2022-23 MMath Mathematics Programme Design Document

	A	C	F	G	I	K	L	M	N	O	P	Q	R	S	T	U	V	W	X	Y	Z	AA	AB	AC	AD	AE	AF	AG	AH	AI	AJ	AK	AL	AM	AN
1	Programme Information & PLOs
2	Title of the new programme – including any year abroad/ in industry variants
3	MMath Mathematics
4	Level of qualification
5	Please select:				Level 7
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 Abroad Please 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:		n/a
11	Programme Leader
12	Prof Michael Bate
13	Purpose and learning outcomes of the programme
14	Statement of purpose for applicants to the programme
15	The MMath degree in Mathematics at York is designed to take students who are fascinated by mathematics on a journey which has the time to go more deeply into modern mathematics than the BSc. You will develop your mathematical skills to be able to understand the advanced techniques in mathematics which prepare you for postgraduate research. Throughout the degree your core mathematical skills (calculus, algebra, probability and statistics) will be developed to a high level of sophistication, and your reasoning skills will be sharpened, as you are guided to use mathematics in deeper and more interesting ways. You will develop other skills which will be valuable throughout your career, such as computer programming and the ability to write on technical subjects with clarity and precision. We pride ourselves on being a friendly and inclusive department with high-quality teaching provided in a relaxed atmosphere. You will experience a variety of ways of learning and working, through lectures, small group seminars, group and individual projects, under the careful guidance of our dedicated staff, all of whom are engaged in current research and many of whom are world leaders in their field. In the final year you will use your knowledge, understanding and skills to write a dissertation on a topic of your own interest, under the supervision of an expert mathematician. By the end of the programme you will be ready to engage with research-level mathematics in some area of specialisation in pure or applied mathematics, and have one of the most sought-after qualifications by key employers. The MMath programme is also accredited by the Institute of Mathematics and Its Applications (IMA) to the level of meeting the full educational requirement for Chartered Mathematician status. With York’s reputation as a top university, this makes an MMath degree in Mathematics at York an outstanding choice.
16	Programme Learning Outcomes Please 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, with a high level of confidence and sophistication, the mathematical language and tools that underpin a wide range of research in, and applications to, science, technology and industry
19	2	recognise when an unfamiliar problem is open to mathematical investigation, and be able to formulate their own strategy for the process of such an investigation,
20	3	use logical reasoning as a basis for the critical analysis of ideas or statements which have a mathematical context, and develop independently their own ideas using well-founded reasoning,
21	4	conduct, both independently and as part of a group of peers, a study of a specialised area of mathematics which takes into account recent mathematical progress. They will be able to compare and synthesise multiple sources to produce this study, and be able to check or complete technical details from these sources independently,
22	5	communicate advanced mathematical ideas clearly, in writing and in a presentation, at a level appropriate for the intended audience,
23	6	create mathematical documents, presentations and computer programmes by accurately and efficiently using a range of digital technologies.
24	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.
25	n/a
26	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.
27	n/a
28	Explanation of the choice of Programme Learning Outcomes Please 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:
29	i) Why the PLOs are considered ambitious or stretching?
30	Each PLO represents a challenge to the student to develop existing skills to a higher level. Through each stage the level of challenge is raised, as more depth or complexity is encountered. In studying mathematics each stage builds naturally on the attainments of the previous one, as foundational ideas are developed into fully fledged theories or methodologies. Those who fully rise to this challenge will be prepared to contribute to mathematics at the research frontier.
31	ii) The ways in which these outcomes are distinctive or particularly advantageous to the student:
32	The outcomes identify six basic areas, which can be summarised as: technique, adaptability, critical thinking, scholarship, communication and digital literacy. When possessed together they give each student the abilities and understanding to function in any environment where the precision and clarity of mathematical thinking are valuable.
33	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)?
34	The communication elements require students to master digital literacy for visual presentations and for producing a dissertation. In addition, all students will learn some programming, and a number of modules include the opportunity to use mathematics software (such as R, Maple and MatLab).
