2021-22 BSc Mathematics and Philosophy Programme Design Document

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1	Programme Information & PLOs
2	Title of the new programme – including any year abroad/ in industry variants
3	BSc Mathematics and Philosophy
4	Level of qualification
5	Please select:				Level 6
6	Please indicate if the programme is offered with any year abroad / in industry variants																				Year in Industry Please select Y/N								No
7																					Year AbroadPlease select Y/N								No
8	Department(s): Where more than one department is involved, indicate the lead department
9	Lead Department		Mathematics
10	Other contributing Departments:		Philosophy
11	Programme Leader
12	Dr. Stefan Weigert (Mathematics)
13	Purpose and learning outcomes of the programme
14	Statement of purpose for applicants to the programme
15	Mathematics and Philosophy have substantial areas of overlap. In mathematics and philosophy alike, significant emphasis is placed on building arguments to deduce conclusions from assumed premises. In the case of mathematics, those assumptions are called axioms, and are not questioned. By contrast, in philosophy the assumptions on which we build our arguments, as well as the argument steps themselves, are open to critical scrutiny, leading to a greater degree of uncertainty in philosophy than in mathematics. Nevertheless, in both mathematics and philosophy the development of creative and compelling arguments for conclusions is a key aim. This combined honours degree involves the study of mathematics and philosophy in parallel, with particular attention to their overlap in the formal study of deductive arguments (logic), and the philosophy of mathematics. This is the particular value of studying mathematics and philosophy together. The distinctive nature of the programme as offered at York is that students have the opportunity to study with world-leading experts not only in mathematics and in philosophy, singly, but also with experts in the overlap in these disciplines, such as the philosophy of logic and of mathematics. Mathematics and Philosophy students at York graduate with a firm command of critical thinking and argumentation, both in formal (mathematical) and informal contexts, and the ability to articulate their ideas and present them in a range of formats. Thus, students have particular skills which are relevant to employability, such as analytical thinking, logical reasoning, and problem solving. These skills then afford graduates opportunities in a wide range of industries, such as teaching, research, the public sector, including the civil and diplomatic services, and management, and financial services.
16	Programme Learning OutcomesPlease provide six to eight statements of what a graduate of the programme can be expected to do. Taken together, these outcomes should capture the distinctive features of the programme. They should also be outcomes for which progressive achievement through the course of the programme can be articulated, and which will therefore be reflected in the design of the whole programme.
17	PLO	On successful completion of the programme, graduates will be able to:
18	1	use logical reasoning to build arguments, and to critically analyse statements, arguments, or conjectures made by others, justifying the principles chosen for such a critique;
19	2	to analyse and solve problems for which techniques including calculus, algebra, and formal logic, were developed;
20	3	investigate unfamiliar problems in mathematics by adapting and/or synthesising a range of mathematical approaches (including abstraction or numerical approximation);
21	4	make a measured judgement about what is the best view on a particular problem and present a sustained line of argument in defence of this judgement based on careful consideration of what can be said for and against the proposed solutions;
22	5	critically engage in ongoing scholarly and philosophical debate concerning mathematical truth, knowledge and our use of mathematics in science and modern life
23	6	gain research skills in an area of mathematical or philosophical specialisation;
24	7	work effectively, imaginatively, and productively as a thinker and learner;
25	8	communicate complex and difficult mathematical and philosophical ideas in clear, precise, and accessible terms in a variety of formats.
26	Programme Learning Outcome for year in industry (where applicable) For programmes which lead to the title ‘with a Year in Industry’ – typically involving an additional year – please provide either a) amended versions of some (at least one, but not necessarily all) of the standard PLOs listed above, showing how these are changed and enhanced by the additional year in industry b) an additional PLO, if and only if it is not possible to capture a key ability developed by the year in industry by alteration of the standard PLOs.
27	N/A
28	Programme Learning Outcome for year abroad programmes (where applicable) For programmes which lead to the title ‘with a Year Abroad’ – typically involving an additional year – please provide either a) amended versions of some (at least one, but not necessarily all) of the standard PLOs listed above, showing how these are changed and enhanced by the additional year abroad or b) an additional PLO, if and only if it is not possible to capture a key ability developed by the year abroad by alteration of the standard PLOs.
