Log inSign up
Math

Discrete Math

Get personalized support from expert tutors and AI-powered study tools.

Personalized practice Exam · Set a test date 9 units · 68 topics
Generate study planExplore skills
Your study plan
Free with a Varsity Tutors account
Free
Turn this Discrete Math outline into a plan
A week-by-week plan
Paced to your test date and rebuilt whenever your Discrete Math scores move.
A score projection
See where you stand today and what each study block is worth.
Progress that sticks
Lessons, flashcards, and quizzes tracked in one place, on every device.
Create your free plan
Takes a minute · No credit card required
Your next tutoring session · Discrete Math prep Ready when you are
No upcoming Discrete Math tutoring session scheduled
Book a tutoring session when you are ready to work with an expert.
Book a tutor

Ways to study

Subject resources
Long-form
Long-form Lessons
Open lessons
1,041 questions
Quizzes
Take a quiz
1 test
Full-length Practice Tests
Start a test

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
25 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
2
Determine truth of quantified statements over a domainAvailable
19 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
3
Negate quantified statements correctlyAvailable
22 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems

Logic and Proof · Propositional Logic

4 core skills4% total weight
0/4 completed
4 skills to mastery
1
Translate statements into propositional logicAvailable
23 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
2
Identify logical equivalences (De Morgan’s, implication forms)Available
24 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
3
Use truth tables to evaluate logical expressionsAvailable
19 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
4
Determine validity of arguments using logical rulesAvailable
23 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems

Logic and Proof · Proof Techniques

5 core skills5% total weight
0/5 completed
5 skills to mastery
1
Proof by casesAvailable
23 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
2
Direct proof strategy and structureAvailable
23 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
3
Proof by contrapositiveAvailable
22 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
4
Proof by contradictionAvailable
21 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
5
Mathematical induction (basic and strong induction)Available
19 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems

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
14 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
2
Compute probabilities in finite sample spacesAvailable
17 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
3
Conditional probability and independenceAvailable
17 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
4
Bayes’ theorem and applicationsAvailable
0 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems — not available yet

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
19 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
2
Binomial distribution and applicationsAvailable
19 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
3
Poisson distribution and applicationsAvailable
9 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems

Graph Theory · Graph Basics

4 core skills4% total weight
0/4 completed
4 skills to mastery
1
Bipartite graphs and matchings (intro)Available
15 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
2
Degrees, paths, cycles, and connectivityAvailable
11 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
3
Planar graphs and Euler’s formula (intro)Available
11 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
4
Represent graphs (adjacency list/matrix)Available
21 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems

Graph Theory · Trees and Spanning Trees

3 core skills3% total weight
0/3 completed
3 skills to mastery
1
Tree properties and traversal conceptsAvailable
1 question 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
2
Kruskal’s and Prim’s algorithms (conceptual)Available
18 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
3
Spanning trees and minimum spanning trees (intro)Available
16 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems

Graph Theory · Graph Algorithms

3 core skills4% total weight
0/3 completed
3 skills to mastery
1
Network flow concepts (max flow intro)Available
20 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
2
Shortest path algorithms (BFS/Dijkstra conceptually)Available
14 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
3
Graph coloring concepts and applicationsAvailable
20 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems

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
14 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
2
Inclusion–exclusion principle (intro and applications)Available
7 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
3
Cartesian products and power setsAvailable
18 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
4
Venn diagrams and set identitiesAvailable
10 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems

Sets, Relations, and Functions · Functions and Growth

4 core skills6% total weight
0/4 completed
4 skills to mastery
1
Function composition and inversesAvailable
9 questions 0 flashcards Lesson available
Long-form lessonFlashcards — not available yetPractice problems
2
Functions: injections, surjections, bijectionsAvailable
18 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
3
Asymptotic notation (Big-O, Big-Theta, Big-Omega)Available
10 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
4
Comparing growth rates and common function classesAvailable
19 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems

Counting and Combinatorics · Basic Counting Principles

4 core skills7% total weight
0/4 completed
4 skills to mastery
1
Combinations with repetitionAvailable
9 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
2
Permutations and combinationsAvailable
12 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
3
Sum and product rulesAvailable
9 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
4
Binomial theorem and binomial coefficientsAvailable
10 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems

