Download Mathematics Modules and Programmes

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Mathematics Modules and Programmes Catalogue
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A Guide for Applicants
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2014/15
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Disclaimer: This booklet is a draft prepared in August 2014 and is provided as a guide for
applicants. Although every effort is made to ensure its accuracy, not all details have been
confirmed at the time of writing and changes are possible. We reserve the right to make changes
in regulations, and to modify or withdraw programmes.
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Programmes in Mathematics 2014/15
In the following pages you will find descriptions of the Mathematics programmes available in 2014/15, with details of
Year 1 FHEQ Level 4 compulsory and optional modules for each programme.
For more details of the programmes, including educational and employment aims, key skills, intellectual and thinking
skills, please consult the University Course Catalogue.
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Table 1: Single Honours Programmes
G100
BSc in Mathematics
3 years
Page 9
G101
BSc in Mathematics (with an Integrated Foundation Year)
4 years
Page 11
G103
MMath in Mathematics
4 years
Page 12
G110
BSc in Pure Mathematics
3 years
Page 14
G120
BSc in Applied Mathematics
3 years
Page 16
G190
BSc in Mathematics for Finance
3 years
Page 18
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Table 2: Joint Honours Programmes
GR12
BSc in Mathematics and German
4 years
Page 22
GR14
BSc in Mathematics and Spanish
4 years
Page 24
GC16
BSc in Mathematics and Sports Science
3 years
Page 26
GQ15
BSc in Mathematics and Welsh
3 years
Page 27
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G100 BSc in Mathematics
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Home Department
Mathematics
College
Science
Contributing Departments
None
Duration
3 years
Route code
XMATS
Coordinator
Dr Martin Crossley
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Year 1 FHEQ Level 4
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Compulsory Modules
MA-100
MA-101
MA-102
MA-111
MA-112
MA-121
MA-135
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Key Skills for Mathematicians
Introductory Calculus#
Introductory Analysis#
Foundations of Algebra#
Introductory Linear Algebra#
Methods in Algebra and Calculus
Classical Geometry
Optional Mathematics Modules
MA-142
Classical Mechanics (of particles)
MA-152
Elementary Probability and Statistics
MA-162
Computational Methods
!
TB
1
1
2
1
2
1
1
Credits
5
15
15
15
15
15
10
2
2
2
15
15
15
In addition to the optional mathematics modules, students may take at most 20 credits of elective modules in another
subject area, subject to timetabling constraints and the approval of the Mathematics department.
Students exiting the programme upon completion of Year 1 FHEQ Level 4 will be awarded a Certificate of Higher
Education.
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Year 2 FHEQ Level 5
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Compulsory Modules
MA-201
MA-202
MA-211
MA-212
MA-221
MA-231
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Real Analysis and Metric Spaces#
Vector Calculus and Measure Theory#
Vector Spaces#
Groups and Rings#
Further Methods of Algebra and Calculus
Advanced Geometry
Optional Mathematics Modules
MA-242
Classical Mechanics (of Rigid Bodies)
MA-252
Theoretical Probability and Statistics
MA-262
Numerical Methods
!
TB
1
2
1
2
1
1
Credits
15
15
15
15
15
15
2
2
2
15
15
15
In addition to the optional mathematics modules, students may take at most 20 credits of elective modules in another
subject area, subject to timetabling constraints, prerequisite requirements and the approval of the Mathematics
department.
Students exiting the programme upon completion of Year 2 FHEQ 5 Level 5 will be awarded a Diploma of Higher
Education.
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Year 3 FHEQ Level 6
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Compulsory Modules
MA-300
MA-301
MA-312
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Project
Complex Variables
Higher Algebra
TB
1 and 2
1
2
Credits
30
15
15
The complete list of Year 3 FHEQ Level 6 modules will be finalized and published shortly before you complete Year 2
FHEQ Level 5 of your studies. In addition to the optional mathematics modules, students may take at most 20 credits of
elective modules in another subject area, subject to timetabling constraints, prerequisite requirements and the approval
of the Mathematics department.
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G101
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BSc in Mathematics (with an Integrated Foundation Year)
Home Department
Mathematics
College
Science
Contributing Departments
None
Duration
4 years
Route code
FMATS
Coordinator
Dr Martin Crossley
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Foundation Year FHEQ Level 3
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Compulsory Modules
MA-001
MA-002
MA-003#
MA-004#
MA-005
MA-007
PH-001
PH-002
CS-061
BIO005
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Fundamental Mathematics at Work
Fundamental Calculus
Fundamental Algebra
Fundamental Geometry
Fundamental Mathematics
Fundamental Mathematical Skills
Introductory Physics
Introduction to Optics and Wave Motion
Introduction to Computing I
Dealing with Data
TB
Credits
1
2
2
2
1
1
1
1
1
2
10
15
15
15
10
10
10
10
10
15
Some compulsory modules are also labelled as “core” denoted by the # sign. These modules must not only be pursued
but they must also be passed.
Years 1-3 FHEQ Levels 4-6
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From Year 1 FHEQ Level 4 onwards, this programme is identical to G100 BSc Mathematics; please refer to that
programme for further details.
