Undergraduate Programme and Module Handbook 2012-2013 (archived)
Module MATH1061: Calculus and Probability I
Department: Mathematical Sciences
MATH1061:
Calculus and Probability I
Type |
Open |
Level |
1 |
Credits |
20 |
Availability |
Available in 2012/13 |
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
- Linear Algebra I (MATH1071)
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.
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.
- 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 and
Probability.
- have an awareness of the basic concepts of theoretical
mathematics in Calculus 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.
- 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 |
61 |
3 per week in terms 1 and 2, 4 revision lectures in term
3. |
1 Hour |
61 |
|
Tutorials |
19 |
Weekly in weeks 2-10 and 12-21. |
1 Hour |
19 |
■ |
Practicals |
1 |
Week 1 |
1 Hour |
1 |
■ |
Support classes |
19 |
1 per week in terms 1 and 2 |
1 Hour |
19 |
|
Preparation and Reading |
|
|
|
100 |
|
Total |
|
|
|
200 |
|
Summative Assessment
Component: Examination |
Component Weighting: 100% |
Element |
Length / duration |
Element Weighting |
Resit Opportunity |
Written examination |
3 hours |
100% |
Yes |
- Weekly written assignments 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