Learn how to construct, interpret, and evaluate logical statements and arguments. Develop fluency with truth tables, implications, and basic proof techniques such as direct proof and proof by contradiction.
Maths 1: Discrete Mathematics
This is a Level 1 course from the Data Science and Artificial Intelligence major, part of the Open Bachelor’s programme. It is worth 6 ECTS and takes place in Term 1 in Lisbon.
Course Summary
Dive into the mathematical foundation of the digital age and uncover the secrets behind data. In this course, you’ll explore discrete mathematical structures that power modern technologies, from combinatorics and foundational logic to sequences and beyond. Through hands-on learning in small, collaborative groups, you’ll build confidence in problem-solving while sharpening teamwork skills. By mastering these fundamental concepts, you’ll be prepared to tackle complex challenges in mathematics, data science, and beyond.
Course Learning Outcomes (CLOs) – TBD
| Description | Mapped to Human Intelligence | |
|---|---|---|
| CLO 1 | Apply logical reasoning, set theory, and combinatorics to solve structured mathematical problems and real-world puzzles in data science. | CI3 – Mastery of Theoretical Foundations |
| CLO 2 | Collaborate in small teams to discuss, solve, and explain discrete math problems, providing and receiving constructive feedback. | SEI5 – Collaboration |
| CLO 3 | Recognize patterns, propose solutions, and use logical reasoning and counterexamples to investigate discrete mathematical problems, clearly communicating findings in writing and discussion. | CI6 – Creativity |
Assessment
| Assessment Type | Weighting of Course Grade | Group Assessment? | Invigilated? | CLOs Mapped | |
|---|---|---|---|---|---|
| Assessment 1 | Evaluative – Quiz | 40% | No | Yes | CLO 1 |
| Assessment 2 | Written – Discovery Assignment | 30% | No | No | CLOs 1 & 3 |
| Assessment 3 | Written – Reflective Assignment | 30% | No | No | CLO 2 |
- Assessment 1 Description: This invigilated quiz, held mid-term, assesses students’ grasp of core discrete mathematics topics. It includes both multiple-choice and short-answer questions requiring students to apply logical reasoning, perform set operations, and solve basic counting problems in real-world contexts. Students may be asked to analyze truth tables, compute permutations/combinations, or evaluate simple recurrence relations, reinforcing foundational skills essential for algorithmic thinking.
- Assessment 2 Description: In this individual assignment, students choose a real-world system (e.g. task scheduling, cryptography, or social networks) where discrete mathematics is applied. They investigate the underlying mathematical principles, structure the problem using symbolic representations, and write a report explaining how recurrence relations or graph theory offer insights. The report should include problem formulation, mathematical modeling, and reflective commentary on what was learned during exploration.
- Assessment 3 Description: Students reflect on their participation in group problem-solving sessions throughout the term. They describe challenges in communicating abstract logic, how their teams overcame misconceptions, and what strategies they developed for learning new mathematical content. The submission may take the form of a short written essay or recorded voice memo. Assessment focuses on metacognitive awareness, collaboration, and articulation of logical reasoning skills.
Indicative List
of Topics
Explore how discrete systems are built and related. Work with sets, functions, relations, and symbolic representations to model and analyse abstract and real-world systems.
Master the fundamental principles of counting, including permutations, combinations, and the pigeonhole principle. Apply these tools to solve problems involving probability, decision-making, and algorithmic design.
Understand patterns and recursive processes. Use recurrence relations to describe growth and change, and apply induction to prove statements about numbers, sequences, and algorithms.
Discover how graphs can model networks, systems, and structures. Learn about nodes, edges, paths, and trees, and explore how graph theory underpins applications from task scheduling to data organisation.
