Fitzwilliam College Online Summer School


Optional Subjects

History and Archaeology
Mathematical Economics
Nuclear Science
Computer Science

 Invitation letter 

 About Fitzwilliam College 

Fitzwilliam College is one of the 31 constituent colleges of the University of Cambridge. It was founded in 1869 specifically to broaden access to the University of Cambridge. It is a dynamic, welcoming international community committed to developing the talents of all its 750 undergraduate and postgraduate students.

Fitzwilliam College sustains that tradition of ensuring that every student, whatever their background, can fulfill their potential and make the most of the incomparably rich opportunities offered here. This is also a forward-looking place, consistent with the College's motto of 'The Best of the Old and the New'. Most of its award-winning buildings date from the 1960s onwards, including some of the best student accommodation in Cambridge, a state-of-the-art auditorium and the Olisa Library.


The Fitzwilliam College Online Summer School is the official Summer School Programme of Fitzwilliam College in the University of Cambridge. All the courses will be taught by academic members of Fitzwilliam College or one of the other colleges of the University of Cambridge. The same academics who lecture and supervise the undergraduate students at Cambridge will teach you undergraduate-level content. The core of Fitzwilliam's academic activities is a desire to retain 'the best of the old', while enthusiastically embracing 'the best of the new'. Fitzwilliam has always been characterised by discussion, debate and creativity of ideas and full participation should form a positive, rewarding and sustainable part of an academic course. This programme is designed to provide students with a flavour of undergraduate study at Cambridge, and an opportunity to explore topics beyond what is covered within the school curriculum.

In 2023, Fitzwilliam College and ASDAN China have entered a strategic partnership to open the Fitzwilliam College Online Summer School Programme to outstanding high school students in China. Nine subject areas were opened for the summer of 2023 and the winter of 2024, and more than 160 students from across the country participated in these programmes. In the summer of 2024, we aim to organise the next, even more extensive Summer School Programme!



  Why us? 

 Programme Outcome 

  • Students who attend at least 80% of the classes, write their essay and give their presentation will receive a certificate of completion by Fitzwilliam College.
  • Each student will write an academic mini-research essay and receive individual feedback from the academic course instructor.
  • Top 2 best performing students will receive an award certificate.
  • The authors of the best 2 essays will receive a "Top Essay" certificate.

Certificate of Completion

Certificate of Execellence

 Teaching Faculty 

* Fitzwilliam College reserves the right to changes to the content of the courses or the course instructors.

Sample Schedule

Mathematics for the Natural Sciences

Time Monday to Friday
Week 1

Differentiation 1:

We introduce differentiation, give some simple example; we introduce sketching simple functions.

Integration 1 and differential equations 1: 

We introduce integration of simple functions and the construction of differential equations using simple physical examples where possible.

Exponential and Logarithms:

We introduce, learn to sketch, and learn to differentiate exponentials and logarithmic functions.

Trigonometry and Hyperbolics:

We introduce, learn to sketch, and learn to differentiate several useful trigonometric functions (including inverses and hyperbolics).

Differentiation 2:

We introduce integration by substitution and by parts; we introduce the integration of differential equations.

Week 2

Integration 2 and differential equations 2:

We introduce integration by substitution and by parts; we introduce the integration of differential equations.

Differential equations 3:

We proceed in learning how to work with differential equations, strongly tying it back to physics wherever possible.

Complex Numbers:

We need the formalism of complex numbers to solve harder physics problems; we introduce and use the cartesian and polar forms.

Differential equations 4:

Simple harmonic oscillator physics requires a different style of solution that will use Complex Numbers.

*List of prerequisite knowledge: GCSE, IGCSE or equivalent qualification. No calculus required as we will cover everything from first principles.

*Office hours: Thursdays, 12.30 pm – 1.30 pm.

Elements of Mathematical Economics


Date Monday to Friday
Week 1

Elements of Mathematics I and II

These lectures introduce students to fundamental concepts of mathematics that have useful applications in economics.

