Pure mathematics studies the properties and structure of abstract objects, [1] such as the E8 group, in group theory. This may be done without focusing on concrete applications of the concepts in the physical world. Pure mathematics is the study of mathematical concepts independently of any application outside mathematics. These concepts may ...

Theoretical mathematics is the study of abstract mathematical structures which form the basic framework for the rest of the mathematical sciences. In large part, theoretical mathematics is inspired by intellectual curiosity.

This is a list of mathematical theories.

2024年12月27日 · Theoretical mathematics, also known as pure mathematics, is the branch of mathematics that seeks to uncover and understand abstract mathematical truths and principles. It involves the development and exploration of mathematical theories and models without necessarily being bound by physical reality or specific applications.

This course covers the fundamentals of theoretical mathematics with a particular focus on writing clear and rigorous mathematical proofs. The course introduces mathematical logic, set theory, function theory, equivalence relations, cardinality, and the Axiom of Choice.

Course Description This course covers the foundations of theoretical mathematics and analysis. The principal topics of the course include fundamentals of logic, sets, functions, number systems, order completeness of the real numbers and its consequences, and convergence of sequences and series of real numbers. Logic, quantiers and proof techniques.

Its purpose is to search for a deeper understanding and an expanded knowledge of mathematics itself. Traditionally, pure mathematics has been classified into three general fields: analysis, which deals with continuous aspects of mathematics; algebra, …

2024年12月9日 · The Theoretical Mathematics Major is offers broad training in mathematics to provide a foundation for understanding and utilizing mathematical concepts, techniques, and skills in a wide range of settings.

Modern mathematics is nearly characterized by the use of rigorous proofs. This practice, the result of literally thousands of years of refinement, has brought to mathematics a clarity and reliability unmatched by any other science.

If you are interested in pursuing a graduate degree in mathematics or you enjoy mathematics and are looking to advance your knowledge, consider the theoretical mathematics option.