Math for IT

How to use this topic

The first eight pages are the school mathematics that the rest builds on: numbers and number sets, primes and divisors, powers and logarithms, algebra, equations, functions and graphs, and geometry with trigonometry. The next eleven are the mathematics of computing itself: number bases, binary arithmetic, floating point, units, modular arithmetic, logic, sets, counting, probability, statistics and growth rates. Two pages introduce calculus, and the last four apply everything: graphs and trees, vectors and matrices, cryptography, and error detection and correction.

Every calculation is also shown as a short Python program with its exact output, so you can check the math by running it. Pages 2 to 8 and the two calculus pages, together with the sets and sequences pages, cover the topics of Basiskennis wiskunde voor informatica, the basic mathematics that the Dutch Open Universiteit expects from students starting its bachelor's degree in computer science.

Learning path

1. 01Why Math Matters in ITWhere mathematics turns up in IT work, from subnets and storage to AI and cryptography, and how to read formulas and mathematical notation.Beginner
2. 02Numbers and Number SetsNatural numbers, integers, rationals and reals, the order of operations, fractions, percentages, rounding and scientific notation.Beginner
3. 03Divisibility, Primes, GCD and LCMDivisors and multiples, prime numbers and prime factorization, the greatest common divisor with Euclid's algorithm, and the least common multiple.Beginner
4. 04Powers, Roots and LogarithmsExponents and their rules, square roots and other roots, logarithms and why base 2 is everywhere in computing, and thinking in orders of magnitude.Beginner
5. 05Algebra: Expressions and FactoringWorking with variables: the rules of algebra, expanding and factoring, special products, and fractions, roots and logarithms that contain variables.Beginner
6. 06Equations and InequalitiesSolving linear and quadratic equations, the quadratic formula, exponential and logarithmic equations, systems of two equations, and inequalities with intervals.Intermediate
7. 07Functions and GraphsWhat a function is, domain and range, linear, quadratic, exponential, logarithmic and other basic functions, composing, shifting and inverting functions, and reading their graphs.Intermediate
8. 08Geometry and TrigonometryPoints, lines and angles, the Pythagorean theorem, degrees and radians, sine, cosine and tangent, and distances in two and more dimensions.Intermediate
9. 09Number Bases and ConversionPositional number systems, converting between decimal, binary, octal and hexadecimal, and binary fractions.Beginner
10. 10Binary Arithmetic and Bitwise OperationsAdding and subtracting in binary, two's complement for negative numbers, overflow, shifts, and AND, OR, XOR and masks as used in subnetting and permissions.Intermediate
11. 11Floating-Point NumbersHow computers store real numbers in IEEE 754 format, why 0.1 + 0.2 is not exactly 0.3, rounding errors, special values and when to use decimals instead.Intermediate
12. 12Units, Prefixes and Data SizesBits and bytes, decimal and binary prefixes such as kB and KiB, bandwidth and transfer times, and converting units without mistakes.Beginner
13. 13Modular ArithmeticCalculating with remainders: the mod operation, congruence, clock arithmetic, and its uses in hashing, check digits such as IBAN and Luhn, and scheduling.Intermediate
14. 14Logic and Boolean AlgebraPropositions and connectives, truth tables, the laws of Boolean algebra including De Morgan's laws, implication, and simplifying conditions in code and networks.Beginner
15. 15Sets and RelationsSets and their notation, union, intersection and difference, Venn diagrams and SQL joins, Cartesian products, and relations with their properties.Intermediate
16. 16Counting and CombinatoricsCounting possibilities: the product rule, permutations and combinations, factorials, password and key spaces, and the pigeonhole principle.Intermediate
17. 17ProbabilityProbability rules, independent and dependent events, conditional probability and Bayes' theorem, expected value, and the birthday paradox applied to IT.Intermediate
18. 18Statistics for ITDescribing data: mean, median and percentiles such as p95 latency, spread and standard deviation, distributions, outliers, and correlation versus causation.Intermediate
19. 19Sequences, Sums and Growth RatesArithmetic and geometric sequences, sigma notation and series, exponential growth and halving, and how growth rates lead to Big-O notation.Intermediate
20. 20Derivatives and Rates of ChangeAverage and instantaneous rates of change, the derivative as the slope of a tangent line, standard derivatives and differentiation rules, and gradient descent in machine learning.Advanced
21. 21Integrals and AccumulationAntiderivatives and the definite integral as area under a curve, the basic integration rules, and adding up rates over time, such as energy from power.Advanced
22. 22Graphs and TreesVertices and edges, paths and connectivity, shortest paths as in OSPF, trees and spanning trees as in Spanning Tree Protocol, and directed acyclic graphs for dependencies.Intermediate
23. 23Vectors and MatricesVectors, length and dot product, cosine similarity as used for AI embeddings, matrices and matrix multiplication, and transformations.Advanced
24. 24The Math Behind CryptographyPrime numbers, modular exponentiation and inverses, and how RSA and Diffie-Hellman work, shown with small numbers, plus why hash functions and key sizes matter.Advanced
25. 25Error Detection and CorrectionParity bits, checksums and CRCs, Hamming codes that correct errors, and XOR parity in RAID, with the math that makes them work.Intermediate

Math for IT glossary

Short definitions of the terms used in this topic. The full glossary covers every topic.