Engineering Mathematics
29 articles in this topic
Permutations and Combinations for GATE CS: Counting Questions Solved with a Repeatable Method
One repeatable method (choose, arrange, subtract) applied to 20 GATE-style counting problems, with the four-question decision procedure that replaces formula memorisation for permutations and combinations in GATE CS.
Group Theory and Algebraic Structures: Groups, Rings and Fields Explained
Group theory for GATE CS: binary operations, group axioms, abelian and cyclic groups, subgroups, Lagrange's theorem, rings, fields and a worked Zn example.
Set theory and relations: closures, equivalence and partial orders explained
Antisymmetric is not the negation of symmetric, a transitive closure is not finished after one pass, and a Hasse diagram is what is left once you delete every edge transitivity already implies. Set operations, relation properties, closures, equivalence classes and posets, worked for GATE.
Combinational circuits: multiplexers, decoders and adders explained
A combinational circuit's output depends only on its current inputs, with no stored state. Multiplexers, decoders, encoders and adders are the blocks GATE keeps testing, and a single 4-to-1 MUX can implement any three-variable Boolean function using just one inverter.
Regular expressions and the pumping lemma, with the exam angle
Regular expressions and the pumping lemma explained: the operators, closure properties, and a worked proof that a^n b^n is not regular, with the exam angle.