Optional Subjects

Mathematics
Computer Science
Chemistry
Physics
Biology
Neuroscience
Eengineering

— Invitation letter —

— About Cambridge —

Founded in 1209, the University of Cambridge is the fourth-oldest university in the world. There are 31 Colleges, six Schools and over 150 Faculties and Departments that make up the University of Cambridge, covering a vast array of subjects and specialised areas of research.

— Introduction —

The Cambridge Online Summer School is officially run by Fitzwilliam College, Cambridge. All the courses will be taught by Cambridge faculty members. 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, Cambridge and ASDAN China have entered into a strategic partnership to open the Fitzwilliam College, University of Cambridge, Summer School Program to outstanding high school students in China for the first time. Eight subject areas will be open for the summer of 2023.

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 certicate of completion by Fitzwilliam College.
  • Each student will write an academic essay and receive an individual feedback report from the academic leads.
  • Outstanding students (Top 2 of each class) will receive an award certificate, and their essays will be published on the website of Fitzwilliam College.

Certificate of Completion

Certificate of Execellence

— Teaching Faculty —

* The final lecturer is subject to the official arrangements of Fitzwilliam College, Cambridge.

Sample Schedule

Mathematics for the Natural Sciences

Date: 31st July to 11th August

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 will serve as a recap and extension for those who have done a lot of integration and as an introduction for those who have not seen integration before
Integration 2
Harder physical problems call for harder integrals – we will examine a few examples that require trigonometry
Differential equations 2
Simple harmonic oscillator physics will call for a different style of solution
Differential equations 3
Some examples of differential equations in Chemistry and Earth Sciences, both first and second order
Week 2 Numerical Integration
Introducing the students to Matlab (or equivalent) with some simple examples
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 will focus on definitions and simple applications of div, grad, curl
Integration 3
We will introduce simple forms of multivariable integration (surface, volume, centre of mass)
Differential equations 4
Very simple examples of physics that requires the use of multivariable differential equations
Final presentation

*Office hours: Thursday 3rd Aug & Thursday 10th August, 8 pm

Elements of Mathematical Finance

Date: 17th July – 28th July

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 finance.
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.
Dynamic Choice
This lecture discusses formal choice in a temporal setting and examines financial decisions with varying time-horizons.
Arbitrage and Expected Utility
This lecture investigates arbitrage opportunities with reference to the aforementioned formal theory of choice, as well as the underlying statistical structure that gives rise to them.
Stochastic Dominance
This lecture discusses conditions under which certain financial options outperform others, with reference to some key statistical properties.
Final Presentation

*Office hours: Thursday 20th and Thursday 27th July, 8 pm.

Special Relativity and Quantum Mechanics

Date: 31st July to 11th August

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

*Office hours: Thursday 3rd Aug & Thursday 10th August, 8 pm

Engineering: Sustainable Vehicles

Date: 17th July – 28th July

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: 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

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

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: identification of critical elements in a car; sketch of an

Internal Combustion Engines

  • Duration: 3 hours (1.5 hours of lecture; 1.5 hours 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, hydrogen, fuel cells
  • In-class problems: quantification of carbon dioxide emitted by a car

Electrification of cars
Hybrid cars, fully electric cars, fundamentals of batteries (cells, packs, modules), energy and power density

  • Duration: 3 hours (2 hours of lecture; 1 hour 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 car concepts
Autonomous vehicles, urban air mobility, electric aircraft, smart mobility

  • Duration: 3 hours (1.5 hours of lecture; 1.5 hour of problems/discussion)
  • Syllabus: autonomous vehicles, urban air mobility, electric aircraft, smart mobility
  • 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: ethical questions, patent search, patent reading

Final Presentation

* Office hours: Thursday 20th and Thursday 27th July, 8 pm.

Computer Sciencce

Date: 17th July – 28th July

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
Yirtual 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 & GPUs and accelerators
Ttexture maps, bump mapping, displacement mapping.
Contrasting CPU pipelines with GPUs, understanding vectorizable workloads, OpenGL/CUDA coding.
Final presentation

*Office hours: Tuesday 18th July and Tuesday 25th July, 8 pm.

Supramolecular Chemistry

Date: 24th July – 4th August

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

*Office hours: Thursday 27th July and Thursday 3rd Aug, 19.30 pm.

Microbiology & Microbial Genetics

Date: 24th July – 4th August

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).
Final Presentation

*Office hours: Thursday 27th July & Thursday 3rd August, 8 pm.

Psychology and Neuroscience

Date: 17th July – 28th July

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.

Experimental Psychology: Experimental approaches to studying mental processes in humans and animals.

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

* Office hours: Wednesday 19th and Wednesday 26th July, 1 pm.

Sample Agenda

Beijing Time Monday to Friday
10:00 - 11:30 Extracurricular activity lead by bilingual TA
11:30 - 16:00 Individual study and assignment
16:00 - 19:00 Live Course by Cambridge academics
20:00 - 21:00 Office Hour (once a week)

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

— Programme Information —

Application

  • Date：July - August 2023 (two weeks, weekends off) (Different dates for different subjects)
  • Optional Subjects：Mathematics (2 courses), Computer Science, Chemistry, Physics, Biology, Neuroscience, Engineering
  • Grade：10 - 12
  • Admission quota：10 - 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 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.

— Contact us —