BSc (Hons) Mathematics with Philosophy

"The proposed new degree programme in Mathematics and Philosophy is a very positive development. The course has been carefully crafted to take advantage of the diverse and impressive skills of the teaching staff. Students will enjoy the course and will appreciate the many interesting career possibilities that it opens up." Professor John S. Wilson, University of Oxford, External Accreditation Assessor.

The Course

The BSc (Hons) Mathematics with Philosophy degree provides students with the opportunity to develop a large skill set in pure and applied mathematics while developing a philosophical understanding of the world we live in and the place we occupy within it.

The School of Mathematics and Physics is dedicated to achieving excellence in research and aims to provide a friendly, approachable culture for students to join.

Students have the opportunity to learn from, and work alongside, our team of academics who can support and encourage them to apply imagination, creativity and rigour to the solution of real-world problems. Individual and group projects during the course are designed to develop valuable transferable skills.

This programme will meet the educational requirements of the Chartered Mathematician designation, awarded by the Institute of Mathematics and its Applications, when it is followed by subsequent training and experience in employment to obtain equivalent competences to those specified by the Quality Assurance Agency (QAA) for taught Master's degrees.

Contact Hours and Reading for a Degree

Students on this programme learn from academic staff who are often engaged in world-leading or internationally excellent research or professional practice. Contact time can be in workshops, practical sessions, seminars or lectures and may vary from module to module and from academic year to year. Tutorial sessions and project supervision can take the form of one-to-one engagement or small group sessions. Some courses offer the opportunity to take part in external visits and fieldwork.

It is still the case that students read for a degree and this means that in addition to scheduled contact hours, students are required to engage in independent study. This allows you to read around a subject and to prepare for lectures and seminars through wider reading, or to complete follow up tasks such as assignments or revision. As a general guide, the amount of independent study required by students at the University of Lincoln is that for every hour in class you are expected to spend at least two to three hours in independent study.

Algebra (Core)
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Algebra (Core)

This module begins with refreshing some of the material from A-Level Maths, such as the binomial theorem and division of polynomials. The main part of the module is a systematic study of general systems of simultaneous linear equations and their solutions. Vectors and matrices are introduced in order to describe the properties of these systems and solutions, and complete answers are obtained to such questions as whether a solution exists and if so how many solutions there are.

Calculus (Core)
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Calculus (Core)

This module focuses on the concepts of the derivative and the Riemann integral, which are indispensable in modern sciences.

Two approaches are used: both intuitive-geometric, and mathematically rigorous, based on the definition of continuous limits. Important results are the Mean Value Theorem, leading to the representation of some functions as power series (the Taylor series), and the Fundamental Theorem of Calculus which establishes the relationship between differentiation and integration. Further calculus tools are explored, such as the general properties of the derivative and the Riemann integral, as well as the techniques of integration. In this module, students may deal with many 'popular' functions used throughout mathematics.

Geometrical Optics, Waves and Mechanics (Core)
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Geometrical Optics, Waves and Mechanics (Core)

This module will present an introduction to the fundamentals of waves, geometrical optics and mechanics, including their mathematical foundations.

Ideas of Mathematical Proof (Core)
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Ideas of Mathematical Proof (Core)

The purpose of this module is to introduce students to basic mathematical reasoning such as rigorous definitions and proofs, logical structure of mathematical statements. Students will have the opportunity to learn the set-theoretic notation, get acquainted with various strategies of mathematical proofs such as proof by mathematical induction or proof by contradiction. Rigorous definitions of limits of sequences and functions will form a foundation for other courses on calculus and differential equations. The importance of definitions and proofs will be illustrated by examples of 'theorems' which may seem obvious but are actually false, as well as certain mathematical 'paradoxes'.

Introduction to Moral Philosophy (Core)
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Introduction to Moral Philosophy (Core)

This module is designed to introduce students to the three areas of discussion in contemporary moral philosophy. Metaethics is concerned with the nature of morality itself and questions such as ‘Are there moral facts?’, ‘If there are moral facts, what is their origin?’. Normative ethics is the attempt to provide a general theory that tells us how to live and enables us to determine what is morally right and wrong. Applied ethics involves the application of ethical principles to specific moral issues (e.g., abortion, euthanasia, animal rights) and the evaluation of the answers arrived at through this application. This module aims to introduce students to all three of these branches of ethics.

