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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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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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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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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
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Analysis 1
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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
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Parallel Programming
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Sidequests
GESS
Advanced Finance
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02 ETHZ
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