NSCI0005 / NSCI0006 Mathematical Methods for Natural Sciences A / B#

About: This pair of modules aims to provide the mathematical foundations and techniques for different streams of the Natural Sciences degree programme. The emphasis is on applications, giving you practice in mathematical manipulation and problem solving rather than rigorous proofs and derivations. You should be able to apply these mathematical ideas to a variety of scientific problems, helping develop their interdisciplinary skills.

Highlights: These modules will give students an opportunity to further develop their mathematical and (to a lesser extent) their computing skills using Python.

Prerequisites: NSCI0005 is for students who are studying Physics streams - if you are taking PHAS0011 then you will also be studying NSCI0005 (irrespective of whether you decide not to take a physics stream after term 1). There is some overlap between the topics on this course and students who have taken further mathematics A-level or equivalent.

Students who take all other foundation modules will be on NSCI0006, which is designed to get studnts thinking about data, trends and modelling.

If you have not taken A-level mathematics or equivalent, then you will take the course MATH0039, which is designed as an introduction to calculus taught by the mathematics department. The syllabus can be found here.

Contents (indicative):

  • NSCI0005

  1. Complex numbers

  2. Sequences, series, limits and convergence

  3. Matrices and vectors

  4. Partial differentiation and multivariable calculus

  5. Integration, solids of revolution and arc length

  6. 1st and 2nd order ordinary differential equations

  • NSCI0006

  1. Python Basics - Introduction to the Python programming language and basic computational modelling skills.

  2. Data Trends - Investigating trends using data drawn from research and policy applications

  3. Rates of Change - The concept of the derivative and results for some standard derivatives. Differential equations, their meaning and solutions.

  4. Dynamics Models - Visualising and interpreting flow; finding equilibrium solutions.

Recommended readings:

We recommend that you start reading through our online mathematics books and attempt the problems:

Book 1

Book 2

[Book 3](coming soon!)

For a full reading lists, click here for NSCI0005 and click here for NSCI0006

Teaching:

  • Lectures: The different topics the course covers will be introduced through lectures. Pre-prepared handouts may be provided by the lecturer, either electronically or as a paper copy. The lecturer may additionally require you to make your own notes during the lecture. In addition, you may be referred to material (for example in textbooks or on the web) to read and assimilate. Lectures are Lecturecast where the facilities are available; however attendance at the lectures is considered an indicator of student engagement and is therefore compulsory.

  • Tutorials Your learning is supported by small-group workshops. Problem sets work will be made available towards the start of the week, with lectures first and then tutorials second. Semianrs are an opportunity to receive feedback on your understanding of the module material, hence preparation and active participation is essential if you wish to derive the most benefit, thus seminar attendance is monitored and compulsory.

  • Self-study: In addition to timetabled hours it is expected that you engage in self-study in order to master the material. This can take the form of practicing example questions (workshop questions, additional questions available on Moodle and past exam questions); participating in peer marking, preparing for seminars and further reading in textbooks and online.

Assessment:

NSCI0005

  • 60% Examination

  • 40% Coursework

NSCI0006

  • 50% Coursework

  • 50% Coursework

You can also refer to the UCL Module Catalogue entry for NSCI005 and for NSCI0006