Discrete Mathematics Curriculum

Mathematics

A structured, level-by-level path through Discrete Mathematics. Start with Foundations of Sets & logic and Core methods in Relations & functions at the Intermediate level, then build toward advanced practice and expert-level mastery — with hands-on projects and quizzes at every stage.

3 levels 9 modules 27 topics 6 weeks · about 24 hours · 8 weeks · about 32 hours · 10 weeks · about 40 hours
Intermediate

Intermediate Discrete Mathematics

6 weeks · about 24 hours

3 modules

Advanced

Advanced Discrete Mathematics

8 weeks · about 32 hours

3 modules

Expert

Expert Discrete Mathematics

10 weeks · about 40 hours

3 modules

Discrete Mathematics Course Curriculum

9 modules across 3 levels.

Intermediate

Intermediate Discrete Mathematics

Start with Sets & logic, Relations & functions and Combinatorics. Each module explains the idea, shows a worked example and ends with a short project, so Discrete Mathematics becomes something you can do rather than something you have only read about.

6 weeks · about 24 hours 3 modules

Topics

Project

Write a one-page explanation of Sets & logic in your own words, with an example you chose yourself, and test it against the module checklist.

Learning Path

1

Foundations of Sets & logic

Work through the three topics in this module, complete the project, then answer the self-check questions before moving on.

2

Core methods in Relations & functions

Work through the three topics in this module, complete the project, then answer the self-check questions before moving on.

Prerequisites: Foundations of Sets & logic

3

Applying Combinatorics

Work through the three topics in this module, complete the project, then answer the self-check questions before moving on.

Prerequisites: Core methods in Relations & functions

Practice Problems

EasyExplain Sets & logic to someone who has never studied the subject, using one worked example.
Solution: A strong answer defines sets & logic precisely, gives one concrete example, and names the limitation it runs into.
MediumExplain Relations & functions to someone who has never studied the subject, using one worked example.
Solution: A strong answer defines relations & functions precisely, gives one concrete example, and names the limitation it runs into.
HardExplain Combinatorics to someone who has never studied the subject, using one worked example.
Solution: A strong answer defines combinatorics precisely, gives one concrete example, and names the limitation it runs into.

Glossary

Sets & logic

A central idea in the intermediate Discrete Mathematics path, covered in the module of the same name.

Example: apply Sets & logic to a small, familiar case step by step, then check your reasoning against the walkthrough.

Relations & functions

A central idea in the intermediate Discrete Mathematics path, covered in the module of the same name.

Example: apply Relations & functions to a small, familiar case step by step, then check your reasoning against the walkthrough.

Combinatorics

A central idea in the intermediate Discrete Mathematics path, covered in the module of the same name.

Example: apply Combinatorics to a small, familiar case step by step, then check your reasoning against the walkthrough.

About the Discrete Mathematics curriculum

The Discrete Mathematics curriculum is a complete, self-paced course in mathematics, organised into 3 progressive levels and 9 modules. It opens with Foundations of Sets & logic and Core methods in Relations & functions, moves through Applying Combinatorics and finishes with expert-level work on Leading practice in Algorithms & complexity and Mastering Boolean algebra.

Across the whole path you work through 27 individual topics — from Sets & logic and Hands-on: sets & logic at the start to Hands-on: boolean algebra and Checking your understanding of boolean algebra by the end. The levels are estimated at 6 weeks · about 24 hours, 8 weeks · about 32 hours and 10 weeks · about 40 hours. Each level assumes the one before it, so you can work straight through from Intermediate to Expert, or start at the level that matches what you already know.

It suits analysts, researchers and students who need to reason with numbers and defend a conclusion, not just run a tool. The emphasis is on interpretation: every technique is introduced with the question it answers, the assumption it needs and the way it fails, so you can apply it to unfamiliar data.

Every module pairs a written summary with a worked example, a short quiz to check the idea landed, and a project brief drawn from real practice. You are never asked to take a concept on trust: the reasoning, the common mistakes and the situations where the approach stops working are all laid out, so you finish a module able to explain the idea rather than only recognise it.

What you’ll be able to do

By the end of the Discrete Mathematics path you should be able to work confidently with:

Sets & logic

Hands-on: sets & logic

Checking your understanding of sets & logic

Relations & functions

Putting relations & functions to work

Checking your understanding of relations & functions

Combinatorics

Hands-on: combinatorics

How the Discrete Mathematics curriculum is structured

Intermediate 6 weeks · about 24 hours 3 modules 9 topics

Intermediate Discrete Mathematics

Start with Sets & logic, Relations & functions and Combinatorics. Each module explains the idea, shows a worked example and ends with a short project, so Discrete Mathematics becomes something you can do rather than something you have only read about.

