Mathematics

Information is a fundamental concept in the world around us that can be investigated from several perspectives. The mathematical theory of information provides a framework for a formal description and interpretation of information. In many ways, this mathematical framework (its applications and the interpretations it provides) is based on concepts from probability theory and statistics. This course provides students with an introduction to the field of information theory. Students will learn to apply and interpret a wide range of concepts from statistics and probability theory to develop, model, and understand the concept of information, as well as related ideas, in a structured and organized way. Many of the tools of statistics and probability theory students encounter in the course should be familiar to them from introductory or intermediate statistics courses, while other concepts might be new.

This course provides a detailed introduction to complex function theory which interrelates the geometric and analytic aspects. A principal goal is Cauchy’s famous integral theorem and its many consequences.

This is a second course in real analysis at the University of Edinburgh and builds on ideas in the analysis portion of Fundamentals of Pure Mathematics. The course begins with sequences and series of real numbers, introducing the concept of Cauchy sequences and results for bounded sequences. Subsequently, sequences and series of functions are introduced and concepts of uniform convergence and power series are discussed. The concept of Lebesgue integral on real line is then developed. Finally, the rudiments of Fourier series are introduced.
 

This course introduces students to the statistical computing and programming, with the main focus on R, Python, and SAS. Students learn basic computing and programming concepts including scripting, variables, expressions, assignments, control structures, and data structures. On the statistical side, they will learn to load raw data, make numerical and graphical summaries of data, and conduct various estimation and testing procedures. Topics include descriptive statistics, statistical estimation, robust estimation, categorical data analysis, testing hypotheses, ANOVA, regression analysis, performing resampling methods and simulations. Some basic knowledge of R is assumed.

The use of computers is increasingly pervasive in all areas of mathematics. This course introduces the foundational concepts of programming and some of the many computational tools in common use by mathematicians.

This course explores both theoretical and practical aspects of cryptography, authentication, and information security. Students learn the relevant mathematical techniques associated with cryptography, the principles of cryptographic techniques and how to perform implementations of selected algorithms in this area, and explore the application of security techniques in solving real-life security problems in practical systems.