Core modules
Your first year will establish the foundations of Discrete Mathematics and its applications, covering proof, formal arguments, rigour and calculations, as well as mathematical reasoning, combinatorial analysis and discrete structures.
In your second year, you will develop a rigorous understanding of the subject's theoretical basis, which will prepare you for later specialisation.
In your third year, you will work alongside academics on an individual project as well as focusing on applications of Discrete Mathematics to Computer Science, and completing advanced modules on algorithms and computation.
In your fourth year, you will have the flexibility to choose optional modules, tailoring the degree to your interests.
In each year of their course, students are expected to study a core group of modules and to make up the required normal load for the year by choosing a set of optional modules. There is a choice of optional modules available and there may be requirements to be satisfied by the choices: that a minimum number be chosen from a specific list.
All students complete Refresher Mathematics before the start of term, a 0 credit module designed to reinforce your existing mathematical knowledge.
Year One
Refresher Mathematics
This is a pre-sessional course for incoming first-year undergraduates from mathematics and joint-mathematics courses. The aim is to refresh A level mathematics and certain core items from further mathematics in preparation for starting their degree.
Read more about the Refresher Mathematics module,Link opens in a new window including the methods of teaching and assessment (content applies to 2023/24 year of study).
Programming for Computer Scientists
This module aims to help you develop your programming skills, regardless of your starting skill level. You will develop problem solving skills through the lens of procedural and object-oriented programming. Using the Java programming language, you will engage with practical work that shall enable you to learn concepts such as classes, encapsulations, arrays, inheritance and advanced topics such as multi-threading and reflection. By engaging with the Warwick Robot Maze environment, you can expect to gain skills in errors analysis and debugging that will help you produce well-designed and well-tested code.
Read more about the Programming for Computer Scientists moduleLink opens in a new window, including the methods of teaching and assessment (content applies to 2023/24 year of study).
Design of Information Structures
Following on from Programming for Computer Scientists, on the fundamentals of programming, this module will teach you all about data structures and how to program them. We will look at how we can represent data structures efficiently and how we can apply formal reasoning to them. You will also study algorithms that use data structures. Successful completion will see you able to understand the structures and concepts underpinning object-oriented programming, and able to write programs that operate on large data sets.
Read more about the Design of Information Structures moduleLink opens in a new window, including the methods of teaching and assessment (content applies to 2023/24 year of study).
Discrete Mathematics and its Applications I
In this foundation module, you’ll learn the basic language, concepts and methods of discrete mathematics, while developing your appreciation of how these are used in algorithms and data structures. By the end, you should be able to appreciate the role of formal definitions, mathematical proofs and underlying algorithmic thinking in practical problem-solving. You’ll acquire knowledge of logic, sets, relations and functions, and learn summation techniques (manipulations and finite calculus) and concepts including asymptotics and the big-O notation to prepare you for more advanced techniques in computer science.
Read more about the Discrete Mathematics and its Applications I moduleLink opens in a new window, including the methods of teaching and assessment (content applies to 2023/24 year of study).
Discrete Mathematics and its Applications II
During this module, you will build on your foundations in discrete mathematics through the study of concepts such as discrete probability and graph theory; learning how to apply these methods in problem-solving. By the end of your course, you will be able to use probabilistic techniques to analyse basic discrete structures and algorithms, understand the importance of asymptotic notation, and be able to use it to analyse asymptotic performance for some basic algorithms. Also, you will study the properties of graphs and related discrete structures, and be able to relate these to practical examples.
Read more about the Discrete Mathematics and its Applications II moduleLink opens in a new window, including the methods of teaching and assessment (content applies to 2023/24 year of study).
Linear Algebra
Linear algebra addresses simultaneous linear equations. You will learn about the properties of vector spaces, linear mappings and their representation by matrices. Applications include solving simultaneous linear equations, properties of vectors and matrices, properties of determinants and ways of calculating them. You will learn to define and calculate eigenvalues and eigenvectors of a linear map or matrix. You will have an understanding of matrices and vector spaces for later modules to build on.
Read more about the Linear Algebra moduleLink opens in a new window, including the methods of teaching and assessment (content applies to 2023/24 year of study).
Calculus I/II
Calculus is the mathematical study of continuous change. In this module there will be considerable emphasis throughout on the need to argue with much greater precision and care than you had to at school. With the support of your fellow students, lecturers and other helpers, you will be encouraged to move on from the situation where the teacher shows you how to solve each kind of problem, to the point where you can develop your own methods for solving problems. By the end of the year you will be able to answer interesting questions like, what do we mean by `infinity’?
Read more about these modules, including the methods of teaching and assessment (content applies to 2023/24 year of study):
Sets and Numbers
It is in its proofs that the strength and richness of mathematics is to be found. University mathematics introduces progressively more abstract ideas and structures, and demands more in the way of proof, until most of your time is occupied with understanding proofs and creating your own. Learning to deal with abstraction and with proofs takes time. This module will bridge the gap between school and university mathematics, taking you from concrete techniques where the emphasis is on calculation, and gradually moving towards abstraction and proof.
Read more about the Sets and Numbers moduleLink opens in a new window, including the methods of teaching and assessment (content applies to 2023/24 year of study).
Introduction to Probability
This module takes you further in your exploration of probability and random outcomes. Starting with examples of discrete and continuous probability spaces, you will learn methods of counting (inclusion-exclusion formula and multinomial coefficients), and examine theoretical topics including independence of events and conditional probabilities. You will study random variables and their probability distribution functions. Finally, you will study variance and co-variance and famous probability theorems.
