Engineering Tripos Part IIB, 4A9 Molecular Thermodynamics, 2025-26
Module leader
Lecturers
Dr A J White and Dr M Onn
Timing and Structure
Michaelmas term. 14 lectures + 2 examples classes. Assessment: 100% exam.
Prerequisites
3A5 Helpful but not essential
Content
This module provides an introduction to the relationship between the microscopic and macroscopic descriptions of thermodynamics and fluid mechanics. The module is equally divided between the two main microscopic approaches, kinetic theory and statistical mechanics, each of which has its place for solving different types of problem. If you have ever wondered about the interpretation of viscosity and thermal conductivity at a molecular level; why the Lewis number is taken as unity for combustion calculations; how to estimate the rate of a gaseous chemical reaction; why the speed of sound in a gas isn’t faster (or slower); what are the interpretations of heat, work and entropy at a molecular level; how you can estimate the specific heat of a gas just by counting, how the conservation equations of fluid flow can be derived from microscopic considerations; what the Boltzmann distribution is and why it is so important; why the no-slip boundary condition is such a good approximation for continuum flow; when the Navier-Stokes equations lose their validity; how gases behave under highly rarefied conditions; how to set about calculating the surface temperature of the space shuttle during re-entry; and many other allied phenomena; then you should find many things to interest you in this module.
The main objective is to obtain a good physical understanding of the relationship between the microscopic and macroscopic viewpoints of thermodynamics and fluid mechanics. At first exposure, this can be a profound experience as it gradually emerges that the macroscopic thermo-fluid-dynamic behaviour of gases can be explained, almost in its entirety, by the results of collisions between molecules. On completion of the module students will have a good appreciation of the microscopic basis of a wide range of macroscopic phenomena.
Kinetic theory and statistical mechanics are complementary theories which are used to give quantitative estimates of macroscopic phenomena, often by using quite simple mathematics. Students will be equipped with the tools to estimate, from microscopic data, many macroscopic thermodynamic properties which would otherwise need to be obtained experimentally. They will also be in a position to construct their own simple molecular models to provide working solutions to specific problems where no data exists. To this end, the lectures will stress the importance of physical understanding backed up by simple mathematical modelling.
More accurate and advanced calculations require a more formalised and complex mathematical approach. Examples occur in rarefied gas dynamics where the fluid cannot be treated as a continuum and the Navier-Stokes equations no longer apply, and in statistical mechanical calculations where inter-molecular forces dominate. Although the lectures will not address such topics in detail, a further objective is to put the student in a position where he or she is ready to assimilate the more advanced literature in both kinetic theory and statistical mechanics.
GAS KINETIC THEORY Dr A J White (7 lectures + 1 examples class)
- Elementary kinetic theory
Intermolecular forces and molecular models, Density, Pressure, Internal energy, Kinetic and thermodynamic temperature, Specific heat capacity, Molecular degrees of freedom, Equipartition of energy, Rôle of intermolecular forces, Imperfect gases.
- Transport properties and chemical equilibrium
Collision rates, Mean free path, Viscosity, Thermal conductivity, Prandtl number, Mixtures of different gases, Diffusion, Schmidt and Lewis numbers, Chemical equilibrium, Law of mass action.
- Molecular velocity distributions
Velocity distribution functions, Effect of collisions, Maxwell-Boltzmann distribution, Statistical averages, Nonequilibrium velocity distributions, Boltzmann’s equation, Relaxation time to equilibrium.
- Molecular gas dynamics
Derivation of mass, momentum and energy conservation equations from kinetic theory, Isentropic flow, Navier-Stokes equations, Rarefied gases, Knudsen number, Boundary slip, Collisionless flow and heat transfer.
STATISTICAL MECHANICS Dr A M Boies (7 lectures + 1 examples class)
- Introduction to Statistical Mechanics
Motivation, microstates, statistical analogues of entropy, the Boltzmann relation, probability examples and averaging procedures.
- The Partition Functions
Microcanonical, canonical and grand canonical ensembles, the system partition function and its relation to thermodynamic properties, the single-particle partition function.
- Quantum Mechanics and Energy States
Key results from quantum mechanics, the de Broglie wavelength, the Schrodinger equation and its solution for a particle in a box, density of energy states and energy levels, degeneracy.
