# ESSENTIAL MATHEMATICS - 2019/0

Module code: PHY1034

## Module Overview

This module is designed to provide essential underpinning skills for the whole programme in (a) the mathematics needed by physical scientists, and (b) the foundations of computational mathematics and programming. The mathematics units of assessment are delivered on a supervised self-study basis - to allow flexible learning patterns to students with different mathematics skills and knowledge levels at University entry. The delivery method is by supported workshop classes and occasional lectures to introduce new topics, as required. The Essential Mathematics module consolidates and enhances mathematical skills to beyond (A2) Advanced Level standard, providing the mathematical foundations needed for subsequent Level FHEQ 4 Mathematics components and for the introductory Physics modules at Level FHEQ 4.

The computational physics unit of assessment is delivered in a supervised classroom environment, with online material covering the basics of computer programming. No previous programming experience is assumed. The material starts from basic concepts of what it means to write a program, and the practicalities of doing so. It then covers the syntax of the Python programming language, though some examples in other common languages used in Physics research (C++, Fortran, ...) are also covered. Common programming concepts, such as variables, control structures and data structures are covered, with a strong link to the use of programming as a way to solve mathematical and physical problems.

### Module provider

Physics

GINOSSAR Eran (Physics)

### Module cap (Maximum number of students): N/A

Workshop Hours: 44

Independent Learning Hours: 84

Lecture Hours: 44

Semester 1

None.

## Module content

Indicative content includes:

Mathematics units:

• Finite and infinite series

• Introduction to calculus: limits, continuity, differentiability, asymptotes, Taylor series

• Analysis – elements of differentiation, integration function investigation

• Introducing complex numbers representation

• Complex algebra and Demoivre's theorem

• Matrices

• Determinants and their properties

• Vector spaces (linear independence, basis, dimensions)

• Linear transformations (representations as matrices)

• Orthogonality

Computing units: These are intended to be worked through at an average rate of one unit per week

• Introduction to the course: Meaning of computer programming. Using the linux command line and frequently used commands, editing python scripts, and running them.

• Variables, native types in python: the different variable data types available, how to initialize and combine them, and how to perform basic mathematical operations.

• Flow Control: Conditional statements, boolean data types, and logic operations.

• Loops: while and for constructions, and list comprehensions.

• Functions and modules: how to create and use functions, and create and use modules.

• Data structures: creating and manipulating arrays from numpy.

• Visualizations: creating plots using matplotlib.

• I/O: reading and writing files.

• Algorithm design: Planning solutions to problems.

• Debugging: techniques to fix common coding problems, and consolidation of previous units

## Assessment pattern

Assessment type Unit of assessment Weighting
School-timetabled exam/test MATHEMATICS PC BASED CLASS TEST (1HOUR) 20
Examination MATHEMATICS PC BASED END OF SEMESTER EXAMINATION (1.5 HOUR) 50
Examination COMPUTING END OF SEMESTER EXAMINATION (1 HR) 30

None.

## Assessment Strategy

The assessment strategy is designed to provide students with the opportunity to demonstrate:

• recall of subject knowledge

• ability to apply mathematical knowledge to unseen problems of a nature similar to those studied inclass

• ability to interpret and write short computer programs

Thus, the summative assessment for this module consists of:

• one mathematics class tests 1h

• one final mathematics exam of 1.5h duration. Section A contains compulsory questions worth 20 marks & Section B contains three questions of 20 marks each of which the students attempt two.

• one final computing examination of 1h duration, in which a single question is to be answered.

Formative assessment and feedback

The supervised sessions involve academics and postgraduate demonstrators who engage with the students on a one-to-one basis in a classroom-like setting to provide verbal feedback. There will be weekly formative Mathematics tests (quizzes) on SurreyLearn with instant results available to the student. The computation part features formative exercises, with the debug-compilation-execution process providing instant feedback, with verbal feedback available from the supervisors in the session.

## Module aims

• To provide the background knowledge and practice and to build greater confidence in the language, notation and use of underpinning mathematical skills to a beyond Advanced level (A2) standard in algebra, functions, real and complex numbers, and differential and integral calculus.
• To provide the basic knowledge and skills necessary to plan and to write simple computer programs, to compile them and to run them in order to solve simple problems in their own right and to provide a foundation of knowledge on which to build for more complex problem-solving.

## Learning outcomes

 Attributes Developed 1 Consistently apply mathematical methods and techniques introduced at A-level, especially integration and differentiation, and understand and make first applications of complex numbers and concepts and properties of series. KCT 2 Take simple mathematical problems and write computer programs which correctly implement the mathematics, using correct syntax to give a working problem which the student will be able to debug, compile and run, generating well-presented numerical and graphical output. KCT

Attributes Developed

C - Cognitive/analytical

K - Subject knowledge

T - Transferable skills

P - Professional/Practical skills

## Methods of Teaching / Learning

The learning and teaching strategy is designed to:

• equip students with subjectknowledge

• develop skills in applying subject knowledge to physicalsituations

• provide a basis in mathematics and computation that can be used as a basis for deeper understanding of physics, and fora further study of mathematics and computation

The learning and teaching methods include:

• 44h of combined lectures and workshops as 4h/week x 11 weeks. The material is covered at a self-paced manner by the students using online resources. In addition lectures will take place introducing , commenting and advising the students on the different topics according to the order above in 'Module contents'. During these classes two one-hour multiple PC based formative tests take, a one-hour summative test (usually in weeks 6-8), plus a 1.5 hour end of semester final examination.

• 22h of guided computing self-study as 2h/week x 11 weeks. The taught material is broken down into a series of 11 units,each of which has a formative test to provide feedback on the level of understanding.  An end of semester class test will contain one two-part question, both parts of which should be attempted.

Indicated Lecture Hours (which may also include seminars, tutorials, workshops and other contact time) are approximate and may include in-class tests where one or more of these are an assessment on the module. In-class tests are scheduled/organised separately to taught content and will be published on to student personal timetables, where they apply to taken modules, as soon as they are finalised by central administration. This will usually be after the initial publication of the teaching timetable for the relevant semester.

Upon accessing the reading list, please search for the module using the module code: PHY1034

## Programmes this module appears in

Programme Semester Classification Qualifying conditions
Physics with Nuclear Astrophysics MPhys 1 Compulsory A weighted aggregate mark of 40% is required to pass the module
Physics with Nuclear Astrophysics BSc (Hons) 1 Compulsory A weighted aggregate mark of 40% is required to pass the module
Physics with Astronomy BSc (Hons) 1 Compulsory A weighted aggregate mark of 40% is required to pass the module
Physics BSc (Hons) 1 Compulsory A weighted aggregate mark of 40% is required to pass the module
Physics MPhys 1 Compulsory A weighted aggregate mark of 40% is required to pass the module
Physics with Astronomy MPhys 1 Compulsory A weighted aggregate mark of 40% is required to pass the module
Physics with Quantum Technologies MPhys 1 Compulsory A weighted aggregate mark of 40% is required to pass the module
Physics with Quantum Technologies BSc (Hons) 1 Compulsory A weighted aggregate mark of 40% is required to pass the module

Please note that the information detailed within this record is accurate at the time of publishing and may be subject to change. This record contains information for the most up to date version of the programme / module for the 2019/0 academic year.