Discrete Mathematics (Discrete Structures) Course
Our Discrete Structures course covers propositional and predicate logic, proof techniques and induction, sets, relations and functions, combinatorics and counting, recurrence relations, algebraic structures, graphs and trees, and Boolean algebra. Lessons are live and one-to-one with a verified subject expert, who explains each concept with worked examples, solves problems from your own module and helps you prepare for exams and coursework. Suitable for computer science and engineering students, following university syllabi in the UK, US, Australia and India (including AKTU, VTU and Anna University style courses).
Reviewed by P. Gaurav, B.Tech in Computer Science and EngineeringLast updated
$14 – $44
per hour
Free demo class · pay only if you continue
What you will learn
Learning outcomes
- Basic mathematics
- Basic algebra
- Basic logical reasoning
- Basic computer science knowledge
Prerequisites
- Basic mathematics
- Basic algebra
- Basic logical reasoning
- Basic computer science knowledge
Tags
Course structure
Syllabus(5 modules)
- Set properties
- Relations
- Functions
- Finite and infinite sets
- Partial orders
- Lattices
What is Discrete Structures?
In short: this course gives one-to-one online tutoring in discrete structures and discrete mathematics. A verified tutor explains logic, proofs, sets, relations, functions, combinatorics and graph theory, with step-by-step proofs and problems.
Discrete structures, or discrete mathematics, is the branch of maths that deals with countable, separate objects rather than continuous quantities, such as sets, logical statements, graphs and integers. It is the mathematical foundation of computer science, used in algorithms, databases, cryptography and the theory of computation.
This online course teaches Discrete Structures one to one with a verified tutor who has studied or taught it at university level, at your pace and aligned with your own module.
Related subject: Computer science help.
What does the Discrete Structures course cover?
| Topic | Key content |
|---|---|
| Sets, relations and functions | Set operations, relations and their properties, equivalence relations, partial orders, lattices, functions, finite and infinite sets |
| Graphs | Directed, undirected, acyclic and bipartite graphs, connected components, Eulerian and Hamiltonian graphs, trees |
| Logic | Propositional and predicate logic, truth tables, equivalences, quantifiers, resolution, soundness and completeness |
| Proof techniques | Direct proof, contradiction, contrapositive, mathematical induction |
| Abstract algebra | Groups, rings, fields, Galois fields |
| Number theory | Divisibility, gcd, modular arithmetic, Euler's phi function, Fermat's little theorem, discrete logarithm |
How do you write a proof by mathematical induction?
- State the claim P(n) clearly.
- Base case: prove P(1) (or the smallest value).
- Inductive hypothesis: assume P(k) is true for some k.
- Inductive step: prove P(k + 1) using the hypothesis.
- Conclude that P(n) holds for all n from the base case onwards.
How do you check whether a relation is an equivalence relation?
Check three properties.
| Property | Test |
|---|---|
| Reflexive | Every element is related to itself |
| Symmetric | If a relates to b, then b relates to a |
| Transitive | If a relates to b and b to c, then a relates to c |
If all three hold, the relation partitions the set into equivalence classes.
What does a worked induction proof look like?
Here is a classic proof: show that 1 + 2 + … + n = n(n + 1) ÷ 2 for all n ≥ 1.
| Step | Working |
|---|---|
| Base case (n = 1) | Left side 1; right side 1 × 2 ÷ 2 = 1 ✓ |
| Inductive hypothesis | Assume it holds for n = k |
| Inductive step | 1 + … + k + (k + 1) = k(k + 1) ÷ 2 + (k + 1) |
| Simplify | (k + 1)(k + 2) ÷ 2, the formula for n = k + 1 |
| Conclusion | True for all n ≥ 1 by induction |
Where do students lose marks in Discrete Structures?
Students most often lose marks in Discrete Structures through the habits below. Each is easy to fix with practice and feedback on your own answers.
| Mark-loser | What to do instead |
|---|---|
| Missing base case | Always prove the base case first |
| Hypothesis not used | Show exactly where the hypothesis is applied |
| Relation properties unchecked | Test reflexive, symmetric and transitive separately |
| Counting double-counts | Decide whether order matters and if repetition is allowed |
| Graph terms confused | Learn precise definitions of path, cycle and tree |
How is it assessed, and how can a tutor help?
Discrete structures modules are usually assessed by written exams and problem sheets with proofs, logic, graph and counting questions.
Tutors explain concepts, work through practice problems with you and give feedback on your approach. Graded work you submit must be your own, as set out in our academic integrity policy. For deadline-driven guidance, see assignment help.
How the lessons work
Lessons are live and one to one on video with screen sharing and a shared whiteboard. You can follow a full course or book sessions on the topics you find hardest before exams. See also Theory of Computation, Design and Analysis of Algorithms and our Abstract Algebra subject page.
