Math for Interviews Sheet
The Math for Interviews sheet collects the mathematics that coding interviews actually use: counting and combinatorics, probability and expectation, modular arithmetic, bit manipulation, recurrences and complexity analysis.
The sheet holds 12 patterns and 60 topics, tracked row by row. From any row you can read the theory for a topic, answer knowledge-check questions on it, have the AI coach teach it back to you, keep notes, bookmark a row and mark it done. Progress is saved against your account, so the sheet is also the record of what you have already covered.
Who it is for
It is for candidates who lose questions to the analysis rather than the code — an off-by-one in a combinatorial argument, a probability set up the wrong way, a recurrence solved by guesswork.
How to work through it
Derive each result once by hand before you memorise it. The interview rarely asks the identity directly; it asks a question whose answer collapses the moment you recognise the identity behind it.
Practice runs on the same platform as the sheet: 850+ problems across every track, code execution in 6 languages, and AI mock interviews that follow the pattern you are studying rather than a random question.
What the math for interviews sheet covers
Interview Soon
6 patterns, 30 topics — the ones that come up first
- Counting & Combinatorics — Permutations, Combinations and the Choose Function, Inclusion-Exclusion, Stars and Bars and Distribution Problems, Catalan Numbers and Structural Counting, The Pigeonhole Principle
- Probability Fundamentals — Sample Spaces, Events and the Basic Rules, Conditional Probability and Bayes' Theorem, Expected Value and Linearity of Expectation, Variance, Independence and Covariance, Distributions Worth Recognising
- Modular Arithmetic & Number Theory — Modular Arithmetic Rules and Safe Reduction, GCD, LCM and the Extended Euclidean Algorithm, Primes, Sieves and Factorization, Modular Inverse, Fermat and Fast Exponentiation, Chinese Remainder Theorem and Multiplicative Structure
- Bit Manipulation & Binary Math — Binary Representation and Two's Complement, The Standard Bit Tricks, XOR Properties and Pairing Arguments, Bitmasks and Subset Enumeration, Popcount, Powers of Two and Bit-Length Math
- Complexity, Recurrences & Growth — Asymptotic Notation Done Correctly, Solving Recurrences and the Master Theorem, Amortized Analysis, Logarithms, Growth Rates and Back-of-Envelope Sizing, Summations and Series You Actually Need
- Linear Algebra Essentials — Vectors, Dot Products and Projections, Matrices as Transformations, Matrix Multiplication, Dimensions and Cost, Matrix Exponentiation for Recurrences, Rank, Inverse and Solving Linear Systems
Deep Dive
6 patterns, 30 topics for full coverage
- Randomized Algorithms & Sampling — Random Shuffling and Fisher-Yates, Reservoir Sampling, Randomized Quickselect and Expected Runtime, Weighted Random Selection, Hashing, Collisions and the Birthday Bound
- Statistics & Estimation — Mean, Median, Mode and Robustness, Sampling, Bias and Confidence Intervals, Hypothesis Testing and p-values, Streaming Statistics and Approximate Counting, A/B Testing Math
- Calculus & Optimization — Derivatives and What They Mean Computationally, Gradients, Partial Derivatives and the Chain Rule, Convexity and Why It Matters, Gradient Descent and Learning Rates, Lagrange Multipliers and Constrained Optimization
- Computational Geometry — Points, Vectors and the Cross Product Sign, Line and Segment Intersection, Convex Hull, Area, Centroids and the Shoelace Formula, Closest Pair and Sweep Line
- Numerical Precision & Overflow — Floating Point Representation, Integer Overflow and Safe Arithmetic, Comparing Floats and Choosing Epsilon, Newton's Method and Iterative Roots, Numerical Stability and Catastrophic Cancellation
- Game Theory & Combinatorial Games — Minimax and Game Trees, Nim and the XOR Strategy, Win/Lose State Dynamic Programming, Sprague-Grundy and Game Decomposition, Alpha-Beta Pruning
