NCHNAP444 Mathematical Structures and Methods Course Descriptor

Course Summary

This course introduces mathematical structures and methods that form the foundation of computer science. Learners will study structures such as sets, tuples, sequences, lists, trees, and graphs. Functions, relations, ordering, and equivalence relations and inductive and recursive definitions of structures and functions will be explored. The course covers principles of proof such as truth tables, inductive proof, basic logic, counting techniques and arguments needed to estimate the size of sets, the growth of functions, and the space-time complexity of algorithms.

Course Aims

• Train learners in the mathematical foundations of computer science.
• Train learners in mathematical terminology and core techniques.
• Give learners the tools to solve basic mathematical problems.
• Give learners the underpinning mathematical knowledge and tools required for programming and computer science.

Learning Outcomes

On successful completion of the course, learners will be able to:

Knowledge and Understanding

Subject Specific Skills

Transferable and Professional Skills

Teaching and Learning

This is an e-learning course, taught throughout the year.

This course can be offered as a standalone short course.

Teaching and learning strategies for this course will include: 

• On-line learning
• On-line discussion groups
• On-line assessment

Course information and supplementary materials will be available on the University’s Virtual Learning Environment (VLE).

Learners are required to attend and participate in all the formal and timetabled sessions for this course. Learners are also expected to manage their self-directed learning and independent study in support of the course.

The course learning and teaching hours will be structured as follows:

• Off-the-job learning and teaching (6 days x 7 hours) = 42 hours
• On-the-job learning (12 days x 7 hours) = 84 hours (e.g. 2 days per week for 6 weeks)
• Private study (4 hours per week) = 24 hours

Total = 150 hours

Assessment

Formative

Learners will be formatively assessed during the course by means of set assignments. These will not count towards the final degree but will provide learners with developmental feedback. 

Summative

Assessment will be in two forms:

Feedback

Learners will receive formal feedback in a variety of ways: written (via email or VLE correspondence) and indirectly through online discussion groups. Learners will also attend a formal meeting with their Academic Mentor (and for apprentices, including their Line Manager). These bi- or tri-partite reviews will monitor and evaluate the learner’s progress.

Feedback is provided on summatively assessed assignments and through generic internal examiners’ reports, both of which are posted on the VLE.

Indicative Reading

Note: Comprehensive and current reading lists for courses are produced annually in the Course Syllabus or other documentation provided to learners; the indicative reading list provided below is used as part of the approval/modification process only.

Books

• Rosen, K. H., (2012), Discrete Mathematics and Its Applications, Content Technologies
• Rosen, K. H., (2011), Student’s Solution Guide to accompany Discrete Mathematics and Its Applications, Mcgraw Hill Higher Education
• Lewis, H. R., (2019), Essential discrete mathematics for computer science, Princeton: Princeton University Press

Journals

Learners are encouraged to read material from relevant journals on Mathematical Structures and Methods as directed by their course trainer.

Electronic Resources

Learners are encouraged to consult relevant websites on Mathematical Structures and Methods.

Indicative Topics

• Propositional Logic and Truth Tables
• Binary Numbers
• Sets and Set Operations
• Counting and Combinatorics

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