Engineering Tripos Part IIA, 3M1: Mathematical Methods, 2023-24
Module Leader
Lecturers
Prof M Girolami, Prof G Wells and Prof M Gales
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, 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 (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: 31/12/2023 12:49
Engineering Tripos Part IIA, 3M1: Mathematical Methods, 2024-25
Module Leader
Lecturers
Prof M Girolami, Prof G Wells and Dr H Ge
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, 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, Dr H Ge)
- 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: 22/01/2025 13:56
Engineering Tripos Part IIA, 3M1: Mathematical Methods, 2018-19
Module Leader
Lecturers
Prof G Csanyi, Prof G Wells and Prof M Gales
Lab Leader
Prof G Csanyi
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 (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
Coursework
Exploring Principal Component Analysis for dimensional reduction and data representation.
There is no Full Technical Report (FTR) associated with this module.
Booklists
Please see the Booklist for Part IIA Courses for references for this module.
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: 16/10/2018 16:48
Engineering Tripos Part IIA, 3M1: Mathematical Methods, 2021-22
Module Leader
Lecturers
Prof M Girolami, Dr A Kabla and Prof M Gales
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 (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
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: 20/05/2021 07:40
Engineering Tripos Part IIA, 3F4: Data Transmission, 2018-19
Module Leader
Lecturers
Dr R Venkataramanan, Prof. Ioannis Kontoyiannis
Lab Leader
Timing and Structure
Lent term. 16 lectures
Prerequisites
Knowledge of 3F1 assumed.
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.
- To understand basic congestion control protocols (TCP/IP), and routing algorithms used in the Internet.
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 operation of congestion control protocols (TCP/IP) and routing algorithms used in the internet
Content
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
- Baseband modulation: Desirable properties of the pulse for PAM; Nyquist criterion for no inter-symbol interference; Eye-diagrams
- 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
- 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)
Channel Coding (3L)
- 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.
Network Algorithms (3L)
- Congestion control in the Internet: window-based congestion control: TCP-Reno; slow-start, congestion avoidance
- Routing algorithms in the Internet: Djikstra's algorithm, Bellman-Ford and the similarities to the Viterbi algorithm
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
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
For network algorithms (last 3L):
- R. Srikant and L. Ying, Communication Networks, Cambridge University Press, 2014.
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.
E4
Understanding of and ability to apply a systems approach to engineering problems.
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: 12/12/2018 17:46
Engineering Tripos Part IIA, 3F4: Data Transmission, 2017-18
Module Leader
Lecturers
Dr R Venkataramanan, Prof. Ioannis Kontoyiannis
Lab Leader
Timing and Structure
Lent term. 16 lectures
Prerequisites
Knowledge of 3F1 assumed.
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.
- To understand basic congestion control protocols (TCP/IP), and routing algorithms used in the Internet.
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 operation of congestion control protocols (TCP/IP) and routing algorithms used in the internet
Content
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
- Baseband modulation: Desirable properties of the pulse for PAM; Nyquist criterion for no inter-symbol interference; Eye-diagrams
- 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
- 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)
Channel Coding (3L)
- 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.
Network Algorithms (3L)
- Congestion control in the Internet: window-based congestion control: TCP-Reno; slow-start, congestion avoidance
- Routing algorithms in the Internet: Djikstra's algorithm, Bellman-Ford and the similarities to the Viterbi algorithm
Further notes
The syllabus for this module has been revised for 2017-18, and therefore the lecture notes, examples papers etc. will be different from previous years. A list of relevant past Tripos questions will be provided towards the end of the module.
Coursework
Digital transmission systems
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
For network algorithms (last 3L):
- R. Srikant and L. Ying, Communication Networks, Cambridge University Press, 2014.
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.
E4
Understanding of and ability to apply a systems approach to engineering problems.
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: 18/02/2018 16:43
Engineering Tripos Part IIA, 3F1: Signals & Systems, 2017-18
Module Leader
Lecturers
Lab Leader
Timing and Structure
Michaelmas term. 16 lectures.
Aims
The aims of the course are to:
- Cover three basic topics in signals and systems which provide the basis for further topics in signal processing, communications, control and related subjects.
- Introduce the z-transform, which is the generalisation of the Laplace transform to discrete time systems.
- Introduce digital filtering.
- Introduce stochastic processes.
Objectives
As specific objectives, by the end of the course students should be able to:
- Be familiar with the theory and application of the z-transform.
