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Programme code | 2MATH012U |
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Programme type | Joint Honours (UG) |
Programme director(s) |
Kentaro Fujimoto (Philosophy and Mathematics)
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Faculty | Faculty of Science |
School/department | School of Mathematics |
Second School/department | Department of Philosophy |
Teaching institution | University of Bristol |
Awarding institution | University of Bristol |
Relevant QAA subject benchmark groups |
Mathematics, statistics and operational research (2023) (benchmark statement)
Philosophy (2019) (benchmark statement) |
Mode of study | Full Time |
Programme length | 4 years (full time) |
The programme provides an education in mathematics and philosophy which stresses their interconnection.
Mathematics:
In mathematics it pays particular attention (but is not restricted to) those fields of mathematics which are related to the philosophy of mathematics, and in philosophy. Apart from a basic grounding in core mathematics through compulsory Level C mathematics courses, the other mandatory units on the mathematics side are an H Level Unit in Mathematical Logic which will acquaint students with a modern view of logic and Set Theory. The compulsory M Level Unit on Axiomatic Set Theory which will introduce the notion of sets, whose existence will be discussed in the Phil. of Maths. unit.
The mathematics part of the programme develops skill in mathematical reasoning and problem-solving, facility in handling abstract concepts, and an ability to think logically and critically and to express ideas clearly.
Graduates should combine the facility in logical thinking, mathematical analysis and attention to detail developed through the study of mathematics, with the breadth of intellectual vision and skill in verbal communication developed through the study of philosophy. This should make them particularly valuable to a wide range of employers.
Philosophy:
This programme is designed to offer students a thorough understanding of Philosophy as it is practised in the analytic tradition, and of the strong intellectual links between Philosophy and Mathematics. It provides a firm basis for research in either subject. The wide ranging and flexible curriculum provides a programme of study incorporating progressive intellectual challenges and consolidates previous experience at each new level.
The mandatory units at level C provide all students with (a) a basic knowledge of some fundamental problems of metaphysics, epistemology, ethics and political philosophy (b) a basic competence in logic and the analysis of arguments and (c) the skills of reading and writing required in analytic philosophy. At levels I, H, and M students choose from a wide range of options, taught by specialists in the areas of their own research, some text-based and others topic-based, ranging from ethics and political philosophy to philosophy of physics. Students in this programme take mandatory units (levels I and M) in Philosophy of Mathematics. Students are also expected to write finals essays, giving them the opportunity both to explore areas in more depth and detail and to develop their own research skills.
The programme is designed to provide the advanced level units needed to prepare students for future research in either subject, but also provides training in a wide range of transferable skills which serve as the foundation for many types of career.
Programme Intended Learning Outcomes | Learning and Teaching Methods |
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Acquisition of knowledge and understanding through lectures, seminars and tutorials (1,2,3,4,5,6). Directed reading with a strong emphasis on primary materials (1,3,4,5,6). Regular problem classes (2). Tutorials and seminars to encourage student participation and advance understanding of difficult materials (1,3,4,5,6). Formative feedback on assessment is given through individual tutorials (for most units) and written comments. (1,2,3,4,5,6). |
Methods of Assessment | |
Coursework essays, testing understanding of a single topic in detail (1,3,4,5,6). Exams, testing breadth of knowledge of different subjects (1,2,4,5,6). Class tests and exercises in logic (2). An extended essay, testing the ability of students to research a subject of their own choice in detail (3,4,5,6). Coursework essays, logic exercises, and level C exams are formative; Level I and H exams and Extended essays are summative. |
Programme Intended Learning Outcomes | Learning and Teaching Methods |
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Lectures provide knowledge, enhance understanding, and serve to exemplify the characteristic virtues of analytic philosophy (1-13). Seminars and group tutorials aid understanding, and provide forums in which students can discuss philosophical issues with each other and with tutors (1-13). Problem classes in logic help students develop their analytical and argumentative skills (6,7). Coursework essays give students the opportunity to read widely and reflect carefully on the material covered in lectures and seminars (1-13). The extended essay gives level H students the opportunity for more intensive and independent research into chosen topics in Philosophy (1-13). |
Methods of Assessment | |