- The Ideal Gas Model
The statistical basis of the ideal gas, the high temperature limit and the Boltzmann distribution, the Sackur-Tetrode equation, temperature-dependence of specific heats (vibrational, rotational and electronic excitation energy modes), the equipartation of energy.
- Relationship to Thermodynamics and Probability
Statistical interpretation of heat and work transfers and the First Law. Thermodynamic probability and property fluctuations.
- Other Statistical Models
Other counting methods, the Einstein crystal and the rubber band model.
Booklists
Please refer to the Booklist for Part IIB Courses for references to this module, this can be found on the associated Moodle course.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
IA2
Demonstrate creative and innovative ability in the synthesis of solutions and in formulating designs.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
Last modified: 04/06/2025 13:24
Engineering Tripos Part IIB, 4A3: Turbomachinery, 2025-26
Module Leader
Lecturers
Prof R.J. Miller and Dr J. Taylor
Lab Leader
Dr J. Taylor
Timing and Structure
Michaelmas term. 75% exam / 25% coursework. 12 lectures (including examples classes) + coursework
Prerequisites
3A1 and 3A3 assumed
Aims
The aims of the course are to:
- provide a general understanding of the principles that govern the design of axial flow and radial flow turbomachines.
Objectives
As specific objectives, by the end of the course students should be able to:
- understand the principles underpinning the study of turbomachine aerodynamics.
- know the requirements for different type of turbomachines.
- know the factors which influence the overall design of turbomachine stages and which influence the matching of components.
- know the factors which influence overall design of turbomachines for propulsion and stationary power-plant applications.
- evaluate the performance of turbine and compressor bladerows and stages using mean-line analyses.
- select a design for a given duty.
- present and understand information on stage and machine design.
- describe and understand compressor off-design performance.
- analyse the performance of propulsion systems and stationary power plant.
Content
Applications and Characteristics of Turbomachines (12L, Prof. RJ Miller and Dr J. Taylor)
- Stage design and choice of design parameters.
- Specific speed, dynamic scaling and measures of efficiency.
- Analysis of the mean-line flow in compressors and turbines.
- Radial flow turbomachines.
- Characteristics of compressors, pumps and turbines.
- Matching of components: compressors and turbines; nozzles, throttles and diffusers. Compressor off-design problems; stall and its consequences.
- Application of turbomachines: power plant and aircraft propulsion systems.
Coursework
| Coursework | Format |
Due date & marks |
|---|---|---|
|
Cascade Experiment Testing of a turbine cascade in a small wind tunnel to measure the blade surface pressure distribution, loss coefficient and flow exit angle. Time required: About 3 hours in the lab plus 4 hours write up. Learning objectives:
|
Experimental work done in pairs. Individual report. Anonymously marked. |
Reports are due 2 weeks after the date of the experiment. [15/60] |
Booklists
Please refer to the Booklist for Part IIB Courses for references to this module, this can be found on the associated Moodle course.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
IA2
Demonstrate creative and innovative ability in the synthesis of solutions and in formulating designs.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
D1
Wide knowledge and comprehensive understanding of design processes and methodologies and the ability to apply and adapt them in unfamiliar situations.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P1
A thorough understanding of current practice and its limitations and some appreciation of likely new developments.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US3
An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.
US4
An awareness of developing technologies related to own specialisation.
Last modified: 04/06/2025 13:24
Engineering Tripos Part IIB, 4A2: Computational Fluid Dynamics, 2025-26
Module Leader
Lab Leader
Timing and Structure
Michaelmas term. In-person lectures and demonstrations. Coursework with integrated lectures. Assessment: 100% coursework.
Prerequisites
3A1 and 3A3 assumed. Pre-module reading about Fortran helpful
Aims
The aims of the course are to:
- Provide an introduction to the field of computational fluid mechanics.
- Develop an understanding of how numerical techniques are devised.
- Implement these techniques in a practical computer program.
- Overview the nature of simulation in the future and advanced methods.
Objectives
As specific objectives, by the end of the course students should be able to:
- Formulate numerical approximations to partial differential equations.
- Write computer programs for solving the resulting difference equations and processing their solutions.
- Learn about modern methods to improve simulation accuracy.
- Appreciate the capabilities of numerical methods to predict complex flows.