G103 MMath in Mathematics
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Home Department
Mathematics
College
Science
Contributing Departments
None
Duration
4 years
Route code
4MATS
Coordinator
Dr Martin Crossley
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Year 1 FHEQ Level 4
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Compulsory Modules
MA-100
MA-101
MA-102
MA-111
MA-112
MA-121
MA-135
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Key Skills for Mathematicians
Introductory Calculus#
Introductory Analysis#
Foundations of Algebra#
Introductory Linear Algebra#
Methods in Algebra and Calculus
Geometry
Optional Mathematics Modules
MA-142
Classical Mechanics (of particles)
MA-152
Elementary Probability and Statistics*
MA-162
Computational Methods *
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TB
1
1
2
1
2
1
1
Credits
5
15
15
15
15
15
10
2
2
2
15
15
15
* Students must take at least one of these modules
In addition to the optional mathematics modules, students may take at most 20 credits of elective modules in another
subject area, subject to timetabling constraints and the approval of the Mathematics department.
Students exiting the programme upon completion of Year 1 FHEQ Level 4 will be awarded a Certificate of Higher
Education.
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Year 2 FHEQ Level 5
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Compulsory Modules
MA-201
MA-202
MA-211
MA-212
MA-221
MA-231
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Real Analysis and Metric Spaces#
Vector Calculus and Measure Theory#
Vector Spaces#
Groups and Rings#
Further Methods of Algebra and Calculus
Advanced Geometry
Optional Mathematics Modules
MA-242
Classical Mechanics (of Rigid Bodies)
MA-252
Theoretical Probability and Statistics*
MA-262
Numerical Methods *
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TB
1
2
1
2
1
1
Credits
15
15
15
15
15
15
2
2
2
15
15
15
* Students must take MA-252 if they did not take MA-152 in Year 1 FHEQ Level 4, and they must take MA-262, if
they did not take MA-162 in Year 1 FHEQ Level 4. In other words, all MMath students must have taken at least one of
the Probability/Statistics modules and at least one of the Computational/Numerical modules.
In addition to the optional mathematics modules, students may take at most 20 credits of elective modules in another
subject area, subject to timetabling constraints, prerequisite requirements and the approval of the Mathematics
department.
Students exiting the programme upon completion of Year 2 HEFQ Level 5 will be awarded a Diploma of Higher
Education.
In addition to the standard University Progression rules, in order to proceed to Year 3 FHEQ Level 6 on the
MMath programme a student must achieve an average of at least 60% in Year 2 FHEQ Level 5, and pass all Year
2 FHEQ Level 5 modules at the first attempt. Students failing to meet this requirement will be transferred to the
G100 BSc Mathematics programme.
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Year 3 FHEQ Level 6
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Compulsory Modules
MA-301
MA-312
MA-303
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Complex Variables#
Higher Algebra#
Mathematical Modelling
TB
1
2
1
Credits
15
15
15
The complete list of Year 3 FHEQ Level 6 modules will be finalized and published shortly before you complete Year 2
FHEQ Level 5 of your studies. In addition to the optional mathematics modules, students may take at most 20 credits of
elective modules in another subject area, subject to timetabling constraints, prerequisite requirements and the approval
of the Mathematics department.
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Some Year 3 FHEQ Level 6 and Year 4 FHEQ Level 7 modules will alternate from year to year, so you should choose
your module selection for Year 3 FHEQ Level 6 and for Year 4 FHEQ Level 7 at the same time. The department will
offer advice about which Year 4 FHEQ Level 7 modules will be available in the following year.
Students exiting the programme upon completion of Year 3 FHEQ Level 6 will receive a BSc Ordinary degree.
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Year 4 FHEQ Level 7
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Compulsory Module
MA-M00
Project
TB
1 and 2
Credits
30
In addition to the optional mathematics modules, students may take at most 20 credits of elective modules in another
subject area, subject to timetabling constraints, prerequisite requirements and the approval of the Mathematics
department.
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G110 BSc in Pure Mathematics
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Home Department
Mathematics
College
Science
Contributing Departments
None
Duration
3 years
Route code
XMAPS
Coordinator
Dr Martin Crossley
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Year 1 FHEQ Level 4
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Compulsory Modules
MA-100
MA-101
MA-102
MA-111
MA-112
MA-121
MA-135
MA-152
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Key Skills for Mathematicians
Introductory Calculus#
Introductory Analysis#
Foundations of Algebra#
Introductory Linear Algebra#
Methods in Algebra and Calculus
Classical Geometry
Elementary Probability and Statistics
Optional Mathematics Modules
MA-142
Classical Mechanics (of particles)
MA-162
Computational Methods
!
TB
1
1
2
1
2
1
1
2
Credits
5
15
15
15
15
15
10
15
2
2
15
15
In addition to the optional mathematics modules, students may take at most 15 credits of elective modules in another
subject area, subject to timetabling constraints and the approval of the Mathematics department.
Students exiting the programme upon completion of Year 1 FHEQ Level 4 will be awarded a Certificate of Higher
Education.
!
Year 2 FHEQ Level 5
!
Compulsory Modules
MA-201
MA-202
MA-211
MA-212
MA-221
MA-231
MA-252
!
