OPEN BETAWe're actively improving! Report issues or share suggestions

Home Courses Formula Sheets About

Stay sharp. Stay curious.

Get free formula sheets, course updates, and math tips in your inbox.

Axiom Academyin partnership with BriTheMathGuy

Making math accessible and enjoyable through interactive lessons, engaging explanations, and a passion for teaching.

Learn

All Courses
Formula Sheets
Achievements

Test Prep

SAT Math
ACT Math
GRE Quant
AP Calculus

Company

About
Contact
What's New

Legal

Privacy Policy
Terms of Service

© 2026 Axiom Academy. All rights reserved.

Built with love for math.

Home
Courses
Discrete Mathematics

∀∃

Discrete Mathematics

Logic, sets, combinatorics, graphs, and algorithm analysis

190Modules

11Units

1

Logic and Proofs

Master logic and proofs

17 modules

The Language of LogicINTRO

Detective's DeductionINTRO

Propositions and ConnectivesLESSON

Logical Equivalence PracticePRACTICE

Truth Table ConstructorPRACTICE

Valid ArgumentsLESSON

Proving an Argument ValidEXAMPLE

Inference Rule MatcherPRACTICE

Building Mathematical ArgumentsLESSON

Proving √2 is IrrationalEXAMPLE

Proof WorkshopPRACTICE

Mathematical InductionLESSON

Digital Circuit DesignerLESSON

Evaluating (p → q) ∧EXAMPLE

Logic and Proofs SummaryLESSON

Logic and Proofs ReferenceFORMULA SHEET

Propositional Logic AssessmentQUIZ

2

Set Theory

Master set theory

15 modules

Organizing CollectionsINTRO

Set FundamentalsLESSON

Set Operations VisualizerPRACTICE

Set Operations PracticePRACTICE

Algebraic Properties of SetsLESSON

Proving A ∩ (B ∪ C) = (A ∩ B) ∪EXAMPLE

Set Proof BuilderPRACTICE

Power Sets and ProductsLESSON

Computing PEXAMPLE

Database Queries as SetsLESSON

Finding A ∪EXAMPLE

Relation ExplorerPRACTICE

Set Theory SummaryLESSON

Set Theory ReferenceFORMULA SHEET

Set Theory AssessmentQUIZ

3

Relations and Functions

Master relations and functions

15 modules

Connecting ElementsINTRO

Relations as SetsLESSON

Analyzing a Divisibility RelationEXAMPLE

Relation Property CheckerPRACTICE

Equivalence RelationsLESSON

Functions as Special RelationsLESSON

Testing Injectivity and SurjectivityEXAMPLE

Function MapperPRACTICE

Function CompositionLESSON

Composition and Inverse LabPRACTICE

Cryptography and BijectionsLESSON

Finding Inverse FunctionsEXAMPLE

Functions SummaryLESSON

Functions and Relations ReferenceFORMULA SHEET

Relations and Functions AssessmentQUIZ

4

Combinatorics

Master combinatorics

19 modules

The Art of CountingINTRO

Fundamental Counting PrinciplesLESSON

License Plate PossibilitiesEXAMPLE

Advanced Counting ProblemsPRACTICE

Counting ScenariosPRACTICE

Order Matters vs. Order Doesn't MatterLESSON

Selecting a CommitteeEXAMPLE

Arrangement VisualizerPRACTICE

Circular PermutationsLESSON

The Binomial TheoremLESSON

Expanding (2x - 3)⁵EXAMPLE

Pascal's Triangle ExplorerPRACTICE

Password Strength AnalyzerLESSON

Lottery Odds CalculatorLESSON

Probability and CountingLESSON

Tournament BracketsLESSON

Combinatorics SummaryLESSON

Combinatorics ReferenceFORMULA SHEET

Combinatorics AssessmentQUIZ

5

Graph Theory

Master graph theory

24 modules

Networks EverywhereINTRO

Graph FundamentalsLESSON

Analyzing the Petersen GraphEXAMPLE

Graph Properties PracticePRACTICE

Graph Builder LaboratoryPRACTICE

Social Network AnalysisLESSON

Spanning TreesLESSON

Binary Search TreesLESSON

Minimum Spanning TreesLESSON

Shortest Path AlgorithmsLESSON

Finding Shortest RouteEXAMPLE

Algorithm RacePRACTICE

Internet Routing SimulatorLESSON

Network FlowLESSON

Decision Tree OptimizerLESSON

Hamiltonian CircuitsEXAMPLE

Depth-First vs. Breadth-FirstEXAMPLE

Graph ColoringPRACTICE