35	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 employability objectives should be informed by the University's Employability Strategy:
36	The PLOs cover a list of skills which are desired by employers: analytical reasoning, confidence with high level mathematics, clarity of communication, flexible thinking, the ability to learn complex ideas quickly and precisely, and digital literacy. Employability skills are also embedded in the curriculum in Mathematical Skills 1 and Mathematical Skills 2
37	vi) How will students who need additional support for academic and transferable skills be identified and supported by the Department?
38	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 our Transition Officer. The Mathematics 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 (fortnightly) 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.
39	vii) How is teaching informed and led by research in the department/ centre/ University?
40	The vast majority of teaching staff are active in research, and through lectures, tutorials and seminars communicate the influence foundational ideas have on making progress in research. Students also explicitly connect with the principles of research through projects (in Math Skills 1 & 2, the MMath Group Project in 3rd year and the final year dissertation) as well as having the option to choose modules in the final year which reflect their preferred specialisation and, together with their choice of final year project, enable them to engage with mathematics at the research frontier. The research interests of staff and their industrial collaborations will be integrated into the programme via project work and placements.
41	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.
42	Stage 0 (if your programme has a Foundation year, use the toggles to the left to show the hidden rows)
43	On progression from the first year (Stage 0), students will be able to:											n/a
44	PLO 1		PLO 2			PLO 3					PLO 4					PLO 5					PLO 6					PLO 7					PLO 8
45	n/a		n/a			n/a					n/a					n/a					n/a					n/a					n/a
46	Stage 1
47	On progression from the first year (Stage 1), students will be able to:											n/a
48	PLO 1		PLO 2			PLO 3					PLO 4					PLO 5					PLO 6					PLO 7					PLO 8
49	competently use foundational mathematical techniques		adapt foundational techniques to unfamiliar situations			create and critique elementary mathematical reasoning and understand the importance of sound reasoning					produce, in collaboration with others, a well-researched survey of some elementary idea or foundational tool in mathematics					communicate elementary mathematical ideas clearly and concisely					use computers for (a) elementary mathematical typesetting to produce a written report and slides for presentation (b) elementary statistical analysis
50	Stage 2
51	On progression from the second year (Stage 2), students will be able to:											n/a
52	PLO 1		PLO 2			PLO 3					PLO 4					PLO 5					PLO 6					PLO 7					PLO 8
53	confidently perform calculations, or use methods, which require the combination of several foundational techniques, and identify which of those techniques is appropriate.		recognize when some foundational techniques can be applied outside the standard context, and put together two or more techniques to analyse a problem.			reproduce, with understanding and some insight, important examples of logical reasoning or mathematical argument, and create their own arguments for similar situations					independently perform a literature survey of a renowned or noteworthy mathematical idea, method or process.					write clearly and concisely, with an appropriate balance between mathematics and English, about well-understood mathematical ideas					write basic programmes in Java, typeset using LaTeX and understand how to search for technical information digitally
54	Stage 3
55	(For Integrated Masters) On progression from the third year (Stage 3), students will be able to:											demonstrate the six PLO abilities in dealing with more sophisticated concepts than those studied in the third year, and work with a greater level of initiative. In particular, they will be prepared for a career in which the ability to work with high-level mathematical concepts, and possibly develop them, plays a significant role.
56	PLO 1		PLO 2			PLO 3					PLO 4					PLO 5					PLO 6					PLO 7					PLO 8
57	confidently perform calculations using advanced methods and tools, and be able to select the appropriate method for the context		recognize when a method or tool developed in earlier years can be applied to an unfamiliar problem			reproduce or paraphrase a standard mathematical argument in the correct context, and be able to critically evaluate an argument or the application of a mathematical tool within a familiar context.					make an effective and scholarly contribution to a report on some sophisticated mathematical idea, method or process.					write clearly and concisely, with an appropriate balance between mathematics and English, about sophisticated mathematical ideas, both independently and as a contributor to a shared report. Also, to be able to provide a clear summary of such ideas for presentation.					confidently use computers for producing well-structured written reports and for effective literature research
58	Programme Structure
59	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.
