Just to see how the interactions of **Biology and Applied Mathematics** may proceed in the future, it is helpful to map the present landscapes of Biology and Applied Mathematics. Engineering in Kenya has more articles.

A biological landscape may be drawn as a rectangular table with different columns for different questions and different rows for different biological domains. Biology asks six types of questions. What is it for?How is it built? What goes wrong?How does it work? How is it fixed? How did it begin? These are questions, respectively, about structures, pathologies,mechanisms, origins,repairs, and purposes or functions.

In Biology and Applied Mathematics, the former teleological interpretation of purpose has been substituted for an evolutionary angle/ perspective. Biological domains, or levels of organization in Biology and Applied Mathematics, include molecules, organs,cells, tissues, individuals, communities,populations, ecosystems or landscapes, and the biosphere. Many biological research problems can be categorized as the combination of one or more queries directed to one or more domains.

# Research for Biology and Applied Mathematics

In addition, biological research questions in Biology and Applied Mathematics have important dimensions of time and space. The timescales of great importance to Biology and Applied Mathematics range from the super fast processes of photosynthesis and reproduction to the millions of years of living evolution on earth.

The relevant spatial timescales in Biology and Applied Mathematics range from the molecular to the cosmic (cosmic rays are said to have played a big role in the evolution on earth). The queries and domains of biology behave differently on different temporal and spatial timescales. The challenges and the opportunities that biology offers mathematics arise because the different units at any given level of the biological organization are heterogeneous.

This in Biology and Applied Mathematics therefore says that the outcomes of their interactions (sometimes called ensemble properties or emergent phenomena) on any random temporal and spatial timescale may be substantially affected by the heterogeneous nature and interactions of biological forms at lower and higher levels of the biological organizations and at smaller and larger temporal and spatial timescales.

## Relation in Biology and Applied Mathematics

The relationship between Biology and Applied Mathematics can be in the structure of the two disciplines. The structure of applied mathematics is better seen as a tetrahedron i.e. a pyramid with a triangular base, than as a matrix with spatial and temporal dimensions. Mathematical imagery, such as the matrix for biology and a tetrahedron for applied mathematics, is useful even when trying to visualize the landscapes of Biology and Applied Mathematics. The four main hills of the applied mathematics landscape are

- Algorithms,
- Theories and models (which includes all pure mathematics),
- Data structures, and
- Computers and software.

Data structures in Biology and Applied Mathematics involves ways to organize data, such as the matrix used to describe the biological landscape. Algorithms are procedures useful for manipulating symbols. Some algorithms are used to analyze models, others to analyze data. Theories and models, including the basic theories of pure mathematics in Biology and Applied Mathematics, are used to analyze both data and even ideas. Mathematics and mathematical theories provide a rating ground for ideas in which the strength of the competing theories can be measured. Computers and software are very important, and frequently the most visible vertex of the applied mathematics landscape. However, cheap and easy computing increases the importance of theoretical comprehension of the results of the computation. Theoretical comprehension/ understanding in Biology and Applied Mathematics is required as a check on the great risk of errors in software, and to close the big gap between the computational results and understanding or insight.

### Conclusion on Biology and Applied Mathematics

The landscape of research in Biology and Applied Mathematics contains all combinations of one or more domains, biological questions, spatial scales and time scales with one or more algorithms, data structures, means of computation (typically the software and hardware), and theories or models. E.g. the following example from the biology of cancer illustrates such a combination: -

The question ‘how does it work?’ is approached in the domain of cells (specifically, human cancer cells) with algorithms for correlation and hierarchical clustering in *Biology and Applied Mathematics*.