├── .gitignore ├── .gitmodules ├── .idea ├── .gitignore └── vcs.xml ├── .obsidian ├── appearance.json ├── community-plugins.json ├── core-plugins-migration.json ├── core-plugins.json ├── hotkeys.json ├── plugins │ ├── obsidian-completr │ │ ├── blacklisted_suggestions.txt │ │ ├── callout_suggestions.json │ │ ├── latex_commands.json │ │ ├── main.js │ │ ├── manifest.json │ │ └── styles.css │ ├── obsidian-quickshare │ │ ├── main.js │ │ ├── manifest.json │ │ └── styles.css │ └── obsidian-relative-line-numbers │ │ ├── main.js │ │ └── manifest.json └── themes │ ├── Catppuccin │ ├── manifest.json │ └── theme.css │ ├── Comfort color dark │ ├── manifest.json │ └── theme.css │ ├── Obsidian Nord │ ├── manifest.json │ └── theme.css │ ├── PLN │ ├── manifest.json │ └── theme.css │ ├── Pine Forest Berry │ ├── manifest.json │ └── theme.css │ └── Pisum │ ├── manifest.json │ └── theme.css ├── Books ├── Introduction to Networking.md ├── Link Layer.md ├── Network Architecture.md ├── Packets.md └── Store-and-Forward Networks.md ├── Linear Algebra in Markov Chains.md ├── Numerical Data.md ├── Pasted image 20250601152652.png ├── Pasted image 20250601152707.png ├── Pasted image 20250601152811.png ├── Pasted image 20250608110200.png ├── Pasted image 20250608111847.png ├── Pasted image 20250608113103.png ├── Predictive Modeling.md ├── Probability.md ├── README.md └── TUM ├── .obsidian ├── app.json ├── appearance.json ├── core-plugins.json ├── hotkeys.json └── workspace.json ├── 1. Semester ├── 1. Semester.md └── ERA │ ├── Arithmetische und Logische Operationen.md │ ├── Assembler.md │ ├── Aufbau eines Prozessors.md │ ├── Befehlsverarbeitung.md │ ├── Binaere Entscheidungsdiagramme.md │ ├── Cache.md │ ├── Compilierung und Assemblierung.md │ ├── Das Von-Neumann Konzept.md │ ├── Digitale Schaltungen.md │ ├── Einfuehrung in die Rechnerarchitekur.md │ ├── Endliche Automaten.md │ ├── Hauptspeicher.md │ ├── Instruction Set Architecture.md │ ├── Logiksynthese und - minimierung.md │ ├── Moderne Prozessoren.md │ ├── Multicycle Prozessoren.md │ ├── Multithreading.md │ ├── Pasted image 20221022153649.png │ ├── Pasted image 20221022153654.png │ ├── Pasted image 20221024152907.png │ ├── Pasted image 20221024164257.png │ ├── Pasted image 20221024164610.png │ ├── Pasted image 20221025170103.png │ ├── Pasted image 20221111135009.png │ ├── Pasted image 20221111135724.png │ ├── Pasted image 20221114120856.png │ ├── Pasted image 20221114211241.png │ ├── Pasted image 20221118133821.png │ ├── Pasted image 20221122205406.png │ ├── Pasted image 20221122205448.png │ ├── Pasted image 20221122205553.png │ ├── Pasted image 20221122205604.png │ ├── Pasted image 20221122205722.png │ ├── Pasted image 20221122205849.png │ ├── Pasted image 20221122205905.png │ ├── Pasted image 20221122210042.png │ ├── Pasted image 20221122210051.png │ ├── Pasted image 20221122210103.png │ ├── Pasted image 20221122210123.png │ ├── Pasted image 20221122210342.png │ ├── Pasted image 20221128122641.png │ ├── Pasted image 20221128125755.png │ ├── Pasted image 20221128125806.png │ ├── Pasted image 20221128130200.png │ ├── Pasted image 20221128132144.png │ ├── Pasted image 20221129161417.png │ ├── Pasted image 20221129162651.png │ ├── Pasted image 20221129162707.png │ ├── Pasted image 20221129163006.png │ ├── Pasted image 20221129164144.png │ ├── Pasted image 20221129165727.png │ ├── Pasted image 20221205124540.png │ ├── Pasted image 20221205125448.png │ ├── Pasted image 20221205125459.png │ ├── Pasted image 20221205131215.png │ ├── Pasted image 20221206000536.png │ ├── Pasted image 20221206000612.png │ ├── Pasted image 20221206001128.png │ ├── Pasted image 20221206161821.png │ ├── Pasted image 20221206161829.png │ ├── Pasted image 20221206162000.png │ ├── Pasted image 20221206162057.png │ ├── Pasted image 20221206162213.png │ ├── Pasted image 20221206164229.png │ ├── Pasted image 20221206165809.png │ ├── Pasted image 20221206170720.png │ ├── Pasted image 20221206172301.png │ ├── Pasted image 20221207230007.png │ ├── Pasted image 20221209133934.png │ ├── Pasted image 20221212122849.png │ ├── Pasted image 20221212125721.png │ ├── Pasted image 20221212131442.png │ ├── Pasted image 20221212132121.png │ ├── Pasted image 20221213172856.png │ ├── Pasted image 20221216135920.png │ ├── Pasted image 20221216141452.png │ ├── Pasted image 20221219123924.png │ ├── Pasted image 20221219124929.png │ ├── Pasted image 20221219130951.png │ ├── Pasted image 20221219131013.png │ ├── Pasted image 20221219132359.png │ ├── Pasted image 20221219132419.png │ ├── Pasted image 20221220214034.png │ ├── Pasted image 20221220214131.png │ ├── Pasted image 20230109231022.png │ ├── Pasted image 20230109231035.png │ ├── Pasted image 20230109231058.png │ ├── Pasted image 20230109231110.png │ ├── Pasted image 20230114152702.png │ ├── Pasted image 20230114152724.png │ ├── Pasted image 20230114152747.png │ ├── Pasted image 20230114152843.png │ ├── Pasted image 20230117113227.png │ ├── Pasted image 20230117114108.png │ ├── Pasted image 20230117120833.png │ ├── Pasted image 20230120133849.png │ ├── Pasted image 20230125122843.png │ ├── Pasted image 20230125123922.png │ ├── Pasted image 20230125125456.png │ ├── Pasted image 20230125125524.png │ ├── Pasted image 20230125155911.png │ ├── Pasted image 20230127140430.png │ ├── Pasted image 20230127141037.png │ ├── Pasted image 20230127141139.png │ ├── Pasted image 20230127141151.png │ ├── Pasted image 20230127141203.png │ ├── Pasted image 20230127143143.png │ ├── Pasted image 20230127143154.png │ ├── Pasted image 20230127143207.png │ ├── Pasted image 20230130122858.png │ ├── Pasted image 20230130125256.png │ ├── Pasted image 20230205164416.png │ ├── Pipelining.md │ ├── RISC-V.md │ ├── Speicheraufbau.md │ ├── Speicherbausteine.md │ ├── Speicherhierarchie.md │ ├── Speicherverwaltung.md │ ├── Systembefehle.md │ └── VHDL.md ├── 2. Semester ├── 2. Semester.md ├── FPV │ ├── Assertions and Verification.md │ ├── Correctness.md │ ├── Funktionale Programmierung und Verifikation.md │ ├── Pasted image 20230417211426.png │ ├── Pasted image 20230417212856.png │ ├── Pasted image 20230424132008.png │ ├── Pasted image 20230424222851.png │ ├── Pasted image 20230424223008.png │ ├── Pasted image 20230424223104.png │ ├── Pasted image 20230508123523.png │ ├── Pasted image 20230508133734.png │ ├── Pasted image 20230626194658.png │ ├── Pasted image 20230626194715.png │ ├── Pasted image 20230626200049.png │ ├── Pasted image 20230626202528.png │ ├── Pasted image 20230626202601.png │ ├── Pasted image 20230626203131.png │ ├── Pasted image 20230626203159.png │ ├── Pasted image 20230626203734.png │ ├── Pasted image 20230627195811.png │ ├── Pasted image 20230722162554.png │ ├── Pasted image 20230722163724.png │ ├── Pasted image 20230722164125.png │ ├── Termination.md │ ├── Verification in Ocaml.md │ └── Weakest Pre-Condition.md ├── GAD │ ├── Datenstrukturen fuer Sequenzen.md │ ├── Effizienzmetrik.md │ ├── Graphen.md │ ├── Grundlagen Algorithmen und Datenstrukturen.md │ ├── Hashing.md │ ├── Laufzeitanalyse.md │ ├── Pasted image 20230425143802.png │ ├── Pasted image 20230510132900.png │ ├── Pasted image 20230510133347.png │ ├── Pasted image 20230513180744.png │ ├── Pasted image 20230513180843.png │ ├── Pasted image 20230513180947.png │ ├── Pasted image 20230513181015.png │ ├── Pasted image 20230513192742.png │ ├── Pasted image 20230524130208.png │ ├── Pasted image 20230524153935.png │ ├── Pasted image 20230606145711.png │ ├── Pasted image 20230606150432.png │ ├── Pasted image 20230606151259.png │ ├── Pasted image 20230610130736.png │ ├── Pasted image 20230610141557.png │ ├── Pasted image 20230610142936.png │ ├── Pasted image 20230613195733.png │ ├── Pasted image 20230613200546.png │ ├── Pasted image 20230613201002.png │ ├── Pasted image 20230613204223.png │ ├── Pasted image 20230613204239.png │ ├── Pasted image 20230614132021.png │ ├── Pasted image 20230621135827.png │ ├── Pasted image 20230621142417.png │ ├── Pasted image 20230625160031.png │ ├── Pasted image 20230625162610.png │ ├── Pasted image 20230625162641.png │ ├── Pasted image 20230625162657.png │ ├── Pasted image 20230625163559.png │ ├── Pasted image 20230625165358.png │ ├── Pasted image 20230625170958.png │ ├── Pasted image 20230625171754.png │ ├── Pasted image 20230630193607.png │ ├── Pasted image 20230630195524.png │ ├── Pasted image 20230630195544.png │ ├── Pasted image 20230702200719.png │ ├── Pasted image 20230702201430.png │ ├── Pasted image 20230709154806.png │ ├── Pasted image 20230709154840.png │ ├── Pasted image 20230709154901.png │ ├── Pasted image 20230709154927.png │ ├── Pasted image 20230709161949.png │ ├── Pasted image 20230711190344.png │ ├── Pasted image 20230716182258.png │ ├── Pasted image 20230716182403.png │ ├── Pasted image 20230719223534.png │ ├── Pasted image 20230719223923.png │ ├── Pasted image 20230722205453.png │ ├── Pasted image 20230722215215.png │ ├── Pattern Matching.md │ ├── Priority Queues.md │ ├── Sortieren.md │ └── Suchstrukturen.md └── LinAlg │ ├── Algebraische Strukturen.md │ ├── Basen von Vektorraeumen.md │ ├── Definitheit von Matrizen.md │ ├── Determinante.md │ ├── Eigenwerte und Eigenvektoren.md │ ├── Erzeugendensysteme.md │ ├── Gaussches Eliminationsverfahren.md │ ├── Komplexe Zahlen und Kartesische Koordinaten.md │ ├── Komplexe Zahlen und Polarkoordinaten.md │ ├── Konstruktion der komplexen Zahlen.md │ ├── Kryptologie.md │ ├── Lineare Abbildungen.md │ ├── Lineare Algebra.md │ ├── Lineare Ausgleichsrechnung.md │ ├── Lineare Codes.md │ ├── Lineare Gleichungssysteme.md │ ├── Matrixnormen.md │ ├── Matrizen.md │ ├── Orthogonal- und Orthonormalsystem.md │ ├── Orthogonalithaet.md │ ├── Rechnen mit Matrizen.md │ ├── Restklassengruppen.md │ ├── Saetze.md │ ├── Singulaerwertszerlegung.md │ ├── Skalarprodukt.md │ └── Vektorraeume.md ├── 3. Semester ├── 3. Semester.md ├── Applied Reg │ ├── Applied Regression.md │ ├── Images │ │ ├── Pasted image 20231113091328.png │ │ ├── Pasted image 20231120195334.png │ │ ├── Pasted image 20231205092621.png │ │ ├── Pasted image 20231205092852.png │ │ ├── Pasted image 20231212094243.png │ │ └── Pasted image 20231212094326.png │ ├── Simple Regression.md │ └── Statistical Basics.md ├── GBS │ ├── Betriebssysteme.md │ ├── Dateisysteme.md │ ├── Ein- und Ausgabe.md │ ├── GBS.apkg │ ├── Grundlagen Betriebssysteme und Systemsoftware.md │ ├── Images │ │ ├── Pasted image 20231023150752.png │ │ ├── Pasted image 20231023150812.png │ │ ├── Pasted image 20231023152522.png │ │ ├── Pasted image 20231030080632.png │ │ ├── Pasted image 20231102100432.png │ │ ├── Pasted image 20231102101954.png │ │ ├── Pasted image 20231107172438.png │ │ ├── Pasted image 20231108162046.png │ │ ├── Pasted image 20231108162632.png │ │ ├── Pasted image 20231116215352.png │ │ ├── Pasted image 20231120150824.png │ │ ├── Pasted image 20231123143221.png │ │ ├── Pasted image 20231128164152.png │ │ ├── Pasted image 20231128164552.png │ │ ├── Pasted image 20231128164922.png │ │ ├── Pasted image 20231208105745.png │ │ ├── Pasted image 20231208120223.png │ │ ├── Pasted image 20231208180721.png │ │ ├── Pasted image 20231208181243.png │ │ ├── Pasted image 20231215093523.png │ │ ├── Pasted image 20231215093609.png │ │ ├── Pasted image 20231215094935.png │ │ ├── Pasted image 20231218091243.png │ │ ├── Pasted image 20231218092843.png │ │ ├── Pasted image 20231218171210.png │ │ ├── Pasted image 20231218173916.png │ │ ├── Pasted image 20231218181201.png │ │ ├── Pasted image 20231220151929.png │ │ ├── Pasted image 20240108170521.png │ │ ├── Pasted image 20240108171308.png │ │ ├── Pasted image 20240110155947.png │ │ ├── Pasted image 20240117180844.png │ │ ├── Pasted image 20240117180920.png │ │ ├── Pasted image 20240118095713.png │ │ ├── Pasted image 20240123153800.png │ │ ├── Pasted image 20240123153824.png │ │ ├── Pasted image 20240131101653.png │ │ └── Pasted image 20240131133731.png │ ├── Interprozesskommunikation.md │ ├── Modellierung paralleler Systeme.md │ ├── Parallele Systeme und Synchronisation.md │ ├── Prozessverwaltung.md │ ├── Scheduling.md │ ├── Speichermanagement.md │ └── Virtualisierung.md ├── GDB │ ├── Anfragebearbeitung.md │ ├── Datenintegritaet.md │ ├── GDB.apkg │ ├── Grundlagen Datenbanken.md │ ├── Images │ │ ├── Pasted image 20231018114626.png │ │ ├── Pasted image 20231018123352.png │ │ ├── Pasted image 20231018123412.png │ │ ├── Pasted image 20231018124624.png │ │ ├── Pasted image 20231025111701.png │ │ ├── Pasted image 20231025112648.png │ │ ├── Pasted image 20231025112658.png │ │ ├── Pasted image 20231025131848.png │ │ ├── Pasted image 20231025131909.png │ │ ├── Pasted image 20231025132134.png │ │ ├── Pasted image 20231025132226.png │ │ ├── Pasted image 20231025133027.png │ │ ├── Pasted image 20231025133039.png │ │ ├── Pasted image 20231025133222.png │ │ ├── Pasted image 20231025192743.png │ │ ├── Pasted image 20231025193644.png │ │ ├── Pasted image 20231201154232.png │ │ ├── Pasted image 20231201161614.png │ │ ├── Pasted image 20231201161744.png │ │ ├── Pasted image 20231201161831.png │ │ ├── Pasted image 20231201163407.png │ │ ├── Pasted image 20231201164535.png │ │ ├── Pasted image 20231201165436.png │ │ ├── Pasted image 20231201165449.png │ │ ├── Pasted image 20231207205911.png │ │ ├── Pasted image 20231207213921.png │ │ ├── Pasted image 20231214105825.png │ │ ├── Pasted image 20231214110204.png │ │ ├── Pasted image 20231214192433.png │ │ ├── Pasted image 20231220184419.png │ │ ├── Pasted image 20231220184657.png │ │ ├── Pasted image 20240113094748.png │ │ ├── Pasted image 20240113103237.png │ │ ├── Pasted image 20240113104629.png │ │ ├── Pasted image 20240125114118.png │ │ ├── Pasted image 20240125160340.png │ │ ├── Pasted image 20240128182053.png │ │ ├── Pasted image 20240130181520.png │ │ ├── Pasted image 20240206092253.png │ │ ├── Pasted image 20240206095020.png │ │ ├── Pasted image 20240206104138.png │ │ ├── Pasted image 20240210110750.png │ │ ├── Pasted image 20240210111105.png │ │ ├── Pasted image 20240210111330.png │ │ ├── Pasted image 20240210113804.png │ │ ├── Pasted image 20240210113814.png │ │ ├── Pasted image 20240210120339.png │ │ ├── Pasted image 20240210121748.png │ │ ├── Pasted image 20240210130643.png │ │ └── Pasted image 20240210131909.png │ ├── Konzeptuelle Modellierung.md │ ├── Mehrbenutzersynchronisation.md │ ├── Physische Datenorganisation.md │ ├── Relationale Entwurfstheorie.md │ ├── Relationales Datenmodell.md │ ├── SQL.md │ └── Transaktionen.md ├── ITSec │ ├── Authentisierung.md │ ├── IT Sicherheit.md │ ├── ITSec.apkg │ ├── Images │ │ ├── Pasted image 20231024103533.png │ │ ├── Pasted image 20231024103547.png │ │ ├── Pasted image 20231103082629.png │ │ ├── Pasted image 20231103094425.png │ │ ├── Pasted image 20231107105659.png │ │ ├── Pasted image 20231107111850.png │ │ ├── Pasted image 20231107114845.png │ │ ├── Pasted image 20231114103420.png │ │ ├── Pasted image 20231114105523.png │ │ ├── Pasted image 20231114111610.png │ │ ├── Pasted image 20231114112644.png │ │ ├── Pasted image 20231117101716.png │ │ ├── Pasted image 20231121112039.png │ │ ├── Pasted image 20231128105852.png │ │ ├── Pasted image 20231205113022.png │ │ ├── Pasted image 20231212102909.png │ │ ├── Pasted image 20231212103916.png │ │ ├── Pasted image 20231212110134.png │ │ ├── Pasted image 20231212111558.png │ │ ├── Pasted image 20231214095259.png │ │ ├── Pasted image 20231219161020.png │ │ ├── Pasted image 20231220122809.png │ │ ├── Pasted image 20240109151035.png │ │ ├── Pasted image 20240119161955.png │ │ ├── Pasted image 20240122132937.png │ │ └── Pasted image 20240130103249.png │ ├── Kryptographie.md │ ├── Kryptographische Hashfunktionen.md │ ├── Netzwerksicherheit.md │ ├── Public Key Infrastructure.md │ ├── Rechtemanagement.md │ ├── Schluesselmanagement.md │ ├── Schwachtellen und Angriffe.md │ └── Systemsicherheit.md └── NumProg │ ├── Differentialgleichungen.md │ ├── Eigenwertprobleme.md │ ├── Fliesskommazahlen und Rundung.md │ ├── Images │ ├── Pasted image 20231102170305.png │ ├── Pasted image 20231113110446.png │ ├── Pasted image 20231113113035.png │ ├── Pasted image 20231127204453.png │ ├── Pasted image 20231127204508.png │ ├── Pasted image 20231128091239.png │ ├── Pasted image 20231129184049.png │ ├── Pasted image 20231211104351.png │ ├── Pasted image 20240105121149.png │ ├── Pasted image 20240201141432.png │ ├── Pasted image 20240207084111.png │ └── Pasted image 20240207084245.png │ ├── Integration.md │ ├── Interpolation.md │ ├── Iterative Verfahren.md │ ├── Loesen linearer Gleichungssysteme.md │ ├── NumProg.apkg │ └── Numerisches Programmieren.md ├── 4. Semester ├── 4. Semester.md ├── DWT │ ├── Diskrete Wahrscheinlichkeitsraeume.md │ ├── Diskrete Wahrscheinlichkeitstheorie.md │ ├── Images │ │ └── Pasted image 20240708102651.png │ ├── Induktive Statistik.md │ ├── Kontinuierliche Wahrscheinlichkeitsraeume.md │ └── Stochastische Prozesse.md ├── GRnVS │ ├── Grundlagen Rechnernetze und Verteilte Systeme.md │ ├── Images │ │ ├── Pasted image 20240416151100.png │ │ ├── Pasted image 20240416151114.png │ │ ├── Pasted image 20240422103331.png │ │ ├── Pasted image 20240424181002.png │ │ ├── Pasted image 20240424181017.png │ │ ├── Pasted image 20240513122656.png │ │ ├── Pasted image 20240514162328.png │ │ ├── Pasted image 20240514162347.png │ │ ├── Pasted image 20240514162609.png │ │ ├── Pasted image 20240514162856.png │ │ ├── Pasted image 20240515124638.png │ │ ├── Pasted image 20240515125359.png │ │ ├── Pasted image 20240515130126.png │ │ ├── Pasted image 20240515134156.png │ │ ├── Pasted image 20240515134351.png │ │ ├── Pasted image 20240527103256.png │ │ ├── Pasted image 20240527105422.png │ │ ├── Pasted image 20240531105724.png │ │ ├── Pasted image 20240531160045.png │ │ ├── Pasted image 20240531160806.png │ │ ├── Pasted image 20240605182551.png │ │ ├── Pasted image 20240614135405.png │ │ ├── Pasted image 20240623132429.png │ │ ├── Pasted image 20240706201526.png │ │ ├── Pasted image 20240707101814.png │ │ ├── Pasted image 20240707102131.png │ │ ├── Pasted image 20240714100808.png │ │ └── Pasted image 20240714102418.png │ ├── Physikalische Schicht.md │ ├── Sicherungsschicht.md │ ├── Sitzungs-, Darstellungs- und Anwendungsschicht.md │ ├── Transportschicht.md │ └── Vermittlungsschicht.md ├── ModSim │ ├── Calculus.md │ ├── Directional Fields.md │ ├── Fuzzy Control.md │ ├── Heat Conduction.md │ ├── Images │ │ ├── Pasted image 20240511114119.png │ │ ├── Pasted image 20240516155357.png │ │ ├── Pasted image 20240531093428.png │ │ ├── Pasted image 20240611094423.png │ │ ├── Pasted image 20240611101639.png │ │ ├── Pasted image 20240611102730.png │ │ ├── Pasted image 20240707152818.png │ │ ├── Pasted image 20240715144443.png │ │ ├── Pasted image 20240719174741.png │ │ ├── Pasted image 20240722163726.png │ │ ├── Pasted image 20240722172000.png │ │ ├── Pasted image 20240722172251.png │ │ ├── Pasted image 20240722173211.png │ │ ├── Pasted image 20240722173226.png │ │ ├── Pasted image 20240722173539.png │ │ ├── Pasted image 20240724182350.png │ │ ├── Pasted image 20240726141753.png │ │ └── Pasted image 20240726182819.png │ ├── Job Scheduling.md │ ├── Markov Chains.md │ ├── Modellbildung und Simulation.md │ ├── Nash Equilibrium and Banzhaf Power Index.md │ ├── Ordinary Differential Equations.md │ ├── Population Dynamics.md │ ├── Traffic Modelling.md │ └── Zero-Sum Games and Elections.md └── Theo │ ├── Berechenbarkeit und Entscheidbarkeit.md │ ├── Einfuehrung in die Theoretische Informatik.md │ ├── Grundlagen formaler Sprache.md │ ├── Images │ ├── Pasted image 20240430153859.png │ ├── Pasted image 20240430153959.png │ ├── Pasted image 20240512172953.png │ ├── Pasted image 20240512173003.png │ ├── Pasted image 20240512173115.png │ ├── Pasted image 20240512173121.png │ ├── Pasted image 20240512173746.png │ ├── Pasted image 20240512173806.png │ ├── Pasted image 20240512173823.png │ ├── Pasted image 20240516105507.png │ ├── Pasted image 20240517164650.png │ ├── Pasted image 20240517170505.png │ ├── Pasted image 20240525095154.png │ └── Pasted image 20240603144116.png │ ├── Komplexitaetstheorie.md │ ├── Kontextfreie Sprachen.md │ └── Regulaere Sprachen.md ├── 5. Semester ├── 5. Semester.md ├── ML │ ├── Classification Performance.md │ ├── Clustering.md │ ├── Decision Trees.md │ ├── Deep Learning 1.md │ ├── Deep Learning 2.md │ ├── Dimensionality Reduction.md │ ├── Hyperparameters.md │ ├── Images │ │ ├── Pasted image 20241015122517.png │ │ ├── Pasted image 20241015122632.png │ │ ├── Pasted image 20241018104453.png │ │ ├── Pasted image 20241018160305.png │ │ ├── Pasted image 20241018164717.png │ │ ├── Pasted image 20241021111606.png │ │ ├── Pasted image 20241021144659.png │ │ ├── Pasted image 20241021150209.png │ │ ├── Pasted image 20241023175808.png │ │ ├── Pasted image 20241101110124.png │ │ ├── Pasted image 20241101122901.png │ │ ├── Pasted image 20241104122158.png │ │ ├── Pasted image 20241115150726.png │ │ ├── Pasted image 20241115153017.png │ │ ├── Pasted image 20241115160904.png │ │ ├── Pasted image 20241115170950.png │ │ ├── Pasted image 20241117171042.png │ │ ├── Pasted image 20241125135343.png │ │ ├── Pasted image 20241125135355.png │ │ ├── Pasted image 20241227150349.png │ │ ├── Pasted image 20241227150402.png │ │ ├── Pasted image 20250105174949.png │ │ ├── Pasted image 20250105182441.png │ │ ├── Pasted image 20250106152241.png │ │ ├── Pasted image 20250106152423.png │ │ ├── Pasted image 20250106160351.png │ │ ├── Pasted image 20250107112441.png │ │ ├── Pasted image 20250107114458.png │ │ ├── Pasted image 20250107134616.png │ │ ├── Pasted image 20250111130317.png │ │ ├── Pasted image 20250114110801.png │ │ ├── Pasted image 20250114112112.png │ │ ├── Pasted image 20250121162441.png │ │ ├── Pasted image 20250122144014.png │ │ ├── Pasted image 20250201135446.png │ │ ├── Pasted image 20250201140932.png │ │ ├── Pasted image 20250201160405.png │ │ └── Pasted image 20250201173823.png │ ├── Linear Classification.md │ ├── Linear Regression.md │ ├── Maschinelles Lernen.md │ ├── Optimization.md │ ├── Probabalistic Inference.md │ ├── SVMs and Kernels.md │ └── k-Nearest Neighbors.md └── RTS │ ├── Images │ ├── Pasted image 20241031162537.png │ ├── Pasted image 20241031163456.png │ ├── Pasted image 20241031163504.png │ ├── Pasted image 20241107161304.png │ └── Pasted image 20241107161317.png │ ├── Real-Time Hardware.md │ ├── Real-Time Systems.md │ └── Time and Clocks.md ├── 6. Semester ├── IDSST │ ├── Data Basics.md │ └── Introduction to Data Science and Statistical Thinking.md └── Markovketten │ ├── Definitions.md │ └── Markovketten.md └── TUM.md /.gitignore: -------------------------------------------------------------------------------- 1 | # Obsidian Generated 2 | .obsidian/app.json 3 | .obsidian/workspace.json 4 | .obsidian/graph.json 5 | .obsidian/workspace-mobile.json 6 | 7 | # Plugin Generated 8 | .obsidian/plugins/obsidian-completr/scanned_words.txt 9 | 10 | TUM/2. 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The link layer is responsible for connecting a device to a local area network and moving data across a single hop 3 | - Link layer technologies, such as cellphone towers and wifi networks, are often used my multiple devices at the same location 4 | - Some technologies, such as fiber optic cables are not shared and only used to send data across routers 5 | - The link layer thus has to deal with encoding, transmitting and coordinating the data traffic 6 | ## Packet Transmission 7 | - In order to enable each computer to send packets across the internet, they implement the Carrier Sense Multiple Access with Collision Detection (CSMA/CD) 8 | - Each computer listens, to see if the network is busy 9 | - If it is not, a computer starts sending data, while simultaneously listening to see, if it can receive it's own data 10 | - If it cannot, the network is busy and the computer waits before trying again 11 | - Once a computer has finished sending a packet, it pauses, so that other devices get a chance to send theirs -------------------------------------------------------------------------------- /Books/Network Architecture.md: -------------------------------------------------------------------------------- 1 | [[Link Layer]] -------------------------------------------------------------------------------- /Books/Packets.md: -------------------------------------------------------------------------------- 1 | - In order to prevent larger messages from blocking the entire network, a message would be split into packets 2 | - Those packets could then be sent across the network seperately and more quickly 3 | - In order to reassemble the packets at the correct destination, in the correct order, each packet has to contain information about its source and destination adress, as well as its offset 4 | - Routers were developed, which are computers, specialized in sending packets along their shortest route 5 | - Now, computers which were part of a Local-Area-Network, could send data across the Wide-Area-Network by connecting to a router 6 | - The term "Internet" thus captures the idea of connecting multiple local networks together -------------------------------------------------------------------------------- /Books/Store-and-Forward Networks.md: -------------------------------------------------------------------------------- 1 | - Originally, wiring was used to connect computers to one another 2 | - However, in order to send data across large distances, expensive, long-distance connections had to be used 3 | - Instead of relying on these connections, intermediate computers would store and forward data across shorter distances, one hop and one message at a time 4 | - This resulted in cheaper connections, however, large sets of data could easily block entire networks 5 | - This problem was solved with the introduction of [[Packets]] -------------------------------------------------------------------------------- /Linear Algebra in Markov Chains.md: -------------------------------------------------------------------------------- 1 | ## Transition Probabilities 2 | - Given an initial distribution $\mu$ and the transition matrix $\Pi$ of a Markov chain $(X_n)_{n=0}^{\infty}$, the distribution of $X_n$ can be computed as: 3 | $$\mu^T \Pi^{n}$$ 4 | - Additionally, the following holds for the same Markov chain: 5 | $$P(X_{n + m} = j \mid X_n = i) = \Pi^m(i, j)$$ 6 | ## Properties 7 | - Since $\Pi$ is a stochastic matrix, all of it's Eigenvalues are at most $|1|$ 8 | - In fact any $\Pi$ of a Markov Chain has an Eigenvector $\hat{\mu}$, whose Eigenvalue is $1$ 9 | - Because of this, the distribution of $\lim_{n \to \infty} X_n = \hat{\mu}$ -------------------------------------------------------------------------------- /Pasted image 20250601152652.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/AntonScheitler/Notes/3d5813aa060b0433589208e87737db5646ee26ba/Pasted image 20250601152652.png -------------------------------------------------------------------------------- /Pasted image 20250601152707.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/AntonScheitler/Notes/3d5813aa060b0433589208e87737db5646ee26ba/Pasted image 20250601152707.png -------------------------------------------------------------------------------- /Pasted image 20250601152811.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/AntonScheitler/Notes/3d5813aa060b0433589208e87737db5646ee26ba/Pasted image 20250601152811.png -------------------------------------------------------------------------------- /Pasted image 20250608110200.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/AntonScheitler/Notes/3d5813aa060b0433589208e87737db5646ee26ba/Pasted image 20250608110200.png -------------------------------------------------------------------------------- /Pasted image 20250608111847.