Real Analysis and Metric Spaces#
Vector Calculus and Measure Theory#
Vector Spaces#
Groups and Rings#
Further Methods of Algebra and Calculus
Advanced Geometry
Theoretical Probability and Statistics
Optional Mathematics Modules
MA-242
Classical Mechanics (of Rigid Bodies)
MA-262
Numerical Methods
!
TB
1
2
1
2
1
1
2
Credits
15
15
15
15
15
15
15
2
2
15
15
In addition to the optional mathematics modules, students may take at most 20 credits of elective modules in another
subject area, subject to timetabling constraints, prerequisite requirements and the approval of the Mathematics
department.
Students exiting the programme upon completion of Year 2 FHEQ Level 5 will be awarded a Diploma of Higher
Education.
!
Year 3 FHEQ Level 6
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Compulsory Modules
MA-300
MA-301
MA-312
MA-352
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Project
Complex Variables
Higher Algebra
Topology
TB
1 and 2
1
2
2
Credits
30
15
15
10
The complete list of Year 3 FHEQ Level 6 modules will be finalized and published shortly before you complete Year 2
FHEQ Level 5 of your studies. In addition to the optional mathematics modules, students may take at most 20 credits of
elective modules in another subject area, subject to timetabling constraints, prerequisite requirements and the approval
of the Mathematics department.
G120 BSc in Applied Mathematics
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Home Department
Mathematics
College
Science
Contributing Departments
None
Duration
3 years
Route code
XMAAS
Coordinator
Dr Martin Crossley
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Year 1 FHEQ Level 4
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Compulsory Modules
MA-100
MA-101
MA-102
MA-111
MA-112
MA-121
MA-135
MA-142
!
Key Skills for Mathematicians
Introductory Calculus#
Introductory Analysis#
Foundations of Algebra#
Introductory Linear Algebra#
Methods in Algebra and Calculus
Classical Geometry
Classical Mechanics (of particles)
Optional Mathematics Modules
MA-152
Elementary Probability and Statistics
MA-162
Computational Methods
!
TB
1
1
2
1
2
1
1
2
Credits
5
15
15
15
15
15
10
15
2
2
15
15
In addition to the optional mathematics modules, students may take at most 15 credits of elective modules in another
subject area, subject to timetabling constraints and the approval of the Mathematics department.
Students exiting the programme upon completion of Year 1 FHEQ Level 4 will be awarded a Certificate of Higher
Education.
!
Year 2 FHEQ Level 5
!
Compulsory Modules
MA-201
MA-202
MA-211
MA-212
MA-221
MA-231
MA-242
!
Real Analysis and Metric Spaces#
Vector Calculus and Measure Theory#
Vector Spaces#
Groups and Rings#
Further Methods of Algebra and Calculus
Advanced Geometry
Classical Mechanics (of Rigid Bodies)
Optional Mathematics Modules
MA-252
Theoretical Probability and Statistics
MA-262
Numerical Methods
!
TB
1
2
1
2
1
1
2
Credits
15
15
15
15
15
15
15
2
2
15
15
In addition to the optional mathematics modules, students may take at most 20 credits of elective modules in another
subject area, subject to timetabling constraints, prerequisite requirements and the approval of the Mathematics
department.
Students exiting the programme upon completion of Year 2 FHEQ level 5 will be awarded a Diploma of Higher
Education.
!
Year 3 FHEQ Level 6
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Compulsory Modules
MA-300
MA-301
MA-314
MA-312
MA-338
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Project
Complex Variables
Differential Equations
Higher Algebra
Analytical Dynamics
TB
1 and 2
1
1
2
2
Credits
30
15
15
15
15
The complete list of Year 3 FHEQ Level 6 modules will be finalized and published shortly before you complete Year 2
FHEQ Level 5 of your studies. In addition to the optional mathematics modules, students may take at most 20 credits of
elective modules in another subject area, subject to timetabling constraints, prerequisite requirements and the approval
of the Mathematics department.
G190 BSc in Mathematics for Finance
!
Home Department
Mathematics
College
Science
Contributing Departments
None
Duration
3 years
Route code
XMAFS
Coordinator
Dr Martin Crossley
!
Year 1 HFEQ Level 4
!
Compulsory Modules
MA-101
MA-102
MA-111
MA-112
MA-100
MA-121
MA-135
MA-152
MA-162
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!
Introductory Calculus#
Introductory Analysis#
Foundations of Algebra#
Introductory Linear Algebra#
Key Skills for Mathematicians
Methods in Algebra and Calculus
Classical Geometry
Elementary Probability and Statistics
Computational Methods
TB
1
2
1
2
1
1
1
2
2
Credits
15
15
15
15
5
15
10
15
15
Students exiting the programme upon completion of Year 1 HFEQ Level 4 will be awarded a Certificate of Higher
Education.
Year 2 HFEQ Level 5
!
Compulsory Modules
MA-201
MA-202
MA-211
MA-212
MA-221
MA-252
!
Real Analysis and Metric Spaces#
Vector Calculus and Measure Theory#
Vector Spaces#
Groups and Rings#
Further Methods of Algebra and Calculus
Theoretical Probability and Statistics
Optional Mathematics Modules
MA-231
Advanced Geometry
MA-262
Numerical Methods
!
