Dr Alex Carter

Associate Professor of Philosophy and Interdisciplinary Studies, ICE, University of Cambridge College Lecturer in Interdisciplinary Studies, Fitzwilliam College

Alex Carter teaches Philosophy and Creativity Theory at the University of Cambridge, Institute of Continuing Education. He also oversees the Institute's undergraduate research courses. At Fitzwilliam College, Alex supervises philosophy students and provides study skills support to all college members. Alex’s research interests are diverse and include Wittgenstein’s later philosophy, the theology of Simone Weil and the philosophy of humour. Alex’s PhD thesis explored some of the surprising aspects of Wittgenstein’s views concerning freedom and fatalism. Alex is currently researching the relationship between humour and creative practice via the concept of ’serious play’.

■ Course Content

From Isaac Newton to Alan Turing, Francis Bacon to Stephen Hawking, Charles Darwin to Rosalind Franklin, James Fraser to Jane Goodall—Cambridge is renowned for its scientific breakthroughs. In this course, we explore the deeper, philosophical significance of these discoveries and ask: Is space a “stuff”? Are human beings “special”? Is mathematics certain? Can machines think? The course welcomes those new to philosophy, and invites students to apply their knowledge of other subjects in critical and creative ways.

* List of prerequisite knowledge:
No previous study of philosophy is required; although a broad familiarity with the ideas above will enhance your understanding and enjoyment of the classes and good preparation by all students will contribute significantly to the success of the course. It is also hoped that students will apply existing knowledge from other fields, e.g. physics, mathematics, law, in discussing the above topics. Much of philosophy is about making distinctions. So, if you are unsure about your suitability, you could review the below questions. There are few (if any) perfect answers in philosophy, so it is important only that you feel confident arriving at an answer.
* Test your knowledge of the prerequisites! Can you answer the questions below?
1. What is the difference between an argument and an assertion?
2. What is the difference between a paradox and a problem?
3. Can Iknow x if x is false?
* Fitzwilliam College reserves the right to changes to the course content or the course instructor

Dr. Joao Rodrigues

Bye Fellow of St Catharine’s and Wolfson Colleges

Joao After many years working in Quantum Field Theory and Particle Physics, specifically in the parton structure of the nucleons, I changed my field of research to the climate of the polar regions. In the Polar Oceans Physics Group in Cambridge, I studied how the Arctic sea ice cover has changed in recent decades as a consequence of global warming. I examined sea ice thickness data collected by submarines and satellites and attempted to quantify the dramatic thinning of the Arctic Sea ice. At present, I teach several Physics and Mathematics courses for first-, second- and third-year students in the Natural Sciences and the Mathematical Tripos of the University of Cambridge.

■ Course Content

The motion of particles at speeds close to the speed of light is described by equations that are very different from those that we apply to study the motion of the objects in our daily life, such as the planets around the Sun. Special Relativity provides the theoretical framework to study those fast moving particles. We shall study phenomena such as the time dilation, length contraction and the famous twin paradox, which have no counterpart in the classical theory.
And let us explore the Quantum World. The atomic and subatomic particles behave in a way that for us, used to the certainties of Classical Dynamics and Electromagnetism, is unambiguously strange. Quantum Mechanics suggests there is an essential randomness in quantum phenomena and the best theory we have, based on the wave function and Schrodinger equation, can only predict the probabilities of events to occur. Such peculiarities of the theory were not appealing to everyone. We shall look at how Einstein objected to the standard formulation of Quantum Mechanics and how his ideas led to new developments.

* 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)
* Test your knowledge of the prerequisites! Can you answer the questions below?
1. Igor is a cosmonaut in the International Space Station, orbiting the Earth at an altitude of 408 km at speed of 28000 km/h. What is his acceleration and what gravitational force does the Earth exert on him.
2. You apply a 4.9 N force to the free end of a spring, stretching it from its relaxed state by 12 mm. What is the spring constant? What force does the spring exert on you if you stretch it by 17 mm? How much work does the spring force do on your hand?
3. The wavelength of x rays produced in the Stanford Linear Accelerator is 0.067 fm; what is the frequency of these x rays?
* Fitzwilliam College reserves the right to changes to the course content or the course instructor.

