A Universe of Sorts

ยง Siddharth Bhat

  1. Laziness for C programmers
  2. Exact sequence of pointed sets
  3. What is a syzygy?
  4. Under the spell of Leibniz's dream
  5. Normal operators: Decomposition into Hermitian operators
  6. Readable pointers
  7. The grassmanian, handwavily
  8. Lie bracket as linearization of conjugation
  9. Computational Origami
  10. Katex in duktape
  11. Kebab case
  12. Localization: Introducing epsilons
  13. NaN punning
  14. Offline Documentation
  15. Using Gurobi
  16. osqp: convex optimizer in 6000 LoC
  17. stars and bars by generating functions
  18. This is not a place of honor
  19. Topological proof of infinitude of primes
  20. Burnside as space average equals time average
  21. The Ise Grand shrine
  22. Edward Kmett's list of useful math
  23. Cokernel is not sheafy
  24. Von neumann: foundations of QM
  25. Discrete schild's ladder
  26. Derivative of step is dirac delta
  27. Extended euclidian algorithm
  28. In a PID, all prime ideals are maximal, geometrically
  29. Prime numbers as maximal among principal ideals
  30. Axiom of Choice and Zorn's Lemma
  31. Local ring in terms of invertibility
  32. Nullstellensatz for schemes
  33. Perspectives on Yoneda
  34. Germs, Stalks, Sheaves of differentiable functions
  35. Connectedness in terms of continuity
  36. Intuition for limits in category theory
  37. Finite topologies and DFS numbering
  38. Categorical definition of products in painful detail
  39. Why is the spectrum of a ring called so?
  40. Ergo proxy
  41. Satisfied and frustrated equations
  42. Combinatorial intuition for Fermat's little theorem
  43. An incorrect derivation of special relativity in 1D
  44. The geometry and dynamics of magnetic monopoles
  45. Sanskrit and Sumerian
  46. Writing Cuneiform
  47. The code of hammurabi
  48. The implicit and inverse function theorem
  49. Whalesong hyperbolic space in detail
  50. Motivating Djikstra's
  51. Intuitions for hyperbolic space
  52. Product of compact spaces in compact
  53. Hyperbolic groups have solvable word problem
  54. Elementary uses of Sheaves in complex analysis
  55. Snake lemma
  56. Kernel, cokernel, image
  57. The commutator subgroup
  58. Simplicity of A5 using PSL(2, 5)
  59. A5 is not solvable
  60. Complex orthogonality in terms of projective geometry
  61. Arithmetic sequences, number of integers in a closed interval
  62. The arg function, continuity, orientation
  63. Odd partitions, unique partitions
  64. Continued fractions, mobius transformations
  65. Permutations-and-lyndon-factorization
  66. Graphs are preorders
  67. Crash course on domain theory
  68. Parallelisable version of maximum sum subarray
  69. Thoughts on implicit heaps
  70. Discriminant and Resultant
  71. Polynomial root finding using QR decomposition
  72. A hacker's guide to numerical analysis
  73. Mobius inversion on Incidence Algebras
  74. Finite differences and Umbral calculus
  75. Permutahedron
  76. Lyndon + Christoffel = Convex Hull
  77. Geometric proof of e^x >= 1+x, e^(-x) >= 1-x
  78. Ranking and Sorting
  79. Proof of minkowski convex body theorem
  80. Burrows Wheeler
  81. Intuitionstic logic as a Heytig algebra
  82. Edit distance
  83. Evolution of bee colonies
  84. Best practices for array indexing
  85. Algebraic structure for vector clocks
  86. Networks are now faster than disks
  87. Einstein-de Haas effect
  88. Rank-select as adjunction
  89. Bounding chains: uniformly sample colorings
  90. Coupling from the past
  91. Word problems in Russia and America
  92. Encoding mathematical hieararchies
  93. Learning code by hearing it
  94. Your arm can be a spinor
  95. Self modifying code for function calls: Look ma, I don't need a stack!
  96. Adjunctions as advice
  97. Reversible computation as groups on programs
  98. Blazing fast math rendering on the web
  99. VC dimension
  100. Symplectic version of classical mechanics
  101. Theorems for free
  102. How to reason with half-open intervals
  103. How does one build a fusion bomb?
  104. Christoffel symbols, geometrically
  105. A natural vector space without an explicit basis
  106. Cache oblivious B trees
  107. Krohn-Rhodes decomposition
  108. Proving block matmul using program analysis
  109. Why I like algebra over analysis
  110. using for cleaner function type typedefs
  111. A walkway of lanterns
  112. Natural transformations
  113. The hilarious commentary by dinosaure in OCaml git
  114. How to link against MLIR with CMake
