Mathematics for Artificial Intelligence and Computer Engineering (I)

Learning Outcomes

Subject Specific Intellectual and Research Skills

Having successfully completed this module you will be able to:

• Recognise, understand and construct rigorous mathematical proofs
• Apply general rules of derivatives and integrals to solve differentiation and integration problems
• Use the language of logic and set theory in order to make precise formal statements
• Apply operations on vectors and matrices and solve systems of linear equations

Knowledge and Understanding

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

• Principles of mathematical proof and sound logical reasoning
• Functions and relations as fundamental structures in computer science
• The interplay of syntax and semantics in mathematics, logic and computer science
• Elementary concepts of linear algebra, pre-calculus and introductory calculus
• The language of set theory and common operations on sets, including infinite sets

Subject Specific Practical Skills

Having successfully completed this module you will be able to:

• Use matrices of numeric data to solve problems derived from example data
• Use symbolic methods to solve systems of equations derived from real problems

Logic

• Propositional logic
• Predicate logic
• Natural deduction
• Mathematical proof
• Induction and recursion

Sets, functions and relations

• Basic set notation and operations
• Tuples, Cartesian Products, Power set
• Relations, equivalence relations and partial orders
• Functions: injections, surjections, bijections
• Cardinality, infinite sets

Single-variable calculus

• Elementary functions: linear, quadratic, polynomials
• Limit
• Differentiation
• Integration

Algebra

• Vector algebra
• Matrix algebra
• Systems of linear equations
• Eigenvectors and eigenvalues

The module consists of:

• Lectures
• Tutorials
• Guided self-study
• Labs as part of the AICE Lab Programme which will cover practical aspects

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.