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/AntonScheitler/Notes/3d5813aa060b0433589208e87737db5646ee26ba/Pasted image 20250608111847.png -------------------------------------------------------------------------------- /Pasted image 20250608113103.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/AntonScheitler/Notes/3d5813aa060b0433589208e87737db5646ee26ba/Pasted image 20250608113103.png -------------------------------------------------------------------------------- /Probability.md: -------------------------------------------------------------------------------- 1 | ## Hypothesis Testing 2 | - In order to make draw conclusions from data, hypotheses need to be made 3 | #### Procedure 4 | - In general, we make a null hypothesis $H_0$, which states that there is nothing to be gained from the data and any observed correlation is coincidence 5 | - Under the assumption that $H_0$ is true we then compute some summary statistic $T(X)$ of our data and check how likely it is that it can even occur 6 | - If there's enough evidence that the observed $T(X)$ is not a coincidence, we can reject $H_0$, otherwise, we assume $H_0$ holds 7 | ## Normal Distribution 8 | - The [[Kontinuierliche Wahrscheinlichkeitsraeume|Normal Distribution]] is very commonly used for statistical analysis 9 | #### Quantiles 10 | - An observation $x$ is considered the $q$-quantile of a distribution function $F$, if the following holds: 11 | $$F(x) = Pr[X \leq x] = q$$ 12 | - Which $q$-quantile an observation is can be obtained using the $\texttt{pnorm}$ function 13 | - Which observation a given $q$-quantile corresponds to can be obtained using the $\texttt{qnorm}$ function 14 | #### The 68-95-99.7 Rule 15 | - If a given dataset follows a normal distribution, about $68$% of the data falls within one standard deviation , $95$% within two standard deviations and $99.7$% within three standard deviations from the mean 16 | #### Normal Probability Plots 17 | - A normal probability plot has the number of standard deviations from the mean on the x-axis and the corresponding sample values on the y-axis 18 | - Samples from the dataset are then drawn on this plot 19 | - If the position of the samples on the plot represents a linear relationship, the data follows a normal distribution 20 | ###### Examples 21 | ![[Pasted image 20250601152707.png]] 22 | ![[Pasted image 20250601152811.png]] -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | ## Notes 2 | - This is a collection of my notes for all sorts of things 3 | #### File Structure 4 | - The most interesting folder for you will likely be TUM 5 | - Inside it, you will find folders organized into semesters and courses 6 | - Inside each course folder there is a file with the same name as the folder 7 | - This file functions as a directory for the course with links to relevant pages 8 | #### Tools 9 | - While GitHub offers markdown support and pages can thus be viewed directly in the browser, the use of [Obsidian](https://obsidian.md/download) is highly recommended 10 | - Inside Obsidian, helpful images are displayed and links behave like intended 11 | -------------------------------------------------------------------------------- /TUM/.obsidian/app.json: -------------------------------------------------------------------------------- 1 | {} -------------------------------------------------------------------------------- /TUM/.obsidian/appearance.json: -------------------------------------------------------------------------------- 1 | { 2 | "accentColor": "" 3 | } -------------------------------------------------------------------------------- /TUM/.obsidian/core-plugins.json: -------------------------------------------------------------------------------- 1 | [ 2 | "file-explorer", 3 | "global-search", 4 | "switcher", 5 | "graph", 6 | "backlink", 7 | "outgoing-link", 8 | "tag-pane", 9 | "page-preview", 10 | "daily-notes", 11 | "templates", 12 | "note-composer", 13 | "command-palette", 14 | "editor-status", 15 | "starred", 16 | "outline", 17 | "word-count", 18 | "file-recovery" 19 | ] -------------------------------------------------------------------------------- /TUM/.obsidian/hotkeys.json: -------------------------------------------------------------------------------- 1 | {} -------------------------------------------------------------------------------- /TUM/1. Semester/1. Semester.md: -------------------------------------------------------------------------------- 1 | ### [[Einfuehrung in die Rechnerarchitekur]] -------------------------------------------------------------------------------- /TUM/1. Semester/ERA/Befehlsverarbeitung.md: -------------------------------------------------------------------------------- 1 | ## Phasen der Befehlsverarbeitung 2 | - Die Ausführung von Befehlen lässt sich in die Interpretations- und Ausführungsphase einteilen 3 | ### Interpretationsphase 4 | - Die Adresse des auszuführenden Befehls wird im Befehlszähler gespeichert 5 | - Über MAR und MDR wird der Befehl in das Instruktionsregister geladen und anschließend dekodiert und ausgeführt 6 | - Nach dem Ausführen wird der Befehlszähler inkrementiert 7 | ### Ausführungsphase 8 | - Die, im Befehl enthaltenen, Daten werden über MAR und MDR aus dem [[Hauptspeicher]] geholt und in Register geladen 9 | - Über die ALU werden die Operanden verrechnet und das Ergebnis im Akkumulator abgespeichert 10 | - Mithilfe von weiteren Befehlen kann das Ergebnis in den [[Hauptspeicher]] zurückgeschrieben werden 11 | ### Beispiel 12 | ![[Pasted image 20221024164610.png]] -------------------------------------------------------------------------------- /TUM/1. Semester/ERA/Binaere Entscheidungsdiagramme.md: -------------------------------------------------------------------------------- 1 | ## Aufbau 2 | - Das Entscheidungsdiagramm ist ein Baum, wobei jeder Knoten einer Funktion entspricht, welche entweder zu 1, oder zu 0 evaluiert 3 | - Eine Kante entspricht dem Wert, den die Funktion annimmt und verbindet sie mit einer weitern Funktion 4 | - Blattknoten, oder Terminale, entsprechen dem Wert, zu dem die Funktion mit der gegebenen Belegung evaluiert 5 | #### Beispiel 6 | ![[Pasted image 20230114152702.png]] 7 | ## Reduktion 8 | #### Isomorphismus 9 | - Sind zwei Knoten isomorph, so koennen sie unter einem zusammengefasst werden 10 | ###### Beispiel 11 | ![[Pasted image 20230114152724.png]] 12 | #### Elimination 13 | - Deuten beide ausgehende Kanten eines Knoten auf denselbsen Knoten, so kann dieser entfernt werden 14 | ###### Beispiel 15 | ![[Pasted image 20230114152747.png]] 16 | #### Shannon Zerlegung 17 | - Eine boolsche Funktion wird in eine Funktion bestehend aus einem Literal und einer aus den Restlichen zerlegt 18 | - Im Entscheidungsdiagramm evaluiert das einzelne Literal zu 1, beziehungsweise zu 0 19 | - Die darauffolgende Funktion ist die aus den restlichen Literalen 20 | - Dieser Vorgang kann rekursiv wiederholt werden, bis das Entscheidungsdiagramm konstruiert wurde 21 | ###### Beispiel 22 | ![[Pasted image 20230114152843.png]] -------------------------------------------------------------------------------- /TUM/1. Semester/ERA/Das Von-Neumann Konzept.md: -------------------------------------------------------------------------------- 1 | ## Sieben Prinzipien eines Rechners 2 | 1. Die Struktur eines Rechners ist problemunabhängig 3 | 2. Ein Rechner besteht aus vier Werken 4 | - Speicherwerk (speichert Programme und Daten) 5 | - Leitwerk (interpretiert Programme) 6 | - Rechenwerk (führt arithmetische Operationen aus) 7 | - Ein-/Ausgabewerk (kommuniziert mit der Umgebung) 8 | 4. Der [[Hauptspeicher]] ist in adressierte, gleich große Zellen unterteilt 9 | 5. Programme und Daten stehen im selben [[Hauptspeicher]] und können durch den Rechner verändert werden 10 | 6. Der Rechner verwendet das Binärsystem 11 | 7. Ein Programm besteht aus einer Folge von Befehlen, welche sequenziell verarbeitet werden ([[Befehlsverarbeitung]]) 12 | 8. Von der Befehlsfolge kann über bedingte und unbedingte Sprünge abgewichen werden 13 | 14 | ## Abweichungen vom Konzept 15 | - Das Leit- und Rechenwerk werden zum Prozessor zusammengefasst 16 | - Das Speicherwerk ist hierarchisch unterteilt ([[Speicherhierarchie]]) 17 | - Auf einem Prozessor befinden sich mehrere Rechenwerke 18 | - Programme und Daten werden in größtenteils getrennten Speichern verwaltet 19 | ## Beispiel 20 | ![[Pasted image 20230205164416.png]] -------------------------------------------------------------------------------- /TUM/1. Semester/ERA/Digitale Schaltungen.md: -------------------------------------------------------------------------------- 1 | ## Repraesentation von Funktionen 2 | - Boolesche Operationen, wie AND, OR oder NOT koennen mithilfe von Schaltungen durch Gatter repraesentiert werden 3 | - Ausgehend von diesen grundlegenden Operationen koennen [[Arithmetische und Logische Operationen]], sowie [[Speicherbausteine]] implementiert werden 4 | - Um Schaltungen zu modellieren, verwendet man [[VHDL]] 5 | #### Beispiel 6 | ![[Pasted image 20221122205448.png]] -------------------------------------------------------------------------------- /TUM/1. Semester/ERA/Einfuehrung in die Rechnerarchitekur.md: -------------------------------------------------------------------------------- 1 | ### [[Das Von-Neumann Konzept]] 2 | ### [[Hauptspeicher]] 3 | ### [[Befehlsverarbeitung]] 4 | ### [[Instruction Set Architecture]] 5 | ### [[Assembler]] 6 | ### [[Compilierung und Assemblierung]] 7 | ### [[Speicherhierarchie]] 8 | ### [[Speicherverwaltung]] 9 | ### [[Systembefehle]] 10 | ### [[Digitale Schaltungen]] 11 | ### [[Arithmetische und Logische Operationen]] 12 | ### [[Speicherbausteine]] 13 | ### [[RISC-V]] 14 | ### [[Aufbau eines Prozessors]] 15 | ### [[Endliche Automaten]] 16 | ### [[Multicycle Prozessoren]] 17 | ### [[Pipelining]] 18 | ### [[Logiksynthese und - minimierung]] 19 | ### [[Binaere Entscheidungsdiagramme]] 20 | ### [[Speicheraufbau]] 21 | ### [[Cache]] 22 | ### [[Moderne Prozessoren]] 23 | ### [[Multithreading]] 24 | ### [[VHDL]] -------------------------------------------------------------------------------- /TUM/1. Semester/ERA/Endliche Automaten.md: -------------------------------------------------------------------------------- 1 | ## Allgemeines 2 | - Ein Automat ist ein Konstrukt, welches ausgehend von einem Ausgangszustand und einer Eingabe in einen Nachfolgezustand wechselt und eine Ausgabe produziert 3 | ## Darstellung 4 | #### Mathematisch 5 | ![[Pasted image 20221212122849.png]] 6 | #### Graphisch 7 | ![[Pasted image 20221212125721.png]] 8 | ## Realisierung 9 | - Um einen Automaten als [[Digitale Schaltungen|digitale Schaltung]] zu realisieren, muessen die erforderlichen Signale kodiert werden 10 | - Ein Automat erhaelt am Eingang ein Zustands- und ein Eingabesignal 11 | - Ein neuer Zustand, sowie ein Ausgabesignal koennen ausgehend von Logikgattern ermittelt werden 12 | - Dieser neue Zustand wird mithilfe von Flipflops gespeichert und im naechsten Takt als Eingang verwendet 13 | #### Beispiel 14 | ![[Pasted image 20221212132121.png]] -------------------------------------------------------------------------------- /TUM/1. Semester/ERA/Hauptspeicher.md: -------------------------------------------------------------------------------- 1 | ## Aufbau 2 | - Ein Speicher ist eine Menge von Zellen fester Wortlänge 3 | - Sämtliche Zellen haben eine Adresse und einen Wert 4 | - Ein Speicher wird in einen Stack, Heap, Data und Code Segment eingeteilt 5 | - Ruecksprungadressen und Registerinhalte koennen im Stack gespeichert werden 6 | - Speicher im Heap kann dynamisch angefragt und freigegeben werden 7 | - Das Data Segment enthaelt festgelegte, globale Daten 8 | - Das Code Segment enthaelt das eigentliche Programm 9 | #### Beispiel 10 | ![[Pasted image 20221025170103.png]] 11 | ## Datenzugriff 12 | - Zugriffe auf Daten werden über das Memory Access Register und das Memory Data Register verwaltet 13 | - Über das MAR wird die gewünschte Zelle adressiert 14 | - Über das MDR können Daten gelesen oder überschrieben werden 15 | - Obwohl ein Speicher in Worten organisiert ist, sind Lese- und Schreibzugriffe auf nicht ausgerichtete Daten möglich 16 | #### Beispiel 17 | ![[Pasted image 20221024152907.png]] 18 | 19 | ## Ausrichtung von Daten 20 | - Ein Datum der Größe n Byte ist korrekt ausgerichtet, falls für seine Adresse A gilt: A mod n = 0 21 | - Da ein Speicher in Worten organisiert ist, werden bei korrekter Ausrichtung die Anzahl der Speicherzugriffe minimiert 22 | - Inkorrekte Ausrichtung bietet effizientere Speichernutzung, führt allerdings neben mehr Speicherzugriffen auch zu einem höheren Hardwareaufwand 23 | #### Endianness 24 | - Endianness beschreibt die Reihenfolge von Bytes in einem Datum 25 | - Bei Little Endian stehen signifikantere Bytes an höheren Adressen 26 | - Bei Big Endian stehen signifikantere Bytes an niedrigeren Adressen 27 | -------------------------------------------------------------------------------- /TUM/1. Semester/ERA/Instruction Set Architecture.md: -------------------------------------------------------------------------------- 1 | ## Allgemeines 2 | - Die Instruction Set Architecture bietet die Schnittstelle zwischen dem Programmierer und dem Rechner 3 | - Die Kommunikation erfolgt mithilfe von [[Assembler]] 4 | - Die ISA umfasst Informationen ueber Ausfuehrungsmodelle, den Prozessor und seine Register, sowie den Befehlssatz 5 | ## Ausfuehrungsmodelle 6 | - Das Ausfuehrungsmodell beschreibt die Anzahl der Operanden, die in einem Befehl kodiert sind 7 | - **Stack Modell** (Alle Operanden sind durch den Stack impliziert) 8 | - **Akkumulator Modell** (Ein Operand, sowie