Define the object
Students should know what a symbol refers to before they are asked to manipulate it.
Teaching
Make the objects visible first.
I prefer teaching that begins with clear definitions and concrete mathematical objects, then moves toward examples, reasoning, computation, and problems that require students to make their own connections.
Teaching approach
Understanding before shorthand.
These are the principles I try to carry into notes, exercise sheets, and classroom discussion.
Use examples as evidence
Examples should expose the idea and its limits, not merely decorate a definition.
Build difficulty gradually
Exercises can begin accessibly and still lead toward proof, abstraction, and open reasoning.
Use computation with purpose
Computation is most useful when it reveals structure or tests an idea that has already been made clear.
Experience
Courses and teaching work
Selected university teaching, exercise classes, and curriculum work.
University of Warsaw · Introduction to Topological Data Analysis
Exercise classes built around guided theoretical and computational problems, with exercise sheets designed to support discussion and problem solving in person.
University of the Philippines Baguio
Teaching Associate for Elementary Analysis II and Introduction to Calculus; module writing and revision for Elementary Analysis I; and a bridging lecture for students preparing for Algebraic Structures I.
Resources
Material meant to be reused.
Older presentations remain available while newer exercise material and mathematical notes are being reorganised into clearer resources.
Algebra
Group Theory
A lecture presentation introducing core ideas from group theory.
Topological data analysis
Exercise Bank
A growing collection of theoretical and computational exercises intended for students with different levels of mathematical experience.