**MTH ****101: Introduction to Mathematics ****(3)**

*Course Contents*:

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. Sequences and series of real and complex numbers.

Matrices, Determinant, Solving system of linear equations.

Symmetry of Plane Figures: Translations, Rotations, Reflections, Glide-reflections, Rigid motion.

*If time permits: Divisibility of integers.

*Suggested 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).
- R. Goldberg, "Methods of Real Analysis", Oxford & IBH Publishing Co. Pvt. Ltd, New Delhi, 1976.
- R. G. Bartle and D. R. Sherbert, "Introduction to Real Analysis", John Wiley & Sons, 1992.

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