Course content (17 lessons)

1. About This Course — 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…
2. Unit 1: Set Theory — Types, Operations & De Morgan's Laws — 1.1 What is a Set? A set is a well-defined, unordered collection of distinct objects, called its elements . "Well-defined" means membership is never ambiguous: for any object x…
3. Unit 1: Relations, Equivalence Relations & Partial Orders — 2.1 Binary Relations A binary relation R from set A to set B is any subset of A × B: R ⊆ A × B. If (a, b) ∈ R we write a R b . A relation on A is a subset of A × A. Since A × A =…
4. Unit 1: Functions, Composition, Inverse & the Pigeonhole Principle — 3.1 Functions as Special Relations A function f: A → B is a relation from A to B in which every element of A is related to exactly one element of B. A is the domain , B the…
5. Unit 2: Propositional Logic, Truth Tables & Normal Forms — 4.1 Propositions and Connectives A proposition is a declarative sentence that is definitively true (T) or false (F). "2 + 2 = 5" is a (false) proposition; "x + 1 = 3" and "Close…
6. Unit 2: Predicate Logic, Quantifiers & Rules of Inference — 5.1 Predicates and Quantifiers Propositional logic cannot express "every prime greater than 2 is odd" — it has no way to talk about all or some objects. A predicate P(x) is a…
7. Unit 2: Proof Techniques — Direct, Contradiction & Induction — 6.1 The Proof Toolkit A proof is a finite chain of statements, each an axiom, a premise, or a consequence of earlier statements by a valid inference rule. For a claim of the form…
8. Unit 3: Combinatorics — Permutations, Combinations & Binomial Theorem — 7.1 The Two Basic Rules Product rule: a task done in a sequence of stages with n1, n2, ..., nk choices per stage has n1·n2···nk outcomes. Example: passwords of 3 letters followed…
9. Unit 3: Recurrence Relations — Hanoi, Fibonacci & Characteristic Roots — 8.1 What is a Recurrence Relation? A recurrence relation defines a sequence by expressing a(n) in terms of earlier terms, plus enough initial conditions to pin the sequence down.…
10. Unit 3: Generating Functions — An Introduction — 9.1 The Idea: Sequences as Power Series The (ordinary) generating function of a sequence a(0), a(1), a(2), ... is the formal power series G(x) = a(0) + a(1)x + a(2)x^2 + ... = Σ…
11. Unit 4: Graph Theory — Handshaking, Euler, Planarity & Coloring — 10.1 Terminology and the Handshaking Lemma A graph G = (V, E) is a set of vertices and a set of edges joining pairs of vertices. Type Multiple edges? Loops? Directed? :--- :---…
12. Unit 4: Trees, Spanning Trees & Traversals — 11.1 What is a Tree? A tree is a connected graph with no cycles. For a graph T with n vertices, the following are all equivalent characterizations — any one can serve as the…
13. Unit 4: Boolean Algebra, K-Maps & Logic Gates — 12.1 Axioms of Boolean Algebra A Boolean algebra is a set B = {0, 1} with operations + (OR), · (AND), and ' (complement) satisfying the Huntington postulates : Postulate + form ·…
14. Unit 5: Divisibility, Primes, GCD & Euclid's Algorithms — 13.1 Divisibility and the Division Algorithm For integers a ≠ 0 and b, a divides b (written a b) iff b = a·c for some integer c. Properties: if a b and a c then a (bx + cy) for…
15. Unit 5: Modular Arithmetic, Congruences & Cryptography — 14.1 Congruences a ≡ b (mod m) iff m (a − b), equivalently a and b leave the same remainder on division by m. Congruence mod m is an equivalence relation on Z (Unit 1) whose…
16. Unit 5: Matrices, Determinants & Linear Systems — 15.1 Matrices and Their Types An m × n matrix is a rectangular array of numbers with m rows and n columns; A[i][j] denotes the entry in row i, column j. Type Definition :--- :---…
17. PYQ: End Term December 2023

About This Course

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

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 Foc

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Frequently asked questions

Is the Mathematical Foundation of CS course really free?

Yes. The entire Mathematical Foundation of CS course on Siksha Sarovar is free to read with no account required. You can optionally sign in with Google to save your progress.

Do I get a certificate for Mathematical Foundation of CS?

Yes — finish the lessons and pass the quiz to earn a free, verifiable certificate you can share on LinkedIn or with recruiters.

Can I run code while learning?

Yes. The built-in online compiler runs C, C++, Python, Java, PHP, JavaScript, C# and SQL directly in your browser — no installation needed.