29	N/A
30	Explanation of the choice of Programme Learning OutcomesPlease explain your rationale for choosing these PLOs in a statement that can be used for students (such as in a student handbook). Please include brief reference to:
31	i) Why the PLOs are considered ambitious or stretching?
32	The PLOs include the development of substantial subject specific knowledge and techniques across two subjects, as well as significant attention to their overlap in formal logic and the philosophy of mathematics. The course provides a distinct intellectual challenge in being able to learn, relate, and combine the complementary methods of mathematics with the methods of philosophy and apply them to a range of problems across both disciplines, particularly in regard to debates concerning mathematical truth, mathematical knowledge, and our use of mathematics in science and modern life.
33	ii) The ways in which these outcomes are distinctive or particularly advantageous to the student:
34	As per the statement of purpose, the first PLO emphasizes logical reasoning as the common core to both mathematics and philosophy. It is a distinctive feature of Mathematics and Philosophy as a degree that there is this close overlap in the key role of deductive argument. Students will have the advantage of studying two subject areas that provide valuable subject-specific knowledge in their own right, as well as reflecting on the shared techniques of both, and specifically on the nature of mathematical reasoning.
35	iii) How the programme learning outcomes develop students’ digital literacy and will make appropriate use of technology-enhanced learning (such as lecture recordings, online resources, simulations, online assessment, ‘flipped classrooms’ etc)?
36	In the process of meeting these outcomes, students will be exposed to a range of digital and technology-enhanced resources in the individual modules that make up the programme, including gaining experience of programming.
37	iv) How the PLOs support and enhance the students’ employability (for example, opportunities for students to apply their learning in a real world setting)? The programme's employablity objectives should be informed by the University's Employability Strategy:
38	The PLOs support development of a range of transferrable skills. In particular, graduates will be flexible-thinking problem solvers, with the ability to deal with both formal/technical material and to communicate clearly verbally and in writing. In addition, students will teamworking skills in collaborative work in seminars and problem solving. Employability skills are also embedded in the curriculum in Mathematical Skills 1.
39	vi) How will students who need additional support for academic and transferable skills be identified and supported by the Department?
40	Primarily via supervisors in the two supporting departments, who monitor progress and meet regularly with their supervisees to discuss their development throughout their degree. Students are allocated a primary supervisor in one of the two Departments, but all are given a contact person in their second Department who they can speak to if they have any subject specific concerns that their own supervisor cannot help with. Additionally, in the Philosophy Department the Director of First Year Programme helps to monitor performance in first year and support students who need it (in close collaboration with our first year seminar tutors). Our first year Beginning Philosophy module highlights basic skills and its online component emphasizes key points. Students are warmly encouraged to make use of module tutors’ office hours where they are struggling with material. For first year students regular "drop-in" academic support sessions are scheduled into the timetable, as optional support for all first year students. These are run by the Transition Officer in the Mathematics Department. The Maths Society runs weekly "Cake and Calculus" sessions in the Department's undergraduate social space (Maths Student Study Centre) during Autumn and Spring term. These sessions are an opportunity for later year students to help first year students, but also a place where all years can come together to work in groups on weekly homework. Mathematical Skills 1 has optional timetabled drop-in sessions during Spring term to help with the written assignments (particularly the use of LaTeX). Specific student needs related to disability are identified through statements of needs, with the oversight of the department's Disability Coordinator and each student's academic supervisor.
41	vii) How is teaching informed and led by research in the department / centre / University
42	The vast majority of teaching staff are active in research, which informs their teaching at all levels. In the Philosophy Department the third year modules are particularly research led, focussing on topics in which the module tutor is active in research. Students are introduced to research methods in Mathematics via project work in Maths Skills 1, and can develop their research skills in a mathematical setting if they choose to complete a Final Year Project in Mathematics. In Philosophy 'Beginning Philosophy' provides an introduction to research methods. Students who do not take the Maths project in third year instead display their independent research skills in philosophy via one or more Advanced Module. In Philosophy, departmental teaching skills workshops for staff feature participation by staff from ASO who ensure our discussions and work take contemporary pedagogical research into account.
