Studies

Courses I have completed at ETHZ so far:

• Basic Structures 5 ECTS First-Order Logic, Introduction to Model Theory, Soundness & Gödel's Completeness Theorem, ZF(C), Ordinal, Cardinal and Real Numbers, Introductory Graph Theory, Elementary Number Theory
• Histories and Philosophies of Mathematics 3 ECTS History: how mathematical research is done in practice, the historical emergence of number, geometry, proof and infinity, and the development of the theory / practice distinction. Philosophy: Hilbert's formalism, Brouwer–Heyting intuitionism, Hersh's humanism, Rotman's semiotics, Ernest's social constructivism, Wittgenstein's later philosophy and the ethical considerations of mathematical thought. Primary texts: Lakatos's "Proofs and Refutations"; Hersh's "What is Mathematics, Really?"; Hilbert's "On the Infinite"; Heyting's "Disputation"; Rotman's "Mathematics as Sign"; Wittgenstein's "Lectures on the Foundations of Mathematics"; Ernest's "The Ethics of Mathematics". As to be expected from a philosophy course, it left me with more questions than answers. Nonetheless, I thoroughly enjoyed it.
• Algebra I 7 ECTS Group Theory: Groups, Subgroups, Quotient Groups, Homomorphisms, Group Actions, Sylow theorems; Ring Theory: Rings, Homomorphisms, Ideals, Factorization; Field Theory: Fields, Field Extensions
• Data Analysis for Physics 5 ECTS Introduction to Python (Numpy, Matplotlib), Introduction to Probability & Error Propagation, (Auto)-Covariance, DFT & Filters, Introduction to Bayesian Inference, Introduction to Machine Learning (Regression, Neural Networks, Deep Learning, Encoding, Clustering, PCA)
• Waves & Electromagnetism 7 ECTS Waves, Electrostatics, Conductors, Currents, Introduction to Special Relativity, Fields of Moving Charges, Magnetic Fields, Induction, AC Circuits, Maxwell's Equations & EM Waves, EM Fields in Matter
• C++ Programming 5 ECTS Expressions & Control Flow, Functions, Vectors & Reference Types, Recursion, Pointers & Dynamic Memory, Dynamic Datastructures, Introduction to OOP
• Classical Mechanics & Thermodynamics 7 ECTS Newtonian Mechanics, Non-Inertial Frames, Energy, Many-body Systems, Oscillations, Thermodynamics
• Analysis I & II 20 ECTS Single and Multivariable Real Analysis: Real Numbers, Introductory Topology, Limits, Sequences & Series, (Total) Differentiability, (Multiple) Riemann Integration, Vector Analysis / Field Theory, Introduction to Manifolds and Differential Forms
• Linear Algebra I & II 14 ECTS Vector Spaces, Linear Maps, Duality & Quotient Spaces, Eigenspaces, Inner Product Spaces, Spectral Theorem, Generalized Eigenspaces, Multilinear Algebra & Tensor Products
• Digital Circuits 4 ECTS Boolean Algebra, Logic Synthesis, CMOS Technology, Latches & Flip-Flops, Number Systems & Arithmetic Circuits, Finite State Machines, Registers and Microprocessors