Mathematical models I.

Description:

The aim of the course to introduce the first-year students to the Python programming via mathematical and data-driven problems. We use Python, since it is widely used in the industry and even research, proper for working with algorithms and data-related problems, enables symbolic computation via special packages and supported by the most population notebook framework, the Jupyter. The course is driven by the following aspects: mathematics and programming are used at the same time, fulfilling the industrial standards via working with modern infrastructure and forcing working in groups, applying symbolic and interactive tools for deepening mathematical topics.

Curriculum:

I. Handling tabular data with numpy

OOP 1.: class, instance, constructor, methods, attributes
basics of Python: variables, data structures, data types
numpy: vectorized operations, broadcasting, logical indexing

II. Symbolic calculations with sympy

algebra: polynomials, solving equations on different domains
linear algebra: linear equations, matrices
calculus: differentiation, integration

III. Interactive applications, visualization practices

geometric transformations
functions, transformations on functions
2D, 3D graphics

IV. Handling tabular data with pandas

pandas: reading data, transformations, visualizations

V. Basics of object-oriented programming in Python

OOP 2.: inheritance, static method, visibility
clean code: documentation, PEP8 design, exception handling

Evaluation:

Quizzes (20 pts)
Project about coding for an topic from elementary mathematics (30 pts)
Complex project (group work, implementation + presentation) (50 pts)