43	Stage-level progression Please complete the table below, to summarise students’ progressive development towards the achievement of PLOs, in terms of the characteristics that you expect students to demonstrate at the end of each year. This summary may be particularly helpful to students and the programme team where there is a high proportion of option modules. Note: it is not expected that a position statement is written for each PLO, but this can be done if preferred (please add information in the 'individual statement' boxes). For a statement that applies across all PLOs in the stage fill in the 'Global statement' box.
44	Stage 0 (if your programme has a Foundation year, use the toggles to the left to show the hidden rows)
45	Stage 1
46	On progression from the first year (Stage 1), students will be able to:											Global statement
47	PLO 1		PLO 2			PLO 3					PLO 4					PLO 5					PLO 6					PLO 7					PLO 8
48	recognise and use logical symbols and terminology to formalise simple arguments and discuss their validity.		competently use foundational mathematical and logical techniques appropriately.			adapt some foundational techniques in mathematics to unfamiliar situations.					appreciate some problems and puzzles in some central areas of philosophy and its history, and begin to consider how these problems may be solved.					appreciate and critically engage with some core issues concerning the nature of knowledge.					grasp some basic mathematical and philosophical research skills.					engage in productive collaborative inquiry (e.g. in seminars) and work independently on problems set by lecturers.					communicate basic ideas in seminars and written work.
49	Stage 2
50	On progression from the second year (Stage 2), students will be able to:											Global statement
51	PLO 1		PLO 2			PLO 3					PLO 4					PLO 5					PLO 6					PLO 7					PLO 8
52	recognise and use logical symbols and terminology to formalise simple arguments and discuss their validity. Provide logical derivations and countermodels to answer questions concerning the validity of arguments in formal logic.		competently use foundational mathematical and logical techniques appropriately. Confidently perform calculations, or use methods, which require the combination of several foundational techniques, and identify which of those techniques is appropriate.			adapt some foundational techniquest to unfamiliar situations. Recognize when some foundational techniques can be applied outside their standard context, and put together two or more techniquest to analyse a problem.					Appreciate a range of problems and puzzles across core areas of philosophy and its history, and understand and critically evaluate available solutions.					appreciate, and critically engage with, metaphysical issues relevant to mathematics, via discussions of metaphysics and/or the philosophy of science.					develop use of mathematical and philosophical research skills through independent study in support of taught modules.					engage in productive collaborative inquiry (e.g. in seminars) and work independently on problems set by lecturers and arising out of individual and group reflection.					Communicate basic and more complex ideas clearly, concisely, and accurately in seminars and written work.
53	Stage 3
54	(For Integrated Masters) On progression from the third year (Stage 3), students will be able to:											Global statement
55	PLO 1		PLO 2			PLO 3					PLO 4					PLO 5					PLO 6					PLO 7					PLO 8
56	Individual statements
57	Programme Structure
58	Module Structure and Summative Assessment Map Please complete the summary table below which shows the module structure and the pattern of summative assessment through the programme. ‘Option module’ can be used in place of a specific named option. If the programme requires students to select option modules from specific lists these lists should be provided in the next section. From the drop-down select 'S' to indicate the start of the module, 'A' to indicate the timing of each distinct summative assessment point (eg. essay submission/ exam), and 'E' to indicate the end of the module (if the end of the module coincides with the summative assessment select 'EA') . It is not expected that each summative task will be listed where an overall module might be assessed cumulatively (for example weekly problem sheets). If summative assessment by exams will be scheduled in the summer Common Assessment period (weeks 5-7) a single ‘A’ can be used within the shaded cells as it is understood that you will not know in which week of the CAP the examination will take place.
59	Stage 0 (if you have modules for Stage 0, use the toggles to the left to show the hidden rows)
60	Stage 1
61	Credits	Module				Autumn Term										Spring Term										Summer Term
62		Code		Title		1	2	3	4	5	6	7	8	9	10	1	2	3	4	5	6	7	8	9	10	1	2	3	4	5	6	7	8	9	10
63	10	PHI00001C		Beginning Philosophy			S																	A	EA
64	20	PHI00005C		Reason and Argument A			S								EA	A
65	20	PHI00008C		Knowledge and Perception													S								E	A
66	10	PHI00003C		Metaphysics																						S			E		A
67	30	MAT00001C		Calculus			S									A													E	A
68	20	MAT00010C		Algebra			S									A													E	A
69	10	MAT00011C		Mathematical Skills 1: Reasoning and Communication			S									A									A		EA
70	Stage 2
71	Students take 60 credits of Philosophy including Key Ideas: Intermediate Logic and at least one of Key Ideas in Metaphysics and Key Ideas in Philosophy of Science. They need to take a further 20 credits in Philosophy, which can either be one more full Key Ideas module, or two Short Key Ideas modules, each worth 10 credits. Students take the 40 credit Pure Mathematics stream in Mathematics, plus Linear Algebra (10 cr) and Vector Calculus (10 cr).
