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01 Semesters (BSc)
Semester 1
Algorithms and Data Structures
Lecture Notes
01 Intro To Algorithms
02 Star Search
03 Max Subarray Sum
04 Searching and Sorting
05 Sorting, Data Structures
06 Abstract Data Types, Binary AVL Search Trees
07 Dynamic Programming, Jump Game, Longest Common Subsequence, Edit Distance
08 Subset Sum, Knapsack, Longest Increasing Subsequence
09 Graph Theory, Eulerian Cycle Algorithm
10 Topological Ordering, Directed Graphs, Representing Graphs on Computers, Topological Sort Algorithm
11 Shortest Path Algorithms, Cheapest Walks in Weighted Graphs, Acyclical Graphs and Topological Sort, Dijkstra's Algorithm
12 Cheapest Path Problem, Negative Cost, Bellman-Ford, Minimum Spanning Trees, Boruvka's Algorithm, Prim's Algorithm, Priority Queues
13 Kruskal's Algorithm, Union Find, Self-Adapting Data Structures and Amortized Analysis
14 All Source Shortest Paths, Floyd-Warshall, Johnson's Algorithm, Matrices and Graphs, Connected Components in Digraphs, Efficient Matrix Operations
15 Quick Select and Finding the Median
Study Notes
Algorithms
Searching and Sorting
Searching Algorithms
Sorting Algorithms
Fundamentals
Growth
Asymptotic Notation
Master Theorem
Comparing Algorithms and Properties
Fundamental Concepts in Graph Theory
Graph Theory
Intro to General Algorithms
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Material
Useful Resources
Discrete Maths
Lecture Notes
01 Intro and Statements
02 Propositional Logic and Formulas
03 Logical Equivalence, Tautological Implication and Modus Ponens
04 Quantifiers
05 Proof Types
06 Set Theory and Russels Paradox
07 Equality, Ordered Pairs, Cartesian Product, Power Set and Relationships
08 Relations, Compositions and Properties
09 Equivalency Relation and Classes, Partitions, Partially Ordered Sets
10 Posets, Hasse Diagrams, Lexicographical Ordering, Special Elements, Functions, Countability, Infinities
11 Functions, Relations, Cardinality, Countability, Cantor's Diagonalization Argument
12 Cardinality, Number Theory, Rings, Euclidian Rings, Ideal, Congruence, Modular Arithmetic, Diophantine Equations
13 Modular Arithmetics, Set of Residues, Diffie-Hellman, Multiplicative Inverse, Chinese Remainder Theorem
14 Algebraic Structures and Operations, Monoids, Inverses, Groups, Group Properties, Landscape of Groups
15 Groups, Homomorphism, Isomorphism, Preservation of Identity and Inverses
16 Isomorphism, Powers, Order, Generators, Lagrange's Theorem, Multiplicative Groups, Euler's Totient Function, RSA
17 Rings, Polynomial Rings, Integral Domains, Units
18 Rings, Fields, Real Polynomial Fields, Polynomial Fields, Galois Fields
19 Factorizations, Polynomial Fields and Division, Polynomial Interpolation, Constructing Galois Fields
20 Generators in Finite Fields, Properties of Finite Fields, Error Correcting Codes, Reed-Solomon Codes
21 Logic, Proof Systems, Logical Consequence, Syntactic Derivation
22 Proof Systems, Syntax, Semantics, Equivalence, Satisfiability, Tautologies, Normal Forms, Types of Statements
23 Predicate Logic Reintroduced, Syntax, Semantics, Universe Size
24 Evaluating and Proving Formulas in Predicate Logic, Equivalences, Transformations, Variable Substitution, Universal Instantiation, Equality, Prenex Normal Form
25 Skolem Normal Form, Russell's Paradox, Cantor's Diagonalization, Existence of Uncomputable Functions, Higher-Order Logic, Calculi
26 Syntactic Derivation vs Semantic Entailment, Logic Calculus, Sequent Calculus, Resolution Calculus
27 Soundness and Completeness of Resolution Calculus, NP and SAT problem
Script
Chapter 2 - Math. Reasoning, Proofs, and a First Approach to Logic
Chapter 3 - Sets, Relations, and Functions
Chapter 4 - Number Theory
Chapter 5 - Algebra
Chapter 6 - Logic
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Material
Useful Resources
Intro To Programming
Lecture Notes
01 EBNF
02 Java (Intro)
