Dr. Bivash Majumder | Academic Profile | BMLabs Mathematics

Academic contributor

Profile and affiliation

Assistant Professor in Mathematics

Prabhat Kumar College, Contai

Purba Medinipur, West Bengal, India

Academic contributions

Contribution roadmap

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Authored subject

Discrete Mathematics

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Abstract Algebra

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Authored subject

Real Analysis

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Functional Analysis

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Curated pathways

Comprehensive module covering 5 sections in Functional Analysis.

Comprehensive module covering 6 sections in Discrete Mathematics.

Assistant Professor in Mathematics

Contribution roadmap

Basic Logical Connectives and Truth Tables

Statements and Primitive Statements

Negation and Compound Statements

Conjunction and Disjunction

Implication and Biconditional

Open Sentences and Truth Values

Truth Tables for Basic Connectives

Symbolic Translation of Compound Statements

Conditional Statements and Programming Decisions

Parentheses in Compound Truth Tables

Tautologies, Contradictions, and Valid Arguments

Truth-Table Applications

Logical Equivalence and the Laws of Logic

Equivalent Forms of Compound Statements

De Morgan's Laws

Distributive Laws for Logical Connectives

Laws of Logic

Duality in Logical Equivalence

Substitution Rules for Logical Equivalence

Negation and Duals of Conditional Statements

Converse, Inverse, and Contrapositive

Nested Conditionals and Program Logic

Simplification of Compound Statements

Switching Networks and Logical Equivalence

NAND and NOR Connectives

Logical Implication and Rules of Inference

Valid Arguments and Logical Implication

Direct Rules of Inference

Invalid Conditional Reasoning

Conjunction and Disjunction Rules

Contradiction and Indirect Proof

Proofs Using Several Rules of Inference

Invalid Arguments and Counterexamples

Predicates and Quantifiers

Open Statements and Universe of Discourse

Existential and Universal Quantifiers

Implicit Quantification and Universe Dependence

Quantifiers in Programming Statements

Truth Conditions for Quantified Statements

Logical Equivalence and Implication of Predicates

Converse, Inverse, and Contrapositive of Quantified Implications

Logical Laws for Quantified Statements

Negation of Quantified Statements

Multiple and Nested Quantifiers

Negation of Nested Quantified Statements

Unique Existence

Quantifiers Definitions And Proofs Of Theorems

Biconditional Definitions with Quantifiers

Proof by Exhaustion and Theorem Terminology

Universal Specification in Quantified Arguments

Universal Generalization in Theorem Proofs

Quantifier Laws and Existential Rules

Integer Parity Definitions and Direct Proofs

Indirect Proof Methods for Theorems

Definition and Examples of Groups

Additive Groups Number Systems

Binary Operations on Sets

First Nonexamples of Groups

Four Group Axioms

Group Definition

Multiplicative Groups Nonzero Numbers

Verify Group Axioms

Standard Examples of Groups

Additive Groups Modulo N

Alternating Groups

Groups From Number Systems

Klein Four Group

Permutation Groups

Roots of Unity Groups

Semigroup Conditions for Groups

Finite Cancellative Semigroups

Idempotents in Finite Semigroups

Semigroup Equation Criterion for Groups

Semigroups

Unique Idempotent Semigroups

Elementary Properties of Groups

Cancellation Laws in Groups

Equations in Groups