Elements of Statistics I and II

These lectures provide the statistical foundations necessary for the analysis of financial processes and relations.

Rational Choice Theory I

This lecture introduces a formal theory of choice and examine some applications in financial transactions.

Week 2

Rational Choice Theory II

This lecture introduces a formal theory of choice and examine some applications in financial transactions.

Stochastic Dominance

This lecture discusses conditions under which certain options outperform others, with reference to some key statistical properties.

Dynamic Choice

This lecture discusses formal choice in a temporal setting and examines financial decisions with varying time-horizons.


This lecture investigates the ways in which rational agents can incorporate newly acquired pieces of information into their decision-making process.

Final Presentation

*List of prerequisite knowledge: Basic differentiation is necessary and basic integration is desirable.
Special Relativity and Quantum Mechanics

Time Monday to Friday
Week 1

The Lorentz Transformation:

We highlight the successes and difficulties of the pre-relativistic physics. The latter was very effective in predicting, for instance, the motion of the planets, but Einstein noticed what appeared to be an inconsistency between Newton’s dynamics and Maxwell’s electromagnetism. This led him to propose a new physical theory and a new transformation law for the coordinates of the same event in two different reference frames. Different observers may assign different times to the same event, a curious feature of what became known as the Lorentz transformation.

Relativistic Kinematics:

The fact that time flows at different rates in different systems of reference has interesting consequences. We shall follow a fast moving interstellar spaceship and compare the magnitudes of time intervals, distances and velocities measured by those in the ship with the corresponding measurements made by observers at rest. In this context, we shall examine in detail the well-known Twin Paradox.

Relativistic Dynamics:

We introduce the notions of relativistic momentum and energy and study some examples of the conversion of mass into energy and vice-versa. We derive the famous formula E=mc^2 and explore its implications in some physical systems.

Relativistic Optics:

The Doppler effect and the aberration of light were known phenomena in non-relativistic physics. We shall assess how Relativity modifies the classic formulas and explore some of the consequences of these changes.

Appearance of rapidly moving objects:

When taking a photograph of a moving object, all rays generated at its boundaries arrive simultaneously at the camera. If the object has a non-negligible size, light rays must then leave its surface at different times. In most instances this causes a significant distortion on the appearance of objects that move at speeds close to the speed of light. However, perhaps surprisingly, some objects keep their shape in the photographs.

Week 2

The historical development of Quantum Mechanics:

The first quarter of the twentieth century is often regarded as one of the most productive periods in the history of science. We shall study the ideas of Planck, de Broglie, Heisenberg, Schrodinger, and others which culminated in 1925-1926 with the formulation of the Quantum Theory.

The postulates of Quantum Mechanics and simple applications:

We introduce the notion of wave function, quantised energy levels and solve Schrodinger’s equation for simple systems. We discuss how the equation can be applied to more complicated systems such as the hydrogen atom.

The EPR paradox and the Bohr-Einstein debate:

The new ideas were not accepted without reluctance by some, among them Einstein. In 1935, together with Podolsky and Rosen, he wrote an article in which an apparent paradox suggested that the formulation of Quantum Mechanics was incomplete. We shall discuss their reasoning and the more modern version of the paradox due to Bohm.

Bell’s Inequality:

Almost 30 years after the EPR argument was formulated, Bell wrote what has been described as one of the most important scientific works of the 20th century, in which it was shown that Quantum Mechanics could not be completed with the so-called hidden variables. We shall have a good discussion of Bell’s theorem and some of its variants, namely due to d’Espagnat.