03 Java (Basics)
04 Java (Input, Random, Control Flow)
05 Java (Functions, Value vs Reference Semantics, Variable Scope)
06 Java (Functions, Loops, Side Effects, Do-While)
07 Sequences
08 Array Operations, Recursion
09 Solution Strategies, Logical Conclusions, Assertions, Hoare Logic
10 Hoare Logic
11 Loop Invariants, Classes and Objects, Attributes, Reference Semantics
12 Null, Class Methods, Constructors
13 Visibility Modifiers, Object Invariants, Static Methods, Final and Attributes
14 Enums, Code Style, Conventions, Refactoring, Linked Lists
15 Linked Lists, Inner Classes, Methods, Recursive Methods, Built-in Lists
16 Java Built-in Lists, LinkedList, ArrayList, Wrapper Classes, Inheritance Basics
17 Visibility Modifiers, Sub Typing, Typecasts, Dynamic Binding, Polymorphism
18 Object Class, Comparing Objects (Override Equals), Shadowing, Inheritance Design Principles, Files, Cursor and Tokens
19 Files, File Output, Exceptions, Checked vs Unchecked, Throwing, Exception Handling Best Practices
20 Interfaces, Java Collection Framework, Interface Collection, Interface List
21 Interface List, Comparing Elements, Interface Set, Hashing and Hashcode
22 Java Collection Framework, Interface Set, Interface Map, Comparator Interface
23 Java Collections Framework, Comparator Interface, Iterator Interface, Generics, ArrayList Example
24 Type Erasure, Advanced Generics (Covariance, Contravariance, Invariance), Type Bounds, Packages
25 Chat Application, Client-Server Architecture, GUI, (De)Serialization, Websockets, Dependency Management, Introspection and Reflection
26 Memory Management, Stack & Heap, Garbage Collection
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Useful Resources
Linear Algebra
Lecture Notes
01 Vectors
02 Vectors
03 Linear Dependence and Independence
04 Matrices and Linear Combinations
05 Transpose and Multiplication
06 CR-Factorization and Linear Transformations
07 Linear Transformations, Linear Systems of Equations, PageRank
08 Gauss Elimination, Elimination Matrices and Solution Sets
09 Elementary Row Operations, Gauss Elimination, Inverse Matrices, Inverse Theorem
10 Calculating the Inverse, LU and LUP Decomposition
11 Gauss-Jordan, REF, RREF, Properties of REF
12 Vector Spaces, Subspaces
13 Vector Spaces, Bases, Dimension
14 Fundamental Subspaces, Column Space, Row Space, Nullspace
15 Orthogonal Vectors and Orthogonal Complements of Subspaces
16 Orthogonal Complementary Subspaces, Projections, Normal Form
17 Projections, Least Squares, Linear Regression
18 Orthonormal Bases, Properties of Orthogonal Matrices
19 Gram-Schmidt Process, QR-Decomposition, Properties of Q and R
20 Pseudoinverses, Constructing Pseudoinverses
21 Certificates, Linear Systems of Inequalities, Projections of Polyhedra, Farkas Lemma
22 Determinants, Permutations, Properties, Cofactors, Cramers Rule
23 Eigenvalues and Eigenvectors, Complex Numbers
24 Explicit Fibonacci Formula, Eigenvalue and Eigenvector properties, Trace
25 Eigenvalues, Eigenvectors, Complete Set of Eigenvectors, Diagonalization, Eigendecomposition
26 Symmetric Matrices, Spectral Theorem, Rayleigh Quotient
27 Positive (Semi)Definite Matrices, Gram Matrices, SVD
28 SVD Theorem and Proof, SVD Abstraction, Pseudoinverse
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Semester 2
Algorithms and Probability
Lecture Notes
01 Introduction, Connectedness, Blocks
02 Finding Cut Vertices and Bridges, Cycles and Circuits, Hamiltonian Cycles and Gray Codes
03 Hamiltonian Cycles, Dirac's Theorem, Complexity Theory, Traveling Salesman
04 Cycles, Travelling Salesman Problem, Metric TSP, Matching, Augmenting Paths, Hall's Marriage Theorem
05 Matchings in Bipartite Graphs
06 Augmenting Paths, Hopcroft-Karp, 1.5 Approximation for Metric TSP
07 Graph Coloring, Greedy Coloring, Smallest-Last Heuristics, Block Graph Colorings
08 Five-Color Theorem, Brooks Theorem, 3-Colorable Coloring Approximation, Randomness