Discrete mathematics for computer science: who this course is for, prerequisites and study plan
Discrete mathematics for computer science covers the logic, sets, relations, graphs, counting and proofs that algorithms, databases and cryptography are built on, and this course teaches them with a 1-to-1 tutor.
This discrete mathematics course suits first- and second-year computer science, IT and BCA students taking a discrete structures or discrete mathematics module, and anyone preparing for algorithms or theory of computation.
Prerequisites: school-level algebra and basic logical reasoning. No university maths is needed to start.
Course length: 36 one-hour lessons across 5 modules.
| Stage | Module | What you can do afterwards |
|---|---|---|
| 1 | Sets, relations and functions | Prove a relation is an equivalence relation and check bijections |
| 2 | Logic | Build truth tables, use predicate logic and write proofs by induction and contradiction |
| 3 | Graphs | Find Euler and Hamilton paths, work with trees and colour graphs |
| 4 | Abstract algebra, number theory | Identify groups, use modular arithmetic and apply Fermat's little theorem |
Where it leads: discrete mathematics prepares you for our Theory of Computation course and Design and Analysis of Algorithms.
Discrete Mathematics (Discrete Structures) Course: frequently asked questions
What is discrete mathematics, with examples?
Discrete mathematics studies objects that are separate and countable rather than continuous. Examples include sets of students, logic statements that are true or false, graphs such as road or computer networks, counting the passwords that can be made from given characters, and modular arithmetic used in cryptography. It is the mathematics behind computer science.
Why do computer science students study discrete maths?
It underpins algorithms, data structures, databases, cryptography and theory of computation.
What is the difference between propositional and predicate logic?
Predicate logic adds variables and quantifiers such as 'for all' and 'there exists'.
What is an Eulerian graph?
A graph with a circuit that uses every edge exactly once.
What is a group?
A set with an operation that is closed and associative, with an identity and inverses.
What is Fermat's little theorem?
If p is prime and a is not divisible by p, then a^(p−1) ≡ 1 (mod p).
Is discrete maths hard?
Proofs take practice, but a step-by-step approach makes it manageable.
Can you help me prepare for my discrete maths exam?
Yes. Tutors practise proofs, logic and graph questions.
How much does a Discrete Structures tutor cost?
The price depends on the tutor and session length. You see the hourly rate before booking, with no subscription.
Can a tutor do my assignment for me?
No. Tutors explain, guide and give feedback so you can complete your own work, in line with our academic integrity policy.
How do I write a proof by induction?
Prove the base case, assume the statement for k, then prove it for k + 1 using that assumption.
What is an equivalence relation?
A relation that is reflexive, symmetric and transitive.
What is the difference between permutations and combinations?
Permutations count ordered arrangements; combinations count unordered selections.
What is a bijection?
A function that is both one-to-one and onto.
What is the pigeonhole principle?
If more items are placed into fewer containers, at least one container holds more than one item.
Is CSE possible without maths?
Not really. Computer science and engineering degrees include compulsory maths, usually discrete mathematics, calculus, linear algebra and probability. You do not need to be a maths specialist, but you must be comfortable with logic and problem solving. Discrete mathematics is the most directly useful, and a tutor can build it up from the basics.
What is a truth table?
A table showing the truth value of a logical expression for every combination of inputs.
What is proof by contradiction?
Assuming the statement is false and deriving a contradiction.
Is discrete mathematics the same as discrete structures?
Mostly, yes. Discrete structures is the name many computer science courses use for discrete mathematics: logic, sets, relations, functions, counting, recurrence relations, graphs, trees and algebraic structures such as groups. Some syllabi weight the topics differently, so your tutor works from your own course outline and past papers.
Do you offer lessons in my time zone?
Yes. Lessons are online, so you can book times that suit your time zone.
Why is discrete mathematics important for computer science?
Discrete mathematics is the language of computer science. Logic underlies programming and circuits, graphs model networks, counting and probability help analyse algorithms, relations underpin databases, and number theory powers cryptography. Learning to write proofs also trains the precise reasoning you need for algorithms and theory of computation.
Keep learning
Related courses
Student reviews
What students say about Discrete Mathematics (Discrete Structures) Course
Used FLN Tutors? Be one of the first to share how it went, in writing or in a short video.
Money-Back Guarantee
Full refund if we miss the agreed deadline, can't find a suitable expert, or major errors can't be fixed by revision.
Learn more →100% Confidential
Your identity, order details and institution are never shared with any third party.
Learn more →Deadline-Backed Delivery
Every order has an agreed deadline. If we don't deliver by it, you can claim a full refund.
Learn more →Get started today
Ready to get expert help?
Tell us what you need and get matched with a tutor who teaches your subject. Delivered on time, every time.