Mathematics and Philosophy BA (Joint Hons)

Students take four modules from the Philosophy Year One programme.

Philosophy modules:

• Reading and Writing Philosophy 1
• Reading and Writing Philosophy 2 Critical, Analytical, and Creative Thinking
• Symbolic Logic 1

Students take the core foundation modules from the Mathematics Year One programme:

• Foundation Module I: Calculus
• Foundation Module II: Complex Numbers and Linear Algebra
• Foundation Module III: Multivariable Calculus

And one of the following:

• Numbers, Groups and Codes
• Mathematical Reasoning and Problem Solving

• Calculus I (MATH101) Level 1 Credit level 15 Semester First Semester Exam:Coursework weighting 80:20 Aims

  1. To introduce the basic ideas of differential and integral calculus, to develop the basic skills required to work with them and to apply these skills to a range of problems.

  2. To introduce some of the fundamental concepts and techniques of real analysis, including limits and continuity.

  3. To introduce the notions of sequences and series and of their convergence.

  Learning Outcomes

  After completing the module students should be able to:

  · differentiate and integrate a wide range of functions;

  · sketch graphs and solve problems involving optimisation and mensuration;

  · understand the notions of sequence and series and apply a range of tests to determine if a series is convergent.

• Calculus Ii (MATH102) Level 1 Credit level 15 Semester Second Semester Exam:Coursework weighting 80:20 Aims

  · To discuss local behaviour of functions using Taylor’s theorem.

  · To introduce multivariable calculus including partial differentiation, gradient, extremum values and double integrals.

  Learning Outcomes

  After completing the module, students should be able to:

  · use Taylor series to obtain local approximations to functions;

  · obtain partial derivatives and use them in several applications such as, error analysis, stationary points change of variables;

  · evaluate double integrals using Cartesian and polar co-ordinates.

• Introduction To Linear Algebra (MATH103) Level 1 Credit level 15 Semester First Semester Exam:Coursework weighting 80:20 Aims
  • To develop techniques of complex numbers and linear algebra, including equation solving, matrix arithmetic and the computation of eigenvalues and eigenvectors.
  • To develop geometrical intuition in 2 and 3 dimensions.
  • To introduce students to the concept of subspace in a concrete situation.
  • To provide a foundation for the study of linear problems both within mathematics and in other subjects.
  Learning Outcomes

  After completing the module students should be ableto:

  • manipulate complex numbers and solve simple equations involving them
  • solve arbitrary systems of linear equations;
  • understand and use matrix arithmetic, including the computation of matrix inverses;
  • compute and use determinants;
  • understand and use vector methods in the geometry of 2 and 3 dimensions;
  • calculate eigenvalues and eigenvectors and, if time permits, apply these calculations to the geometry of conics and quadrics.
• Reading and Writing Philosophy 1 (PHIL107) Level 1 Credit level 15 Semester First Semester Exam:Coursework weighting 0:100 Aims

• To introduce the academic skills and knowledge necessary for the critical reading and writing of philosophy.

• ​To foster in students an appreciation of the value of philosophy.

• ​To enable students to read effectively and to takes notes efficiently.

• To develop students'' skill in presenting complex ideas to an audience and in practicing the intellectual virtues associated with philosophical discussion.
• To promote students'' skill in writing rigorously argued, well-written and well-presented philosophical essays.

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• ​To promote students'' research skills.

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• Learning Outcomes

  Students will be able to explain and evaluate some central work in aesthetics and the philosophy of art.

  ​Students will be able to explain and evaluate some work relevant to a selected specialist topic in ethics. (This topic may vary from year to year. Examples include: human treatment of animals; ethics and the environment.)

  ​Students will be able to explain and evaluate some central work about political liberty.

  ​Students will be able to give structured seminar presentations and to conduct discussion in a manner that displays the intellectual virtues associated with philosophy.

  ​Students will be able to write essays that embody a philosophically-informed approach to argumentation.

  Students will be able to use the Harvard referencing system. ​

  Students will be able to conduct independent research in support of their work, using appropriate print and online resources (including the Routledge Encyclopedia of Philosophy and the Philosopher''s Index). ​
• Reading and Writing Philosophy 2 (PHIL108) Level 1 Credit level 15 Semester Second Semester Exam:Coursework weighting 0:100 Aims

• To consolidate the academic skills and knowledge necessary for the critical reading and writing of philosophy.