Dr Andrea Giusti

Bye-Fellow, Fitzwilliam College, University of Cambridge, Senior Lecturer in Thermofluids, Department of Mechanical Engineering, Imperial College London

Andrea is a Senior Lecturer in Thermofluids at Imperial College London, Department of Mechanical Engineering and Bye-Fellow at Fitzwilliam College, Cambridge. He studied Mechanical and Energy Engineering in Florence (Italy). Following his PhD, Andrea joined the Engineering Department at the University of Cambridge as a RollsRoyce Research Associate. He was appointed Lecturer by Imperial College in October 2018. In addition to the academic role at Imperial College, Andrea supervises undergraduate students at Fitzwilliam College. He is also Editor-in-Chief of the International Journal of Spray and Combustion Dynamics.

Dr Daniel Fredrich

Research Associate, Engineering Department, University of Cambridge

Daniel is a senior researcher and entrepreneur in the field of thermofluids engineering. His research focuses on the numerical prediction of thermoacoustic instabilities and the active control of reacting multiphase flows using external electrostatic fields and non-equilibrium plasma discharges. He holds a PhD in computational fluid dynamics from Imperial College London and an MSc in aeronautics and astronautics from TU Berlin. He is the co-founder of Pinepeak Ltd, a University of Cambridge spinout aiming to solve the problem of wildfires.

■ Course Content

The module we propose focuses on the design of new vehicles with sustainability at the centre of all engineering choices. The student will learn the fundamentals of vehicle dynamics, aerodynamic forces, electrification and new vehicle concepts. Theoretical lectures are paired with practical sessions which will guide the student towards a conceptual design of the vehicle of the future.

* 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. Chemical reactions (reading reactants and products; balancing the reaction).
* Test your knowledge of the prerequisites! Can you answer the questions below?
1. Consider a block sliding on a table with speed U=10 m/s. The kinematic friction coefficient between the block and the table is μ= 0.1. The block is pushed against the table with a normal force equal to 10 N. What is the force parallel to the table that must be applied to the block to keep it moving at constant speed? How much power is needed to move the block?
2.A ball of mass 1 kg is launched vertically from the ground with speed 20 m/s. Assuming that gravity is the only force acting on the ball, what is the maximum height reached by the ball?
3. Methane, CH4, reacts with oxygen, O2. Find the minimum mass of oxygen per unit mass of methane to completely convert carbon into CO2 and hydrogen into H2O.
* Fitzwilliam College reserves the right to changes to the course content or the course instructor.

Dr John Fawcett

Churchill College, University of Cambridge

Since completing his PhD, John Fawcett has been working in industry alongside lecturing, tutoring, supervising and directing studies in Computer Science at Cambridge. Over more than 15 years, John has seen around 500 students through to graduation. John has delivered courses in summer schools for over 10 years and is active in undergraduate admissions, including as Subject Convenor for the Computer Science undergraduate course. John served as University Senior Proctor in the 2021/22 academical year after being Praelector for 6 years at Churchill.

■ Course Content

Artificial intelligence (AI) and machine learning (ML) have featured in the news regularly in recent years as technology continues to transform our social and work lives. This course explores the problems that we can solve with AI and ML and takes a deep dive into how we create them, including the key maths and algorithms. It moves from narrow-focused classical AI systems to solving openended problems that humans cannot necessary solve. Looking beyond today's AI and ML systems, the course looks at the challenges that the technology has still to overcome, posturing you to understand the next wave of developments.

* List of prerequisite knowledge:
No computer science knowledge is assumed but programming experience is always useful.
* Test your knowledge of the prerequisites! Can you answer the questions below?
Suppose you have a function that can tell you which of two items, A and B, should come first in asorted list.
1. What is the difference between a tree and a graph data structure?
2. Why might breadth first search not perform well on a graph?
3. Why might depth first search not perform well on a graph?
* Fitzwilliam College reserves the right to changes to the course content or the course instructor.

Dr Aude Rauscent

Visiting Research Fellow, Department of Psychology, Bye-Fellow at Homerton College, Fitzwilliam College and Hughes Hall, Director of Studies for Psychological and Behavioural Sciences and Natural Sciences

Dr Aude Rauscent is a visiting research fellow at the Department of Psychology, University of Cambridge, and one of the Directors of Studies in Psychological and Behavioural Sciences and Natural Sciences at various colleges across the University. Ten years ago, Aude moved to Cambridge University and continued her research on the neurological and psychological mechanisms subserving individual vulnerability to addiction in the CLIC, Cambridge Laboratory for research on Impulsive and Compulsive disorders, in the Department of Psychology

Dr Alexandra Krugliak

Research Associate at MRC Cognition and Brain Sciences Unit, University of Cambridge, Supervisor, Trinity College, University of Cambridge

Dr Alexandra Krugliak studied Psychology and Cognitive Neuroscience at The University of Maastricht (The Netherlands), before obtaining a PhD from the University of Birmingham (United Kingdom). Currently, Alexandra is a Research Associate at the MRC Cognition and Brain Sciences Unit at the University of Cambridge.

