Mathematics is playing an increasing important role in society and the sciences, enhancing our ability to use models and handle data. While pure mathematics is mostly interested in abstract structures, applied mathematics sits at the interface between this abstract world and the world in which we live. This area of mathematics takes its nourishment from society and science and, in turn, provides a unified way to understand problems arising in diverse fields.
This Very Short Introduction presents a compact yet comprehensive view of the field of applied mathematics, and explores its relationships with (pure) mathematics, science, and engineering. Explaining the nature of applied mathematics, Alain Goriely discusses its early achievements in physics and engineering, and its development as a separate field after World War II. Using historical examples, current applications, and challenges, Goriely illustrates the particular role that mathematics plays in the modern sciences today and its far-reaching potential.
Shortly after receiving his Ph.D. from the University of Brussels, Alain Goriely joined the Department of Mathematics at the University of Arizona. In 2010, he moved to the University of Oxford as the Chair of Mathematical Modelling. He is currently the Director of the Oxford Centre for Industrial and Applied Mathematics. At the scientific level, he is an applied mathematician with broad interests in mathematics, mechanics, sciences, and engineering, which led him to collaborate closely with researchers from many disciplines. His current research includes the mechanics of biological growth and its applications to plants and physiology; the modelling of new photovoltaic devices; the foundations of elasticity; the modelling of cancer; the mechanics of the human brain; and more generally the development of mathematical methods for applied sciences.
1: What's so Funny 'bout Applied Mathematics? Modelling, Theory, and Methods
2: Do You Want to Know a Secret? Turkeys, Giants, and the Atomic Bomb
3: Do You Believe in Models? Simplicity and Complexity
4: Do You Know the Way to Solve Equations? Spinning Tops and Chaotic Rabbits
5: What's the Frequency, Kenneth? Waves, Quakes, and Solitons
6: Can You Picture That? X-rays, DNA, and Photos
7: Mathematics, What is it Good for? Quaternions, Knots, and more DNA
8: Where are We Going? Networks and the Brain