Cambridge Mathematics Summer School
Mathematics is a powerful tool and its influence can be found in almost all walks of life. From engineering, medicine and the sciences to finance, economics and business, maths is a broad subject that offers many avenues.
Some of our most influential thinkers and most prominent theories have their grounding in mathematics. By opting to study mathematics, students are placing themselves in an excellent position to embark on a challenging yet highly rewarding career.
The gulf between mathematics at undergraduate and school level can be large. This often leaves students unprepared and overwhelmed by tertiary education maths. Cambridge Immerse addresses this imbalance by introducing students to undergraduate level content in an comprehensible and engaging manner. Students leave with a new found confidence in approaching challenging material, something that will prove invaluable at university.
Mathematics summer courses held in Cambridge University colleges
The design of courses at Cambridge Immerse are formulated to give students a solid foundation in the principles of mathematics. Participants will learn how to comprehend mathematical language which can act as a springboard to future learning.
From here participants are able to progress to more advanced content and begin to apply it to real life scenarios. Although the material is challenging, tutors are specifically recruited on their ability to portray complex material in an engaging and understandable manner, something that is crucial when considering the nature of a mathematics course. In addition to this, prior to the course commencing students will be instructed to complete preparatory material in order for them to feel confident approaching the new material
What will I study during the Cambridge Mathematics Summer School?
The engaging two week summer school programme encompasses 10 diverse topics which will teach you the both the theory and practice of mathematics, taught by experts from Cambridge Immerse. Here is just a taster of what is on offer on the course:
Constructive mathematics is the mathematics of iterative methods, which arise everywhere in the subject. For example, Niels Abel famously proved that we cannot in general write down the solution to polynomial equations of degree 5 or higher; but of course there will be cases where we need to know the answer! The first place to turn to is an iterative method – a process in which we continually apply the same “action” to a given input, in the (mathematically justified) hope that this process eventually outputs something close to the true answer that we seek.
However, in the context of real world applications, imagine that the solution of this problem is an
essential parameter in the design of say, a satellite or a heavy load carrying bridge. In this case, you need to be sure that the approximate solution is sufficiently close to the true solution – this requires careful, rigorous, and rewarding mathematical analysis.
The famous “Monty Hall problem” will tell you that the theory of probability is not always as simple as you may think; what does it really mean to say that two events occur independently (successively flipping a coin for example)? What is your probability of success in a game of dice? There are numerous problems in probability, however where the events are not independent, for example: two golfers (A and B) are at a driving range, their golf balls are both different, but they have ended up in the same bucket. After picking out 5 balls at random, what is the probability that all of the balls belong to “golfer A”? Of course, we need more information to determine the answer in this case, but it is immediately clear that this “conditional probability” makes things more complex.
In one dimension, the integral of a function gives the area under a curve, and in two dimensions, the volume under a surface. Integration (often seen as the counterpart of differentiation) is one of the main tools of calculus, since one can use integration in many variables, generalising the intuitive notion of area and volume to that of higher dimensional objects (hypercubes, for example). We will introduce some powerful tools in integration, in particular, integration by parts and integration by substitution. We will also look into the approximation of integrals, for example by the trapezium rule; the approximation of integrals or “numerical integration” comes up a lot in real world applications, where one will need to accurately approximate the value of an integral, but will only be given a finite set of data points.
What are the benefits of enrolling on the Cambridge Immerse Mathematics Course?
If you are considering studying maths at university, Cambridge Immerse is the perfect first step to success.
Students benefit from 40 hours of expert tuition in a setting that has been specifically designed by expert tutors to accelerate the learning process and optimise student engagement. This means that we purposefully keep class sizes small in order to allow tutors to address the needs of each individual student whilst also creating an atmosphere where participants feel encouraged to involve themselves in debate and discussion. Tutors are carefully chosen based on their experience tutoring undergraduates and their abilities to make challenging content understandable to our students.
Quick Mathematics summer course facts and stats:
- Maximum tutorial size: 12 students
- expert teaching from university tutors
- Skills development workshops
- Inclusive of excursions
- Reside in a central University of Cambridge college
- Develop your own sketch book / portfolio
- Dedicated university and subject specific advice
- A variety of carefully planned skills workshops
- Inclusive of all excursions and extracurriculars
- Diverse range of international participants
- Participant Assessment
- Certificate of Participation
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