KL3005 - Introduction to Logic and Algorithms

You will learn on this module via a group approach where you and the staff will work together on developing methods and solving problems.

The module is assessed by means of two examinations, weighting 30% and 70% of the final mark, respectively. The written examination will assess your competence on the theoretical content of the module. The in-course assessment will assess algorithms and your knowledge of Python syntax and coding skills.

Feedback will be provided individually and also generically to indicate where the cohort has a strong or a weaker answer to questions. You will receive both written and oral feedback from the assessment, as well as formative feedback throughout the course, in particular during exercise classes/seminars.

You will be supported through lectures and exercise classes/seminars which will provide you with a formal teaching environment for core learning. In particular, exercise classes/seminars will provide you with opportunities for one-to-one interactions. Half of the lectures and all the seminars will be held in an IT laboratory to allow you to develop your practical use of algorithms and Python.. Outside formal scheduled teaching, you will be able to contact the module team (module tutor, module demonstrator when assigned) either via email or the open door policy operated throughout the programme. Further academic support will be provided through technology-enhanced resources via the e-learning portal. You will also have the opportunity to give your feedback formally through periodic staff-student committees and directly to the module tutor at the end of the foundation year.

All modules at Northumbria include a range of reading materials that students are expected to engage with. The reading list for this module can be found at: http://readinglists.northumbria.ac.uk
(Reading List service online guide for academic staff this containing contact details for the Reading List team – http://library.northumbria.ac.uk/readinglists)

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. Time limited open book coding assessment (30%)
Module Learning Outcomes addressed: MLO1, 3
Feedback will be made available within 20 working days.

2. Exam - 3 hour closed book, lab based examination (70%) Module Learning Outcomes addressed: MLO1,2,3, 4, 5. Feedback will be made available within 20 working days.

Formative Assessments

1. Problem-solving workshops
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 introduces you to elementary the principles of mathematical logic and algorithms.

The module further shows how these concepts can be used in a variety of ways to produce algorithms. Smaller group exercise classes/seminars will allow you to obtain help with specific problems. The module is assessed by means of two examinations, with a weighting of 30% and 70% of the final mark, respectively. The module provides a good grounding for computational mathematics and problem solving for your undergraduate degree.

In this module you will learn the principles of mathematical logic and algorithms. In particular you will learn to

• learn basic types of mathematical proofs, such as proof by induction, by contradiction and by contrapositive
• use a formal language for mathematical statements that allows compact and convenient notation and how to translate it into the natural language
• offer clear and unambiguous interpretation of such statements
• implement mathematical statements into algorithms
• test your understanding using the Python programming language and the Jupyter Notebook software
• learn the methods of numerical and symbolic computations, elements of data analysis and visualization in Python

Upon completion of the module you will have acquired fundamental knowledge that is valuable in itself and will serve as the foundation in mathematics and physics, and it will also constitute an important foundation for applications. For example, software engineers strongly rely on mathematical logic theories in their work. Indeed, when dealing with applied problems, researchers have to switch between the descriptive language, mathematical language, the language of numerical methods and algorithms, and specific programming languages. The language of mathematical logic and algorithms offers a great opportunity to practice this translation between languages and is used as a powerful formalised tool for problem solving and composing mathematical proofs.