Modules: Foundations of Sets & logic · Core methods in Relations & functions · Applying Combinatorics

  • Sets & logic: Sets & logic is where many Discrete Mathematics learners first get stuck, so the module slows down, isolates the difficult step and rebuilds it with you.
  • Hands-on: sets & logic: This module treats Sets & logic as a tool: the question it answers, what it assumes, and what a correct use of it looks like in Discrete Mathematics.
  • Checking your understanding of sets & logic: Sets & logic is where many Discrete Mathematics learners first get stuck, so the module slows down, isolates the difficult step and rebuilds it with you.

Project: Write a one-page explanation of Sets & logic in your own words, with an example you chose yourself, and test it against the module checklist.

Advanced 8 weeks · about 32 hours 3 modules 9 topics

Advanced Discrete Mathematics

Build on the intermediate level through Graph theory, Recurrence relations and Number theory basics. The emphasis shifts from knowing the ideas to choosing between them — trade-offs, failure modes and the reasoning behind each decision.

Modules: In depth Graph theory · Patterns and trade-offs in Recurrence relations · Scaling Number theory basics

  • Graph theory: Graph theory is pushed past the textbook case: competing approaches, their trade-offs and the situations where each one breaks down.
  • Putting graph theory to work: The module examines Graph theory closely, including the assumptions beneath it and what changes when those assumptions stop holding.
  • Common pitfalls in graph theory: Graph theory is pushed past the textbook case: competing approaches, their trade-offs and the situations where each one breaks down.

Project: Produce a short case analysis in which Graph theory drives the recommendation, including the alternatives you rejected and why.

Expert 10 weeks · about 40 hours 3 modules 9 topics

Expert Discrete Mathematics

Work at the edge of Discrete Mathematics through Proof techniques, Algorithms & complexity and Boolean algebra. The modules assume fluency and ask for judgement: designing, critiquing and defending work at a professional standard.

Modules: Frontiers of Proof techniques · Leading practice in Algorithms & complexity · Mastering Boolean algebra

  • Proof techniques: Proof techniques is examined at the frontier, with an emphasis on open problems, rigorous argument and decisions you can defend.
  • Hands-on: proof techniques: This module asks you to critique and extend Proof techniques rather than simply apply it, producing work another expert could review.
  • Checking your understanding of proof techniques: Proof techniques is examined at the frontier, with an emphasis on open problems, rigorous argument and decisions you can defend.

Project: Write a professional-standard brief on Proof techniques — argument, evidence, limitations — plus a plan for taking the work further.

How to study Discrete Mathematics, phase by phase

  1. 1

    Phase 1 — Intermediate

    Set aside around 6 weeks · about 24 hours. Work through 3 modules, starting with Foundations of Sets & logic and Core methods in Relations & functions. Finish the phase by completing the project brief: Write a one-page explanation of Sets & logic in your own words, with an example you chose yourself, and test it against the module checklist.

  2. 2

    Phase 2 — Advanced

    Set aside around 8 weeks · about 32 hours. Work through 3 modules, starting with In depth Graph theory and Patterns and trade-offs in Recurrence relations. Finish the phase by completing the project brief: Produce a short case analysis in which Graph theory drives the recommendation, including the alternatives you rejected and why.

  3. 3

    Phase 3 — Expert

    Set aside around 10 weeks · about 40 hours. Work through 3 modules, starting with Frontiers of Proof techniques and Leading practice in Algorithms & complexity. Finish the phase by completing the project brief: Write a professional-standard brief on Proof techniques — argument, evidence, limitations — plus a plan for taking the work further.

  4. 4

    Phase 4 — Consolidate

    Return to the sections that felt weakest, redo their quizzes from memory, and rebuild the Write a one-page explanation of Sets & logic in your own words, with an example you chose yourself, and test it against the module checklist. without following along. Explaining Discrete Mathematics to someone else in plain language is the clearest signal that the Expert level has landed.

Once you have finished, the Discrete Mathematics path is a reasonable foundation for analytics, data science, research and quantitative roles. Because the curriculum is generated and kept as a structured outline rather than fixed videos, you can revisit any module, regenerate the outline at a different depth, or save it to your library and work through it over weeks rather than in one sitting.

Discrete Mathematics — Frequently Asked Questions

Common questions about studying Discrete Mathematics on LearnAnyCourse.

What does the Discrete Mathematics curriculum cover?

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The Discrete Mathematics curriculum is organised into 3 levels (Intermediate, Advanced and Expert) and 9 modules, including Foundations of Sets & logic, Core methods in Relations & functions, Applying Combinatorics, In depth Graph theory, Patterns and trade-offs in Recurrence relations and Scaling Number theory basics.

How long does it take to learn Discrete Mathematics?

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Each level is designed to take about 6 weeks · about 24 hours, 8 weeks · about 32 hours and 10 weeks · about 40 hours. Most learners work through one level at a time at their own pace.

Is the Discrete Mathematics curriculum free?

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Yes. Every Discrete Mathematics curriculum on LearnAnyCourse is free to read and study — create an account only if you want to save curricula to your personal library.

Do I need prior experience to study Discrete Mathematics?

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The curriculum starts at the intermediate level and builds upward, so you can begin with the fundamentals and progress to expert-level Discrete Mathematics topics without jumping ahead.

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