!
TB
1
2
1
2
1
2
Credits
15
15
15
15
15
15
1
2
15
15
This list is provisional and subject to change.
In addition to the optional mathematics modules, students may take at most 20 credits of elective modules in another
subject area, subject to timetabling constraints, prerequisite requirements and the approval of the Mathematics
department.
Students exiting the programme upon completion of Year 2 FHEQ level 5 will be awarded a Diploma of Higher
Education.
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Year 3 HFEQ Level 6
!
Compulsory Modules
MA-350
MA-301
MA-312
MA-341
MA-357
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Dissertation in the Mathematics of Finance
Complex Variables
Higher Algebra
Stochastic Processes
Financial Mathematics
TB
1 and 2
1
2
1
1
Credits
30
15
15
15
15
The complete list of Year 3 HFEQ Level 6 modules will be finalized and published shortly before you complete Year 2
FHEQ Level 5 of your studies. In addition to the optional mathematics modules, students may take at most 20 credits of
elective modules in another subject area, subject to timetabling constraints, prerequisite requirements and the approval
of the Mathematics department
!!
!
GR12 BSc in Mathematics and German
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Home Department
Mathematics
College
Science
Contributing Departments
German
Duration
4 years
Route code
SMATAGRM
Coordinator
Dr Martin Crossley
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!
Year 1 FHEQ Level 4
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Compulsory Modules
MA-101
Introductory Calculus#
MA-102
Introductory Analysis#
MA-111
Foundations of Algebra#
MA-112
Introductory Linear Algebra#
MLG100
Introduction to German Culture
And either: A) For a student with an A or AS level in German:
MLG110
German General Language 1
MLG117
German for Professional Purposes 1
Or: B) For students who have not studied German before:
MLG108
German for Beginners I
MLG109
German for Beginners II
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!
TB
1
2
1
2
1 and 2
Credits
15
15
15
15
20
1 and 2
1 and 2
20
20
1
2
20
20
Students exiting the programme upon completion of Year 1 FHEQ Level 4 will be awarded a Certificate of Higher
Education.
Year 2 FHEQ Level 5
!
Compulsory Modules
MA-201
Real Analysis and Metric Spaces#
MA-202
Vector Calculus and Measure Theory#
MA-211
Vector Spaces#
MA-212
Groups and Rings#
And either: A) For a student with an A or AS level in German:
MLG201
German General Language 2
Or: B) For students who have not studied German before:
MLG234
Intermediate German
!
TB
1
2
1
2
Credits
15
15
15
15
1 and 2
20
1 and 2
20
In addition to the compulsory modules, students are required to take a further 40 credits of modules in German, subject
to timetabling constraints and the approval of the German Department. These must include at least 20 credits chosen
from MLG200, MLG210, MLG235, MLG244.
Students exiting the programme upon completion of Year 2 FHEQ Level 5 will be awarded a Diploma of Higher
Education.
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Level S: Intercalary Year Abroad
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Following successful completion of Year 2 FHEQ Level 5 students will spend an intercalary year at the University of
Ulm or at Georg-August University at Göttingen, studying at least 30 ECTS credits of Mathematics through the
medium of German A Learning Agreement between the home and host institution will be drawn up for each student,
specifying the courses to be studied. Satisfactory progress is required for students to progress into Year 3 FHEQ level 6.
Exemption from the Year Abroad can be granted only in exceptional cases and in accordance with the College of Arts
and Humanities Year Abroad Exemption Policy.
!
!
!
Year 3 FHEQ Level 6
!
Compulsory Modules
MA-301
MA-312
MA-325
MA-384
MLG301
!
Complex Variables
Higher Algebra
Applied Algebra: Coding Theory
Fourier Analysis
German General Language 3
TB
1
2
1
2
1 and 2
Credits
15
15
15
15
20
The complete list of Year 3 FHEQ Level 6 modules will be finalized and published shortly before you complete Year 2
Level 5 of your studies, and students are required to take 40 credits of optional modules in German. All module
selections are subject to timetabling constraints, prerequisite requirements and the approval of the Mathematics
department.
Students may not take the module MA-300 as part of this programme.
!
GR14 BSc in Mathematics and Spanish
!
Home Department
Mathematics
College
Science
Contributing Departments
Spanish
Duration
4 years
Route code
SMATAHSS
Coordinator
Dr Martin Crossley
!
Year 1 FHEQ Level 4
!
Compulsory Modules
MA-101
Introductory Calculus#
MA-102
Introductory Analysis#
MA-111
Foundations of Algebra#
MA-112
Introductory Linear Algebra#
MLS100
Introduction to Hispanic Culture
And either: A) For a student with an A or AS level in Spanish:
MLS110 (W)
Spanish General Language I
MLS117
Spanish for Professional Purposes 1
Or: B) For students who have not studied Spanish before:
MLS130 (W)
Spanish for Beginners I
MLS131 (W)
Spanish for Beginners II
MFL130
Introduction to Hispanic Culture
!
!
TB
1
2
1
2
1 and 2
Credits
15
15
15
15
20
1 and 2
1 and 2
20
20
1
2
1 and 2
20
20
20
Students exiting the programme upon completion of Year 1 FHEQ Level 4 will be awarded a Certificate of Higher
Education.