- Analyse the stability of discrete-time systems
- Understand the use of correlation and spectral density functions.
- Analyse the behaviour of linear systems with random inputs.
Content
Enabling theory, application and design, Dr T. O’Leary and Dr F. Forni
Introduction to signals and systems, discrete time signals and systems, Z-transform (5L – O’Leary)
- Discrete signals and systems, LTI systems, convolution.
- z-transform and solution of linear difference equations
- System analysis in the z-domain.
- Impulse and frequency responses.
Applications & digital filtering (8L – Forni)
- Design and properties of digital feedback systems. Nyquist stability criterion.
- Design and properties of Digital Filters, FIR and IIR
- Analysis of systems with discrete/continuous interfaces.
- DTFT/DFT and links to z-transforms
- The Fast Fourier Transform (FFT)
- Windowed spectral analysis of data
- Introduction to 2D filtering, image analysis
Introduction to random processes and linear systems (3L – O’Leary)
- Continuous time random processes, correlation functions, spectral density.
- Response of continuous time linear systems to random excitation.
Coursework
Flight control
Learning objectives:
- Simulation of various aircraft models on the computer.
- Study real-time (manual) control and the limitations imposed by time delays.
- Design of a simple autopilot.
- Illustrate frequency response concepts in analogue and digital control systems, conditions for oscillation in feedback systems and stability.
- Gain familiarity with MATLAB.
Practical information:
-
Sessions will take place in the EIETL laboratory on Wednesdays and Fridays of full term from 11am-1pm.
-
Students will find it helpful to read through the lab sheet in advance of carrying out the experiment.
-
Students will have the option to submit a Full Technical Report.
Full Technical Report:
Students will have the option to submit a Full Technical Report.
Booklists
Please see the Booklist for Part IIA Courses for references for this module.
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.
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.
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: 22/09/2017 18:35
Engineering Tripos Part IIA, 3F1: Signals & Systems, 2018-19
Module Leader
Lecturers
Lab Leader
Timing and Structure
Michaelmas term. 16 lectures.
Aims
The aims of the course are to:
- Cover three basic topics in signals and systems which provide the basis for further topics in signal processing, communications, control and related subjects.
- Introduce the z-transform, which is the generalisation of the Laplace transform to discrete time systems.
- Introduce digital filtering.
- Introduce stochastic processes.
Objectives
As specific objectives, by the end of the course students should be able to:
- Be familiar with the theory and application of the z-transform.
- Analyse the stability of discrete-time systems
- Understand the use of correlation and spectral density functions.
- Analyse the behaviour of linear systems with random inputs.
Content
Enabling theory, application and design, Dr T. O’Leary and Dr F. Forni
Introduction to signals and systems, discrete time signals and systems, Z-transform (5L – O’Leary)
- Discrete signals and systems, LTI systems, convolution.
- z-transform and solution of linear difference equations
- System analysis in the z-domain.
- Impulse and frequency responses.
Applications & digital filtering (8L – Forni)
- Design and properties of digital feedback systems. Nyquist stability criterion.
- Design and properties of Digital Filters, FIR and IIR
- Analysis of systems with discrete/continuous interfaces.
- DTFT/DFT and links to z-transforms
- The Fast Fourier Transform (FFT)
- Windowed spectral analysis of data
- Introduction to 2D filtering, image analysis
Introduction to random processes and linear systems (3L – O’Leary)
- Continuous time random processes, correlation functions, spectral density.
- Response of continuous time linear systems to random excitation.
Coursework
Flight control
Learning objectives:
- Simulation of various aircraft models on the computer.
- Study real-time (manual) control and the limitations imposed by time delays.
- Design of a simple autopilot.
- Illustrate frequency response concepts in analogue and digital control systems, conditions for oscillation in feedback systems and stability.
- Gain familiarity with MATLAB.
Practical information:
-
Sessions will take place in the EIETL laboratory on Wednesdays and Fridays of full term from 11am-1pm.
-
Students will find it helpful to read through the lab sheet in advance of carrying out the experiment.
-
Students will have the option to submit a Full Technical Report.
Full Technical Report:
Students will have the option to submit a Full Technical Report.
Booklists
Please see the Booklist for Part IIA Courses for references for this module.
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.
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.
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: 16/05/2018 13:31
Engineering Tripos Part IIA, 3E10: Operations Management for Engineers, 2021-22
Leader
Lecturer
Dr T Masood
Lab Leader
Timing and Structure
Lent term. 16 lectures and 4 examples classes.
