 Academic Registry
Programme & Unit Catalogues

## MA10274: Foundations, connections, sequences and functions

[Page last updated: 26 August 2021]

Owning Department/School: Department of Mathematical Sciences
Credits: 12 [equivalent to 24 CATS credits]
Notional Study Hours: 240
Level: Certificate (FHEQ level 4)
Period:
Assessment Summary: CW 50%, EX 50%
Assessment Detail:
• Coursework 1 (CW 25%)
• Coursework 2 (CW 25%)
• Examination (EX 50%)
Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Requisites: Students must have a grade A in A-level Mathematics or equivalent in order to take this unit
While taking this module you must take MA10209
Aims:

The unit is split into two parts: foundations and connections, and; sequences and functions.

Aims for foundations and connections: To improve the ability of the students to read and write mathematics well; to enable them to develop effective study skills for individual and group working; to introduce students to the beauty, the ubiquity and the importance of university-level mathematics.

Aims for sequences and functions: To introduce students to topics usually covered in mathematical analysis, primarily in terms of content and intuition. To introduce the notions of convergence and limit precisely, in the context of both (I) sequences and series, and (II) functions of a scalar variable, and to collect a number of essential mathematical tools and methods related to (I) and (II) which shall underpin future studies. Finally, to show connections between (I) and (II).

Learning Outcomes: In the context of foundations and connections, after taking this unit, students should be able to:
* Determine the validity of mathematical arguments;
* Formulate and write simple mathematical proofs using construction, contradiction, induction;
* Evaluate and improve upon the clarity of written mathematical arguments;
* Work independently, through planned and effective reading and practice;
* Work in a group, through effective discussion and collaboration;
* Discuss the breadth of modern mathematical research;
* Discuss the importance of mathematics in work and society;
* Present mathematics verbally;
* Formulate constructive feedback for others, and act on feedback received.

In the context of the analysis of sequences and series, and scalar-valued functions of a scalar variable, after taking this unit students should be able to:
* demonstrate fluency and familiarity with elementary definitions and results;
* apply these concepts to a range of examples;
* appreciate the purpose of analysis in relation to other areas of mathematics (for instance by discussing examples).

Skills: Written and Spoken Communication (T/F A), Problem Solving (T/F), Numeracy, Reasoning (T/F A)

Content: Foundations and connections:
* Study skills for mathematicians.
* Thinking logically.
* Introduction to definitions, theorems and proofs.
* Techniques of proof, including construction, contradiction, induction.
* Mathematical research at the University of Bath.
* Applications of degree-level mathematics in industry and society.

Sequences and functions:
* Logic, quantifiers
* Numbers and inequalities
* Sequences
* Series
* Limits
* Continuity
* Differentiability
* Real power series

Programme availability:

#### MA10274 is Compulsory on the following programmes:

Department of Mathematical Sciences
• USMA-AFB20 : BSc(Hons) Mathematics, Statistics, and Data Science (Year 1)
• USMA-AAB20 : BSc(Hons) Mathematics, Statistics, and Data Science with Study year abroad (Year 1)
• USMA-AKB20 : BSc(Hons) Mathematics, Statistics, and Data Science with Industrial Placement (Year 1)

 Notes: This unit catalogue is applicable for the 2021/22 academic year only. Students continuing their studies into 2022/23 and beyond should not assume that this unit will be available in future years in the format displayed here for 2021/22. Programmes and units are subject to change in accordance with normal University procedures. Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules. Find out more about these and other important University terms and conditions here.