Introduction to Philosophical Logic (Core)
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Introduction to Philosophical Logic (Core)

This module introduces some of the basic ideas and concepts of philosophical logic and the technical vocabulary that is required for understanding contemporary philosophical writing. Students are introduced to logical concepts such as validity, soundness, consistency, possibility, necessity, contingency, inductive and deductive forms of argument, necessary and sufficient conditions, the rudiments of formalisation, and a range of logical fallacies. The emphasis will be on using logic to construct and evaluate arguments.

Linear Algebra (Core)
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Linear Algebra (Core)

This module describes vector spaces and matrices.

Matrices are regarded as representations of linear mappings between vector spaces. Eigenvalues and eigenvectors are introduced, which lead to diagonalization and reduction to other canonical forms. Special types of mappings and matrices (orthogonal, symmetric) are introduced. Applications of linear algebra to geometry of quadratic surfaces are explored.

Probability and Statistics (Core)
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Probability and Statistics (Core)

This module begins with an introduction of a probability space, which models the possible outcomes of a random experiment. Basic concepts such as statistical independence and conditional probability are introduced, with various practical examples used as illustrations. Random variables are introduced, and certain well-known probability distributions are explored.

Further study includes discrete distributions, independence of random variables, mathematical expectation, random vectors, covariance and correlation, conditional distributions and the law of total expectation. The ideas developed for discrete distributions are applied to continuous distributions.

Probability theory is a basis of mathematical statistics, which has so many important applications in science, industry, government and commerce. Students will have the opportunity to gain a basic understanding of statistics and its tools. It is important that these tools are used correctly when, for example, the full picture of a problem (population) must be inferred from collected data (random sample).

Algebraic Structures (Core)
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Algebraic Structures (Core)

The concepts of groups, rings and fields are introduced, as examples of arbitrary algebraic systems. The basic theory of subgroups of a given group and the construction of factor groups is introduced, and then similar constructions are introduced for rings. Examples of rings are considered, including the integers modulo n, the complex numbers and n-by-n matrices. The ring of polynomials over a given field is studied in more detail.

Coding Theory (Core)
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Coding Theory (Core)

Transmission of data may mean sending pictures from the Mars rover, streaming live music or videos, speaking on the phone, answering someone's question “do you love me?”. Problems arise if there are chances of errors creeping in, which may be catastrophic (say, receiving “N” instead of “Y”).

Coding theory provides error-correcting codes, which are designed in such a way that errors that occur can be detected and corrected (within certain limits) based on the remaining symbols. The problem is balancing reliability with cost and/or slowing the transmission. Students will have the opportunity to study various types of error-correcting codes, such as linear codes, hamming codes, perfect codes, etc., some of which are algebraic and some correspond to geometrical patterns.

Complex Analysis (Core)
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Complex Analysis (Core)

Ideas of calculus of derivatives and integrals are extended to complex functions of a complex variable. Students will learn that complex differentiability is a very strong condition and differentiable functions behave very well. Integration along paths in the complex plane is introduced. One of the main results of this beautiful part of mathematics is Cauchy's Theorem that states that certain integrals along closed paths are equal to zero. This gives rise to useful techniques for evaluating real integrals based on the 'calculus of residues'.

Differential Equations (Core)
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Differential Equations (Core)

Calculus techniques already provide solutions of simple first-order differential equations. Solution of second-order differential equations can sometimes be achieved by certain manipulations. Students may learn about existence and geometric interpretations of solutions, even when calculus techniques do not yield solutions in a simple form. This is a part of the existence theory of ordinary differential equations and leads to fundamental techniques of the asymptotic and qualitative study of their solutions, including the important question of stability. Fourier series and Fourier transform are introduced.

This module provides an introduction to the classical second-order linear partial differential equations and techniques for their solution. The basic concepts and methods are introduced for typical partial differential equations representing the three classes: parabolic, elliptic, and hyperbolic.

Existentialism and Phenomenology (Core)
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Existentialism and Phenomenology (Core)

The aim of this module is to give students a thorough understanding of two intimately related philosophical traditions that came to prominence in the 19th and 20th centuries: existentialism and phenomenology. Each attempts to address the nature and meaning of human existence from the perspective of individual, first-person experience, focusing in particular on fundamental questions of being, meaning, death, nihilism, freedom, responsibility, value, human relations, and religious faith.

