Fitzwilliam College Online Winter School Programme

4001-699-686

Optional Subjects


Biology
Physics
Psychology and Neuroscience
Engineering
Mathematics
Mathematical Economics
Chemistry
Artificial Intelligence

 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.

 Introduction 

The Fitzwilliam College Online Winter School Programme is organised by Fitzwilliam College, one of the constituent colleges of the University of Cambridge. The programme will let you experience the type of advanced teaching offered at Cambridge. The same academics who teach the undergraduate students at the university will help you develop your academic skills. The challenging problem-solving and discussion sessions will reflect the style of Cambridge supervisions, which are the core of the excellent teaching offered at the University. 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 ASEEDER have entered a strategic partnership to open the Fitzwilliam College Summer and Winter School Programmes to outstanding high school students in China. Since 2023, more than 300 students from across the country participated in these programmes. In the winter of 2025, we will offer 2-week long courses in Biology, Physics, Psychology and Neuroscience, Engineering, Mathematics, Mathematical Economics, Chemistry and Artificial Intelligence.

可选课程

数学
计算机科学
化学
物理
生物
医学
行为心理学
工程

  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 research essay and presentation and receive detailed 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

Microbiology and Pathogen Evolution (Biology)

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.

Phylogenetics:

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. Students are encouraged to gain some basic computational skills in Linux and coding if they have an opportunity, but this is not necessary for joining the 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):
Brown, T. A. (2002). Mutation, Repair and Recombination. https://www.ncbi.nlm.nih.gov/books/NBK21114/

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). https://doi.org/10.1007/S11306-021-01800-8

Crick, F. (1970). Central Dogma of Molecular Biology. Nature 1970 227:5258, 227(5258), 561–563. https://doi.org/10.1038/227561a0

Foxman, B., & Riley, L. (2001). Molecular Epidemiology: Focus on Infection. American Journal of Epidemiology, 153(12), 1135–1141. https://doi.org/10.1093/AJE/153.12.1135

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). https://doi.org/10.1128/CMR.00020-18

MacPhee, D. G., & Ambrose, M. (1996). Spontaneous mutations in bacteria: chance or necessity? Genetica, 97(1), 87–101. https://doi.org/10.1007/BF00132585

Pitt, T. L., & Barer, M. R. (2012). Classification, identification and typing of micro-organisms. Medical Microbiology, 24. https://doi.org/10.1016/B978-0-7020-4089-4.00018-4

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: 8pm – 9pm Tuesday 21st Jan, 8pm – 9pm Sunday 2nd Feb.

Special Relativity and Quantum Mechanics (Physics)

 

Date 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=mc2 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
Optics: - The laws of reflection and refraction
- Notion of frequency, period, wavelength
Mathematics: - 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);
*Office hours: 7pm – 8pm Tuesday 21st Jan, 8pm – 9pm Sunday 2nd Feb.

Mathematics for the Natural Sciences (Mathematics)

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 product, quotient, and chain rule for differentiation; we introduce implicit differentiation.

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.

Final Presentations

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

Office hours:
8pm - 9pm Monday 20th Jan, 8pm - 9pm Sunday 2nd Feb.

Psychology and Neuroscience

Time Monday to Friday
Week 1 Intro Psychology:

Introduction to the fundamentals of Psychology.

Methods:

The scientific method and how it applies to Psychology and Neuroscience.

Nuclear Safety and Waste disposal:

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

Cognitive Psychology:

Theoretical frameworks of how humans think and process information.

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: the diagnostic process and treatments for mental disorders.

Final Presentations

*List of prerequisite knowledge: Basic knowledge of brain anatomy and function.
*Office hours: 8pm- 9pm Monday 20th Jan, 8pm- 9pm Sunday 2nd Feb.

Sustainable Vehicles (Engineering)

 

Time Monday to Friday
Week 1 Engineering and Innovation:

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

Operating Systems 1:

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

Sustainability and Life cycle assessment:

a. Duration: 3 hours (2 hours of lecture; 1 hour of problems/discussion)
b. 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.
c. In-class problems: life cycle assessment of a car.
d. Assignment: multi-criteria decision analysis.

Vehicle Dynamics:

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

Aerodynamic forces:

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

Internal Combustion Engines:

a. Duration: 3 hours (2 hours of lecture; 1 hour of problems/discussion)
b. Syllabus: overview of internal engines, fundamentals of thermodynamics, torque, power, efficiency.
c. In-class problems: coupling between an engine and a car; introduction to gear box.

Week 2 Fuels and emissions:

a. Duration: 3 hours (2 hours of lecture; 1 hours of problems/discussion)
b. Syllabus: classification of fuels, emissions from engines, biofuels, hydrogen
c .In-class problems: quantification of carbon dioxide emitted by hydrocarbon combustion.

