**Course Coordinator: **Assistant Professor Lu Lanyuan (email: LYLu@ntu.edu.sg)

**Academic Unit: **3 AU

**Availability:** Period 1 – Period 5

**Pre-requisite:** None

**Course Type: **BS-Major-PE (Self-paced course)

**Language of instruction:** English

**Teaching hours:** Lectures: 24 hours; Online Self-assessment Exercises: 12 hours

**Introduction:**

Interaction between mathematics and biology has a long history, but recently this interaction has become more intensive and extensive. One main reason is the explosion of data-rich information in biology, mainly due to the genomics revolution. In addition to enormous data being available, complexity of biological interaction in almost all fields—from embryology to ecology—has created problems which are impossible to solve without the use of mathematics. Most of these complex biological interactions may only be understood through a combination of mathematical, logical, physical/chemical, and computational tools.

The objective of this course is not to even touch upon any of these sophisticated mathematical tools. Rather, we will go back to the early days of biological research to recognize that some great discoveries in biology were possible only through application of mathematics. We will consider few biological phenomena that most of you are familiar with, such as Mendelian genetics, population genetics, gene mapping, bacterial mutation, and enzyme catalysis.

Our approach will be to proceed with a biological phenomenon and reach a point where we ‘get stuck’ until we use a mathematical tool to solve the problem and understand the phenomenon. While doing so, you will learn how to ‘translate’ a biological problem into ‘mathematical language’ called an equation. Then you solve the equation by using mathematical tools and arrive at a ‘solution’ which is one of the equations of life. Then you will apply the equation to life situation to test whether the equation has been able to unravel the mystery that you were concerned with at the beginning.

Regarding mathematical tools, you will not use anything more sophisticate than you have learned at the A-Level mathematics. These will include basic calculus, logarithm, and linear and exponential equations. **Please note:** The whole course material is available online. Please look at it while you register to make sure that the course is useful for you.

**Learning Objective: **

Because the topics will be presented in scientifically investigative style, the students will learn how to translate a biological problem into a simple mathematical language, and to solve and analyze the mathematics to retranslate into biological meaning.

They will learn to discuss the beauty, power and robustness of simple mathematical concepts in understanding biological phenomena.

They will learn to solve the numerical problems related to biology-mathematics cross-talk; and will be able to explain the inherent intimate relationship between the two areas.

A broad objective is to get rid of the unfounded fear of mathematics, and to look forward to undertake challenges related to quantitative biology.

**Content: **

Six biological topics have been selected covering enzyme to ecology. A short description of each equation and the learning outcomes from each topic has been given below. Every topic will be introduced with investigative approach to the point where mathematics comes in to solve the biological problem. The mathematical principles (equations) are rather simple and well within A-level category. On the other hand, these equations have contributed to the fundamental questions of twentieth century biology. Using each of these equations, the students have to solve numerical problems related to cross-talk between biology and mathematics. I must emphasize, the course is not meant to teach mathematics in any rigorous or systematic manner, because it is not a mathematics course; it is a biology course.

**Learning Outcome: **

The students will be able to translate a biological problem into a simple mathematical language, and to solve and analyze the mathematics to retranslate into biological meaning.

The students will be able to discuss the beauty, power and robustness of simple mathematical concepts in understanding biological phenomena.

The students will be able to solve the numerical problems related to biology-mathematics cross-talk; and will be able to explain the inherent intimate relationship between the two areas.

The students will get rid of the unfounded fear of mathematics, and will look forward to undertake challenges related to quantitative biology.

**Textbook / References: **

Any standard A-level book on mathematics and on biology.

***Prerequisites for Incoming Exchange Students:**Equivalent of A-Level Biology and Biology or Biotechnology major