Queen of the Sciences RU
Queen of the Sciences

Chapters

Introduction

  1. 0 Start

I Numbers

  1. 1 Counting
  2. 2 Zero and minus
  3. 3 Primes
  4. 4 Divisibility
  5. 5 Fractions
  6. 6 Root two

II Algebra

  1. 7 Letters
  2. 8 Equations
  3. 9 Functions and graphs
  4. 10 Quadratic equations
  5. 11 Systems and inequalities
  6. 12 Powers and logarithms
  7. 13 Sequences
  8. 14 Polynomials
  9. 15 Complex numbers

III Geometry

  1. 16 Euclid
  2. 17 Triangle
  3. 18 Pythagoras
  4. 19 Circle and π
  5. 20 Area and volume
  6. 21 Trigonometry
  7. 22 Vectors
  8. 23 Symmetry
  9. 24 Conics

IV Calculus

  1. 25 Limits
  2. 26 Derivative
  3. 27 Extrema
  4. 28 Integral
  5. 29 The number e
  6. 30 Series
  7. 31 Differential equations
  8. 32 Several variables
  9. 33 Fourier
  10. 34 Complex analysis

V Linear algebra

  1. 35 Matrices
  2. 36 Elimination
  3. 37 Vector spaces
  4. 38 Eigenvectors
  5. 39 Least squares, SVD

VI Structures

  1. 40 Groups
  2. 41 Modular and ciphers
  3. 42 Rings and fields
  4. 43 Galois theory
  5. 44 Zeta and curves

VII Chance & data

  1. 45 Combinatorics
  2. 46 Graphs
  3. 47 Probability
  4. 48 Random variables
  5. 49 Statistics
  6. 50 Markov chains

VIII Foundations

  1. 51 Logic and sets
  2. 52 Infinities
  3. 53 Real analysis
  4. 54 Measure
  5. 55 Functional analysis
  6. 56 Gödel and Turing

IX Horizons

  1. 57 Topology
  2. 58 Non-Euclidean geometry
  3. 59 Chaos and fractals
  4. 60 The frontier