Essay writing tests the students' ability to read widely, analyse information and present reasoned arguments (1,2,3,4,5,6,7,8,9,10,13). Examinations test the students' ability to assimilate information, assess and present arguments, and criticise difficult material in a concise and lucid manner (1,2,3,4,5,6,7,8,9,10,12,13). Essay tutorials assist the students' ability to respond appropriately to criticism, to articulate and modify positions and arguments, and to develop a number of intellectual virtues (1,2,3,4,5,6,7,8,9,10,11,12,13). The presentation and group discussion of seminar papers develop the students' skills in communication and virtues in intellectual debate (1,2,3,4,5,6,7,8,9,10,11,12,13). Problem classes test the students' ability in logic (3,5,6,7). The extended Essay tests the students' ability to pursue an independent line of research, and to present the fruits of that research in a professional manner (1,2,3,4,5,6,7,8,9,10,13). |
Programme Intended Learning Outcomes | Learning and Teaching Methods |
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Seminars and tutorials are used to develop oral communication by requiring students to engage in class discussions and to give short presentations to initiate discussion, including defending their interpretations and arguments in debate with other students and staff (1,2, 4, 5, 8, 10,11) Research and written communication skills are developed through feedback on essays (2,3, 6, 8, 10). Students are given guidance in the use of electronic resources, and are informed of opportunities for C&IT training (6,7). Writing essays (especially Extended essays) for set deadlines encourages self-motivation and self-reliance, as well as independence of thought (1,6, 8, 9, 10,11). |
Methods of Assessment | |
Examinations test the ability of the students to provide crisp and lucid presentations of difficult ideas and arguments. (3,10,11) Essays (especially Extended essays) test the ability of students to research their materials and to present ideas and arguments in a lucid and professional manner (1,2,3,6,7,8,9,10,11). |
Statement of expectations from the students at each level of the programme as it/they develop year on year.
Level C/4 - Certificate |
Year 1 of the programme has been designed to lay the foundations, both in terms of subject-specific knowledge and skills and in terms of more general abilities, which will allow students to fulfil the programme's aims and objectives. By the end of the year, students should have a basic knowledge of some central areas of the subject (metaphysics, epistemology, ethics and political philosophy) and some crucial philosophical skills, including competence in formal logic and familiarity with the aims and methods of analytic philosophy. They should also be developing their skills in essay-writing and in discussing philosophical issues in tutorials. |
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Level I/5 - Intermediate |
Students further develop their skills and knowledge by choosing from a menu of options. These options are more demanding than level C units both in terms of the difficulty of the materials studied and of the amount of independent critical thinking required of the students. By the end of the year they should be capable of reading difficult and technical material (eg modern journal articles), grasping their arguments, and debating them in seminars with their peers. The mandatory unit, 'Realism' and 'Normativity', provides all level I students with basic knowledge and skills for more advanced level H units. |
Level H/6 - Honours |
Students further develop their skills and knowledge by choosing from a range of advanced options, taught by specialists in the areas of their own research. By the end of the year they should be capable of thinking critically and working independently. Students' capacity for intensive and independent research is further tested by the system of Extended essays. |
Level M/7 - Masters |
All students take the 'History and Philosophy of Mathematics' unit from the PHS M.A. programme. Two finals essays (or a 20-credit project) further test their capacity for independent study. |
The intended learning outcome mapping document shows which mandatory units contribute towards each programme intended learning outcome.
Programme Intended Learning Outcomes | Learning and Teaching Methods |
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Strong support in the first year, more independence encouraged in later years. First year based on lectures supported by two small-group tutorials per week. Second year based on lectures and problem classes. Third and fourth years based on lectures and/or seminars, guided reading, projects, group work etc. depending on the choice of optional units. |
Methods of Assessment | |
written examination, and in the third and fourth years, assessed project work and seminars depending on the choice of optional unit. |
Programme Intended Learning Outcomes | Learning and Teaching Methods |
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lectures supported by weekly assignments of mathematical exercises which are marked and returned to students. See also under Knowledge and Understanding. |
Methods of Assessment | |
as in Knowledge and Understanding. |
Programme Intended Learning Outcomes | Learning and Teaching Methods |
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As above plus computational assignments and project work in mathematics. |
Methods of Assessment | |
As above plus assessed computational assignments and project work in mathematics. |
Statement of expectations from the students at each level of the programme as it/they develop year on year.