• To consolidate students'' appreciation of the value of philosophy.​

• To consolidate students'' ability to read and take notes effectively.​

• To consolidate students'' skill in presenting complex ideas to an audience and in practising the intellectual virtues associated with philosophical discussion.​

• ​To consolidate students'' skill in writing rigorously argued, well-written and well-presented essays.

• To consolidate students'' research skills. ​

• Learning Outcomes

  Students will be able to explain and evaluate some central work from the early modern period, covering the following topics: (i) perception; (ii) personal identity; (iii) freedom and determinism.

  Students will develop greater skill and confidence in giving structured seminar presentations and in conducting discussion in a manner that displays the intellectual virtues associated with philosophy.

  Students will develop greater skill and confindence in writing essays that embody a philosophically-informed approach to argumentation.

  ​Students will be able to use the Harvard system of referencing.

  ​Students will be able to conduct independent research in support of their work, using appropriate print and online resources (including the Routledge Encyclopedia of Philosophy and the Philosopher''s Index).

• Numbers, Groups and Codes (MATH142) Level 1 Credit level 15 Semester Second Semester Exam:Coursework weighting 90:10 Aims

  · To provide an introduction to rigorous reasoning in axiomatic systems exemplified by the framework of group theory.

  · To give an appreciation of the utility and power of group theory as the study of symmetries.

  · To introduce public-key cryptosystems as used in the transmission of confidential data, and also error-correcting codes used to ensure that transmission of data is accurate. Both of these ideas are illustrations of the application of algebraic techniques.

  Learning Outcomes ​​

  After completing this module the student should be able to:

  1. Use the division algorithm to construct the greatest common divisor of a pair of positive integers;

  2. Solve linear congruences and find the inverse of an integer modulo a given integer;

  3. Code and decode messages using the public-key method;

  4. Manipulate permutations with confidence;

  5. Decide when a given set is a group under a specified operation and give formal axiomatic proofs;

  6. Understand the concept of a subgroup and use Lagrange''s theorem;

  7. Understand the concept of a group action, an orbit and a stabiliser subgroup;

  8. Understand the concept of a group homomorphism and be able to show (in simple cases) that two groups are isomorphic;

  9. Understand the principles of binary coding and how to construct error-detecting and error-correcting binary codes.

• Critical, Analytical and Creative Thinking (PHIL112) Level 1 Credit level 15 Semester First Semester Exam:Coursework weighting 60:40 Aims

• T o introduce students to the concepts and methods of informal logic and to enable students to use these concepts and methods in assessing arguments both within and outside philosophy.

• ​To help students to think more logically themselves, and to locate and remove inconsistencies in their own thoughts.

• ​To introduce students to methods of causal, statistical and probabilistic reasoning and to enable students to identify and avoid causal, statistical and probabilistic fallacies.

• ​To enable students to think creatively about problems and to come up with rational solutions to them, and to make logical decisions in the light of available evidence.

• Learning Outcomes

  ​Students will able to explain and apply the basic concepts of logic.

  ​Students will be able to identify conclusions and premises in arguments, including hidden premises.

  Students will be able to reconstruct and evaluate arguments. ​

  Students will be able to distinguish between reasoning and rhetoric and to identify fallacies and rhetorical ploys in arguments. ​

  Students will be able to distinguish between deductive and inductive infererence, including distinguishing between different types of inductive inference (enumerative, statistical, causal, analogical).

  ​Students will be able to tell when a given set of statements is logically consistent and when it is not.

  ​Students will be able to explain some of the problems with relativism about truth.

  Students will be able to explain and apply some of the basic principles of statistics and of probablity theory. ​

  ​Students will be able to demonstrate creative thinking by spotting possibilities missed by less creative thinkers.

• Introduction To Logic (PHIL127) Level 1 Credit level 15 Semester Second Semester Exam:Coursework weighting 60:40 Aims

• To introduce students to the concepts, language and methods of classical sentential logic.

• To introduce students to a language of classical quantificational logic.

• Learning Outcomes

  Students will be able to explain and apply the basic concepts of classical sentence logic.

  Students will be able to translate from English into sentence logic and vice versa.

  ​Students will be able to construct and use truth tables.

  ​Students will...