Tomasz Dudek

Introduction (PL)

A mathematics enthusiast and experienced tutor. In addition to my teaching skills in mathematics, I have a strong theoretical foundation, particularly in topology and geometry.

LinkedIn | Facebook | Mail me!$$\mathrm{Hom}(Y \otimes X,Z) \cong \mathrm{Hom}(Y,\mathrm{Hom}(X,Z))$$

Education

Jagiellonian University (2024 – currently)

Degree: PhD in Mathematics

PhD Topic: Invariant Structures on Homogeneous Spaces of Lie Groups.

Jagiellonian University (2021 – 2024)

Degree: MSc in Mathematics
Specialty: Pure Mathematics

Final grade: very good (5.0)
Recipient of Rector’s Scholarship in academic year 2021/2022.

Member of the Didactics Committee of the Mathematics Insitute in the academic year 2023/2024. Secretary of the Zaremba Society of Mathematicians-Students in the academic year 2023/2024.

Aside from my main studies, I also attended pedagogical courses.

Adam Mickiewicz University (2018 – 2021)

Degree: BSc in Mathematics
Specialty: Statistics and Data Analysis

Final grade: very good (5.0)
Recipient of Rector’s Scholarship in the academic years 2019/2020 and 2020/2021.

$$\int_{\partial M}\omega = \int_M d\omega$$

Professional Experience

I have been a professional tutor for almost four years. During this time, I have:

Helped a student prepare for entry exams to an Italian university.
Prepared students for contests (e.g., Konkurs Kuratoryjny, Olimpiada Matematyczna).
Conducted an intensive course for the Polish Matura exam.
Worked with students in home education.
Prepared students for the International Baccalaureate (IB AA SL/HL).
Ran a mathematics club.

Matplaneta (10.2023 – currently)

Conducting classes in Math Circle method for elementary school students.

Edu-Mat Skawina (09.2022 – currently)

Stationary job in Skawina with young students (ages 10-13).
Classes are conducted using interactive, workshop-style methods: EZO and MAT! PO-MOC.

Elephant Academy (10.2021 – 03.2024)

Individual tutor – both in-person and online.

$$\sqrt{n}(\bar{X}_n - \mu) \overset{d}{\longrightarrow} \mathcal{N}(0,\sigma^2)$$

Academic teaching

Below is a full list of my academic classes. Hopefully, this section will expand soon.

Linear Algebra 1 (summer term, 2024/2025)

$$\chi(M) = \sum_{k=0}^n \dim \mathrm{H}^n(M,\; \mathbb{Z})$$

Other Activities

Actual

Liga Matematyczna I LO w Katowicach,
Jagiellonian University Mathematics Club,
Unofficial seminar on Topological Field Theory at Jagiellonian University.

Past

organized the Ogólnopolska Sesja Studentów Matematyki and International Workshop for Young Mathematicians,
Conducted a workshop on non-Euclidean geometry during Dni Wydziału WMiI UJ 2024,
Gave a talk on generalization in mathematics at the Konkurs Matematyczny “W Świecie Matematyki” im. prof. Włodzimierza Krysickiego 2024,
Helped organize the Jagielloński Turniej Matematyczny.
Ran a mathematicians’ stand at the Krakowski Festiwal Nauki i Sztuki 2024.

Conferences

GKŁW Workshop in Singularity Theory, Warszawa 2022,
Explicit Algebraic Geometry, Będlewo 2023,
Summer School in Quiver Representations, Quiver Varieties and Combinatorics, Bolonia 2023,
26th Intennational Summer School on Global Analysis and Applications, Prešov 2023.

Other

Participation in Stan Młodych 2023,
Participation in BORNinEU.

$$E^{pq}_1 = \left(\mathrm{H}^q\left(X, \Omega^p\right), \:\partial\right) \Rightarrow H^{p+q}(X,\Omega^\bullet)$$

Skills

My skill set consists mainly of substantive knowledge in mathematics and well-developed soft skills. In terms of technical abilities, I am proficient in the following:

LaTeX		Excel		SageMath		R		Python

Additionally, I am fluent in English at the C1 level and – most importantly – I hold a valid driving license.

$$\pi_3(\mathbb{S}^2) = \mathbb{Z}$$