A branch of mathematics concerned with the properties of space that are preserved under continuous transformations.

A set of points equipped with a topology, defining how subsets relate to each other in terms of continuity.

A property of functions where small changes in input result in small changes in output, crucial for topological analysis.

A continuous function between topological spaces that has a continuous inverse, indicating a topological equivalence.

An interdisciplinary field that uses scientific methods and algorithms to extract insights from structured and unstructured data.

A method in data science that applies topological concepts to analyze the shape of data and uncover patterns.

The study of relationships and structures within networks, often using topological methods to optimize connectivity.

A field of mathematics focusing on the properties and applications of graphs, which are structures made of vertices and edges.

A subset of artificial intelligence that enables systems to learn from data and improve performance without explicit programming.

A systematic plan for conducting research, outlining methods for data collection and analysis.

Guidelines that ensure research is conducted responsibly, respecting the rights and well-being of participants.

The process of gathering and measuring information on targeted variables, crucial for empirical research.

The representation of data or concepts in a visual format to aid understanding and communication.

An in-depth examination of a particular instance or example, often used in research to illustrate broader principles.

The skill of effectively communicating research findings to an audience, emphasizing clarity and engagement.

A formal style of writing used in scholarly publications, characterized by evidence-based arguments and structured format.

A comprehensive overview of existing research on a specific topic, identifying gaps and guiding new research directions.

A document outlining the objectives, methodology, and significance of a proposed research project.

Additional resources that support a research report, such as appendices, charts, or datasets.

Questions or statements designed to encourage self-assessment and critical thinking about one's learning process.

A detailed document summarizing research findings, methodologies, and implications, adhering to academic standards.

The conduct, aims, or qualities that characterize a profession, including ethical behavior and commitment to quality.

The ability to convey ideas clearly and persuasively, ensuring the audience understands and values the message.

A category in mathematics that generalizes set theory, providing a framework for discussing topological spaces.

A branch of differential geometry that studies symplectic manifolds, which are essential in classical and quantum mechanics.