Fitzwilliam College Online Winter School


Optional Subjects

History and Archaeology
Mathematical Economics
Computer Science

 Invitation letter 

  Welcome 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 Programme is the official Winter School Programme of Fitzwilliam College in the University of Cambridge. All the courses will be taught by academic members of the University of Cambridge or one of its constituent colleges. The same academics who lecture and supervise the undergraduate students at Cambridge will teach you for university-level curriculum. 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.

Starting in 2023, Fitzwilliam College and ASDAN China have entered into a strategic partnership to open the Fitzwilliam College Online School Programme to outstanding high school students in China. Nine subject areas were opened for the summer of 2023 and more than 110 students from across the country participated in the programme. In the winter of 2024, we are aiming to organise the next, even larger Winter 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 Differential equations 1:  Using physics we introduce the need to use differential equations with some simple examples – possibly including systems of differential equations in nuclear decay.

Integration 1:  A very flexible day on integration – it serves as a recap and extension for those who have done a lot of integration and as an introduction for those who have not seen much integration yet.

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

Manipulating Vectors: Dot Product and Cross Product and a few applications in Physics.

Week 2 Introduction to multivariable calculus: if we need to describe physical phenomena, we need to be able to express quantities in more than one dimension. We look at how to interpret a scalar function of two variables as a surface.

Differential equations 3: We cover simple examples of multivariable differential equations (for example wave equation, Laplace equation, Diffusion Equation)

Integration 2: We introduce simple forms of multivariable integration (surface, volume, centre of mass)

Differential operators: We focus on definitions of vector functions and simple applications of div, grad, curl. We cover very simple examples of physics that requires the use of vector operators.

Final presentation

*List of prerequisite knowledge: Simple derivatives (polynomials, trigonometric, ln), product and chain rules for derivatives, simple integrals (polynomials, trigonometric, ln).

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);

Engineering: Sustainable Vehicles

Time Monday to Friday
Week 1 Engineering and Innovation
  • Duration: 3 hours (2 hours of lecture; 1 hour of problems/discussion)
  • Syllabus: ideal engineering system, S-shape curve, transition to the super-system, micro-scale interactions, systematic innovation, nature-inspired innovation, examples.
  • In-class problems: finding bio-inspired solutions for the improvement of the performance of a car.
  • Assignment: definition of ideal car and identification of barriers to innovation.

Sustainability and Life cycle assessment

  • Duration: 3 hours (2 hours of lecture; 1 hour of problems/discussion)
  • Syllabus: the lifecycle of a component/system, climate crisis, the concept of sustainability, multi-criteria decision analysis, the various phases of the life cycle assessment, example.
  • In-class problems: life cycle assessment of a car.
  • Assignment: multi-criteria decision analysis.


Vehicle Dynamics

  • Duration: 3 hours (2 hours of lecture; 1 hour of problems/discussion)
  • Syllabus: forces on vehicles, wheels and forces exchanged on the ground, power requirements.
  • In-class problems: identification of engine power requirements for a given performance.
  • Assignment: computation of power required for different slope angles.

Hydrodynamics forces

  • Duration: 3 hours (2 hours of lecture; 1 hour of problems/discussion)
  • Syllabus: fundamentals of friction and drag, flow separation, streamlining, wing profiles, lift and downforce.
  • In-class problems: computations of reduction of drag (case study).
  • Assignment: sketch of an aerodynamic vehicle.

Internal Combustion Engines

  • Duration: Duration: 3 hours (2 hours of lecture; 1 hour of problems/discussion)
  • Syllabus: overview of internal engines, fundamentals of thermodynamics, torque, power, efficiency.
  • In-class problems: coupling between an engine and a car; introduction to gear box.
Week 2 Fuels and emissions
  • Duration: 3 hours (2 hours of lecture; 1 hour of problems/discussion)
  • Syllabus:classification of fuels, emissions from engines, biofuels, hydrogen.
  • In-class problems:quantification of carbon dioxide emitted by hydrocarbon combustion.

Electrification of cars

  • Duration: 3 hours (2.5 hours of lecture; 0.5 hours of problems/discussion)
  • Syllabus: hybrid cars, fully electric cars, fundamentals of batteries (cells, packs, modules), energy and power density.
  • In-class problems: coupling between a car and an electrical powertrain.

Future vehicle concepts

  • Duration: 3 hours (1.5 hours of lecture; 1.5 hour of problems/discussion)
  • Syllabus: autonomous vehicles, urban air mobility, electric aircraft.
  • In-class problems: conceptual design of a sustainable vehicle.

