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Mathematical Foundations in CS

The document outlines key concepts in the Mathematical Foundation of Computer Science, including relations, functions, mathematical induction, algebraic structures, calculus, linear equations, determinants, vector spaces, and propositional logic. It covers various types and properties of these mathematical concepts, as well as their applications in computer science. The content serves as a foundational overview for understanding complex mathematical principles relevant to the field.

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Ayush Singh
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52 views2 pages

Mathematical Foundations in CS

The document outlines key concepts in the Mathematical Foundation of Computer Science, including relations, functions, mathematical induction, algebraic structures, calculus, linear equations, determinants, vector spaces, and propositional logic. It covers various types and properties of these mathematical concepts, as well as their applications in computer science. The content serves as a foundational overview for understanding complex mathematical principles relevant to the field.

Uploaded by

Ayush Singh
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOCX, PDF, TXT or read online on Scribd
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Mathematical Foundation of Computer Science

Relation: Type and compositions of relations, Pictorial


representation of relations, Equivalence relations, Partial ordering
relation.
Function: Types, Composition of function, Recursively defined
function.
Mathematical Induction: Piano's axioms, Mathematical Induction,
Discrete Numeric Functions and Generating functions, Simple
Recurrence relation with constant coefficients, Linear recurrence
relation without constant coefficients, Asymptotic Behaviour of
functions
Algebric Structures: Properties, Semi group, monoid, Group,
Abelian group, properties of group, Subgroup, Cyclic group, Cosets,
Permutation groups, Homomorphism, Isomorphism and
Automorphism of groups.
Calculus: Functions, limits and Continuity, differentiation and
Integration, Differential Equations.
Linear equations and Matrices: Row/column operations, Gaussian
Elimination, Decomposition, inverse.
Determinant: Properties of determinants, Cramer's Rule,
determinants to transpose and inverse.
Vector spaces: Linear independence, Bases, subspace and
dimensionality. Inner Products and Norms: Length, angle, direction
cosines; Orthogonalization.
Prepositional Logic: Preposition, First order logic, Basic logical
operations, Tautologies, Contradictions, Algebra of Proposition,
Logical implication, Logical equivalence, Normal forms, Inference
Theory, Predicates and quantifiers, Posets, Hasse Diagram.

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