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Faculty Handbook 2022-2023

# Module Description

Please ensure you check the module availability box for each module outline, as not all modules will run each academic year.

## Department: Mathematical Sciences

### MATH1561: SINGLE MATHEMATICS A

Type Level Credits Availability Module Cap Open 1 20 Available in 2022/23 Durham

#### Prerequisites

• Normally, A level Mathematics at Grade A or better, or equivalent.

• None.

#### Excluded Combination of Modules

• Calculus I (Maths Hons) (MATHNEW1), Calculus (MATH1061), Linear Algebra I (Maths Hons) (NEWMATH2), 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 19 Weekly in weeks 2-10, 12-20, 21. 1 Hour 19 ■ Support classes 18 Weekly in weeks 2-10 and 12-20. 1 Hour 18 Preparation and Reading 100 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 electronic assessments 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. 100% Yes

#### Formative Assessment:

45 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

If you have a query about a specific module or degree programme, please contact the appropriate department.