Content
This is a coursework based project. The students write a Computational Fluid Dynamics (CFD) program to solve the Euler equations in 2D with time marching. There are also some basic mesh generation, pre-processing and post-processing tasks. The assessment is through two reports: The first report demonstrates the performance of a basic CFD program and studies basic properties of finite differencing methods. This is to be submitted in Week 6 of the Michaelmas term. The 2nd report demonstrates the coding and performance of more advanced CFD algorithms with discussion on a selected advanced CFD topic. The performance and traits of the extended CFD code are contrasted with expected traits for a range of subsonic, transonic and supersonic flows. The final report is submitted after the end of the Michaelmas term in Week 10.
Writing a CFD Solver and Numerical Concepts (5L)
- The proper use of CFD and the equations used for compressible flows
- Finite difference, finite volume, finite element approaches
- Program specification and structure
- Difference schemes, stability, dispersion and diffusion errors
- Turbulence modelling, adaptive methods, multi-phase flows and parallel computing
- Hyperbolicity and the upwinding method for advection
- Total variation diminishing (TVD) methods
Coursework
Brief Progress Check Report / Week 6 of Michaelmas term [25%]
Complete Final Report / Week 10 after end of Michaelmas term [75%]
The entire module is expected to take around 80 hours, similar to other exam based modules. It includes:
- 5 hours of lectures
- Approximately 50 hours of demonstrated sessions, you are not expected to attend all and attendance is not recorded
- Report writing
The demonstrated sessions will help you with:
- Examples of basic Fortran programs
- Mesh generation for simplified geometries
- Constructing an initial flowfield guess
- Finite volume discretisation, evaluation of fluxes
- Application of boundary conditions
- Time marching, simple LAX method
- Convergence & accuracy testing
- Solver enhancements to investigate a choice of challenging test cases
- Post-processing to produce final report data
| Coursework | Format |
Due date & marks |
|---|---|---|
|
[Coursework activity #1 / Interim] Coursework 1 brief description Learning objective:
|
Individual Report anonymously marked |
Thu week 6 [25%] |
|
[Coursework activity #2 / Final] Coursework 2 brief description Learning objective:
|
Individual Report anonymously marked |
Wed week 10 [75%] |
Booklists
Main course text is:
LeVeque R. J. 2002. Finite Volume Methods for Hyperbolic Problems, Cambridge University Press.
Also, useful material can be found in these texts:
Ferziger J. H. and Peric M. 2002. Computational Methods for Fluid Dynamics, Springer.
Toro E. F. 2009. Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction, Springer
Hirsch C. 1988-1990 Numerical Computation of Internal and External Flows, Volumes 1 and 2, Wiley
Davies R., Rea A. and Tsaptsinos D. Introduction to FORTRAN 90, Student Notes, Queen's University, Belfast
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
IA2
Demonstrate creative and innovative ability in the synthesis of solutions and in formulating designs.
Knowledge and Understanding
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
US3
An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.
Last modified: 04/06/2025 13:24
Engineering Tripos Part IIA, 3M1: Mathematical Methods, 2025-26
Module Leader
Lecturers
Prof M Girolami, Prof M Gales, Dr J Dean
Lab Leader
Prof M Girolami
Timing and Structure
Lent term. 16 lectures and coursework.
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 (5L, Dr J Dean)
- 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 (6L, 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
Coursework
Exploring Principal Component Analysis for dimensional reduction and data representation.
There is no Full Technical Report (FTR) associated with this module.
Booklists
Please refer to the Booklist for Part IIA Courses for references to this module, this can be found on the associated Moodle course.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
E4
Understanding of and ability to apply a systems approach to engineering problems.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
P8
Ability to apply engineering techniques taking account of a range of commercial and industrial constraints.
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
US3
An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.
Last modified: 02/02/2026 13:48
Engineering Tripos Part IIA, 3G5: Biomaterials, 2025-26
Module Leader
Lecturers
Prof S Huang, Prof A Markaki,
Lab Leader
Prof A Markaki
Timing and Structure
Michaelmas term. 16 lectures.
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)
- Medical devices detailed definitions and classifications
- Classes of biomaterials overview
- Biocompatibility
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
Further notes
Examples papers
Example papers are available on Moodle.