The module will examine selected existential themes through the writings of thinkers such as Kierkegaard, Nietzsche, Heidegger, Sartre, De Beauvoir, and Camus. Since existentialism is as much a artistic phenomenon as a philosophical one, students will also be given the opportunity to explore existentialist ideas in the works of various literary figures, such as Shakespeare, Dostoyevsky, Kafka, and Milan Kundera.

Industrial and Financial Mathematics (Core)
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Industrial and Financial Mathematics (Core)

Students have the opportunity to learn how mathematics is applied to modern industrial problems, and how the mathematical apparatus finds applications in the financial sector.

Philosophy of Science (Core)
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Philosophy of Science (Core)

This module explores a range of philosophical questions relating to the nature of science. How are scientific theories developed? Are scientific theories discovered through a ‘flash of genius’ or is something more methodical involved? How much of scientific discovery is down to careful observation? Do scientific theories tell us how the world really is? Do the entities scientific theories postulate – atoms, electromagnetic waves, and so on – really exist? Or are scientific theories merely useful models of reality? Is science independent of its social context? To what extent is scientific inquiry affected by gender, race or politics? Is there such a thing as truth that is not relative to a particular culture, social class or historical era? Drawing on accessible examples from a variety of scientific fields and by answering these and related questions, we shall try to reach an understanding of how science works.

Scientific Computing (Core)
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Scientific Computing (Core)

Students will have the opportunity to utilise computers for the numerical solution and simulation of models of physical and mathematical systems, including the use of computer procedural programming languages to solve computational problems.

Numerical algorithms will be introduced to exemplify key concepts in computational programming, with the emphasis on understanding the nature of the algorithm and the features and limitations of its computational implementation. In creating programs, the emphasis will be on using effective programming techniques and on efficient debugging, testing and validation methods. Students may also develop skills at using a logbook as a factual record and as reflective self-assessment to support their learning.

Contemporary Problems in Philosophy (Core)
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Contemporary Problems in Philosophy (Core)

This module gives students the opportunity to engage with some key issues and contemporary debates in key areas of philosophy, such as epistemological relativism, the nature of consciousness, the nature of causation in science, the nature of the self. The precise topics addressed will vary from year to year and students will have input into the choice of topics. The aim of the module is to explore in-depth some significant contemporary philosophical issues and to enable students to develop and enhance their key philosophical and debating skills.

Fluid Dynamics (Option)
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Fluid Dynamics (Option)

This module gives a mathematical foundation of ideal and viscous fluid dynamics and their application to describing various flows in nature and technology.

Students are taught methods of analysing and solving equations of fluid dynamics using analytic and most modern computational tools.

Group Theory (Core)
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Group Theory (Core)

Symmetry, understood in most broad sense as invariants under transformations, permeates all parts of mathematics, as well as natural sciences. Groups are measures of such symmetry and therefore are used throughout mathematics.

Abstract group theory studies the intrinsic structure of groups. The course begins with definitions of subgroups, normal subgroups, and group actions in various guises. Group homomorphisms are introduced and the related isomorphism theorems are proved. Sylow p-subgroups are introduced and the three Sylow theorems are proved. Throughout, symmetry groups are used as examples.

Mathematics Pedagogy (Option)
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Mathematics Pedagogy (Option)

This module is designed to provide students with an insight into the teaching of Mathematics at secondary school level and does this by combining university lectures with an experience of a placement in a secondary school Mathematics department.

The module aims to provide students with an opportunity to engage with cutting-edge maths education research and will examine how this research impacts directly on classroom practice. Students will have the opportunity to gain an insight into some of the key ideas in Mathematics pedagogy and how these are implemented in the school Mathematics lessons and will develop an understanding about the barriers to learning Mathematics that many students experience.

Mathematics Project (Core)
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Mathematics Project (Core)

This is a double module in which a student undertakes a project under supervision of a research-active member of staff. The project can be undertaken at an external collaborating establishment. Projects will be offered to students in a wide range of subjects, assigned with consideration of a students' individual preferences and programme of their studies. Some projects will be more focused on a detailed study of mathematical theories or techniques in an area of current interest. Other projects may require solving specific problems that require the formulation of a mathematical model, its development and solution. Student meet regularly with their supervisor in order to receive guidance and review progress.