Final Presentation
*List of prerequisite knowledge:
Newtonian dynamics:
- Newton’s Laws
- Notions of force, mass, momentum, energy and work
- The laws of reflection and refraction
- Notion of frequency, period, wavelength
- Elementary techniques of differentiation and integration
- Techniques for solving simple first and second order differential equations (desired but not strictly necessary)
*Recommended reading list (optional):
Halliday and Resnick, Fundamentals of Physics (Relativity and Quantum Mechanics chapters only);
A Einstein, The Principle of Relativity;
R Feynman, The Feynman Lectures on Physics, Quantum Mechanics (Chapter 1 only).
Nuclear Science and Technology

Time Monday to Friday
Week 1

Introduction to Nuclear Energy:

Nuclear Energy’s role in the global energy infrastructure and strategy to tackle climate change.

Fundamentals of Nuclear Science: 

Common notation, types of radiation, binding energy, radioactive decay, half-life, and nuclear reactions.

Nuclear Safety and Waste disposal:

Regulatory systems, probabilistic risk assessment, waste immobilisation and disposal.

Nuclear Reactor Design:

Components, and types of reactor including pressurised water reactors, boiling water reactors, gas-cooled reactors and liquid-metal reactors.

Week 2

Fundamentals of Materials Science:

intrinsic and extrinsic properties, crystallography, microstructures and mechanics.

Radiation Damage:

Displacement cascades, dislocation loops and void formation.

Nuclear Fuel:

Uranium, plutonium, and future fuel design.

Nuclear Cladding and Moderators:

Cladding - steels and zirconium, Moderators – graphite, Zirconium hydride, and liquid moderators.

Final presentations:

short student presentations on a topic which has caught their interest. There will be feedback given, and the best presentation will be awarded a prize.

*List of prerequisite knowledge: There are no prerequisites for this course except for basic algebra and trigonometry.
*Office hours: Thursdays, noon – 1 pm.
Computer Science


Time Monday to Friday
Week 1

Computer Architecture:

the components inside a computer and styles of interacting with them. Programmed I/O. Interrupts. DMA.

Operating Systems 1:

virtual memory for protection between processes. Address translation. Hardware acceleration.

Operating Systems 2:

cooperative and preemptive multi-tasking. Scheduling algorithms.

Starting Processes:

system calls, fork, the shell.

Interprocess Communications:

understanding Unix pipes, marshalling datatypes into bytes.

Week 2

Network communication:

sockets, server applications, a simple webserver.

Graphics 1:

ray-tracing, Phong shading, imperfect and perfect reflections.

Graphics 2:

triangularisation, Painters’ Algorithm, Z-Buffers.

Graphics 3:

texture maps, bump mapping, displacement mapping.

GPUs and accelerators:

contrasting CPU pipelines with GPUs, understanding vectorizable workloads, OpenGL/CUDA coding.

Final presentation
*List of prerequisite knowledge:
No computer science knowledge is assumed but programming experience is always useful. Later work on graphics assumes knowledge of vectors and basic geometry.
*Recommended reading list (optional):
Computer Architecture and Organisation, S.P. Wang, published by Springer. ISBN 978-981-16-5661-3 (e-book 978-981-16-5662-0).
Supramolecular Chemistry

Time Monday to Friday
Week 1

Non-covalent interactions:

Explore various non-covalent interactions used by supramolecular chemists to link molecules, including electrostatics, hydrogen bonding, π-interactions and Van der Waals forces.

Thermodynamics in supramolecular chemistry:

Learn about Gibbs free energy, enthalpy, entropy and equilibrium constant and the relationship between these quantities.

Analytical Techniques in supramolecular chemistry:

In this session you will be introduced to various techniques, including NMR, UV, and fluorescence spectroscopy, used to identify and analyse the structural and dynamic properties of host-guest complexes.

Quantifying interactions and solvent effects:

Learn about scales to quantify the strength of non-covalent interactions such as H-bonding and how to predict the strength of these interactions. Explore the effect of the solvent on these interactions.

Week 2

Molecular recognition:

Host-guest chemistry: We will discuss molecular recognition in supramolecular chemistry, including the design principles behind cation, anion, and neutral guest recognition. Learn about the impact and significance of this field, as exemplified by the Nobel Prize in Chemistry awarded in 1987.