Year 2 FHEQ Level 5
!
Compulsory Modules
MA-201
Real Analysis and Metric Spaces#
MA-202
Vector Calculus and Measure Theory#
MA-211
Vector Spaces#
MA-212
Groups and Rings#
And either: A) For a student with an A or AS level in Spanish:
MLS201 (W)
Spanish General Language 2
Or: B) For students who have not studied Spanish before:
MLS204
Intermediate Spanish
!
TB
1
2
1
2
Credits
15
15
15
15
1 and 2
20
1 and 2
20
In addition to the compulsory modules, students are required to take a further 40 credits of modules in Spanish, subject
to timetabling constraints, prerequisite requirements and the approval of the Spanish Department. These must include at
least 20 credits chosen from MLS203, MLS208,
MLS 209, MLS210.
Students exiting the programme upon completion of Year 2 FHEQ Level 5 will be awarded a Diploma of Higher
Education.
!
Level S: Intercalary Year Abroad
!
Following successful completion of Year 2 Level 5 students will spend an intercalary year at the University of
Zaragoza, studying at least 30 ECTS credits of Mathematics through the medium of Spanish. A Learning Agreement
between the home and host institution will be drawn up for each student, specifying the courses to be studied.
Satisfactory progress is required for students to progress into Year 3 FHEQ Level 6. Exemption from the Year Abroad
can be granted only in exceptional cases and in accordance with the College of Arts and Humanities Year Abroad
Exemption Policy.
!!
!
Year 3 FHEQ Level 6
!
Compulsory Modules
MA-301
MA-312
MA-325
MA-384
MLS300 (W)
!
Complex Variables
Higher Algebra
Applied Algebra: Coding Theory
Fourier Analysis
Spanish General Language 3
TB
1
2
1
2
1 and 2
Credits
15
15
15
15
20
The complete list of Year 3 FHEQ Level 6 modules will be finalized and published shortly before you complete Year 2
FHEQ Level 5 of your studies, and students are required to take 40 credits of optional modules in Spanish. All module
selections are subject to timetabling constraints, prerequisite requirements and the approval of the Mathematics
department.
Students may not take the module MA-300 as part of this programme.
!
!
GC16 BSc in Mathematics and Sports Science
!
Home Department
Mathematics
College
Science
Contributing Departments
Sports Science
Duration
3 years
Route code
XMATAEDS
Coordinator
Dr Martin Crossley
!
Year 1 FHEQ Level 4
!
Compulsory Modules
MA-101
MA-102
MA-111
MA-112
SR-141
SR-145
SR-146
SR-148
!
!
Introductory Calculus#
Introductory Analysis#
Foundations of Algebra#
Introductory Linear Algebra#
Human Anatomy
Human Physiology
Biomechanics and Technology B
Sports Psychology
TB
1
2
1
2
1
2
2
1
Credits
15
15
15
15
15
15
15
15
Students exiting the programme upon completion of Year 1 FHEQ Level 4 will be awarded a Certificate of Higher
Education.
Year 2 FHEQ Level 5
!
Compulsory Modules
MA-201
MA-202
MA-211
MA-212
SR-253
SR-254
SR-259
SR-260
!
!
Real Analysis and Metric Spaces#
Vector Calculus and Measure Theory#
Vector Spaces#
Groups and Rings#
Exercise Physiology II
Biomechanics and Technology C
Human Nutrition
Psychological Dimensions of Sport 2:
Adolescents
TB
1
2
1
2
1
2
2
2
Credits
15
15
15
15
15
15
15
15
Students exiting the programme upon completion of Year 2 FHEQ Level 5 will be awarded a Diploma of Higher
Education.
Year 3 FHEQ Level 6
!
Compulsory Modules
MA-301
MA-312
MA-325
MA-384
!
Complex Variables
Higher Algebra
Applied Algebra: Coding Theory
Fourier Analysis
TB
1
2
1
2
Credits
15
15
15
15
The complete list of Year 3 FHEQ Level modules will be finalized and published shortly before you complete Year 3
FHEQ Level 6 of your studies, and students are required to take 30 credits of optional modules in Mathematics.
Students may not take the module MA-300 as part of this programme.
!
GQ15 BSc in Mathematics and Welsh
!
Home Department
Mathematics
College
Science
Contributing Departments
Welsh
Duration
3 years
Route code
XMATACYM
Coordinator
Dr Martin Crossley
!
Year 1 FHEQ Level 4
!
Compulsory Modules
MA-101
MA-102
MA-111
MA-112
CY-108
CY-130
CY-131
!
!
Introductory Calculus#
Introductory Analysis#
Foundations of Algebra#
Introductory Linear Algebra#
Llafar
Cyflwyno'r Seiliau
Cymraeg Ysgrifenedig
TB
1
2
1
2
1 and 2
1
2
Credits
15
15
15
15
20
20
20
Students exiting the programme upon completion of Year 1 HFEQ Level 4 will be awarded a Certificate of Higher
Education.
Year 2 FHEQ Level 5
!
Compulsory Modules
MA-201
MA-202
MA-211
MA-212
CY-210
!
