Further Mathematics and Algorithms

Learning Outcomes

Subject Specific Practical Skills

Having successfully completed this module you will be able to:

• Select and apply algorithms appropriate to a simple biomedical engineering problem
• Estimate the performance of algorithms for a given dataset
• Demonstrate the application of logical thinking in problem solving

Knowledge and Understanding

Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:

• Demonstrate knowledge and understanding of the mathematical principles that underpin algorithms for biomedical engineering
• Demonstrate knowledge and understanding of the fundamentals of algorithms and data structures, including time and space complexity analysis.

Subject Specific Intellectual and Research Skills

Having successfully completed this module you will be able to:

• Evaluate theoretically the complexity of algorithms
• Select the most appropriate algorithm considering the constraints of a given problem

1)Fundamental Maths

• Mathematical proof: by case analysis, by contradiction. Induction and recursion.
• Propositional logic. Predicate calculus. Soundness and completeness.
• Sets and relations.
• Graphs: (un)directed, (a)cyclic, (un)connected, and (un)weighted.

2)Algorithms and data representation

• Abstract Data Types (ADTs).
• Arrays.
• Linear and binary search.
• Sorting algorithms.
• Algorithmic analysis framework

* Average, best, and worst-case performance.

* Empirical and relative (order of growth) measurements: Constant,

logarithmic, linear, log linear, quadratic, cubic, and exponential.

* Time and space efficiency.

• Asymptotic complexity analysis: including Big O notation, little o, big Omega and big theta. Efficiency classes.

In-person lectures and tutorials.

Individual study.

Summative

This is how we’ll formally assess what you have learned in this module.

Referral

This is how we’ll assess you if you don’t meet the criteria to pass this module.

Repeat

An internal repeat is where you take all of your modules again, including any you passed. An external repeat is where you only re-take the modules you failed.