Knowledge Subdomain Lister

Arithmetic is a branch of mathematics that deals with the study of numbers, their properties, and their operations. Here is a comprehensive list of all known relevant subdomains within the Arithmetic knowledge domain: Number theory: The study of properties and relationships between numbers, including prime numbers, divisibility, and factorization. Whole numbers: The set of natural numbers and zero, including basic arithmetic operations such as addition, subtraction, multiplication, and division. Fractions: Numbers expressed as a ratio of two integers, including operations such as addition, subtraction, multiplication, and division. Decimals: Numbers expressed in base ten with digits after the decimal point, including operations such as addition, subtraction, multiplication, and division. Percentages: A special type of fraction in which the denominator is 100, used to express proportions and ratios. Ratio and proportion: The comparison of two quantities, often expressed as a fraction or decimal, including solving problems involving direct and inverse proportionality. Integers: The set of whole numbers and their negatives, including operations such as addition, subtraction, multiplication, and division. Rational numbers: Numbers that can be expressed as a ratio of two integers, including fractions and terminating decimals. Irrational numbers: Numbers that cannot be expressed as a ratio of two integers, including non-terminating decimals and numbers such as pi and e. Real numbers: The set of all rational and irrational numbers, including basic arithmetic operations and properties such as ordering and absolute value. Complex numbers: Numbers of the form a + bi, where a and b are real numbers and i is the imaginary unit, including operations such as addition, subtraction, multiplication, and division. Modular arithmetic: A system of arithmetic in which numbers "wrap around" after a certain value, including operations such as addition, subtraction, multiplication, and division. Order of operations: Rules for evaluating arithmetic expressions involving multiple operations, including parentheses, exponents, multiplication, division, addition, and subtraction. Basic properties of numbers: Properties such as commutativity, associativity, distributivity, and the identity and inverse properties of addition and multiplication. Prime numbers: Positive integers greater than 1 that have no positive integer divisors other than 1 and themselves, including properties such as the prime factorization theorem and the distribution of primes. Divisibility: The ability of one number to be divided exactly by another number, including properties such as the divisibility rules for small integers and the Euclidean algorithm for finding the greatest common divisor. Greatest common divisor: The largest positive integer that divides two or more numbers without remainder, including properties such as the Euclidean algorithm and Bézout's identity. Least common multiple: The smallest positive integer that is a multiple of two or more numbers, including properties such as the prime factorization theorem and the Euclidean algorithm. Diophantine equations: Equations in which the variables must be integers, including techniques for solving linear and quadratic Diophantine equations. Sequences and series: The study of ordered lists of numbers and the sums of their terms, including properties such as arithmetic and geometric progressions and the sum formulae for finite series. Logarithms: The inverse of exponentiation, used to solve exponential equations and simplify expressions, including properties such as the laws of logarithms and change of base formula. Exponents: The shorthand notation for repeated multiplication of a number by itself, including properties such as the laws of exponents and negative and fractional exponents. Radicals: The notation for expressing roots of numbers, including properties such as simplification and operations such as addition, subtraction, multiplication, and division. Arithmetic functions: Functions that operate on integers, including properties such as the Möbius function Combinatorics: The study of counting and arranging objects, including basic principles such as permutations and combinations. Probability: The study of randomness and chance, including concepts such as independent and dependent events, conditional probability, and expected value. Statistics: The study of collecting, analyzing, and interpreting data, including concepts such as measures of central tendency, variability, and correlation. Cryptography: The study of secret codes and ciphers, including concepts such as modular arithmetic, prime factorization, and the RSA algorithm. Number systems: The study of different bases and number systems, including binary, octal, hexadecimal, and other positional notation systems. Number patterns: The study of recurring sequences of numbers, including concepts such as Fibonacci numbers, Pascal's triangle, and the Catalan numbers. Diophantine approximation: The study of approximating irrational numbers by rational numbers, including concepts such as continued fractions and the best rational approximations. Arithmetic geometry: The study of the relationship between number theory and geometry, including concepts such as elliptic curves and modular forms. Analytic number theory: The study of number theory using techniques from analysis, including concepts such as the Riemann zeta function and the prime number theorem. Computational number theory: The study of number theory using computational methods, including algorithms for prime factorization, discrete logarithms, and elliptic curve cryptography. Algebraic number theory: The study of number theory using algebraic techniques, including concepts such as algebraic integers, ideals, and class groups. Arithmetic coding: A method of data compression that uses arithmetic operations instead of fixed-length codes, including concepts such as Huffman coding and Lempel-Ziv-Welch coding. Arithmetic logic units (ALUs): The components of a computer's central processing unit (CPU) that perform arithmetic and logical operations on binary numbers. Note that this list is not exhaustive and there may be other relevant subdomains within the Arithmetic knowledge domain that are not included here.