72	Credits	Module				Autumn Term										Spring Term										Summer Term
73		Code		Title		1	2	3	4	5	6	7	8	9	10	1	2	3	4	5	6	7	8	9	10	1	2	3	4	5	6	7	8	9	10
74	40	MAT00032I		Pure Mathematics			S									A													E	A
75	10	MAT00026I		Linear Algebra			S								E	A
76	10	MAT00030I		Vector Calculus			S								E	A
77	20	PHI00096I		Intermediate Logic			S																		EA					A
78	20/10	Various PHI		Key Ideas (Autumn modules)			S								E	A
79	20/10	Various PHI		Key Ideas (Spring/Summer Modules). Includes Metaphysics and Philosophy of Science													S									A			E		A
80	Stage 3
81	Students can choose to weight their degree 80/40 or 60/60. The 20 credit bridge module (Foundations of Mathematics) in Philosophy is compulsory for all students. Each 20-credit taught Philosophy module has an associated 10-credit Advanced Module, which involve private further study of the topic, guided by a supervisor. For 80/40 Maths/Philosophy, students take the Maths Project (40 cr), plus 40 additional credits of Mathematics from the Pure Mathematics stream, and 40 credits from Philosophy including Foundations of Mathematics. For 60/60 Split, students take 60 credits of Mathematics from the Pure Mathematics stream, plus Foundations of Mathematics, plus an additional 20 credit Philosophy module and the corresponding two 10 credit Advanced Modules. For 80/40 Philosophy/Mathematics, students take 40 credits from the Pure Mathematics stream in Mathematics, plus the Foundations of Mathematics bridge module and an additional 60 credits of Philosophy modules including two Advanced Modules.
82	Credits	Module				Autumn Term										Spring Term										Summer Term
83		Code		Title		1	2	3	4	5	6	7	8	9	10	1	2	3	4	5	6	7	8	9	10	1	2	3	4	5	6	7	8	9	10
84	20	PHI00017H		Foundations of Maths													S								E		A
85	20 each	Various PHI		Research-led Taught Modules in Philosophy (Autumn)			S								EA
86	20 each	Various PHI		Research-led Taught Modules in Philosophy (Spring/Summer)													S								E		A
87	10 each	Various PHI		Advanced Module																						S					EA
88	40	MAT00004H		BSc Final Year Project			S								A														EA				A
89	10	Various MAT		Autumn - List A			S								E	A
90	10	Various MAT		Spring - List B													S								E					A
91	Optional module listsIf the programme requires students to select option modules from specific lists these lists should be provided below. If you need more space, use the toggles on the left to reveal ten further hidden rows.
92	Option List A		Option List B			Option List C					Key Ideas (Value)					Key Ideas (Theoretical Philosophy)					Key Ideas (History of Philosophy)					Year 3 Research-Led Taught Modules					Option List H
93											Note: Examples only—modules offered may vary from year to year
94	Algebraic Number Theory MAT00029H		Differential Geometry MAT00006H								Applied Ethics					Metaphysics					Hume					Contemporary Issues in Bioethics
95	Formal Languages and Automata MAT00002H		Galois Theory MAT00008H								Ethical Theory					Philosophy of Science					Kant					Paradoxes
96	Number Theory MAT00023H		Topology MAT00044H								Religious Ethics					Philosophy of Language					Spinoza and Leibniz					Phenomenology and Psychiatry
97	Groups and Actions MAT00056H		Cryptography MAT00034H								Aesthetics					Philosophy of Mind					Aristotle					Philosophy of Art from Hume to Tolstoy
98											Feminist Philosophy										Nietzsche					Philosophy of Christianity
99																										Philosophy of Physics
100																										Philosophy of Psychology