Mathematics for Artificial Intelligence and Computer Engineering (II)

Learning Outcomes

Subject Specific Intellectual and Research Skills

Having successfully completed this module you will be able to:

• Definition and properties of discrete and continuous probability distributions
• Unconstrained and constrained optimization including the use of Lagrange multipliers
• Critical analysis of counting problems on finite, discrete structures
• Analytical and numerical solution of ordinary differential equations
• Nonlinear optimization via gradient methods
• Elements of statistical inference, including hypothesis testing

Subject Specific Practical Skills

Having successfully completed this module you will be able to:

• Simple computation using tools of symbolic mathematics
• Be able to solve systems of ordinary differential equations derived from real-world problems using numeric and symbolic approaches.

Knowledge and Understanding

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

• Advantages and disadvantages of numerical vs symbolic computation.
• Appreciate applications of the above concepts in AI and CE.
• Concepts of probability and statistical inference
• Concepts of partial differentiation and its applications
• Understanding of the use of the Jacobian matrix for stability analysis of a system of ordinary differential equations.

Combinatorics

• Basic principles of counting: product and sum rules, inclusion-exclusion principle, pigeonhole principle.
• Combinations, permutations and arrangements, binomial theorem.

Probability and statistical inference

• Probability and statistics
• Introduction to probability: elementary probability formulae, discrete and continuous probability distributions.
• Introduction to statistics: sampling, confidence intervals, hypothesis testing, regression.

Calculus

• Partial differentiation; Ordinary differential equations; Jacobian matrix and stability analysis; Numerical integration introduction.

Optimization

• Gradient methods
• Lagrange multipliers

Symbolic maths

• Numeric vs symbolic processing for solving ordinary differential equations

Example application of symbolic maths

• Lane centering in an autonomous driving application

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.