Siksha Sarovar

Siksha Sarovar (sikshasarovar.com) is a free educational web application that helps students in India learn programming and prepare for academic and competitive exams. The platform offers structured coding courses (C, C++, Python, Java, HTML, CSS, PHP, Power BI, AI, Machine Learning, Data Science), complete university curriculum notes for BCA/MCA students with previous year question papers, Class 10 and Class 12 CBSE/HBSE school notes, and dedicated preparation material for SSC, UPSC, Banking, Railway and other government exams. Browsing the site is completely free and requires no account. Users may optionally sign in with Google solely to save their learning progress, quiz scores and personal preferences across devices.

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Siksha Sarovar is a free e-learning platform for coding courses, BCA university notes and competitive exam preparation. Optional Google sign-in saves your learning progress across devices.

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About This Course

Lesson 1 of 17 in the free Mathematical Foundation of CS notes on Siksha Sarovar, written by Rohit Jangra.

Mathematical Foundation of Computer Science — BCA I Semester

Discrete mathematics is the language in which computer science is written. Every data structure is a set with structure, every program condition is a proposition, every algorithm's running time is a recurrence, and every network is a graph. This course builds the mathematical toolkit you will reuse in Data Structures, DBMS, Operating Systems, Computer Networks, Theory of Computation, and Cryptography.

Unit-Wise Syllabus

UnitCore TopicsLessons in this Course
Unit 1Set theory (operations, De Morgan's laws, power sets, Cartesian products), relations (equivalence, partial orders, Hasse diagrams, closures), functions (injective/surjective/bijective, composition, inverse, pigeonhole principle)3
Unit 2Propositional logic (connectives, truth tables, tautologies, CNF/DNF), predicate logic (quantifiers, inference rules), proof techniques (direct, contrapositive, contradiction, mathematical & strong induction)3
Unit 3Combinatorics (sum/product rules, permutations, combinations, binomial theorem, inclusion–exclusion), recurrence relations (characteristic equation, Tower of Hanoi, Fibonacci closed form), generating functions3
Unit 4Graph theory (handshaking lemma, Euler & Hamiltonian paths, planarity, coloring), trees (spanning trees, traversals), Boolean algebra (laws, K-maps, logic gates)3
Unit 5Number theory (divisibility, Euclid's & extended Euclid's algorithms, primes, modular arithmetic, Fermat's little theorem, crypto/hashing applications), matrices (determinants, inverse, linear systems, adjacency matrices)3

How the Exam Usually Tests This Subject

  1. One compulsory question of short answers sampling every unit (definitions, one-line computations, true/false with reason).
  2. One long question per unit — typically a "prove" part (De Morgan, induction, handshaking lemma) plus a "solve" part (K-map, recurrence, gcd, determinant).
  3. Marks are awarded for method shown step-by-step, not just final answers. Every worked example in these lessons is written the way an examiner expects the solution on paper.

How to Study This Course

  • Do the algebra by hand. Reading a solved recurrence is not the same as solving one. Re-derive every worked example with the book closed.
  • Memorize the law tables (set identities, logical equivalences, Boolean axioms) — they are direct 2–3 mark questions and the toolkit for every proof.
  • Finish every lesson's 🎯 Exam Focus block. The questions are modeled on actual end-term papers.

Notation Used Throughout

SymbolMeaningSymbolMeaning
∈, ⊆, ∅membership, subset, empty set∀, ∃for all, there exists
∪, ∩, A'union, intersection, complement¬, ∧, ∨, →, ↔not, and, or, implies, iff
Acardinality of Aa ≡ b (mod m)m divides a − b
C(n, r), P(n, r)combinations, permutations⌊x⌋, ⌈x⌉floor, ceiling
x^2, 2^npowers (plain-text exponent)Σ, ∎summation, end of proof
PYQ papers are available at the end of the lesson list — attempt the December 2023 paper after finishing all five units.