Counting and Combinatorics · Pigeonhole and Advanced Counting

3 core skills4% total weight
0/3 completed
3 skills to mastery
1
Pigeonhole principle and applicationsAvailable
7 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
2
Counting with inclusion–exclusion (applications)Available
3 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
3
Counting using recursion (intro)Available
12 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems

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
9 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
2
Chinese remainder theorem (intro)Available
14 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
3
Solving linear congruences (intro)Available
18 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
4
Modular arithmetic operations and congruencesAvailable
12 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems

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
20 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
2
Prime numbers and factorization conceptsAvailable
12 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
3
Modular exponentiation and fast poweringAvailable
10 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems

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
25 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
2
Explain solution steps in a structured wayAvailable
15 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
3
Use correct notation and definitionsAvailable
18 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems

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
23 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
2
Common pitfalls (miscounting, double counting, invalid assumptions)Available
21 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
3
Translate word problems into discrete structures (graphs, sets,Available
19 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
4
Choose an appropriate discrete method to solve a problemAvailable
19 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems

Recurrence Relations

4 core skills11% total weight
0/4 completed
4 skills to mastery
1
Use generating functions conceptually (intro)Available
17 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
2
Solve linear recurrences with characteristic equations (intro)Available
11 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
3
Formulate recurrence relations from problemsAvailable
22 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
4
Solve linear recurrences by iteration/expansionAvailable
5 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems

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
4 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
2
Karnaugh maps concept (intro)Available
18 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
3
Boolean algebra identitiesAvailable
12 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems

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
19 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
2
Equivalence relations and partitionsAvailable
14 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems
3
Partial orders, Hasse diagrams, and lattices (intro)Available
12 questions 0 flashcards Lesson available
Long-form lessonSlide-style lessonFlashcards — not available yetPractice problems

Live Classes

Scheduled, expert-led Discrete Math classes you attend live.
Browse all
Summer Learning: Bridging the Gap to 1st Grade Math
LIVE
Math
Elementary School Math

Summer Learning: Bridging the Gap to 1st Grade Math

Aug 25, 2026·10:00 PM·
Coordinated Universal TimeTimes shown in Coordinated Universal Time (UTC)
Short-term class
Summer Learning: Bridging the Gap to 2nd Grade Math
LIVE
Math
Elementary School Math

Summer Learning: Bridging the Gap to 2nd Grade Math

Aug 25, 2026·11:00 PM·
Coordinated Universal TimeTimes shown in Coordinated Universal Time (UTC)
Short-term class
Algebra 1 Fundamentals
LIVE
Math
Algebra

Algebra 1 Fundamentals

Aug 26, 2026·9:00 PM·
Coordinated Universal TimeTimes shown in Coordinated Universal Time (UTC)
Short-term class
Summer Learning: Bridging the Gap to 3rd Grade Math
LIVE
Math
Elementary School Math

Summer Learning: Bridging the Gap to 3rd Grade Math

Aug 26, 2026·10:00 PM·
Coordinated Universal TimeTimes shown in Coordinated Universal Time (UTC)
Short-term class
Algebra 2 Fundamentals
LIVE
Math
Algebra 2

Algebra 2 Fundamentals

Aug 26, 2026·11:30 PM·
Coordinated Universal TimeTimes shown in Coordinated Universal Time (UTC)
Short-term class
Precalculus Fundamentals
LIVE
Math
Pre-Calculus

Precalculus Fundamentals

Aug 27, 2026·10:00 PM·
Coordinated Universal TimeTimes shown in Coordinated Universal Time (UTC)
Short-term class
High School Geometry Fundamentals
LIVE
Math
Geometry

High School Geometry Fundamentals

Aug 27, 2026·11:30 PM·
Coordinated Universal TimeTimes shown in Coordinated Universal Time (UTC)
Short-term class
LIVE
Math
High School Physics

Math Essentials for High School Physics

Sep 2, 2026·11:30 PM·
Coordinated Universal TimeTimes shown in Coordinated Universal Time (UTC)
Short-term class

Related Discrete Math tutors

Browse tutors who can help with this subject.
View all tutors
Expert tutoring

No related Discrete Math tutors found

Browse the full gallery to find a vetted expert who can help with Discrete Math.