Level C/4 - Certificate |
Mastery of basic mathematical skills, and an understanding of rigorous mathematics. The capacity to take different approaches to solving problems, and to communicate accurately. |
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Level I/5 - Intermediate |
Understanding of abstract mathematical structures and/or (depending on the other subject studied in the Joint programme) more advanced techniques; broadening and/or deepening of mathematical understanding. The capacity to evaluate the appropriateness of different approaches to solving problems. |
Level H/6 - Honours |
Confidence in handling deeper or more complex mathematical structures, and in critically analysing mathematical arguments; initiative in finding information and self-directed learning.Analytical techniques and problem-solving skills that can be applied in many types of employment. The capacity to evaluate evidence, arguments and assumptions, to reach sound judgements, and to communicate effectively. |
Level M/7 - Masters |
For MSci programmes - Mastery of some areas of mathematics at a level approaching the current research literature; capacity for original work in mathematics, either new research or a new synthesis of existing knowledge.The capacity to deal with complex issues both systematically and creatively, and to show originality in tackling and solving problems. |
The intended learning outcome mapping document shows which mandatory units contribute towards each programme intended learning outcome.
For information on the admissions requirements for this programme please see details in the undergraduate prospectus at http://www.bristol.ac.uk/prospectus/undergraduate/ or contact the relevant academic department.
UG Workload Statement
Success as an undergraduate student depends on you being able to make the transition to self-motivated, independent learning. Programmes are designed to assist you in this development, in many cases by starting with units in which timetabled teaching, such as lectures and practical classes, provides the foundations of knowledge and skills in a subject, moving on to individual research-based work. Over time you will be expected to take increasing responsibility for your own learning, guided by the feedback on your work that you will receive. At the heart of your studies at every level there must be regular and disciplined individual reading, reflection and writing and it is this skill of independent studies, above all others, that will serve you best when you leave the University.
Most programmes use credits and a 20 credit unit broadly equates to about 200 hours of student input. This includes all activities related to the teaching, learning and assessment of taught units.
A component of this is the time that you spend in class, in contact with the teaching staff, which includes activities such as lectures, laboratories, tutorials and fieldwork. Some of this activity may be online and could consist of activity that is synchronous (using real-time environments such as Blackboard Collaborate) or asynchronous (using tools such as tutor moderated discussion forums, blogs or wikis).
In some programmes there are field courses and/or placements that will take place in concentrated periods of time.
Outside scheduled activities you are expected to pursue your own independent learning to build your knowledge and understanding of the subjects you are studying. Such independent activities include, reviewing lecture material, reading textbooks, working on examples sheets, completing coursework, writing up laboratory notes, preparing for in-class progress tests and revising for examinations.
We recognise that many students undertake paid employment. To achieve a sensible balance between work and study, you are advised to undertake paid work for no more than 15 hours per week in term-time.
Professional Programmes
Many undergraduates in the Faculty of Health Sciences will be following the professional programmes of:
For these professional programmes, full time attendance is compulsory unless absence is formally approved. Academic activities are timetabled throughout the 5-day week and student workload is around 40 hours per week on average. Where possible, students in the early years are permitted Wednesday afternoons for sport and extra-curriculum activities. This may not be available in later years of professional programmes as when a student progresses through the curricula there is an increasing exposure to clinical and professional activities. Students in clinic or on placements may need to stay later than core times of 08.00 – 18.00 or even overnight to observe out-of-hours activities. This increasing exposure to clinical activities means that students on these professional programmes often have longer term dates than the University standard. Individual years within programmes are likely to vary in length (for example because of the timings of placements) and further information on this will be found in individual programme regulations. Another important point to note is that many of the assessments sit outside of the standard University examination timetable and are likely to be more frequent meaning that students will more oftentimes be engaged in revision activities and self-directed learning.
