Principles of Mathematics and Engineering Sciences

The idea of proof is the guiding light of mathematics. No matter how many examples you can give for 

The engineering sciences (such as statics, dynamics, strength of materials, transport processes, and electricity) can be described as refinements or adaptations of physical fundamentals. Some others, however (such as information theory and control systems), are conceptual in nature and lend themselves well to mathematical manipulation. Hence relevant mathematical attributes have been included here along with engineering sciences not directly related to physics. 

Although mathematical models are, at best, idealizations, and suffer from a certain degree of unreality, they can still be used to gain understanding and to yield predictions. Engineering sciences are highly dependent on these mathematical models their idealizations are necessary for simplified analyses of biological characteristics and responses. 

Mathematics is not by itself a science, and so its contribution to the biological sciences is different from physics and chemistry. It is through mathematics that concepts and organization of principles can be applied mathematics provides the tools for this process. As some required concepts are not entirely math atical, we must also draw upon the engineering sciences such as control theory to help understand biological function. In this section, material relevant to biological systems is presented. 

Appropriate responses require control systems, and each of these needs sensors, actuators, processing, and information pathways. Survival requires that adequate responses are made to environmental stimuli. Information important to the biological unit must be sensed, sent on to some structure that determines the appropriate response, and then action taken. These controls may be simple or elaborate, but the fact that they occur at all in biology is a sign of life. See Sections 4.3 through 4.5. 

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