60	Stage 0 (if you have modules for Stage 0, use the toggles to the left to show the hidden rows)
61	Stage 1
62	Credits	Module				Autumn Term										Spring Term										Summer Term
63		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
64	30	MAT00001C		Calculus		S										A													E	A
65	20	MAT00010C		Algebra		S										A													E	A
66	10	MAT00011C		Mathematical Skills 1: Reasoning and Communication		S										A									EA		A
67	20	MAT00004C		Introduction to Probability and Statistics		S									EA	A
68	20	MAT00005C		Real Analysis													S												E	A
69	20	MAT00003C		Introduction to Applied Mathematics													S												E	A
70	Stage 2
71	Students choose two out of the three 40cr modules Applied Mathematics, Pure Mathematics or Probability and Statistics. To progress into Stage 3 of the MMath the Stage 2 average must be at least 55. Students with a lower Stage 2 average will be transferred to the BSc in Mathematics for Stage 3.
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	MAT00034I		Applied Mathematics		S										A													E	A
75	40	MAT00032I		Pure Mathematics		S										A													E	A
76	40	MAT00035I		Probability & Statistics		S										A													E	A
77	10	MAT00027I		Mathematical Skills 2		S									A										E	A
78	10	MAT00026I		Linear Algebra		S									E	A
79	10	MAT00033I		Vector Calculus		S									E	A
80	10	MAT00024I		Functions of a Complex Variable													S								E					A
81	Stage 3
82	Students take the 20cr MMath Group Project, and then choose 100cr from options in the Streams or from the three out-of-Stream options with a balance of 50cr per term. Options within a Stream are guaranteed not to have timetable clashes with each other or with the out-of-Stream options. Students can also take up to 20cr of M-level modules in Stage 3, but should be aware that the pass mark for these is 50. M-level modules have the same weight for classification as H-level modules. Note that the options Modelling with Matlab and Practical Data Science with R both include an element of summative assessment by coursework during the term. Students may replace up to 20cr of options with electives from other departments subject to the above constraints concerning the total number of credits in each term, and subject to approval by the (Deputy) Chair of the Board of Studies. The elective must be at H-level, with the exception of Languages For All (LFA) modules which may be at any level.
83	Credits	Module				Autumn Term										Spring Term										Summer Term
84		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
85	10			Autumn - Pure Stream		S									E	A
86	10			Spring - Pure Stream													S								E					A
87	10			Autumn - Applied Stream		S									E	A
88	10			Spring - Applied Stream													S								E					A
89	10			Autumn - Statistics and Mathematical Finance Stream		S									E	A
90	10			Spring - Statistics and Mathematical Finance Stream													S								E					A
91	10	MAT00011H		Option - Dynamical Systems		S									E	A
92	10	MAT00034H		Option - Cryptography													S								E					A
93	20	MAT00041H		Option - Numerical Analysis		S							A										A		EA					A
94	20	MAT000043H		MMath Group Project		S																							EA				A
95	Stage 4
96	Students take the 40cr MMath Final Year Project, and then choose 80cr from options in the Streams. The credit balance Autumn/Spring should be 40/40, 30/50 or 50/30. Students cannot take M-level versions of modules which they have already taken at H-level and must have obtained 120cr of M-level modules across Stages 3 & 4. Options within a Stream are guaranteed not to have timetable clashes with each other. Note that the option Modelling with Matlab includes an element of summative assessment by coursework during the term. Students can also choose to take any number of M-level modules from our Statistics and Mathematical Finance MSc programmes, but these are not guaranteed to be clash-free. Students may replace up to 20cr of options with electives from other departments subject to the above constraints concerning the total number of credits in each term, and subject to approval by the (Deputy) Chair of the Board of Studies. The elective must be at M-level, with the exception of Languages For All (LFA) modules which may be at any level but subject to the requirement to obtain 120cr of M-level modules across Stages 3 & 4.
97	Credits	Module				Autumn Term										Spring Term										Summer Term
98		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
99	10			Autumn - Pure Stream		S									E	A
100	10			Spring - Pure Stream													S								E					A