  115. Energy as triangulaizing state space
  116. The cutest way to write semidirect products
  117. My Favourite APLisms
  118. Proof of chinese remainder theorem on rings
  119. monic and epic arrows
  120. The geometry of Lagrange multipliers
  121. Efficient tree transformations on GPUs
  122. Things I wish I knew when I was learning APL
  123. Every ideal that is maximal wrt. being disjoint from a multiplicative subset is prime
  124. Getting started with APL
  125. SpaceChem was the best compiler I ever used
  126. Mnemonic for Kruskal and Prim
  127. Legendre transform
  128. Cartesian Trees
  129. DFS numbers as a monotone map
  130. Self attention? not really
  131. Coarse structures
  132. Matroids for greedy algorithms
  133. Grokking Zariski
  134. My preferred version of quicksort
  135. Geometric proof of Cauchy Schwarz inequality
  136. Dataflow analysis using Grobner basis
  137. Fenwick trees and orbits
  138. Dirichlet inversion
  139. Incunabulum for the 21st century: Making the J interpreter compile in 2020
  140. An example of a sequence whose successive terms get closer together but isn't Cauchy (does not converge)
  141. Krylov subspace method
  142. Good reference to the Rete pattern matching algorithm
  143. Leapfrog Integration
  144. Comparison of forward and reverse mode AD
  145. An invitation to homology and cohomology, Part 1 --- Homology
  146. An invitation to homology and cohomology, Part 2 --- Cohomology
  147. Stuff I learnt in 2019
  148. A motivation for p-adic analysis
  149. Line of investigation to build physical intuition for semidirect products
  150. Topology is really about computation --- part 2
  151. Topology is really about computation --- part 1
  152. PSLQ algorithm: finding integer relations between reals
  153. Geometric characterization of normal subgroups
  154. Handy characterization of adding an element into an ideal, proof that maximal ideal is prime
  155. Radical ideals, nilpotents, and reduced rings
  156. My disenchantment with abstract interpretation
  157. Computing equivalent gate sets using grobner bases
  158. The janus programming language --- Time reversible computation
  159. A = B --- A book about proofs of combinatorial closed forms
  160. Generating k bitsets of a given length n:
  161. Bondi k-calculus
  162. Topology as an object telling us what zero-locus is closed:
  163. Vivado toolchain craziness
  164. What the hell is a Grobner basis? Ideals as rewrite systems
  165. Lie bracket versus torsion
  166. Blog post: Weekend paper replication of STOKE, the stochastic superoptimizer
  167. Collapsing BlockId, Label, Unique:
  168. Spatial partitioning data structures in molecular dynamics
  169. Vector: Arthur Whitney and text editors
  170. Representing CPS in LLVM using the @coro.* intrinsics
  171. Bug in the LLVM code generator: Lowering of MO_Add2 and MO_AddWordC
  172. Discrete random distributions with conditioning in 20 lines of haskell
  173. Everything you know about word2vec is wrong
  174. Hamiltonian monte carlo, leapfrog integrators, and sympletic geometry
  175. Small Haskell MCMC implementation
  176. The smallest implementation of reverse mode AD (autograd) ever:
  177. Timings of passes in GHC, and low hanging fruit in the backend:
  178. Varargs in GHC: T7160.hs
  179. Debugging debug info in GHC
  180. GHC LLVM code generator: Switch to unreachable
  181. Concurrency in Haskell
  182. Handy list of differential geometry definitions
  183. Lazy programs have space leaks, Strict programs have time leaks
  184. Presburger arithmetic can represent the Collatz Conjecture
  185. Using compactness to argue about covers
  186. Japanese Financial Counting system
  187. Stephen wolfram's live stream
  188. Cleave as a word has some of the most irregular inflections
  189. McCune's single axiom for group theory
  190. Word2Vec C code implements gradient descent really weirdly
  191. Arthur Whitney: dense code
  192. How does one work with arrays in a linear language?
  193. Linear optimisation is the same as linear feasibility checking
  194. Quantum computation without complex numbers
  195. Linguistic fun fact: Comparative Illusion
  196. Long-form posts:
  197. Big list of emacs gripes
  198. Big list of Coq
  199. Big list of writing
  200. Big list of Latex
  201. Big list of Architecture
  202. Big list of Recipes
  203. Big list of history
  204. Big list of words
  205. Big list of Music
  206. Big list of Social Science