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Discrete Mathematics: Logic, Proofs, Graphs and Counting – AI Tutor-Enabled Course Book

Original price was: $45.00.Current price is: $30.00.

AI Tutor-enabled
Self-paced
Beginner → Intermediate

Modules: 10
Study time: About 35 hours
Format: Digital course book (PDF)
Projects: 4 + capstone

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Learn to think like a mathematician and a computer scientist: logic, proofs and structures.

TypeNotes & books

DeliveryInstant download after payment

Instant download after payment
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SKU: CB-DISC Categories: Course Books, Mathematics Tags: AI maths tutor, combinatorics, discrete math for computer science, discrete mathematics course, graph theory, logic and proofs

AI Tutor-Enabled Self-Paced Professional Course Book

Learn to think like a mathematician and a computer scientist: logic, proofs and structures.

Discrete Mathematics is a self-paced course book covering logic, proof techniques, sets, functions, relations, induction, counting, recurrences and graph theory. It is designed for computer science, mathematics and engineering students who need both computation and rigorous reasoning.

Is this you?

Proofs feel impossible to start
Logic notation is confusing
Induction proofs never seem complete
Counting problems give different answers each time
Graph theory has too many definitions
Your computer science course assumes you know this

This course book is built to close exactly that gap: clear explanations, worked practice and an AI tutor that guides you instead of just giving answers.

Learn
Practise
Check with your AI Tutor
Build projects
Get assessed

What you’ll learn in 10 practical modules

01 Propositional LogicReason precisely with statements.

Key concepts

Connectives and truth tables
Logical equivalence
Implications and converses

Sample practice

Build a truth table for (p→q)∧¬q
Show p→q ≡ ¬p∨q

02 Predicate LogicReason about statements with variables.

Key concepts

Quantifiers
Negating quantified statements
Translating English to logic

Sample practice

Negate ∀x ∃y P(x,y)
Translate “every student passed some test”

03 Proof TechniquesWrite convincing proofs.

Key concepts

Direct proof
Contrapositive and contradiction
Proof by cases

Sample practice

Prove the sum of two odd numbers is even
Prove √2 is irrational

04 Sets and FunctionsWork with the language of mathematics.

Key concepts

Set operations
Injective, surjective and bijective functions
Cardinality

Sample practice

Prove A∩(B∪C)=(A∩B)∪(A∩C)
Is f(x)=2x+1 a bijection on ℝ?

05 Mathematical InductionProve statements for all natural numbers.

Key concepts

Weak induction
Strong induction
Recursive definitions

Sample practice

Prove 1+2+…+n = n(n+1)/2
Prove every n≥2 has a prime factor

06 RelationsModel connections between objects.

Key concepts

Properties of relations
Equivalence relations and classes
Partial orders

Sample practice

Is “same remainder mod 3” an equivalence relation?
Draw a Hasse diagram

07 CountingCount systematically.

Key concepts

Sum and product rules
Permutations and combinations
Pigeonhole principle

Sample practice

How many 8-bit strings have exactly three 1s?
Apply the pigeonhole principle

08 Recurrence RelationsSolve sequences defined by earlier terms.

Key concepts

Setting up recurrences
Solving linear recurrences
Divide and conquer

Sample practice

Solve aₙ=3aₙ₋₁, a₀=2
Write a recurrence for the Tower of Hanoi

09 Graph TheoryModel networks with graphs.

Key concepts

Paths, cycles and connectivity
Euler and Hamilton paths
Graph colouring

Sample practice

Does a given graph have an Euler circuit?
Find the chromatic number of a cycle

10 Trees and AlgorithmsUse structures behind computing.

Key concepts

Trees and spanning trees
Shortest paths
Algorithm complexity

Sample practice

Find a minimum spanning tree with Kruskal
Run Dijkstra on a small graph

Use AI as your personal tutor, not an answer machine

The course book includes ready-to-use prompts for ChatGPT, Copilot, Gemini or any capable AI assistant. Each mode makes the AI teach, guide, check or challenge you, so you build real understanding.

1TEACH ME

Explain [topic] in Discrete Mathematics to me step by step at a [beginner / intermediate / advanced] level. Use a simple example first, then a harder one, and ask me a question to check I understood.

2GUIDE ME

I am working on this problem: [paste problem]. Do not give me the answer. Give me one hint at a time and wait for my next step.

3CHECK MY WORK

Here is my solution: [paste working]. Check each step, tell me exactly where any mistake is and why, but let me correct it myself.

4CHALLENGE ME

Give me three exam-style Discrete Mathematics questions on [topic], getting harder each time. Wait for my answers, then mark them and explain what I missed.

5HELP ME APPLY IT

Show me how [topic] from Discrete Mathematics is used in a real situation, then give me a small task to try it myself.

Verify before you trust

Ask a clear, specific question
Solve it yourself first
Test the answer by substituting or estimating
Check it against the worked examples in the book
Validate with your teacher if the AI and the book disagree

Don’t just study it. Build evidence you can show.

Project 1

Logic Puzzle Solver

Formalise and solve logic puzzles with truth tables.

Project 2

Proof Journal

Write and revise ten proofs with feedback.

Project 3

Network Analysis

Model a transport or social network as a graph.

Project 4

Algorithm Analysis

Count operations and compare algorithm efficiency.

Final capstone

Discrete Mathematics Portfolio

Combine proofs, counting problems and a graph-based application with explanations.

Who this course book is for

Computer science students
Mathematics students
Engineering students
Coding bootcamp graduates
Students preparing for technical interviews
Self-learners

Where these skills lead

Software engineering
Computer science
Cybersecurity
Data science
Operations research
Teaching

The course builds skills and evidence; it does not guarantee employment or exam results.

What you receive

10 progressive learning modules
Learning objectives, key concepts and practice problems
Ready-to-use AI Tutor prompts for five learning modes
Practical projects and a capstone
Portfolio guide, assessment rubric and completion checklist
Instant download and lifetime access in My Courses

Format	Digital course book (PDF)
Learning mode	Self-paced + AI Tutor
Level	Beginner → Intermediate
Study time	About 35 hours
Created by	NoteStore Academy
Certificate	Optional project and portfolio assessment
Licence	Personal learning use
Updated	November 2, 2026

Certificate pathway

Want a certificate? Submit your work for optional assessment by NoteStore Academy. Certificates reflect demonstrated work, so they are not issued automatically with purchase.

Module practice work20%

Projects 1–440%

Capstone project30%

Portfolio and reflection10%

Frequently asked questions

Do I need calculus?

No. Discrete mathematics uses algebra and logical reasoning, not calculus.

Is it useful for programming?

Yes. Logic, recursion, counting, graphs and complexity are used throughout computer science.

Will I learn to write proofs?

Yes. Module 3 teaches proof techniques step by step, and later modules give lots of practice.

Is it suitable for first-year students?

Yes. It is written for first and second-year university courses.

How do I get the course book after paying?

Your download link appears on the order confirmation page straight away, is emailed to you, and stays in My Courses in your account.

Which AI assistant can I use?

Any capable assistant works, such as ChatGPT, Microsoft Copilot or Google Gemini. The prompts are written to work with all of them.

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