Lectures in Pure Mathematics

Pure mathematics (fundamental mathematics) is mathematics that studies entirely abstract concepts. This has been a recognizable category of mathematical activity from the 19th century onwards, with the trend towards meeting the needs of navigation, astronomy, physics, economics, engineering, furthermore the pure mathematics is the study of the basic concepts and structures that underlie mathematics. Its purpose is to search for a deeper understanding and an expanded knowledge of mathematics itself. In practice there is much overlap in the activity of pure and applied mathematicians. To develop accurate models for describing the real world, many applied mathematicians draw on tools and techniques that are often considered to be "pure" mathematics. On the other hand, many pure mathematicians draw on natural and social phenomena as inspiration for their abstract research.