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## XX20231: Mathematical and statistical methods for the life sciences

Owning Department/School: Programmes in Natural Sciences
Credits: 12      [equivalent to 24 CATS credits]
Notional Study Hours: 240
Level: Intermediate (FHEQ level 5)
Period:
Assessment Summary: CW 25%, EX-TH 75%*
Assessment Detail:
• Coursework* (CW 25%)
• Open Book Examination 24hr Duration* (EX-TH 75%)

*Assessment updated due to Covid-19 disruptions
Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Requisites: Before taking this module you must take MA10202
In taking this module you cannot take PH20107
Description: Aims:
To provide students with the necessary mathematical background to proceed to advanced modelling in mathematical biology, and to give a mathematical background in probability and statistics to enable informed usage of statistics analysis packages with experimental data.

Learning Outcomes:
After taking this unit the student should be able to:
* Undertake standard calculations using multivariable calculus
* Recognise and know how to use simple techniques from vector calculus including the divergence theorem
* Recognise and solve the heat and wave equation in one spatial dimension in a range of contexts
* Understand and implement a range of statistical techniques to analyse data
* Process data to test hypotheses with an appropriate statistical software package.

Skills:
Numeracy T/F A, Problem solving T/F A, Data handling, and analysis T/F A, Written Communication T/F A, Use of statistical computer package T/F.

Content:
Multivariable calculus Partial derivatives, critical points, chain rules. Double integrals over rectangular domains. Triple integrals. Change of variable using Jacobian. Polar and spherical coordinates.
Vector calculus Line integral, gradient, divergence, statement and application of divergence theorem.
Fourier series Definitions and applications.
Partial differential equations Separation of variables for heat equation, d'Alembert formula for wave equation in one spatial dimension. Fundamental solution of heat equation. Boundary conditions. Steady state spatial distributions.
Statistics Revision of A level material - binomial distribution; normal distribution; null hypothesis; alternative hypothesis; significance level; p-value.
Correlation, regression, ANOVA.
Data analysis and interpretation of biological data sets using statistical package.
Programme availability:

#### XX20231 is Optional on the following programmes:

Programmes in Natural Sciences
• UXXX-AFB01 : BSc(Hons) Natural Sciences (Biochemistry with Chemistry stream) (Year 2)
• UXXX-AAB02 : BSc(Hons) Natural Sciences (Biochemistry with Chemistry stream) with Study year abroad (Year 2)
• UXXX-AKB02 : BSc(Hons) Natural Sciences (Biochemistry with Chemistry stream) with Year long work placement (Year 2)
• UXXX-AFB01 : BSc(Hons) Natural Sciences (Biochemistry with Pharmacology stream) (Year 2)
• UXXX-AAB02 : BSc(Hons) Natural Sciences (Biochemistry with Pharmacology stream) with Study year abroad (Year 2)
• UXXX-AKB02 : BSc(Hons) Natural Sciences (Biochemistry with Pharmacology stream) with Year long work placement (Year 2)
• UXXX-AFB01 : BSc(Hons) Natural Sciences (Biology with Chemistry stream) (Year 2)
• UXXX-AAB02 : BSc(Hons) Natural Sciences (Biology with Chemistry stream) with Study year abroad (Year 2)
• UXXX-AKB02 : BSc(Hons) Natural Sciences (Biology with Chemistry stream) with Year long work placement (Year 2)
• UXXX-AFB01 : BSc(Hons) Natural Sciences (Biology with Pharmacology stream) (Year 2)
• UXXX-AAB02 : BSc(Hons) Natural Sciences (Biology with Pharmacology stream) with Study year abroad (Year 2)
• UXXX-AKB02 : BSc(Hons) Natural Sciences (Biology with Pharmacology stream) with Year long work placement (Year 2)
• UXXX-AFB01 : BSc(Hons) Natural Sciences (Chemistry with Biochemistry stream) (Year 2)
• UXXX-AAB02 : BSc(Hons) Natural Sciences (Chemistry with Biochemistry stream) with Study year abroad (Year 2)
• UXXX-AKB02 : BSc(Hons) Natural Sciences (Chemistry with Biochemistry stream) with Year long work placement (Year 2)
• UXXX-AFB01 : BSc(Hons) Natural Sciences (Chemistry with Biology stream) (Year 2)
• UXXX-AAB02 : BSc(Hons) Natural Sciences (Chemistry with Biology stream) with Study year abroad (Year 2)
• UXXX-AKB02 : BSc(Hons) Natural Sciences (Chemistry with Biology stream) with Year long work placement (Year 2)
• UXXX-AFB01 : BSc(Hons) Natural Sciences (Chemistry with Pharmacology stream) (Year 2)
• UXXX-AAB02 : BSc(Hons) Natural Sciences (Chemistry with Pharmacology stream) with Study year abroad (Year 2)
• UXXX-AKB02 : BSc(Hons) Natural Sciences (Chemistry with Pharmacology stream) with Year long work placement (Year 2)
• UXXX-AFB01 : BSc(Hons) Natural Sciences (Environmental Science with Biochemistry stream) (Year 2)
• UXXX-AAB02 : BSc(Hons) Natural Sciences (Environmental Science with Biochemistry stream) with Study year abroad (Year 2)
• UXXX-AKB02 : BSc(Hons) Natural Sciences (Environmental Science with Biochemistry stream) with Year long work placement (Year 2)
• UXXX-AFB01 : BSc(Hons) Natural Sciences (Environmental Science with Biology stream) (Year 2)
• UXXX-AAB02 : BSc(Hons) Natural Sciences (Environmental Science with Biology stream) with Study year abroad (Year 2)
• UXXX-AKB02 : BSc(Hons) Natural Sciences (Environmental Science with Biology stream) with Year long work placement (Year 2)
• UXXX-AFB01 : BSc(Hons) Natural Sciences (Environmental Science with Chemistry stream) (Year 2)
• UXXX-AAB02 : BSc(Hons) Natural Sciences (Environmental Science with Chemistry stream) with Study year abroad (Year 2)
• UXXX-AKB02 : BSc(Hons) Natural Sciences (Environmental Science with Chemistry stream) with Year long work placement (Year 2)
• UXXX-AFB01 : BSc(Hons) Natural Sciences (Pharmacology with Biochemistry stream) (Year 2)
• UXXX-AAB02 : BSc(Hons) Natural Sciences (Pharmacology with Biochemistry stream) with Study year abroad (Year 2)
• UXXX-AKB02 : BSc(Hons) Natural Sciences (Pharmacology with Biochemistry stream) with Year long work placement (Year 2)
• UXXX-AFB01 : BSc(Hons) Natural Sciences (Pharmacology with Biology stream) (Year 2)
• UXXX-AAB02 : BSc(Hons) Natural Sciences (Pharmacology with Biology stream) with Study year abroad (Year 2)
• UXXX-AKB02 : BSc(Hons) Natural Sciences (Pharmacology with Biology stream) with Year long work placement (Year 2)
• UXXX-AFB01 : BSc(Hons) Natural Sciences (Pharmacology with Chemistry stream) (Year 2)
• UXXX-AAB02 : BSc(Hons) Natural Sciences (Pharmacology with Chemistry stream) with Study year abroad (Year 2)
• UXXX-AKB02 : BSc(Hons) Natural Sciences (Pharmacology with Chemistry stream) with Year long work placement (Year 2)
• UXXX-AFM01 : MSci(Hons) Natural Sciences (Biochemistry with Chemistry stream) (Year 2)
• UXXX-AAM02 : MSci(Hons) Natural Sciences (Biochemistry with Chemistry stream) with Study year abroad (Year 2)
• UXXX-AKM02 : MSci(Hons) Natural Sciences (Biochemistry with Chemistry stream) with Professional Placement (Year 2)
• UXXX-AFM01 : MSci(Hons) Natural Sciences (Biochemistry with Pharmacology stream) (Year 2)
• UXXX-AAM02 : MSci(Hons) Natural Sciences (Biochemistry with Pharmacology stream) with Study year abroad (Year 2)
• UXXX-AKM02 : MSci(Hons) Natural Sciences (Biochemistry with Pharmacology stream) with Professional Placement (Year 2)
• UXXX-AFM01 : MSci(Hons) Natural Sciences (Biology with Chemistry stream) (Year 2)
• UXXX-AAM02 : MSci(Hons) Natural Sciences (Biology with Chemistry stream) with Study year abroad (Year 2)
• UXXX-AKM02 : MSci(Hons) Natural Sciences (Biology with Chemistry stream) with Professional Placement (Year 2)
• UXXX-AFM01 : MSci(Hons) Natural Sciences (Biology with Pharmacology stream) (Year 2)
• UXXX-AAM02 : MSci(Hons) Natural Sciences (Biology with Pharmacology stream) with Study year abroad (Year 2)
• UXXX-AKM02 : MSci(Hons) Natural Sciences (Biology with Pharmacology stream) with Professional Placement (Year 2)
• UXXX-AFM01 : MSci(Hons) Natural Sciences (Chemistry with Biochemistry stream) (Year 2)
• UXXX-AAM02 : MSci(Hons) Natural Sciences (Chemistry with Biochemistry stream) with Study year abroad (Year 2)
• UXXX-AKM02 : MSci(Hons) Natural Sciences (Chemistry with Biochemistry stream) with Professional Placement (Year 2)
• UXXX-AFM01 : MSci(Hons) Natural Sciences (Chemistry with Biology stream) (Year 2)
• UXXX-AAM02 : MSci(Hons) Natural Sciences (Chemistry with Biology stream) with Study year abroad (Year 2)
• UXXX-AKM02 : MSci(Hons) Natural Sciences (Chemistry with Biology stream) with Professional Placement (Year 2)
• UXXX-AFM01 : MSci(Hons) Natural Sciences (Chemistry with Pharmacology stream) (Year 2)
• UXXX-AAM02 : MSci(Hons) Natural Sciences (Chemistry with Pharmacology stream) with Study year abroad (Year 2)
• UXXX-AKM02 : MSci(Hons) Natural Sciences (Chemistry with Pharmacology stream) with Professional Placement (Year 2)

 Notes: This unit catalogue is applicable for the 2019/20 academic year only. Students continuing their studies into 2020/21 and beyond should not assume that this unit will be available in future years in the format displayed here for 2019/20. 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. Undergraduates: Find out more about these and other important University terms and conditions here. Postgraduates: Find out more about these and other important University terms and conditions here.