📝 Mathematics Blog
Concepts, theorems, solved problems, and the fascinating history of mathematics — for B.Sc., M.Sc., CSIR NET, GATE & IIT JAM students.
Computing Suprema and Infima: Standard Techniques
Master the two-condition method & ε-characterisation to rigorously compute sup and inf of any bounded set. Worked examples for CSIR NET, GATE, IIT JAM.
The Architect of Matrices: Arthur Cayley
Discover the life and mathematical legacy of Arthur Cayley, the British mathematician who pioneered matrix algebra and group theory.
Bounds and Extrema of Sets: Subsets of an Ordered Field and Boundedness
Upper and lower bounds, bounded above/below, supremum and infimum — definitions, properties, and worked examples for B.Sc., M.Sc., CSIR NET, GATE, IIT JAM.
Évariste Galois — The Young Revolutionary Who Rewrote Algebra
The short, dramatic life of Évariste Galois and the birth of modern algebra through symmetry and groups. Free mathematics notes for BSc, MSc, CSIR NET, GATE and IIT JAM.
Intervals and the Real Line
Intervals and the Real Line — all six interval types, bounded vs unbounded, absolute value form, the Nested Interval Property, and visualisation on the real line. Free mathematics notes for BSc, MSc, CSIR NET, GATE and IIT JAM.
Absolute Value and the Real Line
Absolute Value and the Real Line — covering absolute value real numbers, triangle inequality proof, reverse triangle inequality. Free mathematics notes for BSc, MSc, CSIR NET, GATE and IIT JAM.
Order Relations and Ordered Sets
Order Relations and Ordered Sets — covering order relations mathematics, partial order total order, ordered field real numbers. Free mathematics notes for BSc, MSc, CSIR NET, GATE and IIT JAM.
Foundations of Real Numbers: Understanding the Number System
Foundations of Real Numbers: Understanding the Number System — covering real number system foundations, natural numbers integers rationals, irrational numbers real line. Free mathematics notes for BSc, MSc, CSIR NET, GATE and IIT JAM.
Consequences of Field Axioms
Consequences of Field Axioms — covering consequences field axioms, uniqueness zero identity, cancellation laws fields. Free mathematics notes for BSc, MSc, CSIR NET, GATE and IIT JAM.
Algebraic Structures and Field Axioms
Algebraic Structures and Field Axioms — covering algebraic structures mathematics, field axioms explained, group ring field mathematics. Free mathematics notes for BSc, MSc, CSIR NET, GATE and IIT JAM.
Finite, Infinite, Countable and Uncountable Sets
Finite, Infinite, Countable and Uncountable Sets — covering countable uncountable sets, Cantor diagonal argument, Schroeder Bernstein theorem. Free mathematics notes for BSc, MSc, CSIR NET, GATE and IIT JAM.
Functions and Relations — Mappings Between Sets
Functions and Relations — Mappings Between Sets — covering functions relations mathematics, equivalence relations explained, injective surjective bijective functions. Free mathematics notes for BSc, MSc, CSIR NET, GATE and IIT JAM.
Logic and Proof Methods — The Language of Mathematics
Logic and Proof Methods — The Language of Mathematics — covering mathematical logic proof methods, propositions logical connectives, truth tables explained. Free mathematics notes for BSc, MSc, CSIR NET, GATE and IIT JAM.
Sets and Basic Notation — A Foundation for Mathematics
Sets and Basic Notation — A Foundation for Mathematics — covering set theory basics, set builder notation explained, subsets power sets. Free mathematics notes for BSc, MSc, CSIR NET, GATE and IIT JAM.
Srinivasa Ramanujan — The Man Who Knew Infinity
Srinivasa Ramanujan — The Man Who Knew Infinity — covering Srinivasa Ramanujan biography, Ramanujan mathematics genius, Ramanujan Hardy collaboration. Free mathematics notes for BSc, MSc, CSIR NET, GATE and IIT JAM.