Coursework
Full Technical Report:
Students will have the option to submit a Full Technical Report.
Booklists
Biomedical Engineering: Bridging Medicine and Technology by W. Mark Saltzman
Biomaterial Science: An Introduction to Materials in Medicine. Edited by Ratner et al.
Examination Guidelines
Please refer to Form & conduct of the examinations.
Last modified: 04/06/2025 13:22
Engineering Tripos Part IIA, 3G4: Medical Imaging & 3D Computer Graphics, 2025-26
Module Leader
Lecturers
Prof Andrew Gee, Prof Graham Treece
Timing and Structure
Lent term. 10 flipped classroom interactive seminars and 6 traditional lectures. Lectures (but not seminars) will be recorded.
Aims
The aims of the course are to:
- Introduce state-of-the-art techniques for the acquisition, representation and visualisation of structured 3D data.
Objectives
As specific objectives, by the end of the course students should be able to:
- Explain the principles of operation of CT, nuclear medicine and diagnostic ultrasound and magnetic resonance imaging.
- Be aware of the advantages and risks associated with these techniques and understand the types of diagnostic problems that each can address.
- Be aware of other types of data to which segmentation and visualisation algorithms can be applied (eg. CAD models).
- Understand the different ways to represent 3D data and appreciate the advantages and disadvantages of each technique.
- Know how to extract surfaces from volumetric data.
- Be aware of the range of computer graphics algorithms and hardware used to visualise 3D data.
- Understand how surfaces can be rendered using suitable illumination and reflection models.
- Know how to visualise voxel arrays directly using volume rendering techniques.
Content
The main application area considered in the module is diagnostic medical imaging: 3D data is acquired using one of the clinical imaging modalities (e.g. CT), represented as a voxel array or segmented into surfaces, then visualised using computer graphics techniques. While medical imaging is the focus of the course, many of the techniques used to segment, represent and visualise the 3D data sets are generic and can equally be applied to other types of data, such as CAD models.
Medical Image Acquisition (flipped classroom, 5 interactive seminars, Prof Andrew Gee)
- X-rays and the Radon transform
- Tomographic reconstruction algorithms in both the spatial and frequency domains
- Emission computed tomography
- SPECT and PET
- Iterative reconstruction algorithms
- 2D and 3D ultrasound
- Introduction to Magnetic Resonance Imaging
Extracting information from 3D data (6 lectures, Prof Graham Treece)
Polygonal representations and efficient storage
- Parametric curves and surfaces
- Subdivision and display of parametric surfaces
Surfaces from sampled data
- Thresholding, morphological operators and contours
- Surface extraction - marching cubes
Interpolating sampled data
- Interpolation of isotropic data
- Distance transforms and interpolation of non-isotropic data
- Unstructured data - RBFs and Delaunay triangulation
Direct surface capture
- Laser stripe scanners
- Space encoding: the cubicscope
3D Graphical Rendering (flipped classroom, 5 interactive seminars, Prof Andrew Gee)
- Viewing systems: viewpoints and projection
- Reflection and illumination models: the Phong reflection model
- Surface rendering: incremental shading techniques, hidden surface removal using Z-buffers
- Shadows and textures
- Ray tracing
- Volume rendering
- Computer graphics hardware
Coursework
A computer-based laboratory exploring the visualization and analysis of CT data. Students write algorithms to generate slices through the 3D data set, observing the differences between linear and nearest-neighbour interpolation. They go on to fit surfaces to the data and analyse some basic geometric properties of the surfaces. Finally, they use Vulkan to visualize the surfaces from different viewpoints and under different lighting conditions, including a "fly-through" visualization mode.
Learning objectives:
- To appreciate the 3D nature of the data acquired by many medical imaging devices.
- To investigate how such data can be stored and resliced in a C++ software framework.
- To consider techniques for extracting surfaces from such data.
- To understand how surfaces can be represented by triangular meshes and stored in suitable C++ data structures.
- To analyse properties of such surfaces using basic computational geometry algorithms.
- To experiment with graphical rendering in a Vulkan framework.
Practical information:
- Sessions will take place in the DPO, during weeks 1-8.
- This activity involves preliminary work (reading the handout, around one hour).
Full Technical Report:
Students will have the option to submit a Full Technical Report.
