KL3005 - Introduction to Logic and Algorithms

In this module, you will engage in a collaborative learning approach, working closely with peers and staff to develop methods and solve problems.

Assessment is divided into two components:
• Python coursework (30%): This evaluates your understanding of algorithms, Python syntax, and coding skills.
• Final theory coursework (70%): This focuses on problem-solving and mathematical proofs, testing your grasp of the theoretical content.

You will receive detailed feedback to support your learning. Individual feedback will address your specific performance, while generic feedback will highlight areas of strength and improvement across the cohort. Written and oral feedback will be provided after assessments, and formative feedback will be ongoing, especially during seminars.
This structure ensures you have clear guidance on your progress and areas to refine as you master the module’s material.

You will be supported through a combination of lectures and seminars, offering a structured environment for core learning. Seminars, in particular, provide opportunities for one-to-one interactions, ensuring personalized guidance. Half of the lectures and all seminars will take place in an IT laboratory, enabling you to develop practical skills in algorithms and Python coding. Outside scheduled teaching sessions, you can contact the module team—including the module tutor and instructor (if assigned)—via email or through the open-door policy available throughout the program. Additional academic support is accessible through technology-enhanced resources on the e-learning portal. You will also have opportunities to provide feedback formally via periodic staff-student committees and directly to the module tutor at the conclusion of the foundation year.
This comprehensive support framework ensures you have both the resources and opportunities to succeed while contributing to the continuous improvement of the module.

All modules at Northumbria include a range of reading materials that students are expected to engage with. Online reading lists (provided after enrolment) give you access to your reading material for your modules. The Library works in partnership with your module tutors to ensure you have access to the material that you need.

You will be able to:

Knowledge & Understanding:
MLO1. Develop a firm foundation of number fields and numeral systems, basic algorithms of number theory and
sequences, iterations and of the induction principle
ML02 Learn the basic methods of proof
MLO3. Understand the basics of flow diagrams, logical branching, input and output, loops and algorithms, numerical and symbolic computation, and realise them in the Python programming language.

Intellectual / Professional skills & abilities:
MLO4. Develop a firm foundation of basic logic and formal language.

Personal Values Attributes (Global / Cultural awareness, Ethics, Curiosity) (PVA):
MLO5. Communicate mathematical concepts at a fundamental level and understand the need to work to and meet prescribed deadlines.

Summative Assessments

Summative assessment is by two pieces to test concepts and methods.

1. CW – 1 week-long, open book take-home coding assessment (30%). Module Learning Outcomes addressed: MLO1, 3. Feedback will be made available within 20 working days.

2. CW – 24 hours long, open book take-home theory assessment (70%) involving mathematical proof and problem solving. Module Learning Outcomes addressed: MLO1,2, 4, 5. Feedback will be made available within 20 working days.

Formative Assessments

1. Problem-solving seminars
Module Learning Outcomes addressed: MLO1, 2, 3, 4, 5

Feedback will take several forms, including individual verbal and written comments on the assessment delivered in class and via blackboard; written feedback on the exam.

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Introduction to Logic and Algorithms explores the logic of mathematical proofs and computer algorithms. Through selected topics in discrete mathematics and number theory, such as numeral systems, Euclid’s algorithm, and continued fractions, you will explore relationships between natural, integer, rational, and real numbers. Building on this foundation, you will learn about basic cryptographic algorithms such as the Caesar cipher and implement them using Python—an industry-leading programming language. The module also presents methods of mathematical proof and their analysis through classical logic. Lectures will introduce theoretical concepts, while IT Lab-based sessions use interactive Jupyter notebooks to teach Python syntax and allow hands-on coding practice. Smaller group seminars provide personalized guidance from experienced instructors. Assessment comprises a Python-based coursework (30%) and a final theoretical coursework (70%), designed to evaluate both practical and conceptual understanding. This module offers a good grounding in mathematics, computer science, and problem-solving skills, preparing you for further undergraduate studies.