■ Course Content

Have you ever wondered how humans think? In this course, you will be introduced to fundamental concepts in Psychology and Cognitive Neuroscience. At the lectures you will explore the fundamental mechanisms of the brain which controls various functions, including thought, emotion, motor skills, vision, and motivation. It is a complex organ composed of approximately 86 billion neurons - nearly the same number as the stars in the Milky Way! You will also learn about advanced techniques used to assess psychological and cognitive functions.

* 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 suit students interested in Cognitive, Neuroimaging, Neuropsycho-pharmacology, and Neurobiology
* Test your knowledge of the prerequisites! Can you answer the questions below?
1. One brain area, one cognitive function? Comment.
2. How do the structures in the brain communicate?
3. Can you imagine tests to assess cognitive functions?
* Fitzwilliam College reserves the right to changes to the course content or the course instructor.

Dr Stephen Sawiak

Fellow, Tutor, College Lecturer, Assistant Director of Studies in Mathematics for Natural Sciences , Fitzwilliam College, University of Cambridge, MRI Physicist, Department of Physiology, Development and Neuroscience, University of Cambridge

Dr Sawiak is an experienced lecturer, supervisor and assistant director of studies responsible for organising the mathematics supervisions for students taking physical Natural Sciences, Computer Science and Chemical Engineering courses in Fitzwilliam College. He has interviewed Natural Sciences candidates for over 15 years and supervised students in mathematics for 18 years. Day to day he conducts research in magnetic resonance imaging acquisition and analysis methods with applications to neuroscience.

■ Course Content

This exciting and challenging mathematics course gives a rapid tour from the fundamentals of calculus (differentiation and integration) up to first-year University level with advanced applications including power series expansion of functions, Fourier series and the extension of integration into multiple dimensions and non-Cartesian coordinate systems. The pace of this course will be fast and most suitable for those with already some familiarity with the basic concepts of calculus who are keen for a preview of University level mathematics made accessible to those of a bright high school level.

* List of prerequisite knowledge:
Basic algebra, trigonometry (functions sin, cos, tan; use of radians)
* Test your knowledge of the prerequisites! Can you answer the questions below?
1. What does the gradient of a function mean?
2. If x(a+b/2)=6, what is b in terms of a and x?
3. Sketch the graphs of sin x and cos x, in radians, from -π<x<π
* Fitzwilliam College reserves the right to changes to the course content or the course instructor.

Serena Povia

College Teaching Associate at St John’s College, Supervisor at Magdalene and Jesus, Involved in Cambridge Admissions for the past 7 years in several colleges STEMSMART Supervisor

Mrs. Serena Povia specialises in teaching Mathematics and Physics at the University level. She has been a supervisor in physics and mathematics for the Natural Sciences course for about ten years. Current teaching commitment are the Physics and Mathematics courses for the first year and the second year. Sereba previously taught third year courses too.

■ Course Content

Programme 1: 13th-26th July, 2025 (40-hour course, 2 office hours)
Programme 2: 27th July - 9th August, 2025 (40-hour course, 2 office hours)

* List of prerequisite knowledge:
Derivatives (polynomials, trigonometric, exponentials, ln), product and chain rules for derivatives, integrals (polynomials, trigonometric, exponentials, ln), integrations by substitution, at least some knowledge of complex numbers.
* Note
This course will be very closely targeted at students between lower and upper sixth, those who have not seen and worked on the following pre-requisites will find the course very hard. Those who have already completed pre-university studies might find at least half of the course too easy. A question sheet will be pre-circulated to participants two weeks before the course to ensure that the prerequisites are met.
* Fitzwilliam College reserves the right to changes to the course content or the course instructor.