Booklists
Please refer to the Booklist for Part IIA Courses for references to this module, this can be found on the associated Moodle course.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P1
A thorough understanding of current practice and its limitations and some appreciation of likely new developments.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
P8
Ability to apply engineering techniques taking account of a range of commercial and industrial constraints.
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
US3
An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.
US4
An awareness of developing technologies related to own specialisation.
Last modified: 04/06/2025 13:22
Engineering Tripos Part IIA, 3G3: Introduction to Neuroscience, 2025-26
Module Leader
Lecturers
Prof G Hennequin, Prof M Lengyel
Lab Leader
Prof G Hennequin
Timing and Structure
Lent term. 16 lectures.
Aims
The aims of the course are to:
- Introduce students to how the brain processes sensory information, controls our actions, learns through experience and lays down memories.
- Elucidate the computational and engineering principles of brain function.
Objectives
As specific objectives, by the end of the course students should be able to:
- Have a basic grasp of neuroscience that can act as foundation for further study.
- Understand the basic principles of sensory processing, decision making, learning and memory and how engineering concepts can be applied to them.
Content
Perception and action (8L) (Prof G Hennequin)
- Neurons and synapses
- Introduction to basic cell physiology and ion channels
- How do neurons communicate? The action potential and the Hodgkin-Huxley model
- Perception as Bayesian inference
- Decision making
Learning and memory (8L) (Prof M Lengyel)
- The cellular basis of learning and memory
- Animal learning
- Memory
Coursework
Simulation of different types of neural coding of natural images. Laboratory report and/or Full Technical Report.
Efficient coding in visual cortex
Learning objectives:
- To apply basic techniques from linear algebra, optimization and statistics to understand how the primary visual cortex might efficiently encode natural scenes
- To learn (or consolidate) how to implement simple algorithms in Python
- To consolidate critical analysis and report-writing skills
Practical information:
- Sessions take place in the DPO.
- This activity involves preliminary homework (estimated 30 min duration), consisting of mathematical derivations (including some basic vector calculus) to be performed before coming to the lab.
Full Technical Report:
Students will have the option to submit a Full Technical Report. This will take the form of a unifying review of 2 papers addressing efficient coding of sensory information in the brain.
Booklists
Please refer to the Booklist for Part IIA Courses for references to this module, this can be found on the associated Moodle course.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
US3
An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.
Last modified: 04/06/2025 13:22
Engineering Tripos Part IIA, 3G1: Molecular Bioengineering I, 2025-26
Module Leader
Lecturers
Dr J Molloy, Prof T O'Leary, Prof G Micklem
Lab Leader
Timing and Structure
Michaelmas term. 16 lectures, 1 computational laboratory class. This is an intensive introductory level undergraduate course targeted at third year Engineering students.
Prerequisites
None
Aims
The aims of the course are to:
- provide a basic grounding in biomolecular engineering along with underpinning molecular biology.
- increase awareness for the opportunities for bioengineering within modern biology.
- have enough background knowledge and familiarity with the terminology to be able to play a productive role collaborating with biologists.
Objectives
As specific objectives, by the end of the course students should be able to:
- appreciate the potential of engineering living systems
- appreciate the capabilities of applying evolution in a laboratory setting
- understand the fundamental molecules and processes required for gene expression and replication
- understand gene structure and regulation in simple organisms
- understand what is feasible with genetic engineering, and the underpinning molecular techniques
- design synthetic genetic circuits: understanding basic mathematical and molecular biological frameworks
- design synthetic genetic circuits: living systems vs cell-free systems
- understand the latest technologies for genome sequencing, genome analysis, and genome-scale experimental methods
- appreciate DNA as a construction material for information storage and other applications
Content
The structure of the course will be as follows.
Lectures 1-5 (GM): Evolution; genetic information; molecular cloning, DNA amplification; example applications
Lectures 6-12 (SB): Gene expression and regulation; circuit design, construction and characterisation; noise; cell-free systems
Lectures 13-16 (GM): Genomes, genome sequencing and transcriptomics; sequence alignment; sequencing applications; DNA for construction and data storage; DNA dynamics
Further notes
Normal teaching 2022-2023
We hope that this year all teaching and activities will take place as they were before the pandemic. Please be respectful of any individuals who still need to wear masks.