Electrification of cars:

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

Future vehicle concepts:

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

Ethics and Intellectual property:

a. Duration: 3 hours (2 hours of lecture; 1 hour of problems/discussion)
b. Syllabus: patents, copyright, registered design, trademark, confidentiality, professional ethics, engineering ethics.
c. 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 on physics for high school.

*Office hours: 6pm – 7pm Tuesday 21st Jan, 6pm – 7pm Sunday 2nd Feb.

Elements of Mathematical Economics (Mathematics and Economics)

Time 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 economic processes and relations.
Rational Choice Theory I and II:
These lectures introduce a formal theory of choice and examine some applications in economic transactions.
Week 2 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.
Information:
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.
*Office hours: 8pm – 9pm Tuesday 21st Jan, 8pm – 9pm Sunday 2nd Feb.
Supramolecular Chemistry: Designing and Building Smart Materials (Chemistry)

Time Monday to Friday
Week 1 Introduction to Non-covalent Interactions I and II:
Explore various non-covalent interactions used by supramolecular chemists to link molecules, including electrostatics, hydrogen bonding, π-interactions, and van der Waals forces.
Thermodynamics of Non-covalent Interactions:
Discuss parameters like enthalpy, entropy, and free energy to understand how these forces influence molecular stability and binding.
Analytical Techniques and Solvent Effects:
Explore analytical techniques used in supramolecular systems, including NMR, UV, and fluorescence spectroscopy, to study structure and binding interactions. Discuss solvent effects that influence non-covalent interactions by altering stability, solubility, and molecular behaviour.
Introduction to Molecular Recognition:
Explore the field of supramolecular chemistry through an introduction to key design principles, including the chelate, macrocyclic, and cryptate effects, as well as cooperativity and solvation effects.
Week 2 Supramolecular Systems I and II:
Discuss host-guest recognition in supramolecular chemistry, including the design principles behind cation, anion, and neutral guest recognition. Learn about the significance of this field, exemplified by the Nobel Prize in Chemistry awarded in 1987. Discuss various techniques used to synthesize and study supramolecular systems such as molecular containers and cages.
Self-Assembly and Template Synthesis:
Discuss the process of self-assembly, where large supramolecular structures are formed/organized through non-covalent interactions, with a focus on examples found in nature such as DNA. Additionally, explore template synthesis, where a molecular scaffold guides the formation of specific supramolecular architectures.
Molecular Machines:
Explore molecular machines in supramolecular chemistry—nanoscale devices that perform specific tasks through controlled molecular motion, driven by external stimuli like light, heat, or chemical reactions.
Final Presentations
Prerequisite knowledge: 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: 5.30pm – 6.30pm Wed 22nd Jan and 5.30pm – 6.30pm Saturday 1st Feb
Computer Science: Artificial Intelligence

Time Monday to Friday
Week 1 Classic search problems in artificial intelligence:
many problems have a solution; many games have an optimal strategy. But how do we find them? What data structures and algorithms can we use?
Scaling to real world search problems:
redesigning our algorithms to better match the limits of modern hardware and to handle different user requirements.
Interactive decision making:
how can we handle problems that change while we are implementing our solution? Dynamic, or interactive, search problems pose interesting new challenges!
Prolog:
we will learn a new programming language that can help us to implement our AI algorithms!
Understanding knowledge:
each of us has an intuitive understanding of common sense and knowledge, but how can we represent that in a computer, and what format(s) make it usable?
Week 2 Automating a warehouse:
Pulling all the pieces together, let’s design the algorithms that a robot needs to pack items into boxes.
Training a neural network:
generalising our approach, can we design systems that can design themselves?
Bayesian inference in the real world:
guest lecture looking at the opportunities and economics of machine learning in the real world.
Limits of machine learning:
understanding the practicalities of contemporary machine learning solutions and the implications for their reliability, trust worthiness, hallucinations, etc.
*List of prerequisite knowledge: No computer science knowledge is assumed but programming experience is always useful.
*Office hours:5.30 pm – 6.30 pm Monday 20th Jan, 8pm – 9pm Sunday 2nd Feb

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 (Twice during the programme)

* For more detailed schedules, please refer to the brochure. The teaching times may change at the discretion of Fitzwilliam College, Cambridge.
* Fitzwilliam College reserves the right to changes to course instructors or the syllabus of the courses.

 Programme Information 

Application

  • Date: 18th January – 3rd February, 2025 (30-hour live course, 2 office hours)
  • Subject: Biology, Physics, Psychology and Neuroscience, Engineering, Mathematics, Mathematical Economics, Chemistry, Artificial Intelligence
  • Grade:10 - 12
  • Admission quota: 15 high school students for each subject

Requirements

  • 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 ASEEDER
    • Individual application need to submit English language performance (IELTS level 6.5 or TOEFL 90) and A or above in relevant 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 ASEEDER teacher.

 Contact us