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About this page
We will update this page when we make significant changes to course information. This does not necessarily include minor corrections or formatting.
If you ever want to ask us about a change, you can contact us at webeditor at warwick dot ac dot uk.
24th October 2022
Following University approval, we have made changes to the IB standard and contextual offers for this course on the ‘Entry requirements’ tab:
Previous content:
IB typical offer
39 to include 6, 6, 6 in three Higher Level subjects including Mathematics.
IB contextual offer
We welcome applications from candidates who meet the contextual eligibility criteria and whose predicted grades are close to, or slightly below, the contextual offer level. The typical contextual offer is 38 including 6,6,6 in three Higher Level subjects including Mathematics. See if you're eligible.
Revised content:
IB typical offer
39 to include 6, 6, 6 in three Higher Level subjects including Mathematics (Analysis and Approaches).
IB contextual offer
We welcome applications from candidates who meet the contextual eligibility criteria and whose predicted grades are close to, or slightly below, the contextual offer level. The typical contextual offer is 38 including 6,6,6 in three Higher Level subjects including Mathematics (Analysis and Approaches). See if you're eligible.
29th September 2022
We have amended the course overview and module sections to include important updates.
We removed the Important information text from Course Overview and Modules sections:
Important information
Please note the Mathematics and Philosophy (BA/BSc) degree is likely to change for 2023 entry. Changes to the core modules go through the University's rigorous academic processes. As module changes are confirmed, we will update the course information on this webpage. It is therefore very important that you check this webpage for the latest information before you apply and prior to accepting an offer. Sign up to receive updates.
We changed the Core Module information for Year 1 and Year 2:
Previous content
Year One
Mind and Reality
Look around. What if all your experiences were the products of dreams, or neuroscientific experiments? Can you prove they aren’t? If not, how can you know anything about the world around you? How can you even think about such a world? Perhaps you can at least learn about your own experience, what it’s like to be you. But doesn’t your experience depend on your brain, an element of the external world? This course will deepen your understanding of the relationship between your mind and the rest of the world.
Read more about the Mind and Reality moduleLink opens in a new window, including the methods of teaching and assessment (content applies to 2022/23 year of study).
Logic 1: Introduction to Symbolic Logic
This module teaches you formal logic, covering both propositional and first-order logic. You will learn about a system of natural deduction and understand how to demonstrate that it is both sound and complete. You will learn how to express and understand claims using formal techniques, including multiple quantifiers. Key concepts you will consider are logical validity, truth functionality and formal proof quantification.
Read more about the Logic 1: Introduction to Symbolic Logic moduleLink opens in a new window, including the methods of teaching and assessment (content applies to 2022/23 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 2022/23 year of study).
Mathematical Analysis I/II
Analysis is the rigorous study of calculus. In this module, there will be a 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. The module will allow you to deal carefully with limits and infinite summations, approximations to pi and e, and the Taylor series. The module also covers construction of the integral and the Fundamental Theorem of Calculus.
Read more about these modules, including the methods of teaching and assessment (content applies to 2022/23 year of study).
Foundations
It is in its proofs that the strength and richness of mathematics are to be found. University mathematics introduces progressively more abstract ideas and structures and demands more in the way of proof until much 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.
This module also looks at algorithms and operational complexity, including cryptographic keys and RSA.
Read more about the Foundations moduleLink opens in a new window, including the methods of teaching and assessment (content applies to 2022/23 year of study).
Differential Equations
Can you predict the trajectory of a tennis ball? In this module you cover the basic theory of ordinary differential equations (ODEs), the cornerstone of all applied mathematics. ODE theory proves invaluable in branches of pure mathematics, such as geometry and topology. You will be introduced to simple differential and difference equations and methods for their solution. You will cover first-order equations, linear second-order equations and coupled first-order linear systems with constant coefficients, and solutions to differential equations with one-and two-dimensional systems. We will discuss why in three dimensions we see new phenomena, and have a first glimpse of chaotic solutions.
Read more about the Differential Equations moduleLink opens in a new window, including the methods of teaching and assessment (content applies to 2022/23 year of study).
Geometry and Motion
Geometry and motion are connected as a particle curves through space, and in the relation between curvature and acceleration. In this course you will discover how to integrate vector-valued functions and functions of two and three real variables. You will encounter concepts in particle mechanics, deriving Kepler’s Laws of planetary motion from Newton’s second law of motion and the law of gravitation. You will see how intuitive geometric and physical concepts such as length, area, volume, curvature, mass, circulation and flux can be translated into mathematical formulas, and appreciate the importance of conserved quantities in mechanics.
Read more about the Geometry and Motion moduleLink opens in a new window, including the methods of teaching and assessment (content applies to 2021/22 year of study).
Introduction to Abstract Algebra
This course will introduce you to abstract algebra, covering group theory and ring theory, making you familiar with symmetry groups and groups of permutations and matrices, subgroups and Lagrange’s theorem. You will understand the abstract definition of a group, and become familiar with the basic types of examples, including number systems, polynomials, and matrices. You will be able to calculate the unit groups of the integers modulo n.
Read more about the Introduction to Abstract Algebra moduleLink opens in a new window, including the methods of teaching and assessment (content applies to 2021/22 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, including Chebyshev’s and Cauchy-Schwarz inequalities. The module ends with a discussion of the celebrated Central Limit Theorem.
Read more about the Introduction to Probability moduleLink opens in a new window, including the methods of teaching and assessment (content applies to 2022/23 year of study).
