MTH0001 | 2022/3 | University of Exeter

MODULE TITLE	Principles of Pure Mathematics	CREDIT VALUE	30
MODULE CODE	MTH0001	MODULE CONVENER	Dr Houry Melkonian (Coordinator)

DURATION: TERM	1	2	3
DURATION: WEEKS	11	11

Number of Students Taking Module (anticipated)	30

DESCRIPTION - summary of the module content

This module develops core mathematical skills essential for progression into a degree in mathematics or other quantitative disciplines. It lays the foundation of Algebra, Trigonometry and Calculus for more advanced mathematical studies by bringing you to a level of knowledge and competence equivalent to the pre-requisite for a first year mathematics at any quantitative degree programme. In this module you will get a grasp of Algebra, which is the study of symbolic representations and the rules for manipulating symbols such as the skills required in ‘backwards thinking’. You will develop competency in elementary algebra to confidently manipulate algebraic expressions, to solve equations and inequalities, as well as to explore functional relationships. Calculus is another part of mathematics to cover in this module, which is concerned with the study of continuous changes, and has two branches, differential calculus (the study of measuring rates of change) and integral calculus (the study of accumulation of quantities), which are precisely linked by the Fundamental Theorem of Calculus. While, on the other hand, you will also learn about Trigonometry, which is the part of mathematics that involves sides and angles and the relation between them. Those skills are fundamental tools for the study of mathematics across the physical, engineering, life and environmental sciences.

On successful completion of this module you will be equipped with the skills to apply algebra, and to use calculus in different contexts, and you will have a sound understanding of fundamental mathematical techniques necessary to handle a diverse range of problems in mathematics, engineering and sciences.

This module will run over two terms; each term you will have weekly scheduled sessions led by the module instructor/convenor. During those sessions you will be introduced to the topic through lecture presentations, learning materials, worked examples and provided exercise worksheet. In this module you will learn how to: use theories, definitions and properties; analyse mathematical statements; use logic and critical thinking to perform mathematics; present findings and communicate results in a coherent way. Each term you will be assessed through a combination of summative assessments: online quizzes and a final exam.

AIMS - intentions of the module

This module aims to enhance your ability to think logically, to manipulate and analyse complex relationships, to question given assumptions as well as to recognise the simple ideas underpinning a given problem. It is developed to renew the background knowledge which you have been in contact with in schools, and to advance your experience with doing mathematics in a more rigorous way.

INTENDED LEARNING OUTCOMES (ILOs) (see assessment section below for how ILOs will be assessed)

Module Specific Skills and Knowledge:

1 manipulate algebraic and numerical expressions accurately and with confidence

2 recognise and solve equations involving logarithmic, exponential, trigonometric and hyperbolic functions;

3 sketch the graphs of a variety of functions of one variable

4 perform accurate calculus manipulations using a variety of standard techniques;

Discipline Specific Skills and Knowledge:

5 manipulate basic mathematical objects necessary in order to progress to successful studies in mathematics, engineering and sciences

6 communicate mathematics effectively and clearly

7 demonstrate an ability to model a given problem mathematically, i.e. to find the mathematical formula which represents the problem

Personal and Key Transferable/ Employment Skills and Knowledge:

8 formulate and solve problems and communicate reasoning and solutions effectively in writing;

9 use learning resources appropriately;

10 communicate ideas and plans in a clear and concise way

11 exhibit self-management and time management skills.

SYLLABUS PLAN - summary of the structure and academic content of the module

- Basic algebra: indices; algebraic expressions; arithmetic operations: addition, subtraction, multiplication; division of algebraic expressions; factor and remainder theorem;

- Equations and inequalities: solving linear equations; solving quadratic equations using: factorisation, discriminant method or completed square form; solving linear and quadratic inequalities

- Functions: dependant and independent variables; domain and range; Real functions: sums, differences, product, quotient and function composition; inverse function; continuity of functions;

- Elementary functions and graphs including: polynomials, exponential, logarithm and natural logarithm;

- Trigonometric functions and identities including solving equations

- Introduction to MATLAB: basic skills, e.g. conditional statement, loops, functions of one output, curve sketching

- Basic Differential Calculus (one variable): definition of the derivative; derivatives of standard functions;

- Differentiation techniques: chain, product and quotient rules; implicit differentiation

- Application of differentiation: maxima and minima of functions with curve sketching; Mean Value Theorem; tangent and normal lines to a curve; Taylor series

- Basic Integral Calculus: definition of the integral as a limit of a sum and graphical principles of integration; Fundamental Theorem of Calculus; definite and indefinite integrals; integration of standard functions;

- Integration methods: Integration by substitution, integration using partial fractions, integration by parts;

- Applications of integration: areas under curves or between two curves; volumes of solid of revolution; numerical integration using Taylor series - MATLAB: integration and differentiation, curve sketching.

