Interaktivní osnova

This is an introductory course on computer-aided mathematics, with a particular focus on computing and programming using SageMath. SageMath is a free, open-source software designed for mathematics and informatics, built on Python as its core language. 

This course complements the material covered in the first two mathematics block courses (MDA101-MAD102), and assumes no prior programming experience.

We will focus on implementing mathematical concepts and solving problems using SageMath (with some use of Matlab), while learning to design simple models for practical applications.

We shall shape the individual weeks together.  The work will be based on individually solved tasks and discussions, covering the following schedule: 

• An overview of basic concepts of SageMath (Sage as a calculator) and standard Sage functions  (1 week);  
• Python variables, symbolic variables and applications (1 week);  
• Elementary programming with Sage (1 week);  
• One-variable functions, 2D plotting,  and  basic solving techniques  (1 week);  
  
• Sets, combinatorics and probabilities (1 week); 
• Plane geometry, relations, mappings and difference equations (1 week);  
• Matrix calculus and linear systems (Gaussian elimination) (1 week); 
• Eigenvalues, eigenvectors, diagonalization and quadratic forms (1 week);
• Linear programming, Markov processes and the Matplotlib library in SageMath (1 week);  
• Polynomial interpolation and applications (1 week);
  
• Limits of functions, continuous functions and derivatives (1 week); 
• Series,  Taylor series and integrals  (1 week); 
• Numerical differentiation and numerical integration, Fourier series (1 week).

The main material for this course will be available online via CoCalc (https://cocalc.com)