Graph Algorithms LabPRACTICE

Traversal AnimatorPRACTICE

Planar GraphsLESSON

Graph Theory SummaryLESSON

Graph Theory ReferenceFORMULA SHEET

Graph Theory AssessmentQUIZ

6

Number Theory

Master number theory

19 modules

Factors and MultiplesINTRO

Clock ArithmeticINTRO

Division AlgorithmLESSON

The Euclidean AlgorithmEXAMPLE

Divisibility PatternsPRACTICE

GCD Calculator WorkshopPRACTICE

The Building BlocksLESSON

Testing PrimalityEXAMPLE

Prime ExplorerPRACTICE

Congruences and ResiduesLESSON

Solving 7x ≡ 3EXAMPLE

Modular Arithmetic LabPRACTICE

Fermat's Little TheoremLESSON

Calendar CalculationsLESSON

RSA EncryptionLESSON

Number Theory ChallengesPRACTICE

Number Theory SummaryLESSON

Number Theory ReferenceFORMULA SHEET

Number Theory AssessmentQUIZ

7

Boolean Algebra

Master boolean algebra

18 modules

Switches and SignalsINTRO

Boolean Operations and LawsLESSON

Simplifying Boolean ExpressionsEXAMPLE

Logic Gate FundamentalsLESSON

Circuit MinimizerPRACTICE

Karnaugh MapsLESSON

Minimizing a 4-Variable FunctionEXAMPLE

Combinational Circuit DesignLESSON

Seven-Segment Display DriverLESSON

Memory ElementsLESSON

Designing a CounterEXAMPLE

State Machine DesignerPRACTICE

Memory and RegistersLESSON

CPU Control UnitLESSON

Digital Logic PracticePRACTICE

Boolean Algebra SummaryLESSON

Digital Logic ReferenceFORMULA SHEET

Boolean Algebra AssessmentQUIZ

8

Discrete Probability

Master discrete probability

21 modules

Updating BeliefsINTRO

Games of ChanceINTRO

Probability SpacesLESSON

Rolling Two DiceEXAMPLE

Basic Probability PracticePRACTICE

Probability CalculatorPRACTICE

Conditional Probability and IndependenceLESSON

The Monty Hall ProblemEXAMPLE

Conditional Probability LabPRACTICE

Bayes' TheoremLESSON

Disease Testing AnalysisLESSON

From Outcomes to NumbersLESSON

Expected Value in GamesLESSON

Analyzing Binomial DistributionEXAMPLE

Probability Distributions PracticePRACTICE

Distribution ExplorerPRACTICE

Indicator Random VariablesLESSON

Monte Carlo MethodsLESSON

Discrete Probability SummaryLESSON

Probability ReferenceFORMULA SHEET

Discrete Probability AssessmentQUIZ

9

Recurrence Relations

Master recurrence relations

20 modules

Patterns in SequencesINTRO

Recurrence Relations FundamentalsLESSON

Modeling Compound InterestEXAMPLE

Recurrence Modeling PracticePRACTICE

Sequence GeneratorPRACTICE

Characteristic Equation MethodLESSON

Solving Fibonacci RecurrenceEXAMPLE

Recurrence SolverPRACTICE

Non-Homogeneous RecurrencesLESSON

Generating FunctionsLESSON

Catalan NumbersEXAMPLE

Generating Function LabPRACTICE

Divide and Conquer RecurrencesLESSON

Merge Sort AnalysisEXAMPLE

Tower of HanoiLESSON

Dynamic ProgrammingLESSON

Advanced Recurrences PracticePRACTICE

Recurrences SummaryLESSON

Recurrences ReferenceFORMULA SHEET

Recurrence Relations AssessmentQUIZ

10

Algorithm Analysis

Master algorithm analysis

19 modules

Racing AlgorithmsINTRO

Big-O NotationLESSON

Analyzing Nested LoopsEXAMPLE

Complexity Analysis PracticePRACTICE

Search Algorithm ShowdownLESSON

Sorting Algorithm VisualizerPRACTICE

Algorithm Efficiency ComparisonLESSON

Lower BoundsLESSON

Complexity Theory PracticePRACTICE

Graph Algorithm ComplexityLESSON

Cache-Efficient AlgorithmsLESSON

The P vs NP ProblemLESSON

Traveling Salesman AnalysisEXAMPLE

Reduction DemonstratorPRACTICE

Algorithm Selection GuideLESSON

QuickSort AnalysisEXAMPLE

Algorithm Analysis SummaryLESSON

Algorithm Analysis ReferenceFORMULA SHEET

Algorithm Analysis AssessmentQUIZ

11

Course Conclusion

Master course conclusion

3 modules

Bridge to Advanced TopicsLESSON

Master ReferenceFORMULA SHEET

Comprehensive Final ExamQUIZ