Master of Physics (MPhys)

MPhys Physics

Join a physics Department of international renown that offers great choice and flexibility, leading to master's qualification.

  • Duration: 4 years
  • Year of entry: 2025
  • UCAS course code: F305 / Institution code: M20
  • Key features:
  • Scholarships available
  • Accredited course

Full entry requirementsHow to apply

Fees and funding

Fees

Tuition fees for home students commencing their studies in September 2025 will be £9,535 per annum (subject to Parliamentary approval). Tuition fees for international students will be £36,500 per annum. For general information please see the undergraduate finance pages.

Policy on additional costs

All students should normally be able to complete their programme of study without incurring additional study costs over and above the tuition fee for that programme. Any unavoidable additional compulsory costs totalling more than 1% of the annual home undergraduate fee per annum, regardless of whether the programme in question is undergraduate or postgraduate taught, will be made clear to you at the point of application. Further information can be found in the University's Policy on additional costs incurred by students on undergraduate and postgraduate taught programmes (PDF document, 91KB).

Scholarships/sponsorships

The University of Manchester is committed to attracting and supporting the very best students. We have a focus on nurturing talent and ability and we want to make sure that you have the opportunity to study here, regardless of your financial circumstances.

For information about scholarships and bursaries please visit our undergraduate student finance pages and our Department funding pages .

Course unit details:
Random Processes in Physics

Course unit fact file
Unit code PHYS10471
Credit rating 10
Unit level Level 1
Teaching period(s) Semester 1
Offered by Department of Physics & Astronomy
Available as a free choice unit? No

Overview

Random Processes in Physics

Aims

To introduce and develop the mathematical skills and knowledge needed to understand and use probability theory in physics.

Learning outcomes

On completion of the course, students will be able to: 

  1. Be cognizant of and be able use appropriately, the fundamentals of probability theory.
  2. Set up and solve models of physical processes involving randomness.
  3. Be aware of and be able to critically apply, some of the important probability distributions that are used by physicists.

Syllabus

1.  Elements of probability                                                                                        

  • Introduction:  What is probability?
  • How to calculate probabilities:  permutations and combinations
  • Conditional probability

 2.  Probability distributions                                                                                     

  • Discrete random variables; expectation value and variance
  • Example:  the geometric distribution
  • Continuous random variables; the probability density function
  • Examples:  the uniform distribution; the normal (or Gaussian) distribution

 3. Exponential Probability Distribution                                                                    

  • Probability of radioactive decay
  • Probability of collisions in a gas; mean free path
  • Generalisation: “hazard rate” and survival probability

 4. Poisson Probability Distribution                                                                           

  • Probability of occurrence of n random events
  • Properties of the Poisson distribution
  • Gaussian limit of the Poisson distribution

 5. Binomial Probability Distribution                                                            

  • Binomial distribution for n trials
  • Irreversible expansion of a gas
  • Poisson and Gaussian limits of the binomial distribution
  • Random walks and diffusion

Assessment methods

Method Weight
Written exam 100%

Feedback methods

Feedback will be provided through self assessed problems, and on-line assessment of weekly examples sheets. General feedback will also be given during the weekly Q&A session.

Recommended reading

A suitable introduction to probability can be found in:

Chapters 39 and 40 of Mathematical Techniques, 3rd edition, Jordan, D. & Smith, P.

Chapters 20 & 21 of Mathematics for Engineers and Scientists, Weltner, K., Gorsjean, J., Schuster, P. & Weber, W.

Chapter 3 of Statistics, Barlow, R.J.

Study hours

Scheduled activity hours
Assessment written exam 1.5
Lectures 22
Seminars 6
Independent study hours
Independent study 70.5

Teaching staff

Staff member Role
Michael Keith Unit coordinator
Benjamin Stappers Unit coordinator

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