## LLLC0188 Discrete Mathematics and Calculus

### 40 creditsClass Size: 50

Module manager: Dr Katy Dobson
Email: k.l.dobson@leeds.ac.uk

Taught: Semesters 1 & 2 (Sep to Jun) View Timetable

Year running 2021/22

### This module is mutually exclusive with

 LLLC0190 Mathematical and Analytical Methods for Science

This module is not approved as a discovery module

### Module summary

This module aims to develop your understanding of fundamental mathematical techniques required for progression onto your chosen degree programme.

### Objectives

During this module students will be introduced to core concepts and techniques in mathematics. They will gain experience and confidence using these techniques and learn how mathematics is applied in Science.

Learning outcomes
On successful completion of this module, students will be able to:
1. Explore and manipulate a variety of basic mathematical objects
2. Perform calculations and solve problems in abstract mathematical and real world scenarios
3. Present mathematical ideas using precise mathematical language in various forms
4. Develop a learning practice which is modelled on continual assessment, formative and summative, across the module and reflection on feedback in order to feedforward and inform future learning

Skills outcomes
Writing using correct and appropriate mathematical language.

### Syllabus

The content will be delivered through lectures and workshops and will cover areas such as:
-Revision of basic arithmetic, algebra and equations.
- Manipulation of surds, logarithms and exponentials.
- Solution of equations; Trigonometry, Sin, Cos, Tan and their graphs.
- Introduction to vectors and representing vector quantities; Co-ordinate geometry of the straight line; gradients, lengths and perpendicularity; Co-ordinate geometry of circles and simple curves; gradients, tangents and perpendicularity.
- Manipulating and sketching functions; graph transformations.
- Differentiation of simple polynomial functions; Finding maxima and minima values using differentiation of polynomial functions. Differentiation of products, quotients and functions of a function; Differentiation of complex functions; sin x, cos x, tan x, e×, log x
- Integration of standard functions; Definite and indefinite integrals; Integration by parts and by substitution; Area under a curve and between curves, volumes of revolution.
- Applying numerical calculus techniques.
- Differentiation and integration of vectors and links to applications in science and engineering.
- Formulation and solution of differential equations.
- Complex Numbers; Argand diagram, Cartesian and polar forms, complex conjugate, modulus.
- Applying discrete mathematical techniques; Truth tables, proof, sets and matrices.

### Teaching methods

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

 Delivery type Number Length hours Student hours Group learning 40 1.00 40.00 Lecture 40 2.00 80.00 Independent online learning hours 80.00 Private study hours 200.00 Total Contact hours 120.00 Total hours (100hr per 10 credits) 400.00

### Private study

Independent on-line learning:
Using VLE resources 40
Weekly quizzes / using online resources 40
Private study:
Working example problems 50
Preparing coursework 50
Revision for examinations 70

### Opportunities for Formative Feedback

In the first semester coursework will be predominately summative to encourage student engagement with the academic content and with the practice of independent study. In the second semester this scaffolding is removed and the focus shifts to more formative assessment to further develop the appropriate skills as independent learners to support undergraduate study.
General feedback on assignment performance will be posted on Minerva, while individual feedback will also be provided upon marking of assignments. Students will also participate in self and peer review across the foundation year.
Weekly / online resources; reflection with exam wrapper activities (formative); problem sets and coursework.

### Methods of assessment

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

Coursework
 Assessment type Notes % of formal assessment Written Work 6 x 2 hour problem sets 15.00 In-course Assessment 40 minute in course exam 5.00 Total percentage (Assessment Coursework) 20.00

Due to the developmental and pedagogical nature of some assessments and timings, there is not a viable opportunity to provide a resit for the following: Science mid-terms in the first semester; laboratory sessions provided by external departments, or after a coursework deadline has passed and the model answers have been shared. Students who miss any of these learning opportunities can apply for mitigating circumstances and potentially could be given consideration at the exam board

Exams
 Exam type Exam duration % of formal assessment Unseen exam 2 hr 20.00 Unseen exam 2 hr 60.00 Total percentage (Assessment Exams) 80.00

Resits for the exam component of the module will be assessed by the same methodology as the first attempt during the July Resit period, in most cases, or during the next available opportunity.