Aims

The aims of the course are to:

• Teach some mathematical techniques that have wide applicability to many areas of engineering.

Objectives

As specific objectives, by the end of the course students should be able to:

• Find the SVD of a matrix, and understand how this can be used to calculate the rank and pseudo-inverse of the matrix.
• Calculate the least squares solution of a set of linear equations.
• Understand how to apply Principal Component Analysis (PCA) to a problem.
• Apply PCA to reduce the dimensionality of an optimization problem and/or to improve the solution representation.
• Represent linear iterative schemes using linear algebra and understand what influences the rate of convergence.
• Understand the definitions and application areas of Stochastic Processes.
• Understand the principle of Markov Chains.
• Implement various sampling schemes to enable parameters of stochastic processes to be estimated.
• Understand the concepts of local and global minima and the conditions for which a global minimum can be obtained.
• Understand the algorithms of the different gradient search methods.
• Solve unconstrained problems using appropriate search methods.
• Solve constrained linear and non-linear optimization problems using appropriately selected techniques.
• Understand how Markov Chain-based algorithms can be used to give reasonable solutions to global optimisation problems.

Content

Linear Algebra provides important mathematical tools that are not only essential to solve many technical and computational problems, but also help in obtaining a deeper understanding of many areas of engineering.  Stochastic (random) processes are important in fields such as signal and image processing, data analysis etc. Optimization methods are routinely used in almost of every branch of engineering, especially in the context of design.

Linear Algebra (4L, Prof G Wells)

• Revision of IB material
• Matrix norms, condition numbers, conditions for convergence of iterative schemes
• Positive definite matrices
• Singular Value Decomposition (SVD), pseudo-inverse of a matrix and least squares solutions of Ax = b
• Principal Component Analysis
• Markov matrices and applications

Stochastic Processes (5L, Prof S Godsill)

• Definition of a stochastic process, Markov assumption (with examples), the Chapman-Kolmogorov (CK) equation, conversion of a particular CK integral equation into a differential equation (for the case of Brownian motion)
• The general Fokker-Planck equation with particular examples (Brownian motion, Ornstein-Uhlenbeck process)
• Introduction to sampling Gibbs sampler, Metropolis Hastings, Importance sampling with applications.

Optimization (7L, Prof M Girolami)

• Introduction: Formulation of optimization problems; conditions for local and global minimum in one, two and multi-dimensional problems
• Unconstrained Optimization: gradient search methods (Steepest Descent, Newton’s Method, Conjugate Gradient Method)
• Linear programming (Simplex Method)
• Constrained Optimization: Lagrange and Karush-Kuhn-Tucker (KKT) multipliers; penalty and barrier functions
• Global optimisation: Simulated Annealing

This syllabus contributes to the following areas of the UK-SPEC standard:

Toggle display of UK-SPEC areas.

 
Last modified: 28/08/2020 11:10

Aims

The aims of the course are to:

• Teach some mathematical techniques that have wide applicability to many areas of engineering.

Objectives

As specific objectives, by the end of the course students should be able to:

• Find the SVD of a matrix, and understand how this can be used to calculate the rank and pseudo-inverse of the matrix.
• Calculate the least squares solution of a set of linear equations.
• Understand how to apply Principal Component Analysis (PCA) to a problem.
• Apply PCA to reduce the dimensionality of an optimization problem and/or to improve the solution representation.
• Represent linear iterative schemes using linear algebra and understand what influences the rate of convergence.
• Understand the definitions and application areas of Stochastic Processes.
• Understand the principle of Markov Chains.
• Implement various sampling schemes to enable parameters of stochastic processes to be estimated.
• Understand the concepts of local and global minima and the conditions for which a global minimum can be obtained.
• Understand the algorithms of the different gradient search methods.
• Solve unconstrained problems using appropriate search methods.
• Solve constrained linear and non-linear optimization problems using appropriately selected techniques.
• Understand how Markov Chain-based algorithms can be used to give reasonable solutions to global optimisation problems.