Aims
The aims of the course are to:
- Introduce Operations Management to students coming specifically from an engineering background.
- Give a foundation course for any engineering student who aims to join large manufacturing firms or go into management consultancy.
Objectives
As specific objectives, by the end of the course students should be able to:
- Understand the role, objectives and activities of Operations Management
- Be familiar with the main Operations Management concepts and techniques, which they can apply in practice.
Content
Operations management is concerned with the processes by which organisations deliver goods and services. The course will be covering the basic concepts and techniques used in managing modern manufacturing and service operations, from the composition of a manufacturing system, to planning and scheduling at factory level, and the coordination of supplier networks
- Process Fundamentals, Types of Manufacturing and Service Operations.
- Inventory Management.
- Forecasting.
- Machine-level Scheduling and Assembly Line Balancing.
- Factory-level Scheduling and MRP Systems.
- Toyota Production System and Lean Thinking.
- Quality Management, Six Sigma and Project Management
- Supply Chain Management
Further notes
TEACHING METHODS
A mixture of:
- Interactive lecture sessions
- Group discussion of case studies
- In-class exercises
Coursework
To be announced in lectures.
There is no Full Technical Report (FTR) associated with this module.
[Coursework Title]
Learning objectives:
Practical information:
- Sessions will take place in [Location], during week(s) [xxx].
- This activity [involves/doesn't involve] preliminary work ([estimated duration]).
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.
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.
D3
Identify and manage cost drivers.
D5
Ensure fitness for purpose for all aspects of the problem including production, operation, maintenance and disposal.
S1
The ability to make general evaluations of commercial risks through some understanding of the basis of such risks.
S2
Extensive knowledge and understanding of management and business practices, and their limitations, and how these may be applied appropriately to strategic and tactical issues.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E4
Understanding of and ability to apply a systems approach to engineering problems.
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).
P7
Awareness of quality issues.
P8
Ability to apply engineering techniques taking account of a range of commercial and industrial constraints.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
Last modified: 01/12/2021 08:16
Engineering Tripos Part IIA, 3E10: Operations Management for Engineers, 2019-20
Leader
Lecturer
Dr F Erhun-Oguz
Lab Leader
Dr F Erhun-Oguz
Timing and Structure
Lent term. 16 lectures and 4 examples classes.
Aims
The aims of the course are to:
- Introduce Operations Management to students coming specifically from an engineering background.
- Give a foundation course for any engineering student who aims to join large manufacturing firms or go into management consultancy.
Objectives
As specific objectives, by the end of the course students should be able to:
- Understand the role, objectives and activities of Operations Management
- Be familiar with the main Operations Management concepts and techniques, which they can apply in practice.
Content
Operations management is concerned with the processes by which organisations deliver goods and services. The course will be covering the basic concepts and techniques used in managing modern manufacturing and service operations, from the composition of a manufacturing system, to planning and scheduling at factory level, and the coordination of supplier networks
- Process Fundamentals, Types of Manufacturing and Service Operations.
- Inventory Management.
- Forecasting.
- Machine-level Scheduling and Assembly Line Balancing.
- Factory-level Scheduling and MRP Systems.
- Toyota Production System and Lean Thinking.
- Quality Management, Six Sigma and Project Management
- Supply Chain Management
Further notes
TEACHING METHODS
A mixture of:
- Interactive lecture sessions
- Group discussion of case studies
- In-class exercises
Coursework
To be announced in lectures.
There is no Full Technical Report (FTR) associated with this module.
[Coursework Title]
Learning objectives:
Practical information:
- Sessions will take place in [Location], during week(s) [xxx].
- This activity [involves/doesn't involve] preliminary work ([estimated duration]).
Full Technical Report:
There is no Full Technical Report (FTR) associated with this module.
Booklists
Please see the Booklist for Part IIA Courses for references for this module.
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.
D3
Identify and manage cost drivers.
D5
Ensure fitness for purpose for all aspects of the problem including production, operation, maintenance and disposal.
S1
The ability to make general evaluations of commercial risks through some understanding of the basis of such risks.
S2
Extensive knowledge and understanding of management and business practices, and their limitations, and how these may be applied appropriately to strategic and tactical issues.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E4
Understanding of and ability to apply a systems approach to engineering problems.
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).
P7
Awareness of quality issues.
P8
Ability to apply engineering techniques taking account of a range of commercial and industrial constraints.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
Last modified: 15/05/2019 09:30
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