09Mathematics162–271Chapter overviewOverviewIntroduction to the mathematics section162Boolean Algebra167Bit operations168Bitwise Set Operations169High-Precision Computation170Fast Exponentiation171Permutations and arrangements172Radians and Coordinate Systems173Complex Numbers268Order theory269Young Tableau270Matroid271Berlekamp–Massey AlgorithmNumeral Systems163Introduction to Numeral Systems164Positional Numeral System165Balanced Ternary166Gray codeNumber Theory174Basic Number Theory175Introduction to Modular Arithmetic176Prime177Greatest common divisor178Euler's Totient Function179Sieve Methods180Prime factorization181Bezout's Lemma & Linear Diophantine Equations182Fermat's Little Theorem & Euler's Theorem183Modular Multiplicative Inverse184Linear Congruence Equation185Chinese Remainder Theorem186Lifting the Exponent Lemma187Factorial Modulo188Lucas Theorem189Congruence Equations190Quadratic residues191Order & Primitive Roots192Discrete Logarithm193Higher-Order Residues & Roots of Unity194Number-Theoretic Block Decomposition195Dirichlet Convolution196Möbius Inversion197Du Sieve198Powerful Number Sieve199Min_25 sieve200Zhou Sieve201Euclidean-like Algorithm202Meissel–Lehmer Algorithm203Continued fraction204Stern–Brocot Trees and Farey Sequences205Quadratic Fields206Pell EquationPolynomials and Generating Functions207Introduction to Polynomials and Generating Functions208Fundamental Theorem of Algebra209Fast Fourier Transform210Number-Theoretic Transform211Fast Walsh Transform212Chirp Z transform213Polynomial Newton iteration214Polynomial Multipoint Evaluation and Fast Interpolation215Elementary Polynomial Functions216Constant-coefficient Homogeneous Linear Recurrences217Polynomial Shift | Continuous Point-Value Shift218Symbolic Method219Lagrange Inversion220Formal Power Series Composition and Compositional Inverse221Ordinary Generating Function222Exponential Generating FunctionsCombinatorics223Permutations and Combinations224pigeonhole principle225Inclusion–Exclusion Principle226The Fibonacci Sequence227Derangements228Catalan Numbers229Stirling Numbers230Bell Numbers231Bernoulli Numbers232Entringer Number233Eulerian Numbers234Partition Numbers235Vandermonde's convolution236Pólya Enumeration237Graph EnumerationLinear AlgebraOverviewAn Introduction to Linear Algebra238Vectors239Inner and Outer Products240Matrix241Elementary transformations242Determinant243Linear Space244Linear Basis245Linear Mapping246Characteristic Polynomial247Diagonalization248Jordan canonical formLinear Programming249WQS binary search250Simplex MethodAbstract Algebra251Basic concepts252Group theory253Ring Theory254Field Theory255Schreier–Sims algorithmProbability Theory256Basic concepts257Conditional Probability and Independence258Random Variables259Numerical Characteristics of Random Variables260Probability InequalitiesGame Theory261Introduction to Game Theory262Impartial Combinatorial Games263Zero-Sum GameNumerical Algorithms264Interpolation265Numerical Integration266Gaussian Elimination267Newton's Method