Method of Mathematical Proofs: Induction, Construction, Contradiction, Contrapositive.
Set: Union and Intersection of sets, Distributive laws, De Morgan's Law, Finite and infinite sets.
Relation: Equivalence relation and equivalence classes.
Function: Injections, Surjections, Bijections, Composition of functions, Inverse function, Graph of a function.
Countable and uncountable sets, Natural numbers via Peano arithmetic, Integers, Rational numbers, Real Numbers and Complex Numbers. Matrices, Determinant, Solving system of linear equations, Gauss elimination method, Linear mappings on R2 and R3, Linear transformations and Matrices.
Symmetry of Plane Figures: Translations, Rotations, Reflections, Glide-reflections, Rigid motions.
- G. Polya, “How to Solve It”, Princeton University Press, 2004.
- K. B. Sinha et. al., “Understanding Mathematics”, Universities Press (India), 2003.
- M. Artin, “Algebra”, Prentice-Hall of India, 2007 (Chapters 1, 4, 5).
- J. R. Munkres, “Topology”, Prentice-Hall of India, 2013 (Chapter 1).