Year Two
Combinatorics
In this module you learn the basics about discrete structures that lie at the heart of many real-world problems. A key notion is that of a graph, which is an abstract mathematical model for a network, such as a street network, a computer network, or a network of friendships. You learn to argue about these structures formally, and to prove interesting theorems about them. This will train your ability to think outside of the box.
Read more about the Combinatorics moduleLink opens in a new window, including the methods of teaching and assessment (content applies to 2023/24 year of study).
Algorithmic Graph Theory
This module is concerned with studying properties of graphs and digraphs from an algorithmic perspective. The focus is on understanding basic properties of graphs that can be used to design efficient algorithms. The problems considered will be typically motivated by algorithmic/computer science/IT applications.
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Formal Languages
You will gain a fundamental understanding of formal languages and how the Chomsky hierarchy classifies them. You’ll study techniques for exploring the regularity of languages using closure properties and pumping lemmas, whilst also considering automata models, alongside the notion of computability. These concepts are central to computer science, and completion will see you able to specify between, and translate, various forms of formal language descriptions. You’ll learn methods of lexical analysis and parsing, and be able to argue whether a formal language is regular or context free. The teachings will discuss Turing machines and philosophical concepts such as decidability, reducibility and the halting problem.
Read more about the Formal Languages moduleLink opens in a new window, including the methods of teaching and assessment (content applies to 2023/24 year of study).
Algorithms
Data structures and algorithms are fundamental to programming and to understanding computation. In this module, you will be using sophisticated tools to apply algorithmic techniques to computational problems. By the close of the course, you’ll have studied a variety of data structures and will be using them for the design and implementation of algorithms, including testing and proofing, and analysing their efficiency. This is a practical course, so expect to be working on real-life problems using elementary graph, greedy, and divide-and-conquer algorithms, as well as gaining knowledge on dynamic programming and network flows.
Read more about the Algorithms moduleLink opens in a new window, including the methods of teaching and assessment (content applies to 2023/24 year of study).
Metric Spaces
This module lays the basis for many subsequent mathematically-inclined modules, and it is concerned with fundamental notions of distances, measuring and continuity. Making these foundations into a consistent theoretical framework has kept many great mathematicians busy for many centuries, and in this module you walk in their footsteps.
Read more about the Metric Spaces moduleLink opens in a new window, including the methods of teaching and assessment (content applies to 2023/24 year of study).
Year Three
Discrete Mathematics Project
Through this practical module, you’ll gain experience in undertaking a significant individual design and development exercise in discrete mathematics, from conception through to design, implementation and delivery. Starting with the selection of a topic and location of a suitable supervisor, you’ll be responsible for regular progress reports, and a presentation of your final results alongside a detailed written report. In addition to enhancing your technical knowledge, this process will help you develop important skills such as self-discipline, time management, organisation and professional communications.
Read more about the Discrete Mathematics Project moduleLink opens in a new window, including the methods of teaching and assessment (content applies to 2023/24 year of study).
Complexity of Algorithms
Are you ready for a challenge? In this module, you’ll learn to analyse the intrinsic difficulty of various computational challenges, and to specify variations that may be more tractable. This will require you to learn notions of the complexity of algorithms, and what makes some computational problems harder than others. You’ll undertake a close study of what makes an algorithm efficient, and study various models of computation, in particular, models of classical deterministic and non-deterministic computations.
Read more about the Complexity of Algorithms moduleLink opens in a new window, including the methods of teaching and assessment (content applies to 2023/24 year of study).
Approximation and Randomised Algorithms
In this module, you will gain an introductory understanding of approximation and randomised algorithms, which often provide a simple, viable alternative to standard algorithms. You’ll learn the mathematical foundations underpinning the design and analysis of such algorithms. Whilst gaining experience of using suitable mathematical tools to design approximation algorithms and analyse their performance. You’ll also learn techniques for designing faster but weaker algorithms for particular situations, such as large running times. You can expect to cover important concepts, including linearity of expectation, Chernoff bounds, and deterministic and randomised rounding of linear programs.
Read more about the Approximation and Randomised Algorithms moduleLink opens in a new window, including the methods of teaching and assessment (content applies to 2023/24 year of study).
Combinatorics II
This module expands your knowledge about reasoning and working with discrete structures, and moves you to more advanced topics beyond graphs. In particular, you will learn about partially ordered sets, matroids and set systems. This will enable you to see and appreciate the role of combinatorial reasoning in a broader context of mathematics and computer science.
Read more about the Combinatorics II moduleLink opens in a new window, including the methods of teaching and assessment (content applies to 2023/24 year of study).
Year Four
In the fourth year you will select from an extensive range of both Computer Science and Mathematics optional modules, as well as some options from other departments.
Optional modules
Optional modules can vary from year to year. Example optional modules may include:
- Professional Skills
- Functional Programming
- Computer Security
- Logic and Verification
- Groups and Rings
- Combinatorial Optimisation
- Introduction to Number Theory
- Stochastic Processes
- Introduction to Mathematical Statistics
In the fourth year, the following optional modules may be of interest:
- Advanced Topics in Algorithms and Complexity
- Quantum Computing
- Agent Based Systems
- Algorithmic Game Theory
- Graph Theory
- Advanced Topics in Data Science
The precise modules available to students may depend on module prerequisites (i.e. for some module choices it is necessary for you to have taken a particular module in a previous year).
