The CCIMI invites applications for fully funded PhD studentships in Mathematics of Information. We held an Open Day on Thursday 15th November. Where prospective students came along and discovered more about our Cambridge Mathematics of Information (CMI) PhD programme. Further information is available on our website.
Information is processed, organised and structured data. It provides context for data and enables decision making process. For example, a single customer’s sale at a restaurant is data – this becomes information when the business is able to identify the most popular or least popular dish.
CCIMI Fully Funded PhD Studentships in the Mathematics
The advance of data science and the solution of big data questions heavily relies on fundamental mathematical techniques and in particular, their intra-disciplinary engagement. This is at the heart of the center for the Mathematics of Information which involves mathematical expertise ranging from statistics, applied & computational analysis, to topology and discrete geometry – all with the common goal of advancing data science questions.
See Also: LMS Fully Founded Ph.D. Studentship at London in UK
Alongside this, specific questions which feed into fundamental methodology development arise naturally in applications we focus on in interdisciplinary engagements with, for instance, economists and social scientists on questions about financial markets and the internet, with physicists and engineers on software and hardware development questions in the context of security, imaging, and structured data processing, as well as biomedical scientists on data science in healthcare and biology.
More info – CCIMI invitation on Funded PhD Studentships
Both this general advancement of data science, and its applications to specific questions is realised by key mathematical expertise represented in the institute including:
- statistics,
- analysis,
- stochastic
- probability
- sparsity
- functional analysis
- discrete geometry
- topology
1. Statistics
Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as “all people living in a country” or “every atom composing a crystal”. Statistics deals with every aspect of data, including the planning of data collection in terms of the design of surveys and experiments.
2. Analysis
Analysis means breaking something down into its various elements and then asking critical thinking questions such as WHY and HOW in order to reach some conclusions of your own.
It is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle, though analysis as a formal concept is a relatively recent development.
3. Stochastic
Stochastic refers to a variable process where the outcome involves some randomness and has some uncertainty. A variable or process is stochastic if there is uncertainty or randomness involved in the outcomes. Stochastic is a synonym for random and probabilistic, although is different from non-deterministic.
Stochastic processes are widely used as mathematical models of systems and phenomena that appear to vary in a random manner. Examples include the growth of a bacterial population, an electrical current fluctuating due to thermal noise, or the movement of a gas molecule.
4. Probability
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur. Or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty.
5. Sparsity
The number of zero-valued elements divided by the total number of elements (e.g., m × n for an m × n matrix) is sometimes referred to as the sparsity of the matrix. Conceptually, sparsity corresponds to systems with few pairwise interactions. Controlled sparsity occurs when a range of values of one or more dimensions has no data; for example, a new variable dimensioned by MONTH for which you do not have data for past months. The cells exist because you have past months in the MONTH dimension, but the data is NA.
6. Functional analysis
Functional analysis is a model of psychological formulation designed to understand the functions of human behaviour. It is a way of helping us to understand why someone is acting in a certain way. So for this example, imagine you are a psychologist working at a medium secure unit.
It is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. inner product, norm, topology, etc.) and the linear functions defined on these spaces and respecting these structures in a suitable sense. The historical roots of functional analysis lie in the study of spaces of functions and the formulation of properties of transformations of functions such as the Fourier transform as transformations defining continuous, unitary etc. operators between function spaces. This point of view turned out to be particularly useful for the study of differential and integral equations.
7. Discrete geometry
Discrete geometry and combinatorial geometry are branches of geometry that study combinatorial properties and constructive methods of discrete geometric objects. Most questions in discrete geometry involve finite or discrete sets of basic geometric objects, such as points, lines, planes, circles, spheres, polygons, and so forth. The subject focuses on the combinatorial properties of these objects, such as how they intersect one another, or how they may be arranged to cover a larger object.
Discrete geometry has a large overlap with convex geometry and computational geometry, and is closely related to subjects such as finite geometry, combinatorial optimization, digital geometry, discrete differential geometry, geometric graph theory, toric geometry, and combinatorial topology.
8. Topology
In mathematics, topology is concern with the properties of a geometric object that are preserve under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or passing through itself.
A topological space is a set endow with a structure, called a topology, which allows defining continuous deformation of subspaces, and, more generally, all kinds of continuity. Euclidean spaces, and, more generally, metric spaces are examples of a topological space, as any distance or metric defines a topology.
Topological insulators are a new state of quantum matter with a bulk gap and odd number of relativistic Dirac fermions on the surface. The bulk of such materials is insulating but the surface can conduct electric current with well-defined spin texture.
We welcome applications for studentships relating to projects and subject areas covering all aspects of the broad field of mathematics of information. Further information on some of the projects currently being investigated by students and faculty can be found on our website, linked here.
Eligibility
The academic requirements for entry to this PhD are a first-class honours degree. Awarded after a four-year course in mathematics or related subject. Or a three-year degree with a one-year postgraduate course on advanced mathematics or related subject. For further details on how to apply for this programme see the relevant entry on the website.
Funding
Fully funded PhD Studentships do include University Composition Fees. And maintenance for the duration of your course to match the RCUK minimum level. The scheme is open to applicants from all countries. Funding is the act of providing resources to finance a need, program, or project. While this is usually in the form of money, it can also take the form of effort or time from an organization or company. Generally, this word is use when a firm uses its internal reserves to satisfy its necessity for cash. While the term financing is use when the firm acquires capital from external sources.
Scholarship Description
- Applications Deadline: Sep 3, 2022
- Course Level: Studentships area unit out there to pursue Doctor of Philosophy programme.
- Study Subject: Studentships area unit awarded in fields of arithmetic of data.
- Scholarship Award: office offers:
- Fully funded Doctor of Philosophy Studentships does embody University Composition Fees.
- Maintenance for the length of your course to match the RCUK minimum level.
- The theme is hospitable candidates from all countries.
- Nationality: The theme is hospitable candidates from all countries.
- Number of Scholarships: ranges not given
- Scholarship may be taken within Britain
Route for application
Apply using the standard PhD application procedure via the University’s Graduate Admissions website.
Deadline
It is very strongly encouraging that applications are receive(d) by 3rd Sep 2022.
Shortlisted candidates will be interview(ed) – the date for interviews will be communicated once shortlisting has taken place.
Please contact https://bit.ly/3mCJIhU in the first instance for any inquiries about the applications process, and for any inquiries regarding the PPh.D.programme.
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