Methods of Mathematical Physics (Option)
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Methods of Mathematical Physics (Option)

The module aims to equip students with methods to analyse and solve various mathematical equations found in physics and technology.

Newton's Revolution (Option)
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Newton's Revolution (Option)

This module examines some of the philosophical issues raised by the Newtonian revolution in the natural sciences, such as: What is the nature of Newton’s distinction between ‘absolute’ and ‘relative’ space? In what sense can forces be said to exist? What is the ontology of force? Is it sufficient to provide a mathematical definition of force (e.g., f=ma)? Is gravity a special kind of force with its own unique set of properties? What is the nature of ‘action at a distance’? Is Newton’s view of space metaphysical? This is an interdisciplinary module that situates Newtonian science in its sociocultural context.

Numerical Methods (Option)
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Numerical Methods (Option)

The module aims to equip students with knowledge of various numerical methods for solving applied mathematics problems, their algorithms and implementation in programming languages.

Tensor Analysis (Core)
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Tensor Analysis (Core)

This module introduces tensors, which are abstract objects describing linear relations between vectors, scalars, and other tensors. The module aims to equip students with the knowledge of tensor manipulation, and introduces their applications in modern science.

†The availability of optional modules may vary from year to year and will be subject to minimum student numbers being achieved. This means that the availability of specific optional modules cannot be guaranteed. Optional module selection may also be affected by staff availability.

Assessment Feedback

The University of Lincoln's policy on assessment feedback aims to ensure that academics will return in-course assessments to students promptly – usually within 15 working days after the submission date (unless stated differently above)..

Methods of Assessment

The way students are assessed on this course may vary for each module. Examples of assessment methods that are used include coursework, such as written assignments, reports or dissertations; practical exams, such as presentations, performances or observations; and written exams, such as formal examinations or in-class tests. The weighting given to each assessment method may vary across each academic year. The University of Lincoln aims to ensure that staff return in-course assessments to students promptly.

Research is a critical part of the academic environment at the University of Lincoln, and as one of our students you can expect to be taught by research academics in the field. Under our “student as producer” initiative students will be expected to contribute to new knowledge yourself. Research will form a part of study from the first year in a variety of ways such as individual and team projects, and will culminate in the final year project.

Student as Producer

Student as Producer is a model of teaching and learning that encourages academics and undergraduate students to collaborate on research activities. It is a programme committed to learning through doing.

The Student as Producer initiative was commended by the QAA in our 2012 review and is one of the teaching and learning features that makes the Lincoln experience unique.

This degree is optionally available in a sandwich mode variant. If students choose the sandwich placement option, they take a year out in industry or at an external research institution (which can be overseas) between years two and three, and have the chance to gain invaluable practical experience. The option is subject to availability and selection criteria set by the industry or external institution.

Placement Year

When students are on an optional placement in the UK or overseas or studying abroad, they will be required to cover their own transport and accommodation and meals costs. Placements can range from a few weeks to a full year if students choose to undertake an optional sandwich year in industry.

Students are encouraged to obtain placements in industry independently. Tutors may provide support and advice to students who require it during this process.

2018/19 UK/EUInternational
Full-time £9,250 per level £14,700 per level
Part-time £77.00 per credit point†  N/A
Placement (optional) Exempt Exempt

 

2019/20UK/EUInternational
Full-time £9,250 per level £15,000 per level
Part-time £77.00 per credit point†  N/A
Placement (optional) Exempt Exempt


†Please note that not all courses are available as a part-time option.

The University undergraduate tuition fee may increase year on year in line with government policy. This will enable us to continue to provide the best possible educational facilities and student experience.

Fees for enrolment on additional modules

Tuition fees for additional activity are payable by the student/sponsor and charged at the equivalent £ per credit point rate for each module. Additional activity includes:

- Enrolment on modules that are in addition to the validated programme curriculum

- Enrolment on modules that are over and above the full credit diet for the relevant academic year

- Retakes of modules as permitted by the Board of Examiners

- In exceptional circumstances, students who are required to re-take modules can do so on an 'assessment only' basis. This means that students do not attend timetabled teaching events but are required to take the assessments/examinations associated with the module(s). The 'assessment only' fee is half of the £ per credit point fee for each module.