Real Analysis and Metric Spaces#
Vector Calculus and Measure Theory#
Vector Spaces#
Groups and Rings#
Sgiliau Iaith: Cadarnhau
TB
1
2
1
2
1
Credits
15
15
15
15
20
In addition to the compulsory modules, students are required to take a further 40 credits of modules in Welsh, subject to
timetabling constraints and prerequisite requirements.
Students exiting the programme upon completion of Year 2 FHEQ Level 5 will be awarded a Diploma of Higher
Education.
!
Year 3 FHEQ Level 6
!
Compulsory Modules
MA-301
MA-312
MA-325
MA-384
Complex Variables
Higher Algebra
Applied Algebra: Coding Theory
Fourier Analysis
TB
1
2
1
2
Credits
15
15
15
15
CY-351
Sgiliau Iaith: Meistroli
1
20
!
!
The complete list of Year 3 HFEQ Level 6 modules will be finalized and published shortly before you complete Year 2
FHEQ Level 5 of your studies, and students are required to take 40 credits of optional modules in Mathematics and
Welsh. All module selections are subject to timetabling constraints, prerequisite requirements and the approval of the
Mathematics department.
Students may not take the module MA-300 as part of this programme.
!
Year 1 FHEQ Level 4 Mathematics Modules 2014/15
!
!
In the following pages you will find descriptions of the Year 1 FHEQ Level 4 Mathematics modules available in
2014/15.
!
MA-100 Key Skills for Mathematicians: 5 credits, Semester 1
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Lecturer: Dr Andrew Neate
Examination period: January
Assessment: Coursework 80%, Presentation 20%
!
Syllabus
- Mathematica;
- Mathematical writing and presenting skills;
- Problem Solving
!
!
At the end of this module, the student should be able to:
1) Complete simple tasks in Mathematica,
2) Present mathematical work in an appropriate written format,
3) Present mathematical work in an oral presentation,
4) Know how to begin solving problems in mathematical or other settings
!
Recommended Reading
!!
o Kevin Houston, How to think like a Mathematician: a companion to undergraduate
mathematics, CUP, 2009
o Lara Alcock, How to study for a mathematics degree, OUP, 2012
MA-101 Introductory Calculus: 15 credits, Semester 1
!
Lecturer: Professor Ian Davies
Examination period: January
Assessment: 80% by examination and 20% by coursework
!
Syllabus
Manipulation of real numbers, natural numbers, integers, rational numbers;
Basic operation with sets;
The absolute value, inequalities;
Sets characterised by inequalities;
Mathematical induction, binomial theorem;
Functions (graph, domain, co-domain, range), polynomials, rational functions;
Injective, surjective, bijective functions;
Composition of functions, inverse function;
Limit of functions, rules for limits;
Derivatives of functions, basic rules;
The derivative as a tool to investigate functions;
Elementary transcendental functions
!
At the end of this module, the student should be able to:
1) explain basic set theory and logic;
2) give a formally correct proof;
3) Use the concept of induction:
4) determine properties of functions such as injectivity, surjectivity, bijectivity and continuity
4) explain the basic idea of limits of sequences and functions
5) explain differentiation and integration of functions
6) apply the rules of differentiation, integration and the fundamental theorem of calculus
7) sketch the graphs of elementary functions
!
Recommended Reading
o MH Protter, CB Morrey, A First Course in Real Analysis, Springer-Verlag c1991
o DA Brannan, A first Course in Mathematical Analysis, CUP, 2006
o S Lang, A First Course in Calculus, Springer-Verlag, c1986
!
Corequisites: MA-111
!
MA-102 Introductory Analysis: 15 credits, Semester 2
!
Lecturer: Professor Ian Davies
Examination period: May/June
Assessment: 80% by examination and 20% by coursework
!
Syllabus
!
Basic inequalities (Bernoulli, Cauchy-Schwarz, Minkowski);
Sequences and their limits;
Convergence of series;
Cauchy sequences, completeness of the real numbers, Bolzano-Weierstrass theorem; principle of
nested intervals;
Convergence criteria for series;
Countable sets;
Open and closed subsets of R, infimum and supremum, limit superior and limit inferior;
Continuous functions and their basic properties
Compact sets, Heine-Borel theorem in R; - Uniform continuity, continuous functions on compact
sets;
Differentiation: definition, basic properties and rules;
Higher order derivatives
Rolle's theorem, mean-value theorem;
L'Hospital's rules;
Local extreme values of a function;
Partition of an interval, the lower and upper Riemann sums;
Riemann integral, criteria of integrability;
Inequalities and the mean value property of integral;
The fundamental theorem of calculus for integrable functions.
!
At the end of this module, the student should be able to:
1) identify suitable tests for convergence of sequences and series;
2) discuss the problems of completeness of the real numbers and outline solutions;
3) outline properties of continuous and differentiable functions;
4) explain the importance of compactness;
5) state and apply Hölder’s and Minkowski’s inequality;
6) use the Riemann integral and know its properties.
!
Recommended Reading:
o MH Protter, CB Morrey, A First Course in Real Analysis, Springer-Verlag c1991
o DA Brannan, A first Course in Mathematical Analysis, CUP, 2006
o S Lang, A First Course in Calculus, Springer-Verlag, 1986
!