Faculty of Health Sciences
Faculty Assessment and Feedback Statement for Undergraduate Students. University of Bristol access only.
School of Mathematics Administration Team – math-info@bristol.ac.uk
This integrated Masters programme has been designated as type II: Specialised or Advanced Masters in accordance with the QAA Degree Characteristics Statement. Please see the Regulations and Code of Practice for Taught Programmes for further information on this type of programme.
MATH10015, MATH10012 and MATH10011 are must pass units. The definition of must pass units can be found in the Regulations and Code of Practice for Taught Programmes Glossary of Terms.
Unit Name | Unit Code | Credit Points | Status | |
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Analysis | MATH10011 | 20 | Mandatory | TB-4 |
Linear Algebra | MATH10015 | 20 | Mandatory | TB-4 |
ODEs, Curves and Dynamics | MATH10012 | 20 | Mandatory | TB-4 |
Introduction to Proofs and Group Theory | MATH10010 | 20 | Mandatory | TB-4 |
Introduction to Philosophy A | PHIL10005 | 20 | Mandatory | TB-1 |
Introduction to Philosophy B | PHIL10006 | 20 | Mandatory | TB-2 |
Certificate of Higher Education | 120 |
This integrated Masters programme has been designated as type II: Specialised or Advanced Masters in accordance with the QAA Degree Characteristics Statement. Please see the Regulations and Code of Practice for Taught Programmes for further information on this type of programme.
Unit Name | Unit Code | Credit Points | Status | |
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You must take 60cp of Mathematics and 60cp of Philosophy units, with no more than 70cp in either teaching block. | ||||
60cp Mathematics units: | ||||
Select at least one of the following Mathematics Units: | ||||
Metric Spaces | MATH20006 | 20 | Optional | TB-1 |
Algebra 2 | MATH21800 | 20 | Optional | TB-2 |
Linear Algebra 2 | MATH21100 | 20 | Optional | TB-1 |
Select up to 40cp additional Mathematics units from the following list: | ||||
Applied Partial Differential Equations 2 | MATH20402 | 20 | Optional | TB-2 |
Introduction to Geometry | MATH20004 | 20 | Optional | TB-2 |
Multivariable Calculus and Complex Functions | MATH20015 | 20 | Optional | TB-1 |
Ordinary Differential Equations 2 | MATH20101 | 20 | Optional | TB-1 |
60cp Philosophy units: | ||||
Take both of the following mandatory units: | ||||
Realism and Normativity | PHIL20046 | 20 | Optional | TB-1 |
Philosophy of Mathematics | PHIL20039 | 20 | Optional | TB-2 |
Select 20cp Philosophy units from the following list: | ||||
Death, dying and disease | PHIL20049 | 20 | Optional | TB-2 |
Philosophy of Mind | PHIL20010 | 20 | Optional | TB-1 |
Ethics | PHIL20011 | 20 | Optional | TB-2 |
Political Philosophy | PHIL20012 | 20 | Optional | TB-1 |
Philosophy of Language | PHIL20017 | 20 | Optional | TB-1 |
Ancient Philosophy | PHIL20040 | 20 | Optional | TB-2 |
Themes in Modern European Philosophy 1 | PHIL20051 | 20 | Optional | TB-1 |
Space, Time and Matter | PHIL20053 | 20 | Optional | TB-2 |
Diploma of Higher Education | 120 |
This integrated Masters programme has been designated as type II: Specialised or Advanced Masters in accordance with the QAA Degree Characteristics Statement. Please see the Regulations and Code of Practice for Taught Programmes for further information on this type of programme.