Exceptionally, tuition fees may not be payable where a student has been granted a retake with approved extenuating circumstances.

For more information and for details about funding your study, please see our UK/EU Fees & Funding pages or our International funding and scholarship pages. [www.lincoln.ac.uk/home/studyatlincoln/undergraduatecourses/feesandfunding/] [www.lincoln.ac.uk/home/international/feesandfunding/]

Additional Costs

For each course students may find that there are additional costs. These may be with regard to the specific clothing, materials or equipment required, depending on their subject area. Some courses provide opportunities for students to undertake field work or field trips. Where these are compulsory, the cost for the travel, accommodation and meals may be covered by the University and so is included in the fee. Where these are optional students will normally (unless stated otherwise) be required to pay their own transportation, accommodation and meal costs.

With regards to text books, the University provides students who enrol with a comprehensive reading list and our extensive library holds either material or virtual versions of the core texts that students are required to read. However, students may prefer to purchase some of these for themselves and will therefore be responsible for this cost. Where there may be exceptions to this general rule, information will be displayed in a section titled Other Costs below.

GCE Advanced Levels: BBB, including grade B from A Level Maths.

International Baccalaureate: 30 points overall, with Higher Level grade 5 in Maths.

Applicants will also need at least three GCSEs at grade 4 (C) or above, which must include English, Maths and Science. Equivalent Level 2 qualifications may also be considered.

EU and International students whose first language is not English will require English Language IELTS 6.0 with no less than 5.5 in each element, or equivalent http://www.lincoln.ac.uk/englishrequirements

The University accepts a wide range of qualifications as the basis for entry and will consider applicants who have a mix of qualifications.

We also consider applicants with extensive and relevant work experience and will give special individual consideration to those who do not meet the standard entry qualifications.

For applicants who do not meet our standard entry requirements, our Science Foundation Year can provide an alternative route of entry onto our full degree programmes:
https://www.lincoln.ac.uk/home/course/sfysfyub/mathematicsandphysics/

If you would like further information about entry requirements, or would like to discuss whether the qualifications you are currently studying are acceptable, please contact the Admissions team on 01522 886097, or email admissions@lincoln.ac.uk

Learn from Experts

Throughout this degree, students may receive tuition from professors, senior lecturers, lecturers, researchers, practitioners, visiting experts or technicians, and they may also be supported in their learning by other students.


Your Future Career

Mathematics with Philosophy graduates may be well placed to progress into careers including science and technology, engineering, computing, medicine, education, consultancy, business and finance, and with government bodies. Some choose to undertake further study at postgraduate level.

Careers Service

The University Careers and Employability Team offer qualified advisors who can work with students to provide tailored, individual support and careers advice during their time at the University. As a member of our alumni we also offer one-to-one support in the first year after completing a course, including access to events, vacancy information and website resources; with access to online vacancies and virtual resources for the following two years.

This service can include one-to-one coaching, CV advice and interview preparation to help you maximise our graduates future opportunities.

The service works closely with local, national and international employers, acting as a gateway to the business world.

Visit our Careers Service pages for further information http://www.lincoln.ac.uk/home/campuslife/studentsupport/careersservice/.


Facilities

The School of Mathematics and Physics forms part of the new Isaac Newton Building, which comprises additional spaces such as workshops and computer laboratories. The School also hosts its own supercomputer.

At Lincoln, we constantly invest in our campus as we aim to provide the best learning environment for our undergraduates. Whatever the area of study, the University strives to ensure students have access to specialist equipment and resources, to develop the skills, which they may need in their future career.

Students also make the most of the University's award-winning Great Central Warehouse Library, which provides access to more than 250,000 printed books and over 400,000 electronic books and journals, as well as databases and specialist collections. The Library has a range of different spaces for shared and individual learning.


This course has not been running at the University of Lincoln for a period long enough to provide its own data for the Key Information Set provided by Unistats.com. Data is currently drawn from similar subjects at the University of Lincoln rather than from this specific subject. If you would like to know more about this course we would strongly recommend that that you meet us at our next open day. Alternatively, talk to us about your future at the University of Lincoln by calling +44 (0) 1522 886644.
The University intends to provide its courses as outlined in these pages, although the University may make changes in accordance with the Student Admissions Terms and Conditions.