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▪ Abstract  Since mathematical sociology was firmly established in the 1960s, it has grown tremendously. Today it has an impressive scope and deals with topical problems of social structure and social change. A distinctive feature of today's use of mathematics in sociology is the movement toward a synthesis between process, structure, and action. In combination with an increased attention to social mechanisms and the problems of causality and temporality, this synthesis can add to its relevance for sociology in general. The article presents recent advances and major sociological research streams in contemporary sociology that involve the application of mathematics, logic, and computer modeling.

My educational career path began as an elementary school teacher, then as an assistant principal, and now as a principal. With the educational experiences that I had at each level of my career, I was certain I would be able to handle an increase in the mathematical rigor presented to our students through the new Mathematics Standards of Learning for Virginia Public Schools (SOL) [1]. I found that, yes, I was able to understand the rigor. However, I found the challenge was providing the needed assistance to bring about results that would ultimately help our teachers and students be successful. I knew that something was needed, but what that something was I was not sure. Fortunately, Richneck Elementary was provided a wonderful opportunity of being assigned a mathematics coach for three years by way of a grant that the Newport News Public School division was awarded to support military-connected students. In addition, the grant supported teachers to work toward their Mathematics Specialist degree. As a result, Karen Joos, Mathematics Coach, received her master's in education with an endorsement as a Mathematics Specialist. David Hundley, Mathematics Coach Facilitator, provided support for coaches under this grant. This article will provide a road map for the journey: working with the mathematics coaches and understanding their processes, promoting my leadership philosophy in relation to the new rigor of the state standards, improving communication through lessons learned, and identifying the collaboration process to achieve the best results for the school and community.

This Element explores the relationship between phenomenology and mathematics. Its focus is the mathematical thought of Edmund Husserl, founder of phenomenology, but other phenomenologists and phenomenologically-oriented mathematicians, including Weyl, Becker, Gödel, and Rota, are also discussed. After outlining the basic notions of Husserl's phenomenology, the author traces Husserl's journey from his early mathematical studies. Phenomenology's core concepts, such as intention and intuition, each contributed to the emergence of a phenomenological approach to mathematics. This Element examines the phenomenological conceptions of natural number, the continuum, geometry, formal systems, and the applicability of mathematics. It also situates the phenomenological approach in relation to other schools in the philosophy of mathematics-logicism, formalism, intuitionism, Platonism, the French epistemological school, and the philosophy of mathematical practice.