das Ergebnis werden in den Akkumulator geladen) 9 | - **Register Modell** (Beide Operanden werden uebergeben, wobei einer vom Ergebnis ueberschrieben wird) 10 | - **Register-Register Modell** (Alle Operanden, sowie das Ergebnisregister werden separat spezifiziert) 11 | ## Befehlssatz 12 | - Der Befehlssatz ist die Menge an Befehlen, mit der der Programmierer mit einem Rechner interagieren kann 13 | - Man unterscheidet drei Klassen von Befehlen 14 | - Arithmetische und logische Operationen 15 | - Befehle fuer den Datentransfer, welche Daten aus und in den [[Hauptspeicher]] laden 16 | - Sprungbefehle, welche den Befehlszaehler ausgehend von Statusregistern aendern koennen 17 | #### Complex Instruction Set Architecture (CISC) 18 | - Grosser, komplexer Befehlssatz 19 | - CISC Rechner werden durch Mikroprogramme realisiert 20 | - Viele Befehle bleiben allerdings ungenutzt und sind meist langsamer 21 | #### Reduced Instruction Set Architecture (RISC) 22 | - Kleiner, elementarer Befehlssatz 23 | - RISC Rechner werden durch feste Verdrahtung realisiert 24 | - Die Befehle sind einfach und schnell ([[RISC-V]]) -------------------------------------------------------------------------------- /TUM/1. Semester/ERA/Moderne Prozessoren.md: -------------------------------------------------------------------------------- 1 | ## Out-of-Order Execution 2 | - Bei der sequentiellen Befehlsverarbeitung in einem pipelined Prozessor kann es zu Hazards kommen 3 | - Manche Hazards koennen ueber das umsortieren von Befehlen behoben werden 4 | - Out-of-Order Prozessoren sind deutlich komplexer, bieten allerdings auch eine effizientere Nutzung von Parallelitaet 5 | ## Parallelitaet 6 | #### Superskalaritaet 7 | - Mehrere unabhaengige Maschinenbefehle koennen parallel ausgefuehrt werden 8 | - Hierfuer verwendet der Prozessor mehrere Funktionseinheiten und Dekodierer 9 | - Zudem werden Pipelinestufen nach der Art des Befehls unterschieden 10 | ###### Beispiel 11 | ![[Pasted image 20230125122843.png]] 12 | #### VLIW Prozessoren 13 | - Ein Instruktionswort enthaelt mehrere Befehle 14 | - Diese Befehle sind unabhaengig voneinander und koennen parallel bearbeitet werden 15 | ###### Beispiel 16 | ![[Pasted image 20230125123922.png]] 17 | #### SIMD 18 | - Bei Single Instruction Multiple Data wird eine Operation parallel auf mehrere Datenstroeme angewandt 19 | - Dies eignet sich besonders fuer Vektoroperationen 20 | ###### Beispiel 21 | ![[Pasted image 20230125125524.png]] 22 | #### [[Multithreading]] 23 | ## Speedup 24 | - Der Speedup eines parallelen Programms ergibt sich aus der Relation der sequentiellen und der parallelen Laufzeit 25 | - Ein paralleles Programm besteht stets aus sequentiellen und parallelen Abschnitten 26 | #### Amdahl's law 27 | - Beschreibt den moeglichen Speedup bei konstanter Problemgroesse 28 | ###### Berechnung 29 | ![[Pasted image 20230127141037.png]] 30 | ![[Pasted image 20230127141139.png]] 31 | ![[Pasted image 20230127141151.png]] 32 | ![[Pasted image 20230127141203.png]] 33 | #### Gustafson's law 34 | - Beschreibt den moeglichen Speedup bei proportionaler Problemgroesse 35 | ###### Berechnung 36 | ![[Pasted image 20230127143143.png]] 37 | ![[Pasted image 20230127143154.png]] -------------------------------------------------------------------------------- /TUM/1. Semester/ERA/Multicycle Prozessoren.md: -------------------------------------------------------------------------------- 1 | ## Allgemeines 2 | - Statt ganze Instruktionen in einem Takt abzuarbeiten, wird die [[Befehlsverarbeitung]] in mehrere Schritte mit kuerzerem Takt unterteilt 3 | - Eine Instruktion benoetigt somit mehrere Takte zum durchlaufen 4 | ## Realisierung 5 | - Multicycle Prozessoren werden mithilfe von [[Endliche Automaten|endlichen Automaten]] realisiert 6 | - Je nach auszufuehrendem Befehl, wechselt der Prozessor in unterschiedliche Zustaende 7 | #### Zustaende 8 | ![[Pasted image 20221216141452.png]] 9 | #### Beispiel 10 | ![[Pasted image 20221213172856.png]] -------------------------------------------------------------------------------- /TUM/1. Semester/ERA/Multithreading.md: -------------------------------------------------------------------------------- 1 | ## Allgemeines 2 | - Ein Hardware-Thread ist eine Ausfuehrungseinheit, welche aus einem Befehlszaehler und Registern besteht 3 | - Andere Ressourcen, wie Speicher und Rechenwerke werden von Threads geteilt 4 | - Ein Kern ist die Kombination aus Threads und den geteilten Ressourcen 5 | - Kerne teilen sich wiederum die Cachehierarchie und arbeiten groesstenteils unabhaengig 6 | - Multithreading Architekturen unterscheiden sich darin, wie sich Threads, Ressourcen teilen 7 | ## Architekturen 8 | - Einfaches Multithreading 9 | - Threads wechseln sich zu einem festen Takt ab 10 | - Simultaneous Multithreading 11 | - Threads laufen echt parallel, falls sie unterschiedliche Teile der Ressourcen benoetigen 12 | #### Beispiel 13 | ![[Pasted image 20230125155911.png]] 14 | ## Cacheorganisation 15 | - Manche [[Cache|Caches]] werden von mehreren Kernen geteilt 16 | - Bei Schreibzugriffen geht die Kohaerenz der Daten verloren 17 | - Die Cachekohaerenz kann mithilfe von Protokollen gewahrt werden 18 | #### MESI Protokoll 19 | - Bei dem MESI Protokoll wird die Kohaerenz von Caches mithilfe eines Automaten gewahrt 20 | ###### Zustaende 21 | - Modified 22 | - Eine Cachezeile wurde lokal veraendert 23 | - Exclusive 24 | - Wert liegt in genau einer Cachezeile vor 25 | - Shared 26 | - Wert liegt in mindestens zwei Cachezeilen vor 27 | - Invalid 28 | - Wert ist nicht gueltig 29 | ###### Beispiel 30 | ![[Pasted image 20230130122858.png]] 31 | #### False Sharing 32 | - Schreiben mehrere Threads auf nicht ausgerichtete Daten, so kommt es zu zusaetzlichen Misses im Cache, da die Daten staendig ueberschrieben und neu geladen werden 33 | - False Sharing kann durch die Ausrichtung von Daten vermieden werden 34 | ###### Beispiel 35 | ![[Pasted image 20230130125256.png]] -------------------------------------------------------------------------------- /TUM/1. 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Semester/ERA/Speicherbausteine.md: -------------------------------------------------------------------------------- 1 | ## Allgemeines 2 | - Speicherbausteine basieren auf dem Konzept der Rueckkopplung 3 | - Indem der Ausgang einer Schaltung als Eingang wiederverwendet wird, wird Speicherverhalten simuliert 4 | #### Beispiel 5 | ![[Pasted image 20221129161417.png]] 6 | ## RS-Latch 7 | - Indem zwei NOR Gatter parallel rueckgekoppelt werden, kann mithilfe eines SET und eines RESET Signals ein Bit gespeichert werden 8 | #### Beispiel 9 | ![[Pasted image 20221129162651.png]] 10 | ![[Pasted image 20221129162707.png]] 11 | ## D-Latch 12 | - Anstelle eines RS-Latches koennen sowohl SET, als auch RESET von einem Eingangssignal abgeleitet werden 13 | - Um das Latch anzusteuern, wird ein ENABLE Signal mit dem Eingangssignal verundet 14 | #### Taktgesteuerte D-Flipflops 15 | - Im Gegensatz zu Latches, koennen Flipflops nur zu steigender Taktflanke angesteuert werden 16 | - Ueber OR Gatter kann das Signal des Takts verzoegert werden, sodass ein Speicherbaustein nur zum Zeitpunkt der aufsteigenden Flanke angesteuert werden kann 17 | #### Beispiel 18 | ![[Pasted image 20221129163006.png]] 19 | ![[Pasted image 20221129165727.png]] 20 | ## Mehrstellige Speicher 21 | - Mehrstellige Binaerzahlen koennen mithilfe einer Kombination aus Adressbits, sowie D-Latches und Multiplexern ueberschrieben und ausgelesen werden 22 | #### Beispiel 23 | ![[Pasted image 20221129164144.png]] -------------------------------------------------------------------------------- /TUM/1. Semester/ERA/Speicherhierarchie.md: -------------------------------------------------------------------------------- 1 | ## Allgemeines 2 | - Da die Arbeit alleine mit dem [[Hauptspeicher]] zu langsam ist, wird das Speicherwerk in der Regel hierarchisch unterteilt 3 | ## Aufteilung 4 | - Je naeher ein Speicherkonstrukt am Prozessor ist, desto geringer ist seine Kapazitaet und desto schneller ist seine Zugriffszeit 5 | #### Speicherkonstrukte 6 | - Register 7 | - [[Cache|Caches]] 8 | - Es gibt unterschiedliche Level von Caches 9 | - Je niedriger das Level, desto geringer die Kapazitaet und die Zugriffszeit 10 | - [[Hauptspeicher]] 11 | - Hintergrundspeicher -------------------------------------------------------------------------------- /TUM/1. Semester/ERA/Speicherverwaltung.md: -------------------------------------------------------------------------------- 1 | ## Speicherorganisation 2 | - Jeder Prozess hat einen eigenen Platz im [[Hauptspeicher]], samt Stack, Heap, Data- und Codesegment 3 | - Laufen mehrere Prozesse parallel, so muss das Betriebssystem, den Speicher eines Prozesses vor allen anderen schuetzen 4 | #### Virtueller Adressraum 5 | - Mithilfe eines virtuellen Adressraums kann der Speicher eines Prozesses geschuetzt werden 6 | - Ein Prozess kann seinen virtuellen Adressraum beliebig nutzen, der Adressraum anderer Prozesse bleibt allerdings verborgen 7 | - Fuer tatsaechliche Speicherzugriffe werden allerdings die physikalischen Adressen benoetigt 8 | #### Memory Management Unit 9 | - Um virtuelle Adressen in Physikalische zu uebersetzen, wird die Memory Management Unit verwendet 10 | - Der Uebersetzungsprozess erfolgt mithilfe von Page Tables 11 | - Ein [[Cache]] kann wahlweise vor, oder nach dem Zugriff auf die MMU verwendet werden 12 | ###### Pages 13 | - Ein [[Hauptspeicher]] wird in Pages fester Groesse eingeteilt 14 | - In Page Tables werden virtuelle Adressen und ihre physikalischen Gegenstuecke gespeichert 15 | ###### Page Directory 16 | - Ueber ein Page Directory wird auf die Page Tables eines Prozesses verwiesen 17 | - Ein Spezialregister verweist wiederum auf das Page Directory 18 | - Bei einem Prozesswechsel wird somit nur dieses Spezialregister veraendert 19 | ###### Swapping 20 | - Um bei der Ueberschreitung der Speicherkapazitaet einen Absturz zu vermeiden, koennen Pages auf den externen Speicher ausgelagert werden -------------------------------------------------------------------------------- /TUM/1. Semester/ERA/Systembefehle.md: -------------------------------------------------------------------------------- 1 | ## Aufgaben des Betriebssystems 2 | - Ueber das Betriebssystem werden Datein, Prozesse und Speicher verwaltet ([[Speicherverwaltung]]) 3 | - Um alle Rechnerkomponenten verwalten zu koennen, verfuegt das Betriebssystem ueber einen priviligierten Modus 4 | #### Moduswechsel 5 | - Um vom Benutzer- zum Systemmodus zu wechseln, kann ein System Call ausgefuehrt werden 6 | - Bei einem System Call wird an eine vordefinierte Adresse im Betriebssystem gesprungen, eine Routine ausgefuehrt und anschliessend in den Benutzermodus zurueckgekehrt 7 | #### Interrupts 8 | - Der Prozessor kann ueber Interrupts auf externe, asynchrone Ereignisse reagieren 9 | - Die Ruecksprungadresse und Registerinhalte werden gesichert, bevor der Interrupt-Handler des Betriebssystems ausgefuehrt wird 10 | #### Exceptions 11 | - Beim Auftreten einer Exception wird das Programm mithilfe des Exception-Handlers des Betriebssystems korrigiert oder abgebrochen -------------------------------------------------------------------------------- /TUM/2. Semester/2. Semester.md: -------------------------------------------------------------------------------- 1 | ### [[Funktionale Programmierung und Verifikation]] 2 | ### [[Lineare Algebra]] 3 | ### [[Grundlagen Algorithmen und Datenstrukturen]] 4 | ### [[Einfuehrung in die Softwaretechnik]] -------------------------------------------------------------------------------- /TUM/2. Semester/FPV/Assertions and Verification.md: -------------------------------------------------------------------------------- 1 | ## Assertions 2 | - In order to verify the correctness of a given program, assertions can be used 3 | - Assertions throw an exception if the program state does not imply the assertion 4 | - In order to verify a program, every program points needs to be annotated with an assertion 5 | - The assertion before an operation is called a pre-condition 6 | - The assertion after an operation is called a post-condition 7 | #### Example 8 | ![[Pasted image 20230417211426.png]] 9 | ## Verification 10 | - Each program points needs to be annotated with an assertion with the start being annotated with true 11 | - For each statement (or conditional ) $s$ the given assertion $A$ needs to imply the [[Weakest Pre-Condition|weakest pre-condition]], derived from the post-condition $B$ (or $B_0$ and $B_1$) of $s$ 12 | - If this is fulfilled, the assertions is considered locally consistent -------------------------------------------------------------------------------- /TUM/2. Semester/FPV/Correctness.md: -------------------------------------------------------------------------------- 1 | ## Correctness of a Program 2 | #### Program State 3 | - The state of any given program $\sigma$ can be described by it's variables and their values 4 | - A program state $\sigma$ satisfies a statement $A$, if the statement is true for the current values of all variables 5 | - The correctness of a statement can thus be determined by substituting in all current values 6 | ###### Example 7 | ![[Pasted image 20230424132008.png]] 8 | #### Execution Trace 9 | - The execution trace $\pi$ of a program is a series of program states $\sigma_0 ... \sigma_m$ with their designated program points $u_0 ... u_m$ 10 | - An execution trace $\pi$ can therefore be described by $$(u_0, \sigma_0)s_1(u_1, \sigma_1)...s_m(u_m, \sigma_m)$$where $s_i$ represents statements, such as basic operations and assignments in the program 11 | #### Theorem 12 | - Using execution traces, the correctness of a program can be verified as follows: 13 | - Given a program with the execution trace $\pi$ that ranges from the program point $u$ to $v$ 14 | - The program point $u$ is annotated with the Assertion $A$ and $v$ with $B$ 15 | - If the initial state of $\pi$ satisfies $A$, then it's final state will satisfy $B$ -------------------------------------------------------------------------------- /TUM/2. Semester/FPV/Funktionale Programmierung und Verifikation.md: -------------------------------------------------------------------------------- 1 | ### [[Assertions and Verification]] 2 | ### [[Weakest Pre-Condition]] 3 | ### [[Correctness]] 4 | ### [[Termination]] 5 | ### [[Verification in Ocaml]] 6 | ### [Flashcards](https://ankiweb.net/shared/info/754030607) -------------------------------------------------------------------------------- /TUM/2. Semester/FPV/Pasted image 20230417211426.