Labs: the lab will be held in person in a lecture room and carried out on your own laptops - please ensure they are charged.
Recordings: the terms under which the University provides recordings means that they are strictly for your personal use only and should not be distributed further in any form.
Examples papers
See the course Moodle site
Coursework
Laboratory Practical - the lab is computational and will concern the design of a COVID-19 test and vaccine.
Learning objectives:
- To become familiar with basic tools for viewing nucleic acid sequences
- To consider the overall workflow for a PCR-based virus test and design the necessary primer sequences
- To consider the overall workflow for generation of a fusion protein and to design the necessary sequences
Practical information:
- Preliminary work (~1hour) and completing an online test in advance of the lab will be worth 1 point. The test will be available through Moodle.
Full Technical Report:
There is no Full Technical Report (FTR) associated with this module.
Booklists
Please refer to the Booklist for Part IIA Courses for references to this module, this can be found on the associated Moodle course.
Examination Guidelines
Please refer to Form & conduct of the examinations.
Last modified: 17/09/2025 13:09
Engineering Tripos Part IIA, 3F4: Data Transmission, 2025-26
Module Leader
Lecturers
Prof A Guillen i Fabregas, Dr J Sayir
Lab Leader
Dr J Sayir
Timing and Structure
Lent term. 16 lectures
Aims
The aims of the course are to:
- Cover a range of topics which are important in modern communication systems.
- Extend the basic material covered in the Engineering Part IB Communications course to deal with data transmission over baseband (low frequency) channels as well bandpass (higher frequency) channels.
- Analyse the effects of noise in some detail.
- Understand the technique of convolutional coding to protect information transmitted over noisy channels.
- Unferstand the foundations of communications over wireless channels.
Objectives
As specific objectives, by the end of the course students should be able to:
- Understand the different components of a communication network, in particular the role of the physical layer versus the network layer.
- Be able to represent waveforms as vectors in a signal space.
- Appreciate that pulses may be shaped to control the bandwidth of a signal and reduce inter-symbol interference, and be aware of the limits on transmission rate if ISI is to be avoided.
- Be able to describe and analyse demodulation of digital bandpass modulated signals in noise.
- Calculate the probability of error of various modulation schemes as a function of the signal-to-noise-ratio.
- Appreciate how equalisation can correct for undesirable channel characteristics and be able to design simple equalisers.
- Understand the principles of Orthogonal Frequency Division Multiplexing for communication over multi-path wideband channels
- Understand the need for coding, i.e., adding redundancy to control the effects of transmission errors.
- Understand the principles of convolutional coding, and be able to design a Viterbi decoder for convolutional codes.
- Understand the modelling and performance analysis over wireless communications channels.
Content
Channel Coding (4L)
- Introduction to error correction and linear codes
- Convolutional codes: State Diagram and Trellis representations, Viterbi decoding algorithm
- Distance properties of convolutional codes using the transfer function derived from state diagram; free-distance of convolutional codes.
Fundamentals of Modulation and Demodulation (7L)
- Introduction: The overall commuication network and the roles of the physical layer and the network layer
- Signal Space: representing waveforms as elements a vector space
- Modelling the noise as a Gaussian random process. Additive White Gaussian Noise (AWGN)
- Optimal demodulation and detection at the receiver in the presence of AWGN: Matched filter demodulator, optimal detection using the maximum-a-posteriori probability (MAP) rule
- Baseband modulation: Desirable properties of the pulse for PAM; Nyquist criterion for no inter-symbol interference; Eye-diagrams
- Passband modulation: QAM, M-ary FSK (Orthogonal signalling)
- Performance analysis of modulation schemes (PAM, QAM, Orthogonal signaling etc.): probability of detection error and bandwidth efficiency
Advanced Topics in PHY-layer (3L)
- Brief discussion of coded modulation
- Equalisation techniques to deal with inter-symbol interference: ZF and MMSE equalizers
- Orthogonal Frequency Division Multiplexing (OFDM)
Wireless Communications (2L)
- Modelling of wireless communications channels
- Error probability analysis over wireless communications channels
Further notes
The syllabus for this module was updated (with significant changes) in 2017-18. A list of relevant past Tripos questions is available on Moodle.