09 Discrete Probability Space, Properties of Probability, Union of Events, Laplace Space, Composite Probability, Combinatorics
10 Conditional Probability, Independence, and Bayes' Theorem
Practice Sessions
01
Script
Chapter 1
01 Fundamentals, Connectivity
02 Trees, Minimum Spanning Trees
03 Shortest Paths
04 Connectivity, Articulation Points, Bridges, Block Decomposition
05 Cycles, Euler Tours, Hamiltonian Cycles, Traveling Salesman Problem
06 Matchings, Colorings
Chapter 2
01 Fundamentals, Probability Spaces and Events
02 Conditional Probabilities, Independence
03 Random Variables, Expectation, Variance
04 Important Discrete Distributions
05 Multiple Random Variables
Fundamental Definitions and Notations
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Analysis 1
Lecture Notes
01
Lecture Notes 2024
01 Introduction, Real Numbers, Completeness
02 Real Numbers, Min, Max, Bounds, Supremum, Infimum, Cardinality, Euclidian Space
03 Supremum, Infimum, Cross Product, Complex Numbers, Sequences
04 Divergence, Limits, Monotony, Weierstrass Theorem, Limit Superior and Inferior
05 Sandwich Lemma, Cauchy Criterion, and Bolzano-Weierstrass Theorem
06 Accumulation Points, Sequences in Reals and Complex, and Series
07 Series Cauchy Criterion, Absolute and Conditional Convergence, Riemann Rearrangement Theorem, Dirichlet's Theorem
08 More Convergence Criteria, Dirichlet's Theorem, Ratio, Root Tests and Power Series
09 Double Series, Cauchy Products, Exponential Functions and Real-Valued Functions
10 Continuity, Intermediate Value Theorem
11 Continuity, Extreme Value Theorem, Composition of Continuous Functions, Continuity of Inverse Functions
12 Continuity, Exponential Function and Function Sequences
13 Function Sequences, Continuity of Limit Function under Uniform Convergence, Cauchy Criterion for Uniform Convergence, Series of Functions, Uniform Convergence of Power Series, Trig Functions
Script
Chapter 1 - Real Numbers, Euclidean Spaces, and Complex Numbers
Chapter 2 - Sequences and Series, Approaching Infinity, Divergence, Infinity, Algebra of Limits, Monotone Sequences, Weierstrass, Cauchy, Series, Summing Infinitely, Special Series and Operations
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Digital Design and Computer Architecture
Lecture Notes 2023
01 Introduction and Basics
02 Tradeoffs, Metrics & Combinational Logic 1
03 Combinational Logic 2
04 Sequential Logic Design
04.5 Labs Intro and FPGAs
05 Sequential Logic Design II & Hardware Description Languages and Verilog
06 Hardware Description Languages and Verilog II, Timing
06.5 Verification & Testing
07 Von Neumann Model & Instruction Set Architectures
08 Instruction Set Architectures II
09 ISA & Microarchitecture
09.5 Assembly Programming
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Material
Parallel Programming
Lecture Notes 2024
01 Introduction & Course Overview
02 Java Recap and JVM Overview
03 Introduction to Threads and Synchronization (Part I)
04 Introduction to Threads and Synchronization (Part II)
05 Introduction to Threads and Synchronization (Part III)
06 Parallel Architectures - Parallelism on the Hardware Level
07 Basic Concepts in Parallelism
08 Divide & Conquer and Executor Service
09 DAG and ForkJoin Framework
10 Parallel Algorithms (Part I)
11 Parallel Algorithms (Part II)
12 Shared Memory Concurrency, Locks and Data Races
13 Virtual Threads
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Sidequests
GESS
Advanced Finance
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02 ETHZ
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01 Semesters (BSc)
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Semester 2
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Algorithms and Probability
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Practice Sessions
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Apr 13, 2025
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