Mathematics & Programming
Beschrijving
Course goals
1. Carry out the following computational tasks:
- Perform standard algebraic calculations
- Perform standard calculus calculations
- Differentiate functions with multiple variables
- Approximate functions using a Taylor series
- Solve simple differential equations
- Perform basic operations with vectors (addition/subtraction/multiplication)
- Calculate basic statistical descriptors (mean, standard deviation, standard error)
- Perform basic probabilistic calculations
- Work with probability distributions (binomial, continuous, Gaussian)
2. Carry out the following programming tasks in Python:
- Perform basic data handling, including the use of variables and function definitions, numbers, strings, lists, dictionaries and tuples
- Use Python to read and write files
- Plot data and functions in Python
- Write and execute basic Python programs including multiple functions and use loops and conditional statements to control the flow of execution
- Use available resources such as code documentation, online searches and AI queries to aid in programming
Content
In this course students are introduced to mathematical and programming skills that are employed by researchers in the Molecular and Biophysical Life Sciences to analyse and integrate data and to understand the physics of living systems.
Introduction:
Mathematical and programming skills are essential for systematically handling, analysing and integrating data generated using modern analytical techniques. In addition, solid mathematical knowledge and skills are required to understand the physical principles and theories that are used to establish a mechanistic understanding of living processes.
Set up of this course:
This course is divided into two parts that run in series. The mathematics part of the course consists of nine lectures that cover: basic algebra, goniometry, differentiation and integration (including functions of multiple variables), limits, (partial) differential equations (first order and second order), Taylor expansion, basic probability theory and statistics and vectors (including dot product and cross product). Each lecture is followed by a supervised practical session.
The programming part consists of six lectures that introduce the basics of programming by discussing the modular structure of programs (modules, functions, loops), different data types and variables, as well as good practices and the use of available resources. After each lecture, students work individually on a series of practical coding assignments that will familiarize them with the basics of programming in Python during supervised tutorials, where regular instruction and feedback is provided. The programming part ends with a group project as final assignment.
Relation to other courses:
The foundation laid in this course serves as a stepping stone for further development of mathematical and programming skills throughout the curriculum.
Teaching format course (estimation):
Lectures 30%
Tutorials 30%
Self study 40%
In the mathematics part each lecture is followed by a practical session to provide opportunities for students to practice and engage actively with the content delivered in the lectures and textbook so that deeper learning occurs.
In the programming part each lecture is complemented with knowledge clips and an interactive online environment on the subject followed by learning-by-doing in practical computer sessions. During all practical sessions, an instructor circulates among the students, answering and asking questions, pointing out subtle details or possible applications, reviewing exercises, and generally guiding students’ learning.
Grading (check course manual for details):
Mathematics part:
- Written exam (60%)
Programming part:
- An exam (24%)
- A final group assignment (16%; students must hand in their code and demonstrate functionality)
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