Self-assembly of molecular structures:

You will be introduced to the process of self-assembly, where large supramolecular structures are formed/organised through non-covalent interactions, with a focus on examples found in nature such as DNA.

Synthesis and applications of molecular machines:

Discuss the 2016 Nobel Prize in Chemistry and the various techniques used to synthesize molecular machines and their applications.

Uncovering the inspiration for chemistry:

Discuss inspiring stories of researchers and their impactful discoveries and give an insight into a life of a chemist.

Final Presentation
*Prerequisite knowledge:
Simple calculations of position of equilibria, equilibrium constants;
Basic organic chemistry (reactions that would normally be covered at secondary school-level organic ;
chemistry, familiarity with the meaning of curly arrows desirable but not essential).
*Office hours:Saturday 20th July, 11 am – noon, Friday 26th July, 11 am – noon.
Pathogen evolution through bioinformatics

Time Monday to Friday
Week 1

Molecular Epidemiology:

An in-depth introduction to the methodologies and key definitions essential for studying the evolution of pathogens using genomic data. Students will learn the foundational concepts that underpin molecular epidemiology.

DNA Structure:

A comprehensive exploration of cell structure, the intricacies of DNA and RNA molecules, and a deep dive into the Central Dogma of biology. This lecture lays the groundwork for understanding genetic information.

Causes and consequences of mutations:

A detailed examination of mutations, including their definition, classification into types, an exploration of their consequences on genetic material, and an analysis of the diverse factors contributing to mutagenesis.

Principles of Classification of Micro-organisms:

A nuanced discussion on the principles governing the classification of microorganisms, emphasising both phenetic and phylogenetic relationships. Students will gain insights into the taxonomic frameworks that categorise these entities.

Microbes and Disease:

An exploration of infectious diseases, covering the spectrum from foodborne and waterborne to airborne diseases. Students will gain a broad understanding of the diverse microbial agents responsible for various health challenges.

Week 2

Bacterial Genomics:

An introduction to the diverse sequencing techniques employed in bacterial genomics. The lecture will guide students through the process of transforming raw sequencing data into a comprehensible genome, providing essential insights into genomic analyses.


A deep dive into phylogenetic principles, including real-world examples of phylogenies, discussions on phylogenetic tree rooting and topology, applications in diverse contexts, and a critical examination of potential pitfalls in phylogenetic analyses.

Phylogenetic Inference:

Building upon the previous lecture, students will learn the practical aspects of phylogenetic inference. This includes creating alignments, understanding distance matrices, selecting appropriate substitution models, and exploring various approaches to construct phylogenetic trees, such as Neighbour-Joining, Likelihood-based methods, and Bayesian phylogenetic inference.

SARS-CoV-2 Pandemic Response:

A special guest lecture by Dr. Christopher Ruis, offering unique insights into his work during the SARS-CoV-2 pandemic response. Students will gain a first-hand understanding of applying mutational spectra and phylogenetics to decipher pathogen transmission patterns.

Final Presentations:

The culmination of the course, where students present their comprehensive understanding of molecular epidemiology and pathogen evolution. Each presentation will showcase the application of acquired knowledge and skills, providing a tangible demonstration of the course's impact on the students' analytical capabilities and scientific acumen.