Dr Vasileios Kotsidis

College Assistant Professor at Gonville and Caius College

Vasileios Kotsidis uses tools from traditional and evolutionary game theory to analyse social interactions that (potentially) involve strategic motives. His research focuses on the scope and limitations of models based on methodological individualism in interpreting individual behaviour (human or otherwise) as it is manifested in social settings. It spans along three main directions: how individuals think, what they are motivated by, and what the researcher can infer. He obtained his PhD in Economics at the University of Nottingham. His doctorate explored some theoretical aspects of social (strategic) behaviour and investigated its empirical manifestations. He also enjoys practicing karate, studying on the philosophy of mathematics, and reading fantasy literature.

■ Course Content

Programme 1: 13th-26th July, 2025 (40-hour course, 2 office hours)
Programme 2: 27th July - 9th August, 2025 (40-hour course, 2 office hours)

This course explores some fundamental notions and results that are of special importance of economic
analysis. It begins by considering elements of set theory, analysis, optimisation calculus, and statistics. It then applies them to construct a series of progressively more elaborate logical statements which form the basis of formal choice under risk. The result is a robust and analytically tractable approach to reasoning about uncertainty.

* List of prerequisite knowledge:
1. Understanding of limiting reasoning
2. Elementary trigonometry
3. Intuitive understanding of sets
4. Venn diagrams
5. Intuitive understanding of probability
* Test your knowledge of the prerequisites! Can you answer the questions below?
1. What does it meant to state that some function, f, is continuous?
2. What does it mean to state that some function, f, is differentiable?
3. Consider two sets, A and B. Suppose that A is a subset of B. What are then the union and the intersection of A and B?
* Fitzwilliam College reserves the right to changes to the course content or the course instructor.

Dr Andrea Chlebikova

Senior Project Chemist at Isaac Physics, Department of Physics, University of Cambridge, College Teaching Associate at Sidney Sussex College, Special Supervisor at Newnham College, Course lecturer, Yusuf Hamied Department of Chemistry, University of Cambridge

Andrea Chlebikova became involved in undergraduate teaching at Cambridge in 2015 and has been supervising first-year chemistry to students of Natural Sciences as well as more specialised physical chemistry courses ever since. She is also involved with undergraduate admissions in multiple colleges. Andrea is in charge of designing and teaching the chemistry content on the STEM SMART programme run by the University of Cambridge, preparing students from disadvantaged backgrounds for studying STEM subjects at university.

Dr Peter Bolgar

Bye-Fellow at Fitzwilliam College, University of Cambridge, Director of Studies and College Lecturer at Magdalene College, University of Cambridge, Lecturer (Teaching) at University College London

Peter Bolgar is a teaching Bye-Fellow in organic and bio-organic chemistry at Fitzwilliam College. He completed his undergraduate degree in Natural Sciences at Cambridge, followed by a PhD in supramolecular chemistry at the same place. Peter now specialises in teaching chemistry at the university level, lecturing a range of courses from the first, second and third year of the undergraduate curriculum. He is involved with undergraduate admissions at Magdalene College. Peter is a member of the UK Chemistry Olympiad Committee, and he mentors students for the International Chemistry Olympiad both nationally and internationally

■ Course Content

Programme 1: 13th-26th July, 2025 (40-hour course, 2 office hours)
Programme 2: 27th July - 9th August, 2025 (40-hour course, 2 office hours)

This course lets participants explore advanced topics in physical and organic chemistry, each of which are fundamental to your studies of a chemistry degree. The course is built on concepts that you will be familiar with from school curriculum. We will quickly extend your knowledge in the fields of atomic and molecular orbital theory, thermodynamics, kinetics and organic reactivity to give you a significant head start in your university education. You will be able to practice your experimental skills as well through a practical class in physical chemistry. We are looking forward exploring the highlights of first year undergraduatelevel Chemistry curriculum with you!

* List of prerequisite knowledge:
Confidence with algebraic manipulation of expressions, including logarithms
A knowledge of differentiation will be helpful but is not necessary
Familiarity with chemistry of secondary-school level (e.g. representations of molecules and chemical bonding, recognise terminology such as “enthalpy”, some experience handling glassware)
* Test your knowledge of the prerequisites! Can you answer the questions below?
1. Calculate the volume of 0.1 molar sulfuric acid necessary to neutralise 25.6 grams of calcium hydroxide.
2. Rearrange
3. Draw a structural formula for propanoic acid and but-1-enol.
* Fitzwilliam College reserves the right to changes to the course content or the course instructor.