Introduction to Scientific Computing

Introduction to Scientific Computing#

https://oist.github.io/iSciComp/

Kenji Doya
August 2023 in Paris

Aim of this Book#

This book aims to provide students from non-computational backgrounds with the basic knowledge and practical skills of computing that are required in almost all fields of science today.

It also tries help students’ intuitive understanding of basic mathematical concepts like eigenvalues and stability through computation and visualization.

Python is used as the standard programming language, but the concepts covered can be helpful also in using other computing tools for data analysis and simulation.

Jupyter Book#

This book is made by Jupyter Book (https://jupyterbook.org). An important feature is that you can download the source codes as Jupyter Notebook by the Download icon on the top right corner of each chapter.

Rather than just reading the html or pdf text, please run the codes, change parameters, apply your own data, and modify the codes to see how the algorithms really work (or fails).

Book Contents#

Chapter

Topic

Items covered

1

Introduction to Python

python, jupyter; data types, for loop

2

Visualization

matplotlib

3

Vectors and matrices

numpy; eigenvalue/vector

4

Functions and classes

name space, object oriented programming

5

Iterative computation

Newton method, discrete-time dynamics

6

Ordinary differential equation

scipy; Euler method, stability

7

Partial differential equation

finite-difference method

8

Optimization

gradient descent, Gauss-Newton method

9

Sampling methods

Monte Carlo methods, evolutionary algorithms

10

Software management

version control system, GitHub

Why Computation?#

  • Theoretical analysis often requires simplifying assumptions.

  • Thought experiment is limited/biased by the experimenter’s thinking.

  • Huge data set is impossible to comprehend withtout numerical processing.

  • …

Which Tools to Use#

There are a bunch to programming languages and tools to choose from.

General programming languages#

  • Fortran

  • C

  • C++

  • Java

  • MATLAB

  • Python

Special purpose tools#

  • Statistics: SPSS, S, R,…

  • Genomics: BLAST,…

  • MRI: SPM, VBM,…

  • Neuroscience: NEURON, NEST,…

How to select?#

  • Satifsy your present need?

  • Future usability

  • User community

How to Learn?#

  • Textbooks

  • Online documents

  • Online courses

  • Read experts’ codes!

  • Modify for your needs

  • Try coding from scratch

  • …

References#

Python#

Scientific Computing#

Math#

Table of Contents#

Contents