List of prerequisite knowledge:
There is no required prerequisite knowledge for this course, however basic computational skills in Linux and coding are encouraged. A broad familiarity with the items on the list above will greatly enhance your understanding and enjoyment of the classes and good preparation by all students will contribute significantly to the success of the course.
Recommended reading list (optional):
Brown, T. A. (2002). Mutation, Repair and Recombination.
Costa dos Santos, G., Renovato-Martins, M., & de Brito, N. M. (2021). The remodel of the “central dogma”: a metabolomics interaction perspective. Metabolomics: Official Journal of the Metabolomic Society, 17(5).
Crick, F. (1970). Central Dogma of Molecular Biology. Nature 1970 227:5258, 227(5258), 561–563.
Foxman, B., & Riley, L. (2001). Molecular Epidemiology: Focus on Infection. American Journal of Epidemiology, 153(12), 1135–1141.
Hall A. What is molecular epidemiology? (Editorial). Trop Med Int Health 1996;1:407–8.
Lakhundi, S., & Zhang, K. (2018). Methicillin-Resistant Staphylococcus aureus: Molecular Characterization,Evolution, and Epidemiology. Clinical Microbiology Reviews, 31(4). MacPhee, D. G., & Ambrose, M. (1996). Spontaneous mutations in bacteria: chance or necessity? Genetica, 97(1), 87–101.
Pitt, T. L., & Barer, M. R. (2012). Classification, identification and typing of micro-organisms. Medical Microbiology, 24. Tompkins LS. Molecular epidemiology: development and application of molecular methods to solve infectious disease mysteries. In: Miller VL, Kaper JB, Portnoy DA, et al, eds. Molecular genetics of bacterial pathogenesis: a tribute to Stanley Falkow. Part 1. Retrospective look at early advances. Washington, DC: American Society for Microbiology, 1994:63–73
Office hours: Thursdays, 12.30 pm - 1.30 pm.
Psychology and Neuroscience

Time Monday to Friday
Week 1

Introduction to the fundamentals of Psychology and Neuroscience:

The objective of the first lecture is to introduce the fundamental notions of psychology and neuroscience and to provide an overview of the wide array of the methods that can be deployed in psychology and behavioural science research.

The modular and integrative functional architecture of the brain:

In this lecture the students will discover some of the fundamentals of the functional anatomy of brain. They will then become acquainted with the principal neurotransmitter of the central nervous system and what happens if they disfunction.

Towards an understanding of the individual vulnerability to develop psychiatric disorders:

In this lecture, the students will be introduced the principle of individual vulnerability to develop psychiatric disorders and the methods used to study the underlying psychological and neurobiological mechanisms.

Introduction to Computational Neuroscience:

This part of the course will focus on introducing students to the behavioural and neural mechanisms of learning and models used for quantifying learning such as reinforcement learning models.

Application of advanced neuroimaging techniques:

Students will be introduced to a variety of neuroimaging methods such as structural and functional magnetic resonance imaging and magnetic resonance spectroscopy. Their application in psychological and clinical neuroscience will be discussed.

Week 2

Machine learning methods for neuroscience:

This lecture will cover different types of machine learning methods, including linear and non-linear methods. Their use for behavioural and neuroimaging data will be discussed.

Principles of microscopy in neuroscience:

Students will get introduced to the basic principles of microscopy and they will be presented with different use cases in the neurosciences, from simple histological staining to more complex live microscopy and super resolution microscopy.

Fantastic cells and where to find them:

In this lecture, students will get acquainted with the principles of cellular neuroscience, understanding the functional organisation of the brain at the cellular molecular level and the complex interplay of neurons and glia.

Cellular communication in the brain and beyond:

This lecture will discuss the fundamentals of neural function, how excitable cells generate action potentials, their propagation, as well as synaptic transmission. The supportive role of glia in this process will also be highlighted.

*List of prerequisite knowledge:
There is no prerequisite knowledge for this course. Strong analytical skills and a keen interest in Psychological and Behavioural Sciences will be particularly helpful. The course will be suitable for students interested in Cognitive, Computational, Behavioural, Cellular Neuroscience, Neuroimaging, Microscopy, Neuropsychopharmacology, and Neurobiology.
*Office hours:
Reinforcement learning: an introduction – Sutton and Barto.
An Introduction to resting state fMRI functional connectivity – Bijsterbosch, Smith, Beckmann(this is to help the students catch up on the prerequisite topics if they were not familiar with a topic)
*Office hours:
Dr Aude Rauscent: Wednesday 17th July, 1 – 2 pm;
Dr Katharina Zuhlsdorff: Monday 22nd July, 12.30 – 1.30 pm;
Dr Stavros Vagionitis: Thursday 25th July, 12.30 – 1.30 pm.
History and Archaeology of Humanity

