvious, ie., elliptic curves and modular forms, then we formalize theories on finite flat group schemes, automorphic representations, \(p\)-adic Galois representations, Hecke algebras, universal deformation rings, Galois cohomology, local and global class field theory, harmonic analysis, arithmetic algebraic geometry, non-abelain Fourier theory. The funny part is that, it took us 350 years to understand and connect these theories. Then we need to prove some really profound theorems about some of these objects, using rest of these objects. And then Fermat's Last Theorem comes out in the wash.