Course No

M101

Credit

3

Syllabus

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 R

^{2}and R^{3}, Linear transformations and Matrices.Symmetry of Plane Figures: Translations, Rotations, Reflections, Glide-reflections, Rigid motions.

Reference Books

- 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).

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