Time Monday to Friday
Week 1

Aim of the course:

Over these ten lectures, students will be exposed to a range of archaeological and historical case studies that expose and undermine neat explanations for how the past is thought about in the present. The focus is global, shifting towards Europe later in the course, but the emphasis will always be laid on how societies across many environments seek to innovate and operate despite the constraints imposed upon them.

Introduction 1 (TMB + BW):

The scope and scale of human history is vast, and seems confusing. This introduction to the course ties together general trends, including the manner in which societies agglomerate and organise. Instead of understanding the present as a linear progression from the past, the emphasis will be on key markers that have differentiated various polities through history.

Introduction 2 (TMB + BW):

In formulating a view of the past, a wide range of methods and techniques have been utilised by scholars since the 18th century. Segueing between archaeology and history, the session will be spent unpicking the manner in which histories have been interpreted.

Lecture 1 (TMB):

During the course of this lecture, the diversity of earlier human community building will be explored. An emphasis will be placed on the creativity and expression that were discovered and expanded upon by a wide range of cultures.

Lecture 2 (TMB + BW):

States are a current geopolitical ever-present. However, they have never taken the same form, socially, economically, or politically. By evaluating a range of exemplars, the divergence of past institutions will be thought through.

Lecture 3 (TMB):

Empires are often believed to be polities of constant expansion and interconnectivity. The validity of this idea will be evaluated whilst the experience of those within such is underlined. A wide number of examples of imperial ambition and experience are discussed.

Week 2

Lecture 4 (TMB + BW):

There were constant blips in human history. Invasion and plague were often thought to break even the mightiest. Through underlining different kinds of experience, a review will be made of the ways in which societies adapt and change to heed external pressures.

Lecture 5 (BW+TMB):

The early Middle Ages saw the end of the unified Roman Empire and the breakup of Europe into smaller areas. Amidst this contraction of political authority, trade and living standards, great changes occurred in religious and societal organisation.

Lecture 6 (BW):

Between 1000 and 1500 European states took the form which they would hold for the next thousand years; this period is often seen as the crucible or making of modern Europe. This session will discuss whether modern European states really can trace their origins back to this period.

Lecture 7 (BW):

The most recent 500 years have seen enormous increases in life expectancy and living standards; alongside these gains have come other changes, less obviously beneficial. This lecture asks what characterizes the modern age, and whether we really have all benefited.

Final Presentation

Sample Agenda

Beijing Time Monday to Friday
10:00 - 11:30 Online Extracurricular activity lead by bilingual TA
11:30 - 15:00 Individual study and assignment
15:00 - 18:00 Live Course by Cambridge academics
19:00 - 20:00 Office Hour (once a week)

* Please check the syllabus. The teaching times may change at the discretion of Fitzwilliam College, Cambridge.

 Programme Information 


  • Date: 15th - 26th July, 2024 (30-hour live course, 2 office hours)
  • Subject: Mathematics, Computer Science, Physics, Biology, Neuroscience, Nuclear Science, Mathematical Economics, Supramolecular Chemistry, History and Archaeology of Humanity
  • Grade:10 - 12
  • Admission quota: 10 - 15 high school students for each subject


  • Method 1:Direct admission if any one of the following conditions is met
    - Students who received B or above in ASDAN EPQ can be admitted directly
    - Global or national awards in various science assessments in ASDAN China
    - Individual applicants need to show their English language performance (IELTS level 6.5 or TOEFL 90) and A or above in a related subject
  • Method 2:Recommendation letter from an invited teacher (Each teacher can recommend up to two students)
  • Method 3:If you do not meet the above criteria, you will be required to do a telephone interview in English with an ASDAN China teacher.

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