Undergraduate Programme and Module Handbook 2024-2025

# Module MATH1561: SINGLE MATHEMATICS A

## Department: Mathematical Sciences

### MATH1561: SINGLE MATHEMATICS A

Type | Open | Level | 1 | Credits | 20 | Availability | Available in 2024/2025 | Module Cap | Location | Durham |
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#### Prerequisites

- A level Mathematics at Grade A or better, or equivalent.

#### Corequisites

- None.

#### Excluded Combination of Modules

- Calculus I (Maths Hons) (MATH1081), Calculus (MATH1061), Linear Algebra I (Maths Hons) (MATH1091), Linear Algebra I (MATH1071), Mathematics for Engineers and Scientists (MATH1551) may not be taken with or after this module.

#### Aims

- This module has been designed to supply mathematics relevant to students of the physical sciences.

#### Content

- Basic functions and elementary calculus: including standard functions and their inverses, the Binomial Theorem, basic methods for differentiation and integration.
- Complex numbers: including addition, subtraction, multiplication, division, complex conjugate, modulus, argument, Argand diagram, de Moivre's theorem, circular and hyperbolic functions.
- Single variable calculus: including discussion of real numbers, rationals and irrationals, limits, continuity, differentiability, mean value theorem, L'Hopital's rule, summation of series, convergence, Taylor's theorem.
- Matrices and determinants: including determinants, rules for manipulation, transpose, adjoint and inverse matrices, Gaussian elimination, eigenvalues and eigenvectors,
- Groups, axioms, non-abelian groups

#### Learning Outcomes

Subject-specific Knowledge:

- By the end of the module students will: be able to solve a range of predictable or less predictable problems in Mathematics.
- have an awareness of the basic concepts of theoretical mathematics in these areas.
- have a broad knowledge and basic understanding of these subjects demonstrated through one or more of the following topic areas: Elementary algebra.
- Calculus.
- Complex numbers.
- Taylor's Theorem.
- Linear equations and matrices.
- Groups

Subject-specific Skills:

Key Skills:

#### 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.
- Initial diagnostic testing fills in gaps related to the wide variety of syllabuses available at Mathematics A-level.
- Tutorials provide the practice and support in applying the methods to relevant situations as well as active engagement and feedback to the learning process.
- Weekly coursework provides an opportunity for students to consolidate the learning of material as the module progresses (there are no higher level modules in the department of Mathematical Sciences which build on this module). It serves as a guide in the correct development of students' knowledge and skills, as well as an aid in developing their awareness of standards required.
- The end-of-year written examination provides a substantial complementary assessment of the achievement of the student.

#### Teaching Methods and Learning Hours

Activity | Number | Frequency | Duration | Total/Hours | |
---|---|---|---|---|---|

Lectures | 63 | 3 per week for 21 weeks | 1 Hour | 63 | |

Tutorials | 9 | Weeks 3, 5, 7, 9 (Term 1) and 13, 15, 17, 19 (Term 2), plus 1 revision tutorial in Easter term. | 1 Hour | 9 | ■ |

Support classes | 18 | Weekly in weeks 2-10 and 12-20. | 1 Hour | 18 | |

Preparation and Reading | 110 | ||||

Total | 200 |

#### Summative Assessment

Component: Examination | Component Weighting: 90% | ||
---|---|---|---|

Element | Length / duration | Element Weighting | Resit Opportunity |

Written examination | 3 hours | 100% | Yes |

Component: Continuous Assessment | Component Weighting: 10% | ||

Element | Length / duration | Element Weighting | Resit Opportunity |

Fortnightly assessments during the first 2 terms. Normally, each will consist of solving problems. Students will have about one week to complete each assignment. | 100% | Yes |

#### Formative Assessment:

40 minute collection paper in the beginning of Epiphany term. Fortnightly formative assessment.

■ 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