Mathematical modeling in the context of "Engineering"

Biology is the scientific study of life and living organisms. It is a broad natural science that encompasses a wide range of fields and unifying principles that explain the structure, function, growth, origin, evolution, and distribution of life. Central to biology are five fundamental themes: the cell as the basic unit of life, genes and heredity as the basis of inheritance, evolution as the driver of biological diversity, energy transformation for sustaining life processes, and the maintenance of internal stability (homeostasis).

Biology examines life across multiple levels of organization, from molecules and cells to organisms, populations, and ecosystems. Subdisciplines include molecular biology, physiology, ecology, evolutionary biology, developmental biology, and systematics, among others. Each of these fields applies a range of methods to investigate biological phenomena, including observation, experimentation, and mathematical modeling. Modern biology is grounded in the theory of evolution by natural selection, first articulated by Charles Darwin, and in the molecular understanding of genes encoded in DNA. The discovery of the structure of DNA and advances in molecular genetics have transformed many areas of biology, leading to applications in medicine, agriculture, biotechnology, and environmental science.

Neuroscience is the scientific study of the nervous system (the brain, spinal cord, and peripheral nervous system), its functions, and its disorders. It is a multidisciplinary science that combines physiology, anatomy, molecular biology, developmental biology, cytology, psychology, physics, computer science, chemistry, medicine, statistics, and mathematical modeling to understand the fundamental and emergent properties of neurons, glia, and neural circuits. The understanding of the biological basis of learning, memory, behavior, perception, and consciousness has been described by Eric Kandel as the "epic challenge" of the biological sciences.

The scope of neuroscience has broadened over time to include different approaches used to study the nervous system at different scales. The techniques used by neuroscientists have expanded enormously, from molecular and cellular studies of individual neurons to imaging of sensory, motor, and cognitive tasks in the brain.

Mathematical chemistry is the area of research engaged in novel applications of mathematics to chemistry; it concerns itself principally with the mathematical modeling of chemical phenomena. Mathematical chemistry has also sometimes been called computer chemistry, but should not be confused with computational chemistry.

Major areas of research in mathematical chemistry include chemical graph theory, which deals with topology such as the mathematical study of isomerism and the development of topological descriptors or indices which find application in quantitative structure-property relationships; and chemical aspects of group theory, which finds applications in stereochemistry and quantum chemistry. Another important area is molecular knot theory and circuit topology that describe the topology of folded linear molecules such as proteins and nucleic acids.