Coursework
Digital transmission systems
NOTE: This lab is being redesigned for the year 2020-21 and will be released in Week 2 of Lent Term. There will be an option to do the lab remotely for those needing to self-isolate or studying remotely.
The information below refers to the previous version of the lab, and will be updated in due course.
Learning objectives:
- To investigate, using a hardware simulation of baseband transmission channels, the phenomenon of inter-symbol interference, and to measure bit error rate (BER) due to noise
- To use the eye diagram as a diagnostic tool, and to understand its limitations.
- To compare the measured dependence of BER on signal-to-noise Ratio (SNR) with theoretical predictions, and explain the differences by considering how the assumptions made in the theoretical analysis compare with the real situation.
Practical information:
- Sessions will take place in EIETL, during week(s) [xxx].
- This activity involves preliminary work-- reading the lab handout [estimated duration: 1 hour].
Full Technical Report:
Students will have the option to submit a Full Technical Report.
Booklists
For Physical-layer communications (first 13L):
- B. Rimoldi, Principles of Digital Communication: A Top-Down Approach, Cambridge University Press, 2016]
- R. Gallager, Principles of Digital Communication, Cambridge University Press, 2008
- U. Madhow, Fundamentals of Digital Communication, Cambridge University Press, 2008
Examination Guidelines
Please refer to Form & conduct of the examinations.
Last modified: 04/06/2025 13:21
Engineering Tripos Part IIA, 3F3: Statistical Signal Processing, 2025-26
Module Leader
Lecturers
Prof S. J. Godsill, Dr G Cantwell
Lab Leader
Timing and Structure
Michaelmas term. 16 lectures.
Aims
The aims of the course are to:
- Study more advanced probability theory, leading into random process theory.
- Study random process theory and focus on discrete time methods.
- Introduce inferential methodology, including maximum likelihood and Bayesian procedures, and examples drawn from signal processing. Objectives
Objectives
As specific objectives, by the end of the course students should be able to:
- By the end of the course students should be familiar with the fundamental concepts of statistical signal processing, including random processes, probability, estimation and inference.
Content
Lectures 1-8: Advanced Probability and Random Processes
-
Probability and random variables
-
Sample space, events, probability measure, axioms.
-
Conditional probability, probability chain rule, independence, Bayes rule.
-
Random variables (discrete and continuous), probability mass function (pmf), probability density function (pdf), cumulative distribution function, transformation of random variables.
-
Bivariate: conditional pmf, conditional pdf, expectation, conditional expectation.
-
Multivariates: marginals, Gaussian (properties), characteristic function, change of variables (Jacobian.)
-
-
Random processes
-
Definition of a random process, finite order densities.
-
Markov chains.
-
Auto-correlation functions.
-
Stationarity–strict sense, wide sense. Examples: iid process, random-phase sinusoid.
-
Ergodicity, Central limit theorem.
-
Spectral density.
-
Response of linear systems to stochastic inputs – time and frequency domain.
-
Time series models: AR, MA, ARMA
-
Lectures 9-16: Detection, Estimation and Inference
-
Basic linear estimation theory: BLUE, MMSE, bias, variance
-
Wiener filters
-
Matched filters
-
Least squares, maximum likelihood, Bayesian inference.
-
The ML/Bayesian linear Gaussian model
-
Maximum likelihood and Bayesian estimation
-
Example inference models: frequency estimation, AR model, Estimation of parameters for discrete Markov chain.
Coursework
Random variables and random number generation
Learning objectives:
- Understand random variables and functions of random variables and their simulation
- To study the Jacobian as used with random variables
- To experiment with methods for non-uniform random number generation
Practical information:
- Sessions will take place in [Location], during week(s) [xxx].
- This activity involves preliminary work.
Full Technical Report:
Students will have the option to submit a Full Technical Report.
Booklists
Please refer to the Booklist for Part IIA Courses for references to this module, this can be found on the associated Moodle course.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
D4
Ability to generate an innovative design for products, systems, components or processes to fulfil new needs.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P1
A thorough understanding of current practice and its limitations and some appreciation of likely new developments.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
P8
Ability to apply engineering techniques taking account of a range of commercial and industrial constraints.
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
US3
An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.
Last modified: 04/06/2025 13:21
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