Unit Name | Unit Code | Credit Points | Status | |
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You must take 60cp of Mathematics and 60cp of Philosophy units, with no more than 70cp in either teaching block. | ||||
Philosophy of Mathematics | PHIL30090 | 20 | Mandatory | TB-2 |
Logic | MATH30100 | 20 | Mandatory | TB-2 |
Set Theory | MATH32000 | 20 | Mandatory | TB-1 |
Select 20cp Mathematics units | ||||
Group 1 | ||||
Metric Spaces | MATH20006 | 20 | Optional | TB-1 |
Group 2 | ||||
Fields, Forms and Flows | MATH30018 | 20 | Optional | TB-1 |
Ordinary Differential Equations 2 | MATH20101 | 20 | Optional | TB-1 |
Group 3 | ||||
Group Theory | MATH33300 | 20 | Optional | TB-1 |
Fluid Dynamics 3 | MATH33200 | 20 | Optional | TB-1 |
Group 5 | ||||
Measure Theory and Integration | MATH30007 | 20 | Optional | TB-1 |
Numerical Analysis | MATH30029 | 20 | Optional | TB-1 |
Group 6 | ||||
Complex Function Theory | MATH33000 | 20 | Optional | TB-1 |
Quantum Mechanics | MATH35500 | 20 | Optional | TB-1 |
Multivariable Calculus and Complex Functions | MATH20015 | 20 | Optional | TB-1 |
Group 7 | ||||
Combinatorics | MATH30030 | 20 | Optional | TB-1 |
Linear Algebra 2 | MATH21100 | 20 | Optional | TB-1 |
Group 9 | ||||
Group 10 | ||||
Galois Theory | MATHM2700 | 20 | Optional | TB-2 |
Quantum Information Theory | MATH30031 | 20 | Optional | TB-2 |
Group 11 | ||||
Number Theory | MATH30200 | 20 | Optional | TB-2 |
Statistical Mechanics | MATH34300 | 20 | Optional | TB-2 |
Group 12 | ||||
Mechanics 23 | MATH31910 | 20 | Optional | TB-2 |
Functional Analysis 3 | MATH36202 | 20 | Optional | TB-2 |
Group 14 | ||||
Dynamical Systems and Ergodic Theory 3 | MATH36206 | 20 | Optional | TB-2 |
Algebra 2 | MATH21800 | 20 | Optional | TB-2 |
Group 15 | ||||
Introduction to Geometry | MATH20004 | 20 | Optional | TB-2 |
Optimisation | MATH30017 | 20 | Optional | TB-2 |
Random Matrix Theory | MATH30033 | 20 | Optional | TB-2 |
Select 40cp Philosophy units from the following list: | ||||
Philosophy of Science | PHIL30049 | 20 | Optional | TB-2 |
Philosophical Issues of Physical Sciences | PHIL30052 | 20 | Optional | TB-1 |
Philosophy of Biology | PHIL30063 | 20 | Optional | TB-1 |
Philosophy of Psychology | PHIL30077 | 20 | Optional | TB-2 |
The Philosophy and History of Medicine | PHIL30082 | 20 | Optional | TB-1 |
Death, dying and disease | PHIL30115 | 20 | Optional | TB-2 |
Evil, Deviance, and Crime | PHIL30127 | 20 | Optional | TB-1 |
First Extended Essay | PHIL30107 | 20 | Optional | TB-1 |
Second Extended Essay | PHIL30108 | 20 | Optional | TB-2 |
BSc Science (Maths and Philosophy) | 120 |
This integrated Masters programme has been designated as type II: Specialised or Advanced Masters in accordance with the QAA Degree Characteristics Statement. Please see the Regulations and Code of Practice for Taught Programmes for further information on this type of programme.
