Log inSign up
Discrete Math · Lessons

Discrete Math lessons

9 sections · 68 skills · work through the full outline skill by skill — read the long-form lesson or flip through the slide-style version.
Long-form lessonsSlide-style lessons

Discrete Math

Practice 68 skills across this outline.

Recommended next
Translate quantified statements (∀, ∃) into predicate logic
Logic and Proof · Predicate Logic
Long-form lesson
Weighting distribution
19 categories
Recurrence Relations
11%
Counting and Combinatorics · Basic Counting Principles
7%
Problem-Solving & Discrete Modeling · Algorithmic Thinking and Modeling
7%
Discrete Probability · Probability Foundations
6%
Sets, Relations, and Functions · Functions and Growth
6%
Number Theory and Cryptography · Divisibility and Modular Arithmetic
6%

Skills

The comprehensive taxonomy of discrete math — drill into a card to work its skills.

Logic and Proof · Predicate Logic

3 core skills3% total weight
0/3 completed
3 skills to mastery
1
Translate quantified statements (∀, ∃) into predicate logicRecommended
Long-form
2
Determine truth of quantified statements over a domainAvailable
Long-form
3
Negate quantified statements correctlyAvailable
Long-form

Logic and Proof · Propositional Logic

4 core skills4% total weight
0/4 completed
4 skills to mastery
1
Translate statements into propositional logicAvailable
Long-form
2
Identify logical equivalences (De Morgan’s, implication forms)Available
Long-form
3
Use truth tables to evaluate logical expressionsAvailable
Long-form
4
Determine validity of arguments using logical rulesAvailable
Long-form

Logic and Proof · Proof Techniques

5 core skills5% total weight
0/5 completed
5 skills to mastery
1
Proof by casesAvailable
Long-form
2
Direct proof strategy and structureAvailable
Long-form
3
Proof by contrapositiveAvailable
Long-form
4
Proof by contradictionAvailable
Long-form
5
Mathematical induction (basic and strong induction)Available
Long-form

Discrete Probability · Probability Foundations

4 core skills6% total weight
0/4 completed
4 skills to mastery
1
Expected value and variance for discrete random variablesAvailable
Long-form
2
Compute probabilities in finite sample spacesAvailable
Long-form
3
Conditional probability and independenceAvailable
Long-form
4
Bayes’ theorem and applicationsAvailable
Long-form

Discrete Probability · Common Discrete Distributions

3 core skills5% total weight
0/3 completed
3 skills to mastery
1
Geometric and negative binomial distributions (intro)Available
Long-form
2
Binomial distribution and applicationsAvailable
Long-form
3
Poisson distribution and applicationsAvailable
Long-form

Graph Theory · Graph Basics

4 core skills4% total weight
0/4 completed
4 skills to mastery
1
Bipartite graphs and matchings (intro)Available
Long-form
2
Degrees, paths, cycles, and connectivityAvailable
Long-form
3
Planar graphs and Euler’s formula (intro)Available
Long-form
4
Represent graphs (adjacency list/matrix)Available
Long-form

Graph Theory · Trees and Spanning Trees

3 core skills3% total weight
0/3 completed
3 skills to mastery
1
Tree properties and traversal conceptsAvailable
Long-form
2
Kruskal’s and Prim’s algorithms (conceptual)Available
Long-form
3
Spanning trees and minimum spanning trees (intro)Available
Long-form

Graph Theory · Graph Algorithms

3 core skills4% total weight
0/3 completed
3 skills to mastery
1
Network flow concepts (max flow intro)Available
Long-form
2
Shortest path algorithms (BFS/Dijkstra conceptually)Available
Long-form
3
Graph coloring concepts and applicationsAvailable
Long-form

Sets, Relations, and Functions · Set Operations and Counting

4 core skills5% total weight
0/4 completed
4 skills to mastery
1
Set notation and operations (union, intersection, complement)Available
Long-form
2
Inclusion–exclusion principle (intro and applications)Available
Long-form
3
Cartesian products and power setsAvailable
Long-form
4
Venn diagrams and set identitiesAvailable
Long-form

Sets, Relations, and Functions · Functions and Growth

4 core skills6% total weight
0/4 completed
4 skills to mastery
1
Function composition and inversesAvailable
Long-form
2
Functions: injections, surjections, bijectionsAvailable
Long-form
3
Asymptotic notation (Big-O, Big-Theta, Big-Omega)Available
Long-form
4
Comparing growth rates and common function classesAvailable
Long-form

Counting and Combinatorics · Basic Counting Principles

4 core skills7% total weight
0/4 completed
4 skills to mastery
1
Combinations with repetitionAvailable
Long-form
2
Permutations and combinationsAvailable
Long-form
3
Sum and product rulesAvailable
Long-form
4
Binomial theorem and binomial coefficientsAvailable
Long-form

Counting and Combinatorics · Pigeonhole and Advanced Counting

3 core skills4% total weight
0/3 completed
3 skills to mastery
1
Pigeonhole principle and applicationsAvailable
Long-form
2
Counting with inclusion–exclusion (applications)Available
Long-form
3
Counting using recursion (intro)Available
Long-form

Number Theory and Cryptography · Divisibility and Modular Arithmetic

4 core skills6% total weight
0/4 completed
4 skills to mastery
1
Divisibility, gcd, and Euclidean algorithmAvailable
Long-form
2
Chinese remainder theorem (intro)Available
Long-form
3
Solving linear congruences (intro)Available
Long-form
4
Modular arithmetic operations and congruencesAvailable
Long-form

Number Theory and Cryptography · Primes and Cryptography Concepts

3 core skills5% total weight
0/3 completed
3 skills to mastery
1
RSA and public-key cryptography concepts (intro)Available
Long-form
2
Prime numbers and factorization conceptsAvailable
Long-form
3
Modular exponentiation and fast poweringAvailable
Long-form

Problem-Solving & Discrete Modeling · Formal Communication

3 core skills5% total weight
0/3 completed
3 skills to mastery
1
Write clear mathematical arguments and proofsAvailable
Long-form
2
Explain solution steps in a structured wayAvailable
Long-form
3
Use correct notation and definitionsAvailable
Long-form

Problem-Solving & Discrete Modeling · Algorithmic Thinking and Modeling

4 core skills7% total weight
0/4 completed
4 skills to mastery
1
Check solutions and validate reasoningAvailable
Long-form
2
Common pitfalls (miscounting, double counting, invalid assumptions)Available
Long-form
3
Translate word problems into discrete structures (graphs, sets,Available
Long-form
4
Choose an appropriate discrete method to solve a problemAvailable
Long-form

Recurrence Relations

4 core skills11% total weight
0/4 completed
4 skills to mastery
1
Use generating functions conceptually (intro)Available
Long-form
2
Solve linear recurrences with characteristic equations (intro)Available
Long-form
3
Formulate recurrence relations from problemsAvailable
Long-form
4
Solve linear recurrences by iteration/expansionAvailable
Long-form

Relations and Discrete Structures · Boolean Algebra and Logic Circuits

3 core skills5% total weight
0/3 completed
3 skills to mastery
1
Logic gates and circuit simplification (intro)Available
Long-form
2
Karnaugh maps concept (intro)Available
Long-form
3
Boolean algebra identitiesAvailable
Long-form

Relations and Discrete Structures · Relations and Equivalence Classes

3 core skills6% total weight
0/3 completed
3 skills to mastery
1
Determine if a relation is reflexive, symmetric, transitiveAvailable
Long-form
2
Equivalence relations and partitionsAvailable
Long-form
3
Partial orders, Hasse diagrams, and lattices (intro)Available
Long-form