- UCAS course code
- GG41
- UCAS institution code
- M20
Bachelor of Science (BSc)
BSc Computer Science and Mathematics with Industrial Experience
Duration: 4 years
Year of entry: 2025
UCAS course code: GG41 / Institution code: M20
- Key features:
Industrial experience
Scholarships available
- Typical A-level offer: A*A*A including specific subjects
- Typical contextual A-level offer: AAA including specific subjects
- Refugee/care-experienced offer: AAB including specific subjects
- Typical International Baccalaureate offer: 38 points overall with 7,7,6 at HL, including specific requirements
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 £36,000 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 .
Course unit details:
Foundations of Modern Probability
| Unit code | MATH37021 |
|---|---|
| Credit rating | 10 |
| Unit level | Level 3 |
| Teaching period(s) | Semester 1 |
| Available as a free choice unit? | No |
Overview
The Law of Large Numbers (LLN) and the Central Limit Theorem (CLT) are two most important/ fundamental results in classical and modern probability theory with numerous applications.
Extending the intuitive understanding and partial proofs developed in Probability 1 & 2, the unit builds on methods from mathematical analysis to cultivate a rigorous understanding and derive complete proofs of fundamental results in probability theory, focusing in particular on the LLN and the CLT.
Pre/co-requisites
| Unit title | Unit code | Requirement type | Description |
|---|---|---|---|
| Foundations of Modern Probability | MATH20722 | Anti-requisite | Compulsory |
| Mathematical Foundations & Analysis | MATH11121 | Pre-Requisite | Compulsory |
| Probability and Statistics 2 | MATH27720 | Pre-Requisite | Compulsory |
Aims
The unit aims to:
- Introduce students to fundamental concepts, methods, and tools in modern probability
theory in a systematic and rigorous way (by presenting proofs), offering robust theoretical
foundations for subsequent studies in probability theory and related areas (such as Financial
Mathematics).
- Guide students to develop a rigorous understanding and derive complete proofs of
fundamental results in probability theory, such as the Law of Large Numbers and the
Central Limit Theorem, while extending the intuitive understanding and partial proofs
of these results developed in Probability 1 & 2.
Learning outcomes
On the successful completion of the course, students will be able to:
Calculate probabilities and expected values using more advanced probabilistic methods such as the second Borel-Cantelli lemma or Kolmogorov's 0-1 law.-
State and use fundamental inequalities (Markov, Jensen, Holder, Minkowski) and modes of convergence (almost sure, in probability, in distribution, in mean).
State and use monotone convergence theorem, dominated convergence theorem, and Fatou’s lemma.
State and derive the law of large numbers and the central limit theorem in a variety of theoretical and applied settings.
Teaching and learning methods
2 contact hours per week, divided between review class and examples class. Most of content delivered via online videos (approximately 75 minutes per week).
Assessment methods
| Method | Weight |
|---|---|
| Written exam | 80% |
| Written assignment (inc essay) | 20% |
Feedback methods
Preparing questions on video content
Feedback provided during Review class
Weekly exercise sheet (submit attempted solutions)
Feedback provided during Examples class
Midterm test
General feedback provided after test is marked.
Final exam
General feedback provided after exam is marked.
Recommended reading
[1] Williams, D. (1991). Probability with Martingales. Cambridge Univ. Press.
[2] Shiryaev, A. N. (1996). Probability. Springer-Verlag.
Study hours
| Scheduled activity hours | |
|---|---|
| Lectures | 11 |
| Practical classes & workshops | 11 |
| Independent study hours | |
|---|---|
| Independent study | 78 |
Teaching staff
| Staff member | Role |
|---|---|
| Xiong Jin | Unit coordinator |