Year Two
Logic II: Metatheory
In this module, you will learn about the metatheory of propositional and first-order logic; to understand the concept of a sound and complete proof system similar to that of Logic I. You will study elementary set theory and inductive definitions and then consider Tarski's definitions of satisfaction and truth, proceeding to develop the Henkin completeness proof for first-order logic. You will learn to appreciate the significance of these concepts for logic and mathematics, with the ability to define them precisely.
Read more about the Logic II: Metatheory moduleLink opens in a new window, including the methods of teaching and assessment (content applies to 2021/22 year of study).
Algebra I: Advanced Linear Algebra
On this course, you will develop and continue your study of linear algebra. You will develop methods for testing whether two general matrices are similar, and study quadratic forms. Finally, you will investigate matrices over the integers, and investigate what happens when we restrict methods of linear algebra to operations over the integers. This leads, perhaps unexpectedly, to a complete classification of finitely generated abelian groups. You will be familiarised with the Jordan canonical form of matrices and linear maps, bilinear forms, quadratic forms, and choosing canonical bases for these, and the theory and computation of the Smith normal form for matrices over the integers.
Read more about the Algebra I: Advanced Linear Algebra moduleLink opens in a new window, including the methods of teaching and assessment (content applies to 2021/22 year of study).
Mathematical Analysis III
In the first half of this module, you will investigate some applications of year one analysis: integrals of limits and series; differentiation under an integral sign; a first look at Fourier series. In the second half you will study analysis of complex functions of a complex variable: contour integration and Cauchy’s theorem, and its application to Taylor and Laurent series and the evaluation of real integrals.
Read more about the Mathematical Analysis III moduleLink opens in a new window, including the methods of teaching and assessment (content applies to 2023/24 year of study).
Amended content:
Year One
Mind and Reality
Look around. What if all your experiences were the products of dreams, or neuroscientific experiments? Can you prove they aren’t? If not, how can you know anything about the world around you? How can you even think about such a world? Perhaps you can at least learn about your own experience, what it’s like to be you. But doesn’t your experience depend on your brain, an element of the external world? This course will deepen your understanding of the relationship between your mind and the rest of the world.
Read more about the Mind and Reality moduleLink opens in a new window, including the methods of teaching and assessment (content applies to 2022/23 year of study).
Logic 1: Introduction to Symbolic Logic
This module teaches you formal logic, covering both propositional and first-order logic. You will learn about a system of natural deduction and understand how to demonstrate that it is both sound and complete. You will learn how to express and understand claims using formal techniques, including multiple quantifiers. Key concepts you will consider are logical validity, truth functionality and formal proof quantification.
Read more about the Logic 1: Introduction to Symbolic Logic moduleLink opens in a new window, including the methods of teaching and assessment (content applies to 2022/23 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 2022/23 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, including Chebyshev’s and Cauchy-Schwarz inequalities. The module ends with a discussion of the celebrated Central Limit Theorem.
Read more about the Introduction to Probability moduleLink opens in a new window, including the methods of teaching and assessment (content applies to 2022/23 year of study).
Mathematical Analysis I/II
Analysis is the rigorous study of calculus. In this module, there will be a 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. The module will allow you to deal carefully with limits and infinite summations, approximations to pi and e, and the Taylor series. The module also covers construction of the integral and the Fundamental Theorem of Calculus.
Read more about these modules, including the methods of teaching and assessment (content applies to 2022/23 year of study).
Methods of Mathematical Modelling 1 and 2
Methods of Mathematical Modelling 1 introduces you to the fundamentals of mathematical modelling and scaling analysis, before discussing and analysing difference and differential equation models in the context of physics, chemistry, engineering as well as the life and social sciences. This will require the basic theory of ordinary differential equations (ODEs), the cornerstone of all applied mathematics. ODE theory later proves invaluable in branches of pure mathematics, such as geometry and topology. You will be introduced to simple differential and difference equations, methods for obtaining their solutions and numerical approximation.
In the second term for Methods of Mathematical Modelling 2, you will study the differential geometry of curves, calculus of functions of several variables, multi-dimensional integrals, calculus of vector functions of several variables (divergence and circulation), and their uses in line and surface integrals.
Read more about these modules, including the methods of teaching and assessment (content applies to 2022/23 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 2022/23 year of study).
Year Two
Logic II: Metatheory
In this module, you will learn about the metatheory of propositional and first-order logic; to understand the concept of a sound and complete proof system similar to that of Logic I. You will study elementary set theory and inductive definitions and then consider Tarski's definitions of satisfaction and truth, proceeding to develop the Henkin completeness proof for first-order logic. You will learn to appreciate the significance of these concepts for logic and mathematics, with the ability to define them precisely.
Read more about the Logic II: Metatheory moduleLink opens in a new window, including the methods of teaching and assessment (content applies to 2022/23 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).
Multilinear Algebra
In this module, you will develop and continue your study of linear algebra: the Jordan normal form for matrices; functions of matrices; symmetric and quadratic forms; tensors; bilinear forms; dual spaces.
Read more about the Multilinear Algebra is moduleLink opens in a new window, including the methods of teaching and assessment (content applies to 2023/24 year of study).
Groups and Rings
This first abstract algebra module, roughly based on the current version of Algebra-2: Groups and Rings, focuses on developing your understanding and application of the theories of groups and rings, improving your ability to manipulate them and extending your knowledge and understanding of algebra from the Sets and Numbers module in Year One.
Read more about the Groups and Rings moduleLink opens in a new window, including the methods of teaching and assessment (content applies to 2023/24 year of study).