Corequisites: MA-101, MA-111
!
MA-111 Foundations of Algebra: 15 credits, Semester 1
!
Lecturer: Dr Grigory Garkusha
Examination period: January
Assessment: 80% by examination and 20% by coursework
!
Syllabus
Logic: statements, connectives, truth tables, quantifiers, what does it mean ‘to prove’.
Binary operations on sets: commutative, associative operations, manipulations with brackets.
Groups: well-known groups such as (Z,+), (R*, .), Zn, S3, symmetries of square etc.
Rings: including polynomials, Z, Zn, ring of matrices.
Fields: including R, Q.
Algebraic manipulations and manipulation of formulae for fields.
Roots of polynomials.
Elementary combinatorics and the binomial theorem.
Back to rings: divisibility and Euclid’s algorithm with examples in Z and the ring of polynomials
(including division of polynomials), primes, proof that Zp is a field.
!
At the end of this module, the student should be able to:
!
1) explain and apply the basic principles of logic, proof and algebraic manipulation;
2) define groups, rings and fields and describe their basic properties;
3) solve basic algebraic problems in concrete and abstract situations;
4) apply appropriate techniques of algebraic manipulation to a given situation;
5) recognise patterns underlying a variety of algebraic situations.
!
Recommended Reading
o
o
o
o
PM Cohn, Elements of linear algebra, Chapman and Hall, 1994
S Lipschutz, Linear algebra, Schaum, 1994
H Anton, Linear Algebra, (Ed 7), J Wiley, 1995
IDD Hernstein, Topics in Algebra, Blaissdell, 1965
!
Corequisites: MA-101
!
MA-112 Introductory Linear Algebra: 15 credits, Semester 2
!
Lecturer: Dr Grigory Garkusha
Examination period: January
Assessment: 80% by examination and 20% by coursework
!
Syllabus
Relations, orders and countability: examples of ordered sets such as R, Q, Z; Russell’s paradox.
Complex numbers: C as a field, Argand diagram, De Moivre’s theorem, roots of complex numbers;
complex numbers as an unordered field; statement of the fundamental theorem of algebra.
Matrices: Mn(R) as a non-commutative ring.
Linear equations, Gauss elimination.
Vectors and vector spaces: brief revision of vectors, formal definition of a vector spaces as an
abstraction of properties of planar or geometric vectors, examples in Rn, polynomials, functions,
Mn,m(R), Cn, and variants over different fields.
Bases and coordinates.
Linear maps, matrices as linear maps.
Determinants.
!
At the end of this module, the student should be able to:
!
1) explain set orderings and the concept of countability;
2) work with and explain the need for complex numbers;
3) state the fundamental theorem of algebra;
4) define the concept of a vector space and subspace and give standard examples of vector spaces;
5) explain the relationships between vectors, matrices, vector spaces and linear transformations;
6) solve systems of linear equations using Gaussian elimination;
7) define the concepts of bases and coordinates in vector spaces and subspaces,
!
Recommended Reading
o
o
o
o
PM Cohn, Elements of linear algebra, Chapman and Hall, 1994
S Lipschutz, Linear algebra, Schaum, 1994
H Anton, Linear Algebra, (Ed 7), J Wiley, 1995
IDD Hernstein, Topics in Algebra, Blaissdell, 1965
!
Corequisites: MA-101, MA-111
!
MA-121 Methods of Algebra and Calculus: 15 credits, Semester 1
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Lecturer: Dr Carlo Mercuri
Examination period: January
Assessment: 80% by examination and 20% by coursework
!
Syllabus
Manipulation of real numbers
Solutions of equations
Solutions of systems of equations
Matrices
Functions
Graph sketching
Differentiation
Integration
Ordinary differential equations
!
At the end of this module, the student should be able to:
1) select and apply techniques of algebra to problems involving systems of linear equations;
2) work with matrices confidently;
3) investigate and analyses the properties of functions;
4) select and apply techniques of calculus to problems of integration and differentiation;
5) solve simple differential equations.
!
Recommended Reading
o
o
o
o
o
o
o
MH Protter, CB Morrey, A First Course in Real Analysis, Springer-Verlag c1991
DA Brannan, A first Course in Mathematical Analysis, CUP, 2006
S Lang, A First Course in Calculus, Springer-Verlag, c1986
PM Cohn, Elements of linear algebra, Chapman and Hall, 1994
S Lipschutz, Linear algebra, Schaum, McGraw-Hill c2009
H Anton, Linear Algebra, J Wiley, c1994
IDD Hernstein, Topics in Algebra, Blaissdell, 1964
!
Corequisites: MA-101, MA-111
!
MA-135 Classical Geometry: 10 credits, Semester 1
!
Lecturer: Dr Jeffrey Giansiracusa
Examination period: January
Assessment: 80% by examination and 20% by coursework
!
Syllabus
What are “points”, “lines”, “planes” and “space”?