LEARNING AND TEACHING

LEARNING ACTIVITIES AND TEACHING METHODS (given in hours of study time)

Scheduled Learning & Teaching Activities	88	Guided Independent Study	212	Placement / Study Abroad	0

DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS

Category	Hours of study time	Description
Scheduled learning and teaching activities	44	Formal lectures of new material.
Scheduled learning and teaching activities	44	Seminars and tutorials, worked examples, with individual and group support.
Guided independent study	212	Lecture & assessment preparation, wider reading.

ASSESSMENT

FORMATIVE ASSESSMENT - for feedback and development purposes; does not count towards module grade

Form of Assessment	Size of Assessment (e.g. duration/length)	ILOs Assessed	Feedback Method
Weekly exercises (Term 1)	10 x 1 hour	1-11	Exercises discussed in class, solutions provided
Weekly exercises (Term 2)	10 x 1 hour	1-11	Exercises discussed in class, solutions provided

SUMMATIVE ASSESSMENT (% of credit)

Coursework	40	Written Exams	60	Practical Exams	0

DETAILS OF SUMMATIVE ASSESSMENT

Form of Assessment	% of Credit	Size of Assessment (e.g. duration/length)	ILOs Assessed	Feedback Method
4 Online Quizzes (each quiz may be attempted multiple times, but students are required to achieve at least 60% for each quiz - otherwise a score of zero will be recorded.)	4 x 5%	4 x 1 hour	1-10	Electronic
Written Exam A (Jan)	30%	2 hours	1-10	Annotated script
4 Online Quizzes (each quiz may be attempted multiple times, but students are required to achieve at least 60% for each quiz - otherwise a score of zero will be recorded.)	4 x 5%	4 x 1 hour	1-10	Electronic
Written Exam B (May)	30%	2 hours	1-10	Annotated script

DETAILS OF RE-ASSESSMENT (where required by referral or deferral)

Original Form of Assessment	Form of Re-assessment	ILOs Re-assessed	Time Scale for Re-assessment
4 Online Quizzes	4 Online Quizzes (4 x 5%)*	1-10	August Ref/Def period
Written Exam A (Jan)	Written Exam A (30%)	1-10	August Ref/Def period
4 Online Quizzes	4 Online Quizzes (4 x 5%)*	1-10	August Ref/Def period
Written Exam B (May)	Written Exam B (30%)	1-10	August Ref/Def period

(each online quiz (8 in total) may be attempted multiple times, but students are required to achieve at least 60% for each quiz - otherwise a score of zero will be recorded.

RE-ASSESSMENT NOTES

Deferral – if you have been deferred for any assessment, you will be expected to complete relevant deferred assessments as determined by the Mitigation Committee. The mark given for re-assessment taken as a result of deferral will not be capped and will be treated as it would be if it were your first attempt at the assessment.

Referral – if you have failed the module overall (i.e. a final overall module mark of less than 40%) you will be required to undertake re-assessments as described in the table above for any of the original assessments that you failed. The mark given for a re-assessment taken as a result of referral will be capped at 40%.

RESOURCES

INDICATIVE LEARNING RESOURCES - The following list is offered as an indication of the type & level of
information that you are expected to consult. Further guidance will be provided by the Module Convener

Basic reading/Web-based and electronic resources:

• ELE – College to provide hyperlink to appropriate pages

Other resources:

• ‘Fundamentals of University Mathematics’, McGregor, C. M., 3rd ed., Oxford: Woodhead, 2010 [Library]

Reading list for this module:

There are currently no reading list entries found for this module.

CREDIT VALUE	30	ECTS VALUE	15

PRE-REQUISITE MODULES	None
CO-REQUISITE MODULES	None

NQF LEVEL (FHEQ)		AVAILABLE AS DISTANCE LEARNING	No
ORIGIN DATE	Thursday 29th July 2021	LAST REVISION DATE	Wednesday 14th September 2022

KEY WORDS SEARCH	Algebra; Trigonometry; Functions; Calculus

Principles of Pure Mathematics - 2022 entry