Unit Name | Unit Code | Credit Points | Status | |
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You must take 60cp of Mathematics and 60cp of Philosophy units, balanced accross teaching blocks | ||||
Axiomatic Set Theory | MATHM1300 | 20 | Mandatory | TB-1 |
Project | PHILM0008 | 20 | Mandatory | TB-1,TB-2 |
Two units , no more than one unit from each group, from: | ||||
Group 1 - TB2 | ||||
Algebraic Number Theory 4 | MATHM6205 | 20 | Optional | TB-1 |
Group 3 - TB1 | ||||
Representation Theory | MATHM4600 | 20 | Optional | TB-1 |
Group 4 - TB1 | ||||
Quantum Computation | MATHM0049 | 20 | Optional | TB-1 |
Algebraic Topology | MATHM1200 | 20 | Optional | TB-1 |
Group 5 - TB1 | ||||
Complex Function Theory (34) | MATHM3000 | 20 | Optional | TB-1 |
Group 6 - TB1 | ||||
Geometry of Manifolds | MATHM0037 | 20 | Optional | TB-1 |
Project - TB1 | ||||
Project | MATHM2200 | 20 | Optional | TB-4 |
Group 7 - TB2 | ||||
Fields, Forms and Flows | MATHM0033 | 20 | Optional | TB-2 |
Group 8 - TB2 | ||||
Galois Theory | MATHM2700 | 20 | Optional | TB-2 |
Group 9 - TB2 | ||||
Analytic Number Theory | MATHM0007 | 20 | Optional | TB-2 |
Statistical Mechanics 34 | MATHM4500 | 20 | Optional | TB-2 |
Group 10 - TB2 | ||||
Functional Analysis 34 | MATHM6202 | 20 | Optional | TB-2 |
Group 11 - TB2 | ||||
Group 12 - TB2 | ||||
Dynamical Systems and Ergodic Theory 4 | MATHM6206 | 20 | Optional | TB-2 |
Group 13 - TB2 | ||||
Algebraic Geometry | MATHM0036 | 20 | Optional | TB-2 |
Advanced Quantum Theory | MATHM0053 | 20 | Optional | TB-2 |
Group 14 - TB2 | ||||
Topics in Geometry and Discrete Mathematics | MATHM0048 | 20 | Optional | TB-2 |
Two units from: | ||||
The Philosophy and History of Medicine | PHILM0022 | 20 | Optional | TB-1 |
Philosophy of Biology | PHILM0006 | 20 | Optional | TB-1 |
Philosophy of Probability | PHILM0028 | 20 | Optional | TB-2 |
Philosophy of Physics | PHILM0005 | 20 | Optional | TB-1 |
History of Science | PHILM0007 | 20 | Optional | TB-1 |
Epistemology and Metaphysics | PHILM0021 | 20 | Optional | TB-1 |
Philosophy of Psychology | PHILM0020 | 20 | Optional | TB-2 |
Mathematics and Philosophy (MSci) | 120 |
Unit Pass Mark for Undergraduate Programmes:
For details on the weightings for classifying undergraduate degrees, please see the Agreed Weightings, by Faculty, to be applied for the Purposes of Calculating the Final Programme Mark and Degree Classification in Undergraduate Programmes.
For detailed rules on progression please see the Regulations and Code of Practice for Taught Programmes and the relevant faculty handbook.
Please refer to the specific progression/award requirements for programmes with a preliminary year of study, the Gateway programmes and International Foundation programmes.
All undergraduate degree programmes allow the opportunity for a student to exit from a programme with a Diploma or Certificate of Higher Education.
Integrated Master's degrees may also allow the opportunity for a student to exit from the programme with an equivalent Bachelor's degree where a student has achieved 360 credit points, of which 90 must be at level 6, and has successfully met any additional criteria as described in the programme specification.
The opportunities for a student to exit from one of the professional programmes in Veterinary Science, Medicine, and Dentistry with an Award is outlined in the relevant Programme Regulations (which are available as an annex in the Regulations and Code of Practice for Taught Programmes).
An Ordinary degree can be awarded if a student has successfully completed at least 300 credits with a minimum of 60 credits at Level 6.
The pass mark for the professional programmes in Veterinary Science, Medicine and Dentistry is 50 out of 100. The classification of a degree in the professional programmes in Veterinary Science, Medicine, and Dentistry is provided in the Regulations and Code of Practice for Taught Programmes.
Please note: This specification provides a concise summary of the main features of the programme and the learning outcomes that a typical student might reasonably be expected to achieve and demonstrate if he/she takes full advantage of the learning opportunities that are provided.
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