Algebraic Topology is a branch of mathematics which uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism. The word “Topology” comes from the Greek words “topos”, which means place, and “logos”, which means study. Topology is the study of the properties of spaces that are invariant (preserved) under deformations, twisting, and stretching. It is often said that a topologist is a person who cannot tell the difference between their doughnut and their coffee mug, since each can be continuously deformed to the other (each is a solid sphere with one handle).
Cryptography can be summarized at a high level as the theory and practice of controlling information. Simple examples of its applications can be found in many places in modern society-perhaps the most prominent is that of securing electronic commerce. Branches of cryptography touch many areas of mathematics and computer science, including algebra, number theory, combinatorics and complexity theory, to name a few.
Intelligent User Interface (IUI) is a study on the development of human-machine interfaces that work naturally to the users, as well as improve the efficiency and effectiveness of the interaction. The goal of IUI is basically fulfilled by applying various techniques from Artificial Intelligence, Machine Learning, and Statistics, such as knowledge representation and reasoning, user modeling, gesture recognition, natural language processing, etc.
Machine Learning is a field of study that focuses on automatically constructing models from a set of collected examples. The obtained model can be used to predict the properties of the data found in the future. For example, a credit card company may need a model to predict if a payment made through their credit card is fraud or not. Manually constructing a model takes huge efforts and it may miss some fraudulent behaviors. Machine Learning helps reduce the required efforts, and wisely utilize a large amount of collected data.
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