← Higher Math: Discrete Mathematics

⇄ Sync
Length

Program
History and progress transfer
Choose a topic — problems will keep coming one after another for as long as you like

Theory of all steps of the program by blocks. Open a topic to read it.

How a session goes

A session is 10–90 minutes: a warm-up on what you've learned, new steps with short theory and problems, practice. Each problem gives two tries: 100 points on the first, 60 on the second; after the second mistake the correct answer is shown. You move on in the program if 70 % of the problems are solved.

Problems with numbers are generated anew every time a step is repeated. A fractional answer can be entered with a comma, a point or as a fraction: 0,5, 0.5, 1/2. In Practice any topic is available without a timer.

About the course

Relations, functions and cardinality, inclusion–exclusion, combinations with repetition and the binomial theorem, recurrences and generating functions, Boolean functions (DNF, CNF, completeness), graphs: connectivity, trees, Euler circuits, Dijkstra, spanning trees, coloring; modular arithmetic, the Euclidean algorithm, Fermat's theorem and the idea of RSA.

Course program: 35 lessons

Relations, functions, cardinality

  1. Relations and their properties
  2. Equivalence and order
  3. Injection, surjection, bijection
  4. Functions: more
  5. Cardinality of sets
  6. Checkpoint: relations and functions

Combinatorics

  1. Inclusion–exclusion principle
  2. Inclusion–exclusion: more
  3. Combinations with repetition
  4. The binomial theorem
  5. Checkpoint: combinatorics

Recurrence relations

  1. Recurrence relations
  2. The characteristic equation
  3. Recurrences: more
  4. Generating functions (overview)
  5. Checkpoint: recurrence relations

Boolean functions

  1. Boolean functions and tables
  2. DNF and CNF
  3. Completeness (overview)
  4. Checkpoint: Boolean functions

Graphs

  1. Graphs and vertex degrees
  2. Paths, connectivity, trees
  3. Euler and Hamiltonian cycles
  4. Shortest path: Dijkstra
  5. Minimum spanning tree
  6. Graphs: more
  7. Coloring and bipartite graphs
  8. Checkpoint: graphs

Number theory

  1. Remainders and modular arithmetic
  2. GCD and the Euclidean algorithm
  3. Congruences
  4. Congruences: more
  5. Fermat's little theorem
  6. The idea of RSA
  7. Checkpoint: number theory