Content

Linear Algebra provides important mathematical tools that are not only essential to solve many technical and computational problems, but also help in obtaining a deeper understanding of many areas of engineering.  Stochastic (random) processes are important in fields such as signal and image processing, data analysis etc. Optimization methods are routinely used in almost of every branch of engineering, especially in the context of design.

Linear Algebra (4L, Prof G Wells)

• Revision of IB material
• Matrix norms, condition numbers, conditions for convergence of iterative schemes
• Positive definite matrices
• Singular Value Decomposition (SVD), pseudo-inverse of a matrix and least squares solutions of Ax = b
• Principal Component Analysis
• Markov matrices and applications

Stochastic Processes (5L, Prof M Gales)

• Definition of a stochastic process, Markov assumption (with examples), the Chapman-Kolmogorov (CK) equation, conversion of a particular CK integral equation into a differential equation (for the case of Brownian motion)
• The general Fokker-Planck equation with particular examples (Brownian motion, Ornstein-Uhlenbeck process)
• Introduction to sampling Gibbs sampler, Metropolis Hastings, Importance sampling with applications.

Optimization (7L, Prof G Csanyi)

• Introduction: Formulation of optimization problems; conditions for local and global minimum in one, two and multi-dimensional problems
• Unconstrained Optimization: gradient search methods (Steepest Descent, Newton’s Method, Conjugate Gradient Method)
• Linear programming (Simplex Method)
• Constrained Optimization: Lagrange and Kuhn-Tucker multipliers; penalty and barrier functions
• Global optimisation: Simulated Annealing

This syllabus contributes to the following areas of the UK-SPEC standard:

Toggle display of UK-SPEC areas.

 
Last modified: 16/10/2018 16:48

Aims

The aims of the course are to:

• Develop an understanding of the materials issues associated with man-made and naturally-derived materials for medical purposes. Specific case studies will be considered in addition to the general framework.

Objectives

As specific objectives, by the end of the course students should be able to:

• Identify the mechanism by which medical devices and implants come to market.
• Know about the classes of materials used in medical materials and the associated reasons.
• Understand the requirements for materials used in the body and assess potential for implant-body interactions.
• Perform quantitative evaluations of drug delivery.
• Identify appropriate implants and tissue engineering approaches for tissue and body function replacements.
• Understand bioethics and safety regulations associated with medical devices and implants.

Content

Course overview with introduction to biomaterials and medical devices (1L)

Bioethics and Material Sterilisation (1L)

• Origins of bioethics and contemporary challenges
• Definitions, techniques and metrology

Sector Analysis and Regulatory Affairs (1L)

• Areas of growth, market values
• Market trends
• Role of standards
• Approval process

Personalised Medicine and Future Technologies (1L)

• Personalised medinine
• Basic introduction to tissue engineering
• Advanced nanotechnology

Synthetic polymers for biomedical applications (2L)

• Introduction to polymers
• Synthetic biodegradable polymers 

Naturally derived polymers and hydrogels (1L)

• Naturally derived polymers
• Hydrogels

Tissue engineering (1L)

• General concepts of tissue engineering
• Combining cells with scaffolds
• Implant integration and vascularisation

Drug delivery and diffusion (2L)

• Drug delivery systems
• Diffusion controlled systems in drug delivery
• General strategies for drug delivery

Biological response to implants (2L+Q&A)

• Wound healing
• Biological response to biomaterials

Orthopaedic Implants - Hip Replacement (1.5L)

• Types of implant fixation
• Materials in hip implants
• Surface engineering approaches
• In vivo loading of hip joint

Cardiovascular Stents (2.5L)

• Balloon expandable & self expanding stents
• Materials in ​stents
• Stent mechanics and design

Aims

The aims of the course are to:

• Develop an understanding of the materials issues associated with man-made and naturally-derived materials for medical purposes. Specific case studies will be considered in addition to the general framework.

