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01 Semesters (BSc)
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Semester 1
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Discrete Maths
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Lecture Notes
Folder: 01-Semesters-(BSc)/Semester-1/Discrete-Maths/Lecture-Notes
27 items under this folder.
Sep 12, 2025
01 Intro and Statements
Sep 12, 2025
02 Propositional Logic and Formulas
Sep 12, 2025
03 Logical Equivalence, Tautological Implication and Modus Ponens
Sep 12, 2025
04 Quantifiers
Sep 12, 2025
05 Proof Types
Sep 12, 2025
06 Set Theory and Russels Paradox
Sep 12, 2025
07 Equality, Ordered Pairs, Cartesian Product, Power Set and Relationships
Sep 12, 2025
08 Relations, Compositions and Properties
Sep 12, 2025
09 Equivalency Relation and Classes, Partitions, Partially Ordered Sets
Sep 12, 2025
10 Posets, Hasse Diagrams, Lexicographical Ordering, Special Elements, Functions, Countability, Infinities
Sep 12, 2025
11 Functions, Relations, Cardinality, Countability, Cantor's Diagonalization Argument
Sep 12, 2025
12 Cardinality, Number Theory, Rings, Euclidian Rings, Ideal, Congruence, Modular Arithmetic, Diophantine Equations
Sep 12, 2025
13 Modular Arithmetics, Set of Residues, Diffie-Hellman, Multiplicative Inverse, Chinese Remainder Theorem
Sep 12, 2025
14 Algebraic Structures and Operations, Monoids, Inverses, Groups, Group Properties, Landscape of Groups
Sep 12, 2025
15 Groups, Homomorphism, Isomorphism, Preservation of Identity and Inverses
Sep 12, 2025
16 Isomorphism, Powers, Order, Generators, Lagrange's Theorem, Multiplicative Groups, Euler's Totient Function, RSA
Sep 12, 2025
17 Rings, Polynomial Rings, Integral Domains, Units
Sep 12, 2025
18 Rings, Fields, Real Polynomial Fields, Polynomial Fields, Galois Fields
Sep 12, 2025
19 Factorizations, Polynomial Fields and Division, Polynomial Interpolation, Constructing Galois Fields
Sep 12, 2025
20 Generators in Finite Fields, Properties of Finite Fields, Error Correcting Codes, Reed-Solomon Codes
Sep 12, 2025
21 Logic, Proof Systems, Logical Consequence, Syntactic Derivation
Sep 12, 2025
22 Proof Systems, Syntax, Semantics, Equivalence, Satisfiability, Tautologies, Normal Forms, Types of Statements
Sep 12, 2025
23 Predicate Logic Reintroduced, Syntax, Semantics, Universe Size
Sep 12, 2025
24 Evaluating and Proving Formulas in Predicate Logic, Equivalences, Transformations, Variable Substitution, Universal Instantiation, Equality, Prenex Normal Form
Sep 12, 2025
25 Skolem Normal Form, Russell's Paradox, Cantor's Diagonalization, Existence of Uncomputable Functions, Higher-Order Logic, Calculi
Sep 12, 2025
26 Syntactic Derivation vs Semantic Entailment, Logic Calculus, Sequent Calculus, Resolution Calculus
Sep 12, 2025
27 Soundness and Completeness of Resolution Calculus, NP and SAT problem