Euclid’s axiomatic approach to geometry;
Rotations and translations (isometries);
Descartes’ approach by coordinates;
classical geometry in the plane: triangles, polygons, circle, symmetries – groups – congruence;
classical geometry in the plane by vectors: basic operations, applications;
metric geometry in the plane: length, area, some trigonometry;
classical geometry in space: cubes, cuboids, pyramids, ball, cylinder, cylindrical pyramids;
classical geometry in space by vectors: basic operations, applications;
metric geometry in space: length, area, volume
!
At the end of this module, the student should be able to:
!
1) draw relevant diagrams;
2) use vectors in two and three dimensions and perform calculations with them;
3) state properties of basic shapes in two and three dimensions;
3) explain and work with notions such as length, area and volume;
4) illustrate differences between Euclidean and non-Euclidean geometry.
!
Recommended Reading
o R Fenn, Geometry, Springer, 2001
o J Roe, Elementary Geometry, OUP, 1993
!
Corequisites: MA-101, MA-111
!
!
MA-142 Classical Mechanics (of particles): 15 credits, Semester 2
!
Lecturer: Dr Elaine Crooks
Examination period: May/June
Assessment: 80% by examination and 20% by coursework
!
Syllabus
Vectors for mechanics.
Statics: forces and moments, representation by vectors.
Kinematics: position, velocity and acceleration using vectors.
Momentum and collisions.
Impulse.
Newton’s laws and Galilean relativity.
Conservation laws: Energy, momentum, angular momentum. Stability of motion.
Conservative fields.
Resisted motion: air resistance, Stoke's drag.
Variable mass problems: Rocket motion.
Introduction to Keplerian motion: basic planetary motion.
!
!
At the end of this module, the student should be able to:
1) use vector techniques to model physical problems involving systems of particles;
2) explain the concepts of momentum, forces, moments, energy and impulse in mathematical terms;
3) solve given dynamical problems using appropriate methods;
4) apply Newton's laws to form a mathematical model of physical problems involving particles;
5) solve problems involving standard models such as resisted flow, rocket motion and the Kepler
problem;
6) identify and apply the correct techniques from calculus and differential equations to solve
problems.
!
Recommended Reading
o Gregory RD, Classical Mechanics, CUP 2006.
o Collinson CP & Roper T, Particle Mechanics, Arnold 1995.
o Lunn M, A First Course in Mechanics, OUP 1991.
Corequisites: MA-102, MA-112
!
!
MA-152 Elementary Probability and Statistics: 15 credits, Semester 2
!
Lecturer: Dr Zeev Sobol
Examination period: May/June
Assessment: 80% by examination and 20% by coursework
!
Syllabus
Discrete probability spaces;
Independent events;
Conditional probability, partition rule, Bayes’ rule;
Examples of distribution and related combinatorics problems: Bernoulli, binomial, multinomial,
geometric, hypergeometric, negative binomial, Poisson;
Random variable and its distribution, joint distribution of a collection of random variables (joint
density function);
Independent random variables, expectation, including additive and multiplicative properties of
expectation;
Moments, (possibly moment generating function), variance;
Markov and Chebyshev inequalities, first encounter with the law of large numbers;
Sample of a random variable, parameter of a distribution, statistic, estimator, unbiasedness,
consistency, sample mean, sample variance;
Maximal likelihood estimation, examples: binomial distribution, Poisson distribution;
Population, variate, population mean, sampling with and without replacement.
!
At the end of this module, the student should be able to:
!
1) explain the fundamentals of probability theory and statistics;
2) formulate given problems in terms of probabilities;
3) identify concepts from Calculus/Algebra and apply them in a probabilistic setting;
4) state basic statistics of given data;
5) select and apply a valid test for the analysis of data;
6) formulate and test suitable hypotheses.
!
Recommended Reading
!
o
o
o
o
GR Grimmett, D Welsh, Probability: An Introduction Clarendon 1986
DR Stirzacker, Probability and Random Variables: A beginners guide, CUP, 1999
BG Wetherill, Elementary Statistical Methods, Chapman and Hall, 1982
JT McClave, T Sincich, Statistics, Pearson Education, 2009
Corequisites: MA-102, MA-112
!
!
MA-162 Computational Methods : 15 credits, Semester 2
!
Lecturer: Dr Lloyd Bridge
Examination period: May/June
Assessment: 80% by examination and 20% by coursework
!
Syllabus
-
Computational Methods:
History of computation
Representation errors, propagation of error
Algorithms for computation
Computation of functions
Solution of non-linear equations
Introduction to linear multistep methods
- Introduction to numerical quadrature
Matlab:
Syntax and operation
Basic tools
Lists and matrices
Two dimensional graphics
Solving equations
Calculus Toolbox
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At the end of this module, the student should be able to:
1) explain and analyse how an error can propogate through a calculation;
2) select and implement an appropriate algorithm for a given problem;
3) explain which algorithms are efficient and accurate in a given situation;
4) state a variety of algorithms and conditions under which it can be applied;
5) use Matlab as an aid to computation and presentation.
!
Recommended Reading
o Burden RL, Faires JD, Numerical Analysis, Brooks & Cole, 2011.
o Don E, Mathematica (Schaum Outline Series), McGraw Hill 2001.
o Torrence B & Torrence E, The Student's Introduction to Mathematica, CUP, 2009.
Prerequisites: MA-101, MA-112