Studies

Courses I have completed at ETHZ so far:

• Data Structures and Algorithms 8 ECTS Algorithm Efficiency & Correctness, Generic Programming, Searching, Selection, Sorting, Amortized Analysis, (Balanced) Search Trees, Heaps, Hash Tables, Geometric Algorithms (Convex Hull, Sweep Line, Closest Point Pair), Graphs (Traversal, Shortest Path, Minimum Spanning Tree, Maximum Flow), Dynamic Programming, Introduction to Parallel & Concurrent Programming
• 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