# mathematics

- A High-Level Technical Overview of Fully Homomorphic Encryption
- Tabletop Games Based on Math Problems
- MLIR — A Global Optimization and Dataflow Analysis
- MLIR — Lowering through LLVM
- MLIR — Dialect Conversion
- Socks, a matching game based on an additive combinatorics problem
- MLIR — Canonicalizers and Declarative Rewrite Patterns
- Encoding Schemes in FHE
- MLIR — Verifiers
- MLIR — Folders and Constant Propagation
- MLIR — Using Traits
- Computing Percentages Easier
- MLIR — Defining a New Dialect
- MLIR — Using Tablegen for Passes
- MLIR — Writing Our First Pass
- MLIR — Running and Testing a Lowering
- MLIR — Getting Started
- Two's Complement and Group Theory
- Sample Extraction from RLWE to LWE
- Estimating the Security of Ring Learning with Errors (RLWE)
- Negacyclic Polynomial Multiplication
- Polynomial Multiplication Using the FFT
- Carnival of Mathematics #209
- Key Switching in LWE
- Modulus Switching in LWE
- "Practical Math" Preview: Collect Sensitive Survey Responses Privately
- The Gadget Decomposition in FHE
- Group Actions and Hashing Unordered Multisets
- Carnival of Mathematics #197
- Searching for RH Counterexamples — Exploring Data
- Regression and Linear Combinations
- Searching for RH Counterexamples — Scaling Up
- Searching for RH Counterexamples — Performance Profiling
- Searching for RH Counterexamples — Deploying with Docker
- Optimization Models for Subset Cover
- Searching for RH Counterexamples — Unbounded Integers
- Searching for RH Counterexamples — Adding a Database
- Searching for RH Counterexamples — Setting up Pytest
- Taylor Series and Accelerometers
- Silent Duels—Parsing the Construction
- Visualizing an Assassin Puzzle
- A parlor trick for SET
- Earthmover Distance
- NP-hard does not mean hard
- Binary Search on Graphs
- Formulating the Support Vector Machine Optimization Problem
- The Inner Product as a Decision Rule
- Bayesian Ranking for Rated Items
- The Reasonable Effectiveness of the Multiplicative Weights Update Algorithm
- Zero Knowledge Proofs for NP
- Zero Knowledge Proofs — A Primer
- Singular Value Decomposition Part 2: Theorem, Proof, Algorithm
- Singular Value Decomposition Part 1: Perspectives on Linear Algebra
- Tensorphobia and the Outer Product
- Concrete Examples of Quantum Gates
- Hashing to Estimate the Size of a Stream
- Load Balancing and the Power of Hashing
- The Inequality
- A Quasipolynomial Time Algorithm for Graph Isomorphism: The Details
- Serial Dictatorships and House Allocation
- One definition of algorithmic fairness: statistical parity
- The Boosting Margin, or Why Boosting Doesn't Overfit
- The Welch-Berlekamp Algorithm for Correcting Errors in Data
- The Čech Complex and the Vietoris-Rips Complex
- What does it mean for an algorithm to be fair?
- Methods of Proof — Diagonalization
- The Many Faces of Set Cover
- Markov Chain Monte Carlo Without all the Bullshit
- Finding the majority element of a stream
- A Proofless Introduction to Information Theory
- Zero-One Laws for Random Graphs
- The Quantum Bit
- A Motivation for Quantum Computing
- Making Hybrid Images
- Linear Programming and Healthy Diets — Part 1
- A problem that is not (properly) PAC-learnable
- Stable Marriages and Designing Markets
- Martingales and the Optional Stopping Theorem
- (Finite) Fields — A Primer
- On Coloring Resilient Graphs
- Simulating a Biased Coin with a Fair Coin
- Elliptic Curves as Elementary Equations
- Simulating a Fair Coin with a Biased Coin
- Fixing Bugs in "Computing Homology"
- Probably Approximately Correct — a Formal Theory of Learning
- The Two-Dimensional Fourier Transform and Digital Watermarking
- Adversarial Bandits and the Exp3 Algorithm
- Optimism in the Face of Uncertainty: the UCB1 Algorithm
- Guest Post: Torus-Knotted Baklava
- Rings — A Second Primer
- Universal Properties
- Properties of Morphisms
- Categories as Types
- Rings — A Primer
- Categories, What's the Point?
- Probabilistic Bounds — A Primer
- A Sample of Standard ML, the TreeSort Algorithm, and Monoids
- Homology Theory — A Primer
- Conditional (Partitioned) Probability — A Primer
- Methods of Proof — Induction
- Seam Carving for Content-Aware Image Scaling
- Methods of Proof — Contradiction
- Methods of Proof — Direct Implication
- k-Means Clustering and Birth Rates
- Depth- and Breadth-First Search
- The Fundamental Group — A Primer
- Probability Theory — A Primer
- Groups — A Second Primer
- Groups — A Primer
- Decision Trees and Political Party Classification
- Trees—A Primer
- K-Nearest-Neighbors and Handwritten Digit Classification
- Metric Spaces — A Primer
- Dynamic Time Warping for Sequence Comparison
- The Fast Fourier Transform
- Principal Component Analysis
- The Discrete Fourier Transform — A Primer
- Streaming Median
- Thoughts after a Year of Math ∩ Programming
- The Fourier Transform — A Primer
- Double Angle Trigonometric Formulas
- False Proof – 2 = 4, As the Limit of an Infinite Power Tower
- The Fourier Series—A Primer
- Kolmogorov Complexity—A Primer
- Classic Nintendo Games are NP-Hard
- Learning Programming — Finger-Painting and Killing Zombies
- Fundamental Theorem of Algebra (With Picard's Little Theorem)
- Cryptanalysis with N-Grams
- The Fundamental Theorem of Algebra (with Galois Theory)
- Handshake Lemma
- Word Segmentation, or Makingsenseofthis
- Numerical Integration
- Row Reduction Over A Field
- Metrics on Words
- Holidays and Homicide
- Z[√2] has Infinitely Many Units
- The Smallest Non-Cyclic Simple Group has Order 60
- The Square Root of 2 is Irrational (Geometric Proof)
- The Perceptron, and All the Things it Can't Perceive
- Number Theory—A Primer
- Encryption & RSA
- False Proof—All Numbers are Describable in at Most Twenty Words
- Eigenfaces, for Facial Recognition
- Inner Product Spaces—A Primer
- Hunting Serial Killers
- False Proof—The Reals are Countable
- Graph Coloring, or Proof by Crayon
- Optimally Stacking the Deck—Kicsi Poker
- Set Theory—A Primer
- False Proof—31.5 = 32.5
- False Proof—There are Finitely Many Primes
- False Proof—1 = 2
- Geometric Series with Geometric Proofs
- Turing Machines—A Primer
- Determinism and Finite Automata—A Primer
- Turing Machines and Conway's Dreams
- The Wild World of Cellular Automata
- Tiling a Chessboard
- Teaching Mathematics—Graph Theory
- Area of a Triangle
- Sums of the first n numbers, squares
- The Party Problem
- Number of Games in a Tournament
- Google's Page Rank—The Final Product
- Featured Posts
- Linear Algebra—A Primer
- Google's PageRank—A First Attempt
- Big-O Notation—A Primer
- Well Orderings and Search
- Prime Design