Objectives

As specific objectives, by the end of the course students should be able to:

• Identify the mechanism by which medical devices and implants come to market.
• Know about the classes of materials used in medical materials and the associated reasons.
• Understand the requirements for materials used in the body and assess potential for implant-body interactions.
• Perform quantitative evaluations of drug delivery.
• Identify appropriate implants and tissue engineering approaches for tissue and body function replacements.
• Understand bioethics and safety regulations associated with medical devices and implants.

Content

Course overview with introduction to biomaterials and medical devices (1L)

Bioethics and Material Sterilisation (1L)

• Origins of bioethics and contemporary challenges
• Definitions, techniques and metrology

Sector Analysis and Regulatory Affairs (1L)

• Areas of growth, market values
• Market trends
• Role of standards
• Approval process

Personalised Medicine and Future Technologies (1L)

• Personalised medinine
• Basic introduction to tissue engineering
• Advanced nanotechnology

Synthetic polymers for biomedical applications (2L)

• Introduction to polymers
• Synthetic biodegradable polymers 

Naturally derived polymers and hydrogels (1L)

• Naturally derived polymers
• Hydrogels

Tissue engineering (1L)

• General concepts of tissue engineering
• Combining cells with scaffolds
• Implant integration and vascularisation

Drug delivery and diffusion (2L)

• Drug delivery systems
• Diffusion controlled systems in drug delivery
• General strategies for drug delivery

Biological response to implants (2L+Q&A)

• Wound healing
• Biological response to biomaterials

Orthopaedic Implants - Hip Replacement (1.5L)

• Types of implant fixation
• Materials in hip implants
• Surface engineering approaches
• In vivo loading of hip joint

Cardiovascular Stents (2.5L)

• Balloon expandable & self expanding stents
• Materials in ​stents
• Stent mechanics and design

Aims

The aims of the course are to:

• Develop an understanding of the materials issues associated with man-made and naturally-derived materials for medical purposes. Specific case studies will be considered in addition to the general framework.

Objectives

As specific objectives, by the end of the course students should be able to:

• Identify the mechanism by which medical devices and implants come to market.
• Know about the classes of materials used in medical materials and the associated reasons.
• Understand the requirements for materials used in the body and assess potential for implant-body interactions.
• Perform quantitative evaluations of drug delivery.
• Identify appropriate implants and tissue engineering approaches for tissue and body function replacements.
• Understand bioethics and safety regulations associated with medical devices and implants.

Content

Course overview with introduction to biomaterials and medical devices (1L)

Bioethics and Material Sterilisation (1L)

• Origins of bioethics and contemporary challenges
• Definitions, techniques and metrology

Sector Analysis and Regulatory Affairs (1L)

• Areas of growth, market values
• Market trends
• Role of standards
• Approval process

Personalised Medicine and Future Technologies (1L)

• Personalised medinine
• Basic introduction to tissue engineering
• Advanced and nanotechnology

Synthetic polymers for tissue engineering applications (2L)

• Introduction to polymers
• Synthetic biodegradable polymers 

Host response to implants (1L)

• Wound repair
• Innate immunity
• The biological response to biomaterials

Using cells in tissue engineering (1L)

• What happens when biomaterials fail
• Cell therapy
• Combining cells with scaffolds
• Working with biology - implant integration and vascularisation

Naturally derived polymers for tissue engineering application (1L)

Drug delivery and diffusion (2L) + Q&A (1L)

• Drug delivery systems
• Diffusion controlled systems in drug delivery

Orthopaedic Implants - Hip Replacement (1.5L)

• Types of implant fixation
• Materials in hip implants
• Surface engineering approaches
• In vivo loading of hip joint

Cardiovascular Stents (2.5L)

• Balloon expandable & self expanding stents
• Materials in ​stents
• Stent mechanics and design