Discrete Mathematics Professional Certification
The mathematics of logic, structure, and computation
Key facts
- Level: Professional
- Field: Mathematics
- Estimated study time: about 32 hours
- Credential price: $213
- Exam: 88 questions · 140 minutes · pass mark 75%
About the Discrete Mathematics Professional certification
A professional-level certification in discrete mathematics — the rigorous foundation underneath computer science, cryptography, networks, and formal reasoning. You will master propositional and predicate logic, including connectives, truth tables, logical equivalences, quantifiers, and the rules of inference; the major methods of proof — direct, contrapositive, contradiction, and both ordinary and strong mathematical induction; set theory with its operations, power sets, Cartesian products, cardinality and the countable/uncountable distinction; functions and relations, including injective/surjective/bijective maps, equivalence relations and partitions, partial orders and Hasse diagrams; combinatorics — the sum and product rules, permutations and combinations, the pigeonhole principle, inclusion-exclusion, binomial coefficients and an introduction to generating functions; recurrence relations and how to solve linear recurrences, plus an introduction to the Master theorem; number theory — modular arithmetic, the Euclidean algorithm for GCD, primes, congruences, and the idea behind RSA; graph theory — terminology, paths and cycles, connectivity, trees and spanning trees, Euler and Hamilton circuits, planarity, graph coloring, isomorphism and shortest paths; Boolean algebra and logic circuits; and algorithm analysis with Big-O notation and an introduction to complexity classes including P vs NP, finite automata and formal languages. Every topic is taught with worked, step-by-step examples, diagrams, and honest explanations, so you finish able to read, write, and verify rigorous arguments — the working language of professional computer science and mathematics.
What you will learn
The official Discrete Mathematics Professional study course covers:
- Logic & Proof — Propositions, connectives, quantifiers and the rules of inference that make arguments valid.
- Methods of Proof — Direct, contrapositive and contradiction proofs, plus ordinary and strong induction.
- Sets, Functions & Relations — Set operations and cardinality, the three function types, and equivalence relations and orders.
- Combinatorics — Counting principles, permutations and combinations, pigeonhole, inclusion-exclusion and the binomial theorem.
- Number Theory & Recurrences — Modular arithmetic, the Euclidean algorithm, primes and RSA, plus solving recurrence relations.
- Graphs, Logic Circuits & Computation — Graph theory and spanning trees, Boolean algebra and circuits, Big-O and the P vs NP question.
- Hands-on Lab — Logic, Counting & Graphs — A discrete-math capstone in Google Colab: build truth tables and test logical equivalence, count with permutations and combinations, do modular arith…
Prerequisites
Frequently asked questions
- Is the Discrete Mathematics Professional certificate verifiable?
- Yes. Every issued Hootix Academy certificate carries a unique credential code that anyone can verify online.
- How is the Discrete Mathematics Professional exam structured?
- It is a 140-minute ID-verified multiple-choice exam of 88 questions; you need 75% to pass.
- Do I need to buy the course to take the exam?
- Each certification is sold three ways: the exam on its own, the online course on its own, or both together as a Course + exam bundle (the bundle price is the course price plus the exam price).
- How long does the Discrete Mathematics Professional course take?
- About 32 hours of self-paced study.