Core course for B.Sc. (Research) Mathematics. Not available as UWE.

**Credits (Lec:Tut:Lab)**= 3:1:0 (3 lectures and 1 tutorial weekly)

**Prerequisites: **None

**Overview: **Introduction to modern mathematical language and reasoning: Sets and Logic, Proof strategies, Functions, Induction.

**Detailed Syllabus:**

**Sentential Logic:**Deductive reasoning, negation of a sentence, conjunction and disjunction of sentences, equivalence of sentences, truth tables, logical connectives.**Sets:**Operations on sets, Venn diagrams, cartesian product, quantifiers.**Proof Strategies:**Direct proofs, proofs involving negations, conditionals, conjunctions, and disjunctions, existence and uniqueness proofs, proofs involving equivalence.**Relations and Functions:**Ordered pairs, equivalence relations, equivalence classes, partitioning of a set, functions as many-one relations, graphs of functions, one-one functions, onto functions, inverse of a function, images and inverse images of sets.**Mathematical Induction:**Division algorithm, principle of mathematical induction, well ordering principle, strong induction, principle of recursive definition.**More on Sets:**Finite and infinite sets, countable and uncountable sets.

**References:**

- Book of Proof by Richard Hammack, 2nd edition, Richard