This course gives a basic grounding in several key areas of mathematics; calculus, linear algebra, basic skills, statistics and additionally will provide an introduction to Matlab. These topics are grouped into four strands. As students enter this course with differing backgrounds, the aim here is to bring everyone up to a level which will enable them to engage with the later compulsory courses and electives. An initial self- assessment will be completed by all students and the teaching will be adapted based on these results. Finally, the aim of this course is that students can not only solve mathematical problems when presented with them in a mathematical formulation, but also that students are able to independently generate simple mathematical formulations of biological problems and then solve them.
Calculus Students should be able to: ● Appreciate the difference between functions using discrete and continuous time and be able to suggest when each is appropriate. ● Be able to calculate limits ● Be able to integrate and differentiate a wide range of functions ● Solve basic differential equations ● Understand the use of calculus and be able to select the correct method for solving a problem framed solely in a biological context Basic skills and statistics Students should be able to: ● Distinguish between the forms of linear, polynomial, rational, exponential and logarithmic functions and know their properties. ● Work with real and complex numbers, understand their properties and graphical representations. ● Sketch graphs, using function, its first derivative, and the second derivative. ● Apply different types of curve fitting in the biological context. ● Understand the basic principles of probability including Bayes theorem. ● Understand the definitions of discrete and continuous variables, probability and cumulative distribution functions. ● Calculate expectation, variance, covariance and correlation. ● Appreciate the basic components of hypothesis testing. Linear algebra Students should be able to: ● Solve systems of linear equations, understand different types of possible solutions, and use the ideas in applied problems. ● Perform the common operations of matrix algebra and use them to solve applied problems. ● Compute determinant of a square matrix and understand its properties. ● Understands the concepts of linear independence, spanning set, basis, rank of matrix, vector space and subspace, and linear transformation. ● Understand eigenvectors and eigenvalues, how they characterize the action of some linear transformations and how to used them to solve applied problems. ● Use the ideas of inner products, orthogonality, and projections to determine least square solutions to a linear systems. Matlab Students should be able to: ● Use Matlab to import/export data and produce figures based on this data ● Understand and run code provided to them, and interpret the output ● Computationally check results from any of the other strands of the course ● Adapt code provided to them to improve or alter its functionality
There are many good textbooks for all areas of this course, in particular due to their emphasis on the connection between mathematics and biology and their many biological examples, we recommend; ● Calculus for biology and medicine Claudia Neuhauser (2014) Pearson. ● Elementary linear algebra - Applications version Howard Anton and Chris Rorres (10th edition) John Wiley&Sons, Inc. ● Mathematics for the life sciences Erin N. Bodine, Suzanne Lenhart and Louis J. Gross (2014) Princeton University Press