Undergraduate Programme and Module Handbook 2011-2012 (archived)
Module MATH1012: CORE MATHEMATICS A
Department: Mathematical Sciences
MATH1012:
CORE MATHEMATICS A
Type |
Open |
Level |
1 |
Credits |
40 |
Availability |
Available in 2011/12 |
Module Cap |
None. |
Location |
Durham
|
Prerequisites
- Normally, A level Mathematics at grade A or better and AS
level Further Mathematics at grade A or better, or
equivalent.
Corequisites
Excluded Combination of Modules
- Mathematics for Engineers and Scientists (MATH1551), Single
Mathematics A (MATH1561), Single Mathematics B (MATH1571) and Foundation
Mathematics (MATH1641) may not be taken with or after this
module.
Aims
- This module is designed to follow on from, and reinforce, A level
mathematics.
- It will present students with a wide range of mathematics ideas in
preparation for more demanding material later.
- There will be opportunities to gain experience with the Maple
computer package.
- Aim: to give a utilitarian treatment of some important mathematical
techniques.
- Aim: to develop geometric awareness and familiarity with vector
methods.
Content
- A range of topics are treated each at an elementary level
to give a foundation of basic definitions, theorems and computational
techniques.
- A rigorous approach is expected.
- Elementary functions of a real variable.
- Limits, continuity, differentiation and
integration.
- Ordinary Differential Equations.
- Fourier series.
- Linear Algebra in n dimensions with concrete illustrations
in 2 and 3 dimensions.
- Vectors, matrices and determinants.
- Vector spaces and linear mappings.
- Complex numbers.
- Diagonalisation, inner-product spaces and special
polynomials.
- Introduction to group theory.
- Introduction to Probability.
- Discrete and continuous probability
distributions.
Learning Outcomes
- By the end of the module students will: be able to solve a
range of predictable or less predictable problems in Calculus, Linear
Algebra and Probability.
- have an awareness of the basic concepts of theoretical
mathematics in the fields of Calculus, Linear Algebra and
Probability.
- have a broad knowledge and basic understanding of these
subjects demonstrated through one of the following topic
areas:
- Calculus: Elementary Functions of a Real Variable.
- Limits, continuity, differentiation, Taylor's theorem,
integration.
- Ordinary Differential Equations.
- Linear Algebra: Vectors in Rn, matrices and
determinants.
- Vector spaces over R and linear mappings.
- Complex numbers and Cn as a vector space.
- Diagonalisation and Jordan normal form.
- Inner product spaces.
- Introduction to groups.
- Special polynomials.
- Probability: Conditional probability, Bayes Theorem and
independence.
- Discrete random variables and distributions.
- Expected value, variance and the weak law of large
numbers.
- Continuous random variables, particularly the
Normal.
- The Central Limit Theorem.
- Students will have basic mathematical skills in the following
areas: Modelling, Spatial awareness, Abstract reasoning,
Numeracy.
Modes of Teaching, Learning and Assessment and how these contribute to
the learning outcomes of the module
- Lectures demonstrate what is required to be learned and the
application of the theory to practical examples.
- Tutorials provide active engagement and feedback to the
learning process.
- Weekly homework problems provide formative assessment to guide
students in the correct development of their knowledge and skills. They
are also an aid in developing students' awareness of standards
required.
- Initial diagnostic testing and associated supplementary
problems classes fill in gaps related to the wide variety of syllabuses
available at Mathematics A-level.
- Experience with the Maple computer package reinforces the
ability to succeed in routine elementary calculation and to enable
students to recognise their own computational errors.
- The examination provides a final assessment of the achievement
of the student.
Teaching Methods and Learning Hours
Activity |
Number |
Frequency |
Duration |
Total/Hours |
|
Lectures |
132 |
6 per week in terms 1 and 2 |
1 Hour |
132 |
|
Tutorials |
38 |
Twice weekly |
1 Hour |
38 |
■ |
Practicals |
8 |
Distributed over the year |
1 Hour |
8 |
■ |
Other (Diagnostic Tests) |
5 |
Week 1 |
1 Hour |
5 |
■ |
Preparation and Reading |
|
|
|
237 |
|
Total |
|
|
|
400 |
|
Summative Assessment
Component: Examination |
Component Weighting: 100% |
Element |
Length / duration |
Element Weighting |
Resit Opportunity |
Written examination 1 |
3 hours |
50% |
Yes |
Written examination 2 |
3 hours |
50% |
Yes |
- Two written assignments weekly during the first 2
terms. Normally, each will consist of solving problems and will typically
be one to two pages long. Students will have about one week to complete
each assignment. - 45 minute collection paper in the first week of
Epiphany term.
■ Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University