Ethics and Intellectual property

  • Duration: 3 hours (2 hours of lecture; 1 hour of problems/discussion)
  • Syllabus: patents, copyright, registered design, trademark, confidentiality, professional ethics, engineering ethics.
  • In-class problems: patent search, patent reading

Final Presentation

*List of prerequisite knowledge: fundamental concepts of mechanics (Newton’s second law, friction force, velocity, acceleration along a straight line); the concept of energy and power; the concept of pressure. Optional: chemical reactions (reading reactants and products; balancing the reaction).

*Recommended reading list (optional): any book of physics for high school.

Computer Sciencce


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 Introduction to supramolecular chemistry: Explore the exciting field of supramolecular chemistry through an introduction to key design principles, including chelate, macrocyclic, cryptate effect, cooperativity, and solvation effects.

Synthesis of supramolecules/supramolecular synthons: Explore various non-covalent interactions used by supramolecular chemists to link molecules, including electrostatics, hydrogen bonding, π-interactions, and van der Waals forces. Introduce common reactions used to make supramolecular synthons, including the 2022 Nobel Prize-winning click reaction.

Explore Host-Guest interactions: Discuss host-guest 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.

Characterising Host-Guest complexes: Learn about various techniques, including NMR, UV, and fluorescence spectroscopy, used to identify and analyse the structural and dynamic properties of host-guest complexes.

Week 2 Self-assembly of molecular structures: Discuss 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: A Q&A session to explore students' motivations for pursuing chemistry, discuss inspiring stories of researchers and their impactful discoveries and give an insight into a life of a chemist.
Final Presentation

*Prerequisite knowledge:
Basic thermodynamics (entropy, enthalpy, Gibbs free-energy)
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)

Microbiology & Microbial Genetics

Time Monday to Friday
Week 1 Intro Microbiology: Introduces students to the microbial world and its diversity.

Intro Pathogens: Introducing students to the main types of pathogens.

Transmission & Prevention: Methods that are used for pathogen transmission (how do they make us sick?) and approaches for infection prevention.

The Immune System: The role of our immune system in combatting infectious diseases.

Antimicrobial Therapies: The range and mechanisms of antimicrobial medications against infectious pathogens.

Week 2 Antimicrobial Resistance (AMR): what is it and why is it happening? What is the scale of the problem?

Biofilms: An overview of microbial biofilms and their role in infection and AMR.

Vaccines: Introduction to the principle and mechanisms of vaccines.

Microbial Genetics: Introduction to the main aspects of microbial genetic (DNA, RNA, replication…etc).

Pathogens Overview: Overview of some important pathogens and their role in infectious diseases.

Final Presentation

List of prerequisite knowledge:
There is no required prerequisite knowledge for this course. 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):
Anderson, D. Introduction to Microbiology. Mosby, 1980
Not complex but a bit old now. It covers a lot of what we will be covering in the course.

Jacob, Francois and Jacques Monod. Genetic regulatory mechanisms in the synthesis of proteins.

"What is true for E. coli is true for an elephant.....".
A classic paper,

Madigan, M et al. Brock Biology of Microorganisms. Pearson, 2014
A useful (albeit detailed) introduction to microbiology for readers with a good level of background knowledge.

Kenneth Todar's online textbook of microbiology,
A fairly detailed introduction for the interested amateur.

For pure fun (plus easy accessibility of the papers, because they're linked) have a look at the PNAS list of "classics". They're from a variety of sciences, including microbiology, so you'll have to do a bit of sifting/filtering:

Psychology and Neuroscience

Time Monday to Friday
Week 1 Intro Psychology: Introduction to the fundamentals of Psychology.

Methods: Overview of the methods used in research and applied Psychology.

Cognitive Psychology: Theoretical frameworks of how humans think and process information.

The Brain: Brain anatomy and function.

Cognitive Neuroscience: Studying the brain with neuro-imaging methods and computational approaches, and what it reveals about how the mind works.

Week 2 Visual Perception: How visual information is perceived and processed in the brain: organisation of the visual systems in humans and animals, visual illusions, effects of lesions on visual experience.

Memory: Mechanisms underlying the formation and retrieval of memories: short- versus long-term memory, memory formation, remembering, patient studies.

Attention: Attention guides how we perceive the world: theories of attention, selective attention, active perception.

Psychopathology: What happens when the brain and behaviour work atypically: examples of mental disorders.

Final Presentation

*No pre-requisite knowledge is needed

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 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)

* Course schedule may change at the discretion of Fitzwilliam College, Cambridge.

 Programme Information 


  • Date: 3rd - 18th February, 2024 (All the courses offer 30h contact hours, but the exact teaching times will be released in mid January. Not all courses will take place at the same times.)
  • Subject: Mathematics, Computer Science, Physics, Biology, Neuroscience, Engineering, 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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