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/AntonScheitler/Notes/3d5813aa060b0433589208e87737db5646ee26ba/TUM/2. Semester/FPV/Pasted image 20230417211426.png -------------------------------------------------------------------------------- /TUM/2. 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Semester/FPV/Termination.md: -------------------------------------------------------------------------------- 1 | ## General 2 | - It is not guranteed, that an [[Assertions and Verification|assertion]] is always reached, since a program might not terminate 3 | - The termination of a given program must therefore be proven 4 | #### Approach 5 | ###### Indicator Variable 6 | - For any loop, an indicator variable $r$ needs to be determined 7 | - $r$ ist often calculated using an expression $e_r$, composed of local variables 8 | ###### Control Flow 9 | - The necessary operations for creating and updating $r$ are inserted into the program 10 | - The loop invariant is formed around $r$ 11 | ###### Proof 12 | - Locally consistent assertions are calculated inside the loop via [[Weakest Pre-Condition|weakest pre-conditions]], starting with the assertion $r > e_r$ 13 | - If $r$ fulfills all necessary criteria, a given loop will terminate: 14 | - The assertion at the start of the loop implies $r \geq 0$ 15 | - The assertion at the end of the loop implies $r > e_r$ 16 | ###### Example 17 | ![[Pasted image 20230627195811.png]] -------------------------------------------------------------------------------- /TUM/2. Semester/GAD/Grundlagen Algorithmen und Datenstrukturen.md: -------------------------------------------------------------------------------- 1 | ### [[Effizienzmetrik]] 2 | ### [[Laufzeitanalyse]] 3 | ### [[Datenstrukturen fuer Sequenzen]] 4 | ### [[Hashing]] 5 | ### [[Sortieren]] 6 | ### [[Priority Queues]] 7 | ### [[Suchstrukturen]] 8 | ### [[Graphen]] 9 | ### [[Pattern Matching]] 10 | ### [Flashcards](https://ankiweb.net/shared/info/1983647928) -------------------------------------------------------------------------------- /TUM/2. Semester/GAD/Pasted image 20230425143802.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/AntonScheitler/Notes/3d5813aa060b0433589208e87737db5646ee26ba/TUM/2. Semester/GAD/Pasted image 20230425143802.png -------------------------------------------------------------------------------- /TUM/2. 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Semester/GAD/Pattern Matching.md: -------------------------------------------------------------------------------- 1 | ## Problem 2 | - In einem Text der Laenge $n$ wird nach einem Teilwort der Laenge $m \leq n$ gesucht 3 | - Die Indizes dieses Teilworts muessen zurueckgegeben werden 4 | ## Knuth-Morris-Pratt Algorithmus 5 | - Um den Suchbereich zu optimieren, wird der Rand eines Wortes verwendet 6 | #### Rand 7 | - Ein Wort $r$ ist der Rand eines Wortes $w$, falls $r$ sowohl Praefix, als auch Suffix von $w$ ist 8 | - $r$ ist der eigentliche Rand, falls er der groesste moegliche Rand, nach $w$ selbst ist 9 | #### Shifts 10 | - Tritt ein Mismatch auf, so wird das Suchwort so weit verschoben, bis der gematchte Praefix im Suffix liegt, in dem das Mismatch aufgetreten ist 11 | ###### Beispiel 12 | ![[Pasted image 20230722205453.png]] 13 | ###### Sichere Shifts 14 | - Es muss garantiert werden, dass bei einem Shift kein Vorkommen des Teilworts uebersprungen wird 15 | - Hierfuer wird ein Array $borders$ erstellt, welches am Index $i$ die Laenge des eigentlichen Rands des Praefix der Laenge $i$ des Teilworts enthaelt 16 | - Indem bei einem Mismatch an der Stelle $j$ um $j - borders[j]$ geshiftet wird, wird sichergestellt, dass erneut am fruehesten moeglichen Vorkommen des Teilworts gesucht wird 17 | ![[Pasted image 20230722215215.png]] 18 | #### Laufzeit 19 | - Der Algorithmus benoetigt maximal $2n + m$ Vergleiche um ein Teilwort der Laenge $m$ in einem Text der Laenge $n$ zu finden -------------------------------------------------------------------------------- /TUM/2. Semester/LinAlg/Basen von Vektorraeumen.md: -------------------------------------------------------------------------------- 1 | ## Allgemeines 2 | - Es sei $V$ ein $\mathbb{K}$-[[Vektorraeume|Vektorraum]], so bezeichnet man $B \subseteq V$ als Basis von $V$, falls gilt: 3 | - $B$ ist [[Erzeugendensysteme|linear unabhaengig]] 4 | - $B$ erzeugt $V$ 5 | - Jeder $\mathbb{K}$-Vektorraum besitzt eine Basis 6 | #### Basisverkuerzung und -erweiterung 7 | - Ist $B$ eine Basis von $V$, so gilt: 8 | - $B$ ist ein minimales Erzeugendensystem von $V$ 9 | - $B$ ist eine maximale, linear unabhaengige Teilmenge von $V$ 10 | - Jede linear unabhaengige Teilmenge von $V$ kann zu einer Basis von $V$ ergaenzt werden 11 | - Jedes Erzeugendensystem von $V$ kann zu einer Basis von $V$ verkuerzt werden 12 | #### Maechtigkeit von Basen 13 | - Alle Basen von $V$ haben dieselbe Maechtigkeit 14 | - Falls $n = dim(V)$, so gilt: 15 | - Jede linear unabhaengige Menge und jedes Erzeugendensystem mit $n$ Elementen ist eine Basis von $V$ 16 | - Jede Menge mit mehr als $n$ Elementen ist linear abhaengig -------------------------------------------------------------------------------- /TUM/2. Semester/LinAlg/Definitheit von Matrizen.md: -------------------------------------------------------------------------------- 1 | ## Allgemeines 2 | - Es sei $A \in \mathbb{R}^{n \times n}$ symmetrisch 3 | - $A$ ist definit, falls sie unterschiedliche Eigenschaften erfuellt 4 | - Dies kann anhand der [[Eigenwerte und Eigenvektoren|Eigenwerte]] von $A$ ermittelt werden 5 | #### Positiv Definit 6 | - $A$ ist positiv definit, falls gilt: 7 | $$\forall \space v \in \mathbb{R}^n \setminus \{0\}: v^TAv > 0$$ 8 | - Dies ist erfuellt, falls fuer die Eigenwerte $\lambda_i$ von $A$ gilt: 9 | $$\lambda_i > 0$$ 10 | #### Negativ Definit 11 | - $A$ ist negativ definit, falls gilt: 12 | $$\forall \space v \in \mathbb{R}^n \setminus \{0\}: v^TAv < 0$$ 13 | - Dies ist erfuellt, falls fuer die Eigenwerte $\lambda_i$ von $A$ gilt: 14 | $$\lambda_i < 0$$ 15 | #### Semi Positiv Definit 16 | - $A$ ist semi positiv definit, falls gilt: 17 | $$\forall \space v \in \mathbb{R}^n \setminus \{0\}: v^TAv \geq 0$$ 18 | - Dies ist erfuellt, falls fuer die Eigenwerte $\lambda_i$ von $A$ gilt: 19 | $$\lambda_i \geq 0$$ 20 | #### Semi Negativ Definit 21 | - $A$ ist semi negativ definit, falls gilt: 22 | $$\forall \space v \in \mathbb{R}^n \setminus \{0\}: v^TAv \leq 0$$ 23 | - Dies ist erfuellt, falls fuer die Eigenwerte $\lambda_i$ von $A$ gilt: 24 | $$\lambda_i \leq 0$$ 25 | #### Indefinit 26 | - $A$ ist indefinit, falls gilt: 27 | $$\exists \space v, w \in \mathbb{R}^n: v^TAv > 0, \space w^TAw < 0$$ 28 | - Dies ist erfuellt, falls fuer die Eigenwerte $\lambda_1, ..., \lambda_n$ von $A$ gilt: 29 | $$\exists \space \lambda_i, \lambda_j \in \{\lambda_1, ..., \lambda_n\}: \lambda_i > 0, \space \lambda_j < 0$$ -------------------------------------------------------------------------------- /TUM/2. Semester/LinAlg/Erzeugendensysteme.md: -------------------------------------------------------------------------------- 1 | ## Linearkombinationen 2 | - Es sei $V$ ein $\mathbb{K}$-Vektorraum mit $v_1, ..., v_n \in V$ und $\lambda_1, ..., \lambda_n \in \mathbb{K}$ 3 | - Man bezeichnet einen Vektor $v \in V$ als Linearkombination von $v_1, ..., v_n$, falls er dargestellt werden kann durch: 4 | $$v = \lambda_1 v_1 + ... + \lambda_n v_n$$ 5 | - Um zu bestimmen ob ein gegebener Vektor $v$ als Linearkombination von $v_1, ..., v_n$ dargestellt werden kann, kann ein [[Lineare Gleichungssysteme|homogenes lineares Gleichungssystem]] verwendet werden 6 | #### Das Erzeugnis 7 | - Fuer $X \subseteq V$ wird definiert: 8 | $$\langle X \rangle = lin(X) = span(X) = \Big \{ \sum_{i = 1}^{n} \lambda_i v_i \mid n \in \mathbb{N}, \lambda_1, ..., \lambda_n \in \mathbb{K}, v_1, ..., v_n \in \mathbb{X} \Big \}$$ 9 | - Gilt $\langle X \rangle = U$, so bezeichnet man $X$ als Erzeugendensystem von $U$ 10 | #### Lineare Unabhaengigkeit 11 | - Die Vektoren $v_1, ..., v_n$ sind linear unabhaengig, falls gilt: 12 | $$\forall \space T \subset \{v_1, ..., v_n\}: \langle T \rangle \subset \langle v_1, ..., v_n \rangle$$ 13 | - Umgekehrt sind die Vektoren linear abhaengig, falls gilt: 14 | $$\exists \space T \subset \{v_1, ..., v_n\}: \langle T \rangle = \langle v_1, ..., v_n \rangle$$ 15 | ###### Kriterium 16 | - Das lineare Gleichungssystem $\lambda_1 v_1 + ... + \lambda_n v_n = 0$ wird aufgestellt 17 | - Hat das LGS genau eine Loesung, so sind die Vektoren linear unabhaengig 18 | - Hat es mehr als eine Loesung, so sind die Vektoren linear abhaengig -------------------------------------------------------------------------------- /TUM/2. Semester/LinAlg/Gaussches Eliminationsverfahren.md: -------------------------------------------------------------------------------- 1 | ## Eliminationsverfahren 2 | - Ein [[Lineare Gleichungssysteme|LGS]] kann geloest werden, indem es in seine Zeilenstufenform ueberfuehrt wird 3 | - Die Umformung erfolgt mithilfe elementarer Zeilenumformungen 4 | - Nach Erreichen der Zeilenstufenform koennen die Loesungen des LGS durch Rueckwaertseinsetzen bestimmt werden 5 | #### Zeilenumformungen 6 | - Vertauschen zweier Zeilen 7 | - Multiplikation einer Zeile mit einem $\lambda \neq 0$ 8 | - Addition des $\lambda$-fachen einer Zeile zu einer anderen Zeile 9 | #### Beispiel 10 | $$\begin{pmatrix} 11 | 1 & 1 & 2 &| & 2 \\ 12 | 2 & 2 & -1 &| & 1 \\ 13 | 3 & 4 & 2 & | & 2 14 | \end{pmatrix} 15 | \leadsto 16 | \begin{pmatrix} 17 | 1 & 1 & 2 & | & 2 \\ 18 | 0 & 1 & -4 & | & -4 \\ 19 | 0 & 0 & -5 & | & -3 20 | \end{pmatrix} 21 | $$ 22 | -------------------------------------------------------------------------------- /TUM/2. Semester/LinAlg/Komplexe Zahlen und Kartesische Koordinaten.md: -------------------------------------------------------------------------------- 1 | ## Grundlagen von komplexen Zahlen 2 | - Die [[Konstruktion der komplexen Zahlen]] erfolgt mithilfe der Menge $\mathbb{R}^2$ 3 | - Es sei $z$ eine beliebige Zahl aus $\mathbb{C} = \{a + bi | a, b \in \mathbb{R}\}$ 4 | - Man bezeichnet $Re(z) = a$ als Realteil und $Im(z) = b$ als Imaginaerteil von $z$ 5 | - Eine beliebige Zahl $w$ ist zu $z$ aequivalent, falls Real- und Imaginaeteil der beiden Zahlen identisch sind 6 | #### Konjugiert komplexe Zahlen 7 | - Man bezeichnet $\overline{z}=a -bi$ als die zu $z$ konjugiert komplexe Zahl 8 | - $\overline{z}$ entsteht somit durch die Spiegelung von $z$ an der reellen Achse 9 | - Fuer $\overline{z}$ gilt: 10 | $$z\overline{z} = (a + bi) \cdot (a - bi) = a^2 + b^2 \in \mathbb{R}$$ 11 | $$\overline{z+w} = \overline{z} + \overline{w}$$ 12 | $$\overline{z \cdot w} = \overline{z} \cdot \overline{w}$$ 13 | #### Betrag einer komplexen Zahl 14 | - Der Abstand $|z|$ einer komplexen Zahl $z$ zum Ursprung bezeichnet man als Betrag von $z$ 15 | - Der Abstand von $z$ zu einer komplexen Zahl $w$ wird durch $|z - w|$ beschrieben 16 | - Fuer $|z|$ gilt: 17 | $$|z| = \sqrt{a^2 + b^2} = \sqrt{z\overline{z}}$$ 18 | #### Multiplikative Inverse einer komplexen Zahl 19 | - Sei $q = \frac{z}{w}$ eine komplexe Zahl 20 | - Fuer das multiplikative Inverse von $q$ gilt: 21 | $$q^{-1}=q^{-1} \cdot \frac{\overline{w}}{\overline{w}}$$ 22 | #### Dreiecksungleichung 23 | - Fuer zwei komplexe Zahlen $z$ und $w$ gilt: 24 | $$|zw| = |z| \cdot |w|$$ 25 | $$|z + w| \leq |z| + |w|$$ 26 | ## Fundamentalsatz der Algebra 27 | - Jedes Polynom $f = a_nx^n + ... + a_1x + a_0$ mit komplexen Koeffizienten $a_n ... a_0$ kann folgendermassen in Linearfaktoren zerlegt werden: 28 | $$f = a_n(x - z_n)^{v_n} + ... + (x - z_1)^{v_1}$$ 29 | - Hierbei sind $z_n ... z_1$ Nullstellen von $p$ mit den Vielfachheiten $v_n ... v_1$ 30 | - Die Zerlegung kann durch wiederholtes Bestimmen der Nullstellen und Polynomdivision ermittelt werden -------------------------------------------------------------------------------- /TUM/2. Semester/LinAlg/Komplexe Zahlen und Polarkoordinaten.md: -------------------------------------------------------------------------------- 1 | ## Grundlagen der Polardarstellung 2 | - Die komplexen Zahlen bilden die [[Konstruktion der komplexen Zahlen|Gausssche Zahlenebene]] und koennen alternativ zur kartesischen Darstellung $(a, b)$ mithilfe von Polarkoordinaten dargestellt werden 3 | - Eine Zahl z wird durch ihre Laenge $r = |z|$ und ihr Argument, den Winkel $\varphi \in (-\pi, \pi]$ zur positiven reellen Achse, beschrieben 4 | #### Umrechnung von Koordinaten 5 | - Aus $(a, b)$ laesst sich $(r, \varphi)$ folgendermassen ermitteln: 6 | $$r = \sqrt{a^2 + b^2}$$ 7 | $$\varphi = 8 | \begin{cases} 9 | arccos(\frac{a}{r}) &\text{, falls $b \geq 0$} \\ 10 | -arccos(\frac{a}{r}) &\text{, falls $b < 0$} 11 | \end{cases} 12 | $$ 13 | - Umgekehrt gilt: 14 | $$a = cos(\varphi) \cdot r$$ 15 | $$b = sin(\varphi) \cdot r$$ 16 | $$z = cos(\varphi)r + isin(\varphi)r = r(cos(\varphi) + isin(\varphi))$$ 17 | - Letztere Form bezeichnet