Queen of the Sciences RU

Queen of the Sciences

Practice

Problems from every chapter of the course. The generator makes up fresh ones every time, accepts any correct form of the answer and shows a worked solution when you get stuck.

Introduction

Chapter 0 · What mathematics is

Hunting for counterexamplesOpenCollapse
Chords and pieces of a circleOpenCollapse

Numbers

Chapter 1 · Counting: from notches to bits

Converting between basesOpenCollapse

Chapter 2 · Zero and minus

Working with integersOpenCollapse

Chapter 3 · Prime numbers

Breaking numbers into prime factorsOpenCollapse

Chapter 4 · Divisibility and Euclid's algorithm

GCD, LCM and Euclid's algorithmOpenCollapse

Chapter 5 · Fractions

Working with fractionsOpenCollapse
Repeating decimalsOpenCollapse

Chapter 6 · Root two and the real numbers

Rational or irrational?OpenCollapse

Algebra

Chapter 7 · Letters for numbers

Expanding brackets and factoringOpenCollapse

Chapter 8 · Equations: the art of balance

Solving linear equationsOpenCollapse

Chapter 9 · Functions and graphs

Reading graphsOpenCollapse

Chapter 10 · Quadratic equations

Solving quadratic equationsOpenCollapse

Chapter 11 · Systems of equations and inequalities

Systems of two equationsOpenCollapse

Chapter 12 · Powers and logarithms

Powers and logarithmsOpenCollapse

Chapter 13 · Sequences and induction

ProgressionsOpenCollapse

More practice

These practice sets are ready; the chapters they belong to are still being written.

Angle excess and defectOpenCollapse
Antiderivatives and integralsOpenCollapse
Areas and volumesOpenCollapse
How many: countable or the continuumOpenCollapse
Angles and lengths in a circleOpenCollapse
Complex numbersOpenCollapse
Conic sections from their equationsOpenCollapse
Compass, straightedge and powers of twoOpenCollapse
Counting the waysOpenCollapse
DerivativesOpenCollapse
Differential equationsOpenCollapse
Eigenvalues and eigenvectorsOpenCollapse
Adding points on an elliptic curveOpenCollapse
Entropy, codes and chainsOpenCollapse
Euler characteristicOpenCollapse
ExtremaOpenCollapse
Gödel numbers, MIU and Turing machinesOpenCollapse
Fourier coefficientsOpenCollapse
Fractal dimensionOpenCollapse
Graph problemsOpenCollapse
The Hamming (7, 4) codeOpenCollapse
Projections and least squaresOpenCollapse
Computing limitsOpenCollapse
Tables, negations and islandersOpenCollapse
The logistic mapOpenCollapse
Matrices and vectorsOpenCollapse
Measures and Lebesgue integralsOpenCollapse
Modular arithmeticOpenCollapse
Norms, inner products and contractionsOpenCollapse
Partial derivatives and the gradientOpenCollapse
PermutationsOpenCollapse
Polynomial division and rootsOpenCollapse
Computing probabilitiesOpenCollapse
Pythagoras’ theoremOpenCollapse
Random variablesOpenCollapse
Gaussian eliminationOpenCollapse
SeriesOpenCollapse
Statistics: averages, margins, testsOpenCollapse
Subset sumOpenCollapse
Supremum and infimumOpenCollapse
The triangleOpenCollapse
Sines, cosines and trianglesOpenCollapse
VectorsOpenCollapse
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