man als Polardarstellung 18 | #### Arithmetik in Polardarstellung 19 | - Es seien $z_1 = r_1(cos(\varphi_1) + isin(\varphi_1))$ und $z_2 = r_2(cos(\varphi_2) + isin(\varphi_2))$ zwei komplexe Zahlen 20 | ###### Multiplikation 21 | $$z_1 \cdot z_2 = r_1r_2(cos(\varphi_1 + \varphi_2) + isin(\varphi_1 + \varphi_2))$$ 22 | - Um das Produkt zu bilden, werden somit die Laengen der Zahlen multipliziert und ihre Argumente addiert 23 | ###### Potenz 24 | $$z^n = r^n(cos(n\varphi) + isin(n\varphi))$$ 25 | ###### Wurzel 26 | - Fuer jede komplexe Zahl $z$ und jedes $n \in \mathbb{N}$ sind $z_k$ mit $k \in \{0, 1, ..., n-1\}$ genau die $n$-ten Wurzeln von $z$ 27 | - Fuer in $z_k$ gilt: 28 | $$z_k = \sqrt[n]{r}(cos(\frac{\varphi + 2k\pi}{n}) + isin(\frac{\varphi + 2k\pi}{n}))$$ -------------------------------------------------------------------------------- /TUM/2. Semester/LinAlg/Konstruktion der komplexen Zahlen.md: -------------------------------------------------------------------------------- 1 | ## Vorgehen 2 | - Zur Konstruktion von $\mathbb{C}$ wird die Menge $\mathbb{R}^2=\{(a, b) | a, b \in \mathbb{R}\}$ betrachtet 3 | - Die Elemente von $\mathbb{R}^2$ sind somit Punkte in einer zweidimensionalen Ebene 4 | - Diese Ebene besitzt eine reelle und eine imaginaere Achse 5 | - Befinden sich Elemente auf der reellen Achse, so entsprechen Addition und Multiplikation dieser Elemente in $\mathbb{R}^2$ den Operationen in $\mathbb{R}$ 6 | #### Definition von Operationen 7 | - Fuer $\mathbb{R}^2$ werden Addition und Multiplikation definiert 8 | - $\mathbb{R^2}$ bildet somit einen [[Algebraische Strukturen|Koerper]] 9 | ###### Addition 10 | - Die Addition von $(a, b)$ und $(c, d)$ wird ueber $(a, b) + (c, d) = (a+c, b+d)$ definiert 11 | - Das neutrale Element bezueglich der Addition ist $(0, 0)$ 12 | - Jedes Element besitzt ein Inverses 13 | ###### Multiplikation 14 | - Die Multiplikation von $(a, b)$ und $(c, d)$ wird ueber $(a,b) \cdot(c, d)=(ac - bd, ad + bc)$ definiert 15 | - Das neutrale Element bezueglich der Multiplikation ist $(1, 0)$ 16 | - Ausser dem Nullvektor hat jedes Element ein Inverses 17 | #### Notation 18 | - Ein Element $(a, 0)$ wird durch $a$ beschrieben 19 | - Das Element $(0, 1)$ wird durch $i$ beschrieben 20 | - Ein beliebiges Element $(a, b)$ kann somit als $a + bi$ dargestellt werden -------------------------------------------------------------------------------- /TUM/2. Semester/LinAlg/Kryptologie.md: -------------------------------------------------------------------------------- 1 | ## Pohlig-Hellman Verfahren 2 | - Es sei $S$ der Sender einer Nachricht $N \in \mathbb{Z}^{\star}_p$ und $R$ ihr Empfaenger, wobei $p$ eine beliebige, aber grosse Primzahl ist 3 | #### Verschluesselung 4 | - Es wird ein $e$ gewaehlt, sodass $ggT(e, p-1) = 1$ ist 5 | - Somit ist $e \in \mathbb{Z}^{\star}_{p-1}$ und besitzt ein Inverses 6 | - $N$ wird ueber $e$ zu $N^e$ verschluesselt 7 | #### Entschluesselung 8 | - Da $e$ ein Inverses besitzt, kann ueber den euklidischen Algorithmus ein $d$ bestimmt werden, sodass gilt: 9 | $$ed = 1 \mod p-1$$ 10 | - Mithilfe von $d$ kann $N^e$ entschluesselt werden: 11 | $$(N^e)^d = N^{ed} = N^{1 + r(p-1)} = N * N^{r(p-1)} = N * (N^{p-1})^r = N * 1^r = N$$ 12 | ## RSA Verfahren 13 | - Es sei $S$ der Sender einer Nachricht $N \in \mathbb{Z}^{\star}_n$ und R ihr Empfaenger 14 | - Zudem stellt $R$ einen public Key $(n, e)$ zur Verfuegung 15 | #### Public Key 16 | - $n$ setzt sich folgendermassen aus dem beiden Primzahlen $p$ und $q$ zusammen: 17 | $$n = pq$$ 18 | - Fuer die [[Restklassengruppen|prime Restklassengruppe]] $\mathbb{Z}^{\star}_n$ gilt somit: 19 | $$|\mathbb{Z}^{\star}_n| = \varphi(n) = (p-1)(q-1)$$ 20 | - $e$ wird so bestimmt, dass gilt: 21 | $$gTT(e, (p-1)(q-1)) = 1$$ 22 | - Somit ist $e \in \mathbb{Z}^{\star}_{(p-1)(q-1)}$ und bestizt ein Inverses 23 | - $N$ wird ueber $e$ zu $N^e$ verschluesselt 24 | #### Private Key 25 | - Da $e$ ein Inverses besitzt, kann ueber den euklidischen Algorithmus ein $d$ bestimmt werden, sodass gilt: 26 | $$ed = 1 \mod (p-1)(q-1)$$ 27 | - Dieses $d$ wird geheim gehalten und kann $N^e$ entschluesseln: 28 | $$(N^e)^d = N^{ed} = N^{1 + r(p-1)(q-1)} = N^1 * (N^{(p-1)(q-1)})^r = N * 1^r = N$$ -------------------------------------------------------------------------------- /TUM/2. Semester/LinAlg/Lineare Algebra.md: -------------------------------------------------------------------------------- 1 | ### [[Komplexe Zahlen und Kartesische Koordinaten]] 2 | ### [[Komplexe Zahlen und Polarkoordinaten]] 3 | ### [[Lineare Gleichungssysteme]] 4 | ### [[Rechnen mit Matrizen]] 5 | ### [[Restklassengruppen]] 6 | ### [[Kryptologie]] 7 | ### [[Erzeugendensysteme]] 8 | ### [[Basen von Vektorraeumen]] 9 | ### [[Lineare Codes]] 10 | ### [[Determinante]] 11 | ### [[Orthogonalithaet]] 12 | ### [[Lineare Ausgleichsrechnung]] 13 | ### [[Lineare Abbildungen]] 14 | ### [[Eigenwerte und Eigenvektoren]] 15 | ### [[Singulaerwertszerlegung]] 16 | ### [[Definitheit von Matrizen]] 17 | ### [[Matrixnormen]] 18 | ### [Flashcards](https://ankiweb.net/shared/info/921866146) -------------------------------------------------------------------------------- /TUM/2. Semester/LinAlg/Lineare Ausgleichsrechnung.md: -------------------------------------------------------------------------------- 1 | ## Orthogonalraum 2 | - Es sei $V$ ein [[Orthogonalithaet|euklidischer Vektorraum]] mit einem Untervektorraum $U$, wobei gilt $dim(V) = n$, $dim(U) = r$ 3 | - Der Orthogonalraum von $U$ wird definiert durch: 4 | $$U^{\perp} = \{v \in V \mid \forall \space u \in U: v \perp u \space \} \leq V$$ 5 | - Fuer den Orthogonalraum $U^{\perp}$ gilt: 6 | $$U \cap U^{\perp} = \{0\}$$ 7 | $$\forall \space v \in V, \exists_1 \space u \in U, \exists_1 \space u' \in U^{\perp}: v = u + u'$$ 8 | $$dim(U^{\perp}) = n - r$$ 9 | ## Orthogonale Projektion 10 | - Es sei $V = \mathbb{R}^n$ ein und $U \leq V$ 11 | - Die orthogonale Projektion $P_U$ wird beschrieben durch: 12 | $$P_U = \begin{cases} 13 | V \rightarrow U \\ 14 | v = u + u^{\perp} \mapsto u \\ 15 | \end{cases}$$ 16 | - Hierbei ist $u$ das Element aus $U$, fuer das die Distanz $||v - u||$ minimal ist 17 | - Es sei $U = \langle b_1, ..., b_r \rangle$ mit $b_i \in \mathbb{R}^n$ und $A = (b_1, ..., b_r) \in \mathbb{R}^{n \times r}$ 18 | - $u$ kann somit mithilfe von $Ax$ mit $x \in \mathbb{R}^r$ beschrieben werden 19 | - Ueber ein [[Lineare Gleichungssysteme|lineares Gleichungssystem]] ist $x$ so zu bestimmen, dass $||v - Ax||$ minimal ist 20 | - Fuer $x$ gilt hierbei die Normalengleichung: 21 | $$A^TAx = A^Tv$$ 22 | #### Methode der kleinsten Quadrate 23 | - Es sei eine Punktwolke $(x_i, y_i)$ gegeben 24 | - Alle Punkte $(x_i, y_i)$ sollen mithilfe der Funktion $f(x) = \beta_1 f_1(x)+ ... + \beta_r f_r(x)$ moeglichst genau approximiert werden 25 | - Es werden die Matrix $A$, sowie die Vektoren $x$ und $v$ festgelegt, sodass gilt: 26 | $$A = \begin{pmatrix} 27 | f_1(x_1) & ... & f_r(x_1) \\ 28 | \vdots & & \vdots \\ 29 | f_1(x_n) & ... & f_r(x_n) 30 | \end{pmatrix}$$ 31 | $$x = (\beta_1, ..., \beta_r)^T$$ 32 | $$v = (y_1, ..., y_n)^T$$ 33 | - Mithilfe der Normalengleichung kann nun $x$ so bestimmt werden, dass $||v - Ax||$ minimal ist -------------------------------------------------------------------------------- /TUM/2. Semester/LinAlg/Matrixnormen.md: -------------------------------------------------------------------------------- 1 | ## Allgemeines 2 | - Fuer eine Matrix $A \in \mathbb{R}^{n \times n}$ wird die die Norm mithilfe der Abbildung $||\cdot||$ definiert: 3 | $$||\cdot|| = \begin{cases} 4 | V \rightarrow \mathbb{R} \\ 5 | v \mapsto ||v|| 6 | \end{cases}$$ 7 | #### Einsnorm 8 | - Fuer Spaltenvektoren $v$ wird die Norm $||v||_1$ definiert ueber: 9 | $$||v||_1 = |v_1| + ... + |v_n|$$ 10 | - Die Einsnorm einer Matrix ist die maximale Spaltensumme 11 | #### Zweinorm 12 | - Fuer Spaltenvektoren $v$ wird die Norm $||v||_2$ definiert ueber: 13 | $$||v||_2 = \sqrt{{v_1}^2 + ... + {v_n}^2}$$ 14 | - Die Zweinorm einer Matrix wird mithilfe der Spektralnorm bestimmt 15 | #### Unendlichkeitsnorm 16 | - Fuer Spaltenvektoren $v$ wird die Norm $||v||_{\infty}$ definiert ueber: 17 | $$||v||_{\infty} = max\{|v_1|, ..., |v_n|\}$$ 18 | - Die Unendlichkeitsnorm einer Matrix ist die maximale Zeilensumme -------------------------------------------------------------------------------- /TUM/2. Semester/LinAlg/Orthogonal- und Orthonormalsystem.md: -------------------------------------------------------------------------------- 1 | ## Allgemeines 2 | - Es sei $(V, \langle \cdot, \cdot \rangle)$ ein beliebiger euklidischer Vektorraum 3 | #### Orthogonalbasis 4 | - $B \subseteq V$ ist ein Orthogonalsystem, falls gilt: 5 | $$\forall \space b_i, b_j \in B, i \neq j: b_i \perp b_j$$ 6 | - Bildet $B$ eine Basis, so bezeichnet man diese als Orthogonalbasis 7 | #### Orthonormalbasis 8 | - $B \subseteq V$ ist ein Orthonormalsystem, falls gilt: 9 | $$\forall \space b_i, b_j \in B, i \neq j: b_i \perp b_j$$ 10 | $$\forall \space b \in B: ||b|| = 1$$ 11 | - Bildet $B$ eine Basis, so bezeichnet man diese als Orthonormalbasis -------------------------------------------------------------------------------- /TUM/2. Semester/LinAlg/Saetze.md: -------------------------------------------------------------------------------- 1 | ## Satz von Lagrange 2 | - Ist $(\mathbb{G}, \cdot)$ eine endliche [[Algebraische Strukturen|Gruppe]], und $(\mathbb{U}, \cdot)$ eine Untergruppe dieser Gruppe, so gilt: 3 | $$|\mathbb{U}| \space | \space |\mathbb{G}|$$ 4 | ## Satz von Euler 5 | - Ist $(\mathbb{G}, \cdot)$ eine endliche Gruppe, so gilt: 6 | $$a^{|\mathbb{G}|} = e$$ 7 | ## Kleiner Satz von Fermat 8 | - Falls $p \in \mathbb{N}$ prim, so gilt, falls $p \nmid a$ 9 | $$\forall \space a \in \mathbb{Z}: a^{p-1} = 1 \mod p$$ 10 | - Und falls $p \mid a$: 11 | $$\forall \space a \in \mathbb{Z}: a^p = a \mod p$$ 12 | ## Determinanten vom Transponierten 13 | - Es sei $A \in \mathbb{K}^{n \times n}$ beliebig 14 | - Fuer $det(A)$ gilt: 15 | $$det(A) = det(A^T)$$ -------------------------------------------------------------------------------- /TUM/2. Semester/LinAlg/Singulaerwertszerlegung.md: -------------------------------------------------------------------------------- 1 | ## Allgemeines 2 | - Zu einer Matrix $A \in \mathbb{R}^{m \times n}$ werden die orthogonalen Matrizen $U \in \mathbb{R}^{m \times m}$ und $V \in \mathbb{R}^{n \times n}$, sowie die Diagonalmatrix $\Sigma \in \mathbb{R}^{m \times n}$ bestimmt, sodass gilt: 3 | $$A = U\Sigma V^T$$ 4 | - Falls $m \leq n$, so hat $\Sigma$ das Format: 5 | $$\Sigma = \begin{pmatrix} 6 | \sigma_1 & ... & 0 & 0 & ... & 0 \\ 7 | & \ddots & & \vdots & & \vdots \\ 8 | 0 & ... & \sigma_r & 0 & ... & 0 9 | \end{pmatrix}$$ 10 | - Falls $n \leq m$, so hat $\Sigma$ das Format: 11 | $$\Sigma = \begin{pmatrix} 12 | \sigma_1 & & 0 \\ 13 | & \ddots & \\ 14 | 0 & & \sigma_r \\ 15 | 0 & ... & 0 \\ 16 | \vdots & & \vdots \\ 17 | 0 & ... & 0 18 | \end{pmatrix}$$ 19 | - Hierbei ist $r = min\{m, n\}$ 20 | #### Bestimmen von $\Sigma$ 21 | - Die Eigenwerte $\lambda_1, ..., \lambda_r, ..., \lambda_n$ von $A^TA$ werden bestimmt 22 | - Von den Eigenwerten werden $\lambda_1, ..., \lambda_r$ betrachtet und absteigend sortiert 23 | - Fuer die Singulaerwerte $\sigma_i$ von $\Sigma$ gilt: 24 | $$\sigma_i = \sqrt{\lambda_i}$$ 25 | #### Bestimmen von V 26 | - Da $A^TA$ symmetrisch ist, bilden die Eigenvektoren $v_1, ..., v_n$ eine [[Orthogonal- und Orthonormalsystem|ONB]] 27 | - Fuer $V$ gilt hierbei: 28 | $$V = (v_1, ..., v_n)$$ 29 | #### Bestimmen von U 30 | - Die Vektoren $u_1, ..., u_r$ werden bestimmt ueber: 31 | $$u_i = \frac{1}{\sigma_i}Av_i$$ 32 | - Falls $r < m$, werden $u_1, ..., u_r$ mithilfe des [[Orthogonalithaet|Gram-Schmidtverfahrens]] zu einer ONB ergaenzt 33 | - Fuer $U$ gilt hierbei: 34 | $$U = (u_1, ..., u_m)$$ -------------------------------------------------------------------------------- /TUM/2. Semester/LinAlg/Skalarprodukt.md: -------------------------------------------------------------------------------- 1 | ## Allgemeines 2 | - Es wird eine Abbildung $\langle \cdot, \cdot \rangle$ wird definiert durch: 3 | $$\langle \cdot, \cdot \rangle: \begin{cases} 4 | V \times V \rightarrow \mathbb{R} \\ 5 | (v, w) \mapsto \langle v, w \rangle \\ 6 | \end{cases}$$ 7 | - Diese Abbildung bezeichnet man als Skalarprodukt, falls sie bilinear, symmetrisch und positiv definit ist: 8 | $$\forall \space v, v', w, \in V: \forall \space \lambda \in \mathbb{R}: \langle \lambda v + v', w \rangle = \lambda \langle v, w \rangle + \langle v', w \rangle$$ 9 | $$\forall \space v, w \in V: \langle v, w \rangle = \langle w, v \rangle$$ 10 | $$\forall \space v \in V: \langle v, v \rangle \geq 0$$ 11 | $$\forall v \in V: \langle v, v \rangle = 0 \equiv v = 0$$ -------------------------------------------------------------------------------- /TUM/3. Semester/3. Semester.md: -------------------------------------------------------------------------------- 1 | ### [[Applied Regression]] 2 | ### [[IT Sicherheit]] 3 | ### [[Numerisches Programmieren]] 4 | ### [[Grundlagen Datenbanken]] 5 | ### [[Grundlagen Betriebssysteme und Systemsoftware]] -------------------------------------------------------------------------------- /TUM/3. Semester/Applied Reg/Applied Regression.md: -------------------------------------------------------------------------------- 1 | ### [[Statistical Basics]] 2 | ### [[Simple Regression]] -------------------------------------------------------------------------------- /TUM/3. Semester/Applied Reg/Images/Pasted image 20231113091328.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/AntonScheitler/Notes/3d5813aa060b0433589208e87737db5646ee26ba/TUM/3. 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Semester/GBS/Betriebssysteme.md: -------------------------------------------------------------------------------- 1 | ## Aufgaben 2 | - Das Betriebssystem bietet Schnittstellen zur Hardware, wie beispielsweise das Lesen und Schreiben von Daten 3 | - Adressraeume und CPU werden ebenfalls von dem Betriebssystem verwaltet 4 | ## Prozesse 5 | - Ein Prozess ist ein Programm, welches ausgefuehrt wird 6 | #### Anforderungen 7 | - Prozesse benoetigen Ressourcen, wie CPU oder Ein- und Ausgabe, um laufen zu koennen 8 | - Jeder Prozess besitzt einen eigenen, abgeschotteten Adressraum, welcher virtualisiert wird 9 | - Ist ein Prozess multi-threaded, so benoetigt er zusaetzliche Register und Befehlszaehler 10 | ## Arbeitsmodi 11 | - Das Betriebssystem bietet unterschiedliche Modi, um Sicherheit zu garantieren 12 | - Programme laufen hauptsaechlich im Benutzermodus und koennen mithilfe von System Calls kontrolliert in den Systemmodus wechseln 13 | - Im Systemmodus kann direkt auf Hardwareressourcen zugegriffen werden 14 | #### Beispiel 15 | ![[Pasted image 20231023150812.png]] 16 | ## Architekturen 17 | - Ein Betriebssystem kann auf unterschiedliche Weisen realisiert werden 18 | #### Monolithisches System 19 | - Das Betriebssystem umfasst eine grosse Menge an Funktionen welche alle im Systemmodus ausgefuehrt werden 20 | - Das System wird hierdurch jedoch unuebersichtlich und schwer zu warten 21 | ###### Beispiel 22 | ![[Pasted image 20231023150752.png]] 23 | #### Mikrokernel System 24 | - Das Betriebssystem wird in mehrere, kleine Module aufgeteilt 25 | - Der Mikrokern laeuft als einziges Modul im Systemmodus und verwaltet Scheduling 26 | - Alle anderen Systemdienste laufen als Serverprozess im Benutzermodus 27 | - Benoetigt ein Programm einen Dienst, so erfolgt die Kommunikation ueber den Mikrokern 28 | ###### Beispiel 29 | ![[Pasted image 20231023152522.png]] 30 | -------------------------------------------------------------------------------- /TUM/3. Semester/GBS/GBS.apkg: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/AntonScheitler/Notes/3d5813aa060b0433589208e87737db5646ee26ba/TUM/3. Semester/GBS/GBS.apkg -------------------------------------------------------------------------------- /TUM/3. Semester/GBS/Grundlagen Betriebssysteme und Systemsoftware.md: -------------------------------------------------------------------------------- 1 | ### [[Betriebssysteme]] 2 | ### [[Prozessverwaltung]] 3 | ### [[Scheduling]] 4 | ### [[Parallele Systeme und Synchronisation]] 5 | ### [[Modellierung paralleler Systeme]] 6 | ### [[Interprozesskommunikation]] 7 | ### [[Speichermanagement]] 8 | ### [[Dateisysteme]] 9 | ### [[Ein- und Ausgabe]] 10 | ### [[Virtualisierung]] 11 | ### Download Flashcards -------------------------------------------------------------------------------- /TUM/3. 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Semester/GDB/Datenintegritaet.md: -------------------------------------------------------------------------------- 1 | ## Referentielle Integritaet 2 | - Fremdschluessel einer Relation muessen auf existierende Tupel verweisen, oder null sein 3 | - Die Intigritaet muss erhalten bleiben, falls sich das referenzierte Tupel aendert oder geloescht wird 4 | - Hierfuer gibt es unterschiedliche Herangehensweisen 5 | #### Cascade 6 | - Mithilfe des **cascade** Schluesselworts werden die Aenderungen kaskadiert 7 | - Wird das referenzierte Tupel beispielsweise geloescht, so wird auch das referenzierende Tupel geloescht 8 | #### Set Null 9 | - Mithilfe des **set null** Schluesselworts wird der Fremdschluessel bei Aenderungen auf null gesetzt 10 | ## Statische Integritaetsbedingungen 11 | - Mithilfe von statischen Integritaetsbedingungen wird festgelegt, welche Werte ein Attribut annehmen kann 12 | - Diese Integritaetsbedingungen werden mithilfe von **check** definiert 13 | ###### Beispiel 14 | ```sql 15 | create table Users( 16 | name varchar(30), 17 | ... 18 | age integer check(age > 0) 19 | ); 20 | ``` 21 | - Es wird sichergestellt, dass das Alter eines Nutzers positiv ist 22 | ```sql 23 | create table Likes( 24 | id integer, 25 | tweet_id integer, 26 | ... 27 | creation_date date check(not exists( 28 | select * from Tweet t 29 | where t.id = tweet_id 30 | and creation_date < t.creation_date 31 | ) 32 | ) 33 | foreign key (tweet_id) references Tweet(id) 34 | ) 35 | ``` 36 | - Es wird sichergestellt, dass ein Like nicht vor seinem entsprechenden Tweet erstellt werden kann -------------------------------------------------------------------------------- /TUM/3. Semester/GDB/GDB.apkg: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/AntonScheitler/Notes/3d5813aa060b0433589208e87737db5646ee26ba/TUM/3. Semester/GDB/GDB.apkg -------------------------------------------------------------------------------- /TUM/3. Semester/GDB/Grundlagen Datenbanken.md: -------------------------------------------------------------------------------- 1 | ### [[Konzeptuelle Modellierung]] 2 | ### [[Relationales Datenmodell]] 3 | ### [[SQL]] 4 | ### [[Datenintegritaet]] 5 | ### [[Relationale Entwurfstheorie]] 6 | ### [[Physische Datenorganisation]] 7 | ### [[Anfragebearbeitung]] 8 | ### [[Transaktionen]] 9 | ### [[Mehrbenutzersynchronisation]] 10 | ### Download Flashcards -------------------------------------------------------------------------------- /TUM/3. 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Semester/GDB/Konzeptuelle Modellierung.md: -------------------------------------------------------------------------------- 1 | ## Entity-Relationship Modell 2 | - Fuer den Konzeptuellen Entwurf einer Datenbank werden Entity-Relationship Modelle verwendet 3 | #### Entities 4 | - Verschiedene Entities stehen in Beziehungen zueinander 5 | - Entities werden zudem mithilfe von Attributen beschrieben 6 | - Das Schluesselattribut ist ein Attribut, welches den Entity eindeutig definiert 7 | ###### Schwacher Entitytyp 8 | - Alle Entities eines schwachen Typs nehmen an einer Beziehung Teil 9 | - Der Schluessel eines schwachen Entities ergibt sich aus seinem partiellen Schluessel und dem des Entites zu dem die Beziehung besteht 10 | ###### Beispiel 11 | ![[Pasted image 20231018114626.png]] 12 | ![[Pasted image 20231018124624.png]] 13 | #### Beziehungen 14 | ###### n-stellige Beziehungen 15 | - Man unterscheidet 1:1, 1:n, sowie n:m Beziehungen 16 | - Hierbei wird jeweils ausgedrueckt wieviele Entities eines Typs in einer Beziehung mit Entities eines anderen Typs stehen 17 | ###### Min-Max Beziehungen 18 | - Bei einer Beziehung wird ausgedrueckt, an wievielen Beziehungen eine Entity mindestens und hoechstens teilnehmen kann 19 | ###### Beispiel 20 | ![[Pasted image 20231018123352.png]] 21 | ![[Pasted image 20231018123412.png]] -------------------------------------------------------------------------------- /TUM/3. Semester/ITSec/IT Sicherheit.md: -------------------------------------------------------------------------------- 1 | ### [[Schwachtellen und Angriffe]] 2 | ### [[Kryptographie]] 3 | ### [[Kryptographische Hashfunktionen]] 4 | ### [[Schluesselmanagement]] 5 | ### [[Authentisierung]] 6 | ### [[Public Key Infrastructure]] 7 | ### [[Netzwerksicherheit]] 8 | ### [[Rechtemanagement]] 9 | ### [[Systemsicherheit]] 10 | ### Download Flashcards -------------------------------------------------------------------------------- /TUM/3. Semester/ITSec/ITSec.apkg: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/AntonScheitler/Notes/3d5813aa060b0433589208e87737db5646ee26ba/TUM/3. Semester/ITSec/ITSec.apkg -------------------------------------------------------------------------------- /TUM/3. 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Semester/ITSec/Netzwerksicherheit.md: -------------------------------------------------------------------------------- 1 | ## Transportsicherheit 2 | - Der Transport von Datenpaketen in einem Netzwerk muss sicher gestaltet werden 3 | - Diese Sicherheitsziele werden auf verschiedene Weisen realisiert 4 | #### Transport Layer Security 5 | - Mithilfe von TLS kann ein sicherer Kommunikationskanal zwischen zwei Entitaeten erzeugt werden 6 | ###### Handshake 7 | - Der Client sendet eine Zufallszahl, eine Menge von Ciphersuites, die entsprechenden [[Schluesselmanagement|Diffie-Hellman]] Parameter und eine Menge von Signaturverfahren an den Server 8 | - Der Server sendet eine Zufallszahl, eine Ciphersuite, einen Diffie-Hellman Parameter, das Zertifikat und $Sig(H(\nabla))$, sowie $HMAC(\nabla)$, verschluesselt mit $k_{SC}$ 9 | - Nun besitzen sowohl der Client, als auch der Server das shared secret und der Client versendet abschliessend $HMAC(\nabla)$, verschluesselt mit $k_{CS}$ 10 | ![[Pasted image 20240109151035.png]] 11 | #### Firewall Architekturen 12 | - Um das Versenden und Empfangen ungewollter Nachrichten zu verhindern, werden Firewalls verwendet 13 | - Firewalls koennen unterschiedliche Formen annehmen 14 | ###### Paketfilter 15 | - Anhand der Headerdaten eines Pakets wird entschieden, ob es weitergeleitet wird, oder nicht 16 | ###### Deep Package Inspection 17 | - Sowohl die Headerdaten, als auch die Payload eines Pakets werden analysiert 18 | - Somit kann Malware blockiert werden 19 | ###### Application Layer Gateway 20 | - Die Kommunikation wird auf Proxys in der Firewall umgeleitet 21 | - Die Firewall hat Einblick in die Applikation und nutzt diesen Hintergrund, um Pakete besser zu filtern -------------------------------------------------------------------------------- /TUM/3. 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Semester/NumProg/NumProg.apkg -------------------------------------------------------------------------------- /TUM/3. Semester/NumProg/Numerisches Programmieren.md: -------------------------------------------------------------------------------- 1 | ### [[Fliesskommazahlen und Rundung]] 2 | ### [[Interpolation]] 3 | ### [[Integration]] 4 | ### [[Loesen linearer Gleichungssysteme]] 5 | ### [[Differentialgleichungen]] 6 | ### [[Iterative Verfahren]] 7 | ### [[Eigenwertprobleme]] 8 | ### Download Flashcards 9 | -------------------------------------------------------------------------------- /TUM/4. Semester/4. Semester.md: -------------------------------------------------------------------------------- 1 | ### [[Grundlagen Rechnernetze und Verteilte Systeme]] 2 | ### [[Einfuehrung in die Theoretische Informatik]] 3 | ### [[Modellbildung und Simulation]] 4 | ### [[Diskrete Wahrscheinlichkeitstheorie]] -------------------------------------------------------------------------------- /TUM/4. Semester/DWT/Diskrete Wahrscheinlichkeitstheorie.md: -------------------------------------------------------------------------------- 1 | ### [[Diskrete Wahrscheinlichkeitsraeume]] 2 | ### [[Kontinuierliche Wahrscheinlichkeitsraeume]] 3 | ### [[Induktive Statistik]] 4 | ### [[Stochastische Prozesse]] -------------------------------------------------------------------------------- /TUM/4. Semester/DWT/Images/Pasted image 20240708102651.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/AntonScheitler/Notes/3d5813aa060b0433589208e87737db5646ee26ba/TUM/4. Semester/DWT/Images/Pasted image 20240708102651.png -------------------------------------------------------------------------------- /TUM/4. Semester/GRnVS/Grundlagen Rechnernetze und Verteilte Systeme.md: -------------------------------------------------------------------------------- 1 | ### [[Physikalische Schicht]] 2 | ### [[Sicherungsschicht]] 3 | ### [[Vermittlungsschicht]] 4 | ### [[Transportschicht]] 5 | ### [[Sitzungs-, Darstellungs- und Anwendungsschicht]] -------------------------------------------------------------------------------- /TUM/4. 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Semester/ModSim/Directional Fields.md: -------------------------------------------------------------------------------- 1 | ## Visualizing Differential Equations 2 | - In order to visualize a differential equation, a directional field, consisting of arrows in a field, can be used 3 | - Each arrow describes how a sepecific point will change over time 4 | #### Construction 5 | - In order to construct a vector field, a few steps are required 6 | ###### Nullclines 7 | - Nullclines are linear lines, at which a differential equation equals zero 8 | - Those nullclines can be thought of as the axes of directional fields 9 | ![[Pasted image 20240722172000.png]] 10 | ###### Steady States 11 | - Steady states are the intersections of nullclines 12 | - Directional fields, in a certain sense, exist only to identify steady states as either attractive, repulsive, or saddle points 13 | ![[Pasted image 20240722172251.png]] 14 | ###### Considering Signs 15 | - The direction of arrows depends on the sign of a differential equation in a sector 16 | - These sectors are defined by the nullclines 17 | - For each sector, the signs of all differential equations are combined 18 | ![[Pasted image 20240722173211.png]] 19 | ![[Pasted image 20240722173226.png]] 20 | ###### Construct Arrows 21 | - Once the direction of arrows has been defined for every sector, they can be drawn 22 | - It is important to consider the fact, that arrows might cross nullclines and don't have to be in line with them 23 | ![[Pasted image 20240722173539.png]] 24 | #### Example 25 | ![[Pasted image 20240722163726.png]] -------------------------------------------------------------------------------- /TUM/4. 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Semester/ModSim/Job Scheduling.md: -------------------------------------------------------------------------------- 1 | ## Scheduling 2 | - A set of tasks $A_1, ..., A_n$ is run on a set of machines $M_1, ..., M_m$, where each task takes a certain amount of time 3 | - The task execution must be ordered such that the resulting schedule is optimal 4 | - Precedences define, which task needs to be executed before which, creating an ordering of tasks 5 | #### Graph View 6 | - Using tasks as vertices and precedences as edges, a graph view of a schedule can be constructed 7 | - A virtual initial vertex $A_S$ and a virtual final vertex $A_E$ serve as the start and end points of the graph 8 | - If tasks are assigned to different machines, they can be iterated through concurrently 9 | ###### Schedule Construction 10 | - One option to construct a schedule, is to start every task, as soon as all preceding tasks have been completed 11 | - Alternatively, the completion time of $A_E$ can be used to determine the latest possible time, a task needs to finish at, in order to still meet the completion time of $A_E$ 12 | - Those approaches are the forward and backward step and they both result in an optimal schedule 13 | ###### Critical Paths 14 | - A path in a schedule is critical, if there can be no downtime between tasks on it 15 | ###### Example 16 | ![[Pasted image 20240516155357.png]] 17 | #### Job Shop 18 | - In a job shop model, tasks are divided into subtasks, which need to run on a specific machine and are all dependent on one another 19 | ###### Disjunctive Edges 20 | - If the subtasks $A_{x, y}$ and $B_{i, j}$ of two different tasks happen to be executed on the same machine, a clear ordering cannot be established immediately 21 | - Instead, disjunctive edges, which face from $A_{x, y}$ to $B_{i, j}$ and the other way around, are created 22 | - In a disjunctive edge assignment, each of the edges is tested out, removing the corresponding one 23 | - Using this assignment, an optimal schedule can be determined -------------------------------------------------------------------------------- /TUM/4. Semester/ModSim/Modellbildung und Simulation.md: -------------------------------------------------------------------------------- 1 | ### [[Calculus]] 2 | ### [[Nash Equilibrium and Banzhaf Power Index]] 3 | ### [[Zero-Sum Games and Elections]] 4 | ### [[Job Scheduling]] 5 | ### [[Population Dynamics]] 6 | ### [[Directional Fields]] 7 | ### [[Ordinary Differential Equations]] 8 | ### [[Fuzzy Control]] 9 | ### [[Heat Conduction]] 10 | ### [[Markov Chains]] 11 | ### [[Traffic Modelling]] -------------------------------------------------------------------------------- /TUM/4. Semester/ModSim/Nash Equilibrium and Banzhaf Power Index.md: -------------------------------------------------------------------------------- 1 | ## Nash Equilibrium 2 | - A Nash equilibrium is reached, if every player's strategy is optimal given the strategies of all other players 3 | - As such, a player would have no interest in changing strategies, since it would only result in a worse result for themselves 4 | ## Banzhaf Power Index 5 | - The Banzhaf power index is used to describe the influence of a party in a political system 6 | - In this system, all parties have a weight $ and can either vote yes, or no 7 | - A vote is passed, if the weights of the parties voting yes exceeds a specific quorum $q$ 8 | #### Computing the Index 9 | - The Banzhaf power index of a party is the number of scenarios, in which it would sway the vote 10 | - More specifically given a set of parties $\{S_1, ..., S_n\}$ with weights $w_1, ..., w_n$, the Banzhaf power index of $S_i$ is defined as 11 | $$|T|, \; \; T \subseteq S \setminus \{S_i\}: \sum_{k \in T} w_k < q \leq \sum_{k \in T \cup \{S_i\}} w_k$$ 12 | ###### Relative Index 13 | - The relative Banzhaf power index of a party is it's absolute index, divided by the sum of power indices of all parties -------------------------------------------------------------------------------- /TUM/4. Semester/Theo/Einfuehrung in die Theoretische Informatik.md: -------------------------------------------------------------------------------- 1 | ### [[Grundlagen formaler Sprache]] 2 | ### [[Regulaere Sprachen]] 3 | ### [[Kontextfreie Sprachen]] 4 | ### [[Berechenbarkeit und Entscheidbarkeit]] 5 | ### [[Komplexitaetstheorie]] -------------------------------------------------------------------------------- /TUM/4. Semester/Theo/Images/Pasted image 20240430153859.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/AntonScheitler/Notes/3d5813aa060b0433589208e87737db5646ee26ba/TUM/4. Semester/Theo/Images/Pasted image 20240430153859.png -------------------------------------------------------------------------------- /TUM/4. 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Semester/Theo/Images/Pasted image 20240603144116.png -------------------------------------------------------------------------------- /TUM/5. Semester/5. Semester.md: -------------------------------------------------------------------------------- 1 | ### [[Maschinelles Lernen]] 2 | ### [[Real-Time Systems]] -------------------------------------------------------------------------------- /TUM/5. Semester/ML/Classification Performance.md: -------------------------------------------------------------------------------- 1 | ## Binary Classification Performance 2 | - In order to determine the performance of a binary classification algorithm, a confusion table is used 3 | #### Confusion Table 4 | - A confusion table for a binary classification algorithm has the following form: 5 | ![[Pasted image 20241018104453.png]] 6 | #### Attributes 7 | - Based on the amounts of true positives and negatives and false ones, a number of attributes can be defined: 8 | - Accuracy: $\frac{TP + TN}{TP + TN + FP + FN}$ 9 | - Precision: $\frac{TP}{TP + FP}$ 10 | - Sensitivity: $\frac{TP}{TP + FN}$ 11 | - Specificity: $\frac{TN}{FP + TN}$ 12 | - Depending on the type of problem at hand, certain attributes are more relevant than others -------------------------------------------------------------------------------- /TUM/5. Semester/ML/Hyperparameters.md: -------------------------------------------------------------------------------- 1 | ## Tuning Hyperparameters 2 | - The goal of tuning hyperparameters is to develop the model, that performs best on unseen data 3 | #### Approach 4 | - To tune hyperparameters, a dataset is split into a training set, a validation set and a test set 5 | - Using the training set and validation set, the optimal hyperparameters can be determined 6 | - These hyperparameters can then be tested against the test set 7 | ###### Example 8 | ![[Pasted image 20241015122517.png]] 9 | #### Overfitting 10 | - Overfitting occurs, when the model is trained too closely on the training data 11 | - In training, the model therefore shows very good results, but since it is generalized poorly, it underperforms on unseen data 12 | ###### Batteling Overfitting 13 | - The model is optimized using the validation data in a training loop 14 | - At the end of training, the model is tested against the test data set 15 | - This test data set must only be used once, to avoid meta optimization on the test data 16 | ###### Example 17 | ![[Pasted image 20241021144659.png]] 18 | #### K-fold Cross-Validation 19 | - In order to optimize training, when the underlying dataset is small, the dataset is split into $K$ sections, where $K - 1$ sections are used for training and one for validation 20 | - A different section is used for training on every training round 21 | - Over mutliple rounds, each section will have been used once for validation and the optimal hyperparameters can be obtained by averaging the best parameters for each round 22 | ###### Leave-one-out cross-validation 23 | - In leave-one-out cross-validation, there are as many sections, as there vectors 24 | - This means that the validation data consists of just a single data vector 25 | - This approach yields the optimal model but is very expensive so it should only be used on small datasets 26 | ###### Example 27 | ![[Pasted image 20241021150209.png]] -------------------------------------------------------------------------------- /TUM/5. 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Semester/ML/Images/Pasted image 20250201173823.png -------------------------------------------------------------------------------- /TUM/5. Semester/ML/Maschinelles Lernen.md: -------------------------------------------------------------------------------- 1 | ### [[k-Nearest Neighbors]] 2 | ### [[Decision Trees]] 3 | ### [[Probabalistic Inference]] 4 | ### [[Linear Regression]] 5 | ### [[Linear Classification]] 6 | ### [[Optimization]] 7 | ### [[Deep Learning 1]] 8 | ### [[Deep Learning 2]] 9 | ### [[SVMs and Kernels]] 10 | ### [[Dimensionality Reduction]] 11 | ### [[Clustering]] -------------------------------------------------------------------------------- /TUM/5. Semester/ML/k-Nearest Neighbors.md: -------------------------------------------------------------------------------- 1 | ## Basic Concepts 2 | - Given a training dataset of categorized vectors, the $k$ nearest neighbors approach yields the category for new vectors 3 | - To determine the category of a new vector, the categories of its $k$ nearest neighbors are counted and the majority is chosen 4 | - The [[Classification Performance|performance of the classification]] can be improved by weighing a vector's neighbors based on their distance from it 5 | #### Distance Measuring 6 | - A number of distance measures can be used, in order to determine the distance between two neighbors 7 | #### Hyperparameter $k$ 8 | - The number $k$ of the neighbors the model considers is a hyperparameter, that needs to be [[Hyperparameters|tuned]] 9 | ###### Example 10 | ![[Pasted image 20241015122632.png]] 11 | ## Classification Pitfalls 12 | - Certain classification errors can appear, if a few of the common pitfalls aren't avoided 13 | #### Standardization 14 | - Many models are sensitive to differences in scale 15 | - To work around this sensitivity, the training data is standardized, so that the mean is always $0$ and variance always $1$ 16 | - Given a set of training vectors $x_i$, the training set can be standardized as follows: 17 | $$x_{i, \text{std}} = \frac{x_i - \mu_i}{\sigma_i}$$ 18 | ###### Handling Input and Output 19 | - Once the model has been trained, and is being used, inputs will not adhere to the standardization automatically 20 | - As such, they need to be standardized before being fed to the model and it's output needs to be destandardized accordingly 21 | #### Dimensionality 22 | - The more dimensions the input space has, the less of the space is covered by the same amount of vectors 23 | - For a precise classification, the number of vectors thus needs to grow exponentially with the number of features 24 | ###### Example 25 | ![[Pasted image 20241018160305.png]] -------------------------------------------------------------------------------- /TUM/5. 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Semester/RTS/Real-Time Hardware.md: -------------------------------------------------------------------------------- 1 | ## Microcontroller 2 | - A microcontroller consists of a few different parts, that are all connected to each other on a single board 3 | #### Microprocessor 4 | - A microprocessor consists of a control unit, an ALU and a few registers 5 | - This microprocessor can be connected to IO, timers and memory via busses to form a microcomputer 6 | ###### Example 7 | ![[Pasted image 20241107161304.png]] 8 | #### Example 9 | ![[Pasted image 20241107161317.png]] -------------------------------------------------------------------------------- /TUM/5. Semester/RTS/Real-Time Systems.md: -------------------------------------------------------------------------------- 1 | ### [[Time and Clocks]] 2 | ### [[Real-Time Hardware]] -------------------------------------------------------------------------------- /TUM/5. Semester/RTS/Time and Clocks.md: -------------------------------------------------------------------------------- 1 | ## Time Measurements in Computers 2 | - Computers measure time based on a multiple of a periodically created microtick 3 | - The granularity of a clock describes the size of the intervals between microticks 4 | ![[Pasted image 20241031162537.png]] 5 | #### Measurement Errors 6 | - Assuming there is a perfect clock $z$, and all other clocks are compared against it 7 | - Given a clock $k$ with a granularity of $g^k$ which is equal to $10$ microticks of $z$, or $n^k$ 8 | - The drift of this clock is described by: 9 | $$\text{drift}_i^k = \frac{z (\text{microtick}^k_{i + 1}) - z(\text{microtick}^k_i)}{n^k}$$ 10 | - The drift is thereforce the relation of the microticks performed by $k$ to the microticks it is supposed to perform 11 | - From this, the drift rate $\rho$ can be computed: 12 | $$\rho_i^k = | \text{drift}_i^k - 1|$$ 13 | - A perfect clock therefore has a drift rate of $0$ 14 | ###### Example 15 | ![[Pasted image 20241031163456.png]] 16 | ![[Pasted image 20241031163504.png]] -------------------------------------------------------------------------------- /TUM/6. Semester/IDSST/Introduction to Data Science and Statistical Thinking.md: -------------------------------------------------------------------------------- 1 | ### [[Data Basics]] 2 | ### [[Numerical Data]] 3 | ### [[Probability]] 4 | ### [[Predictive Modeling]] -------------------------------------------------------------------------------- /TUM/6. Semester/Markovketten/Markovketten.md: -------------------------------------------------------------------------------- 1 | ### [[Definitions]] 2 | ### [[Linear Algebra in Markov Chains]] 3 | ### [[Stationary Distributions]] -------------------------------------------------------------------------------- /TUM/TUM.md: -------------------------------------------------------------------------------- 1 | ### [[1. Semester]] 2 | ### [[2. Semester]] 3 | ### [[3. Semester]] 4 | ### [[4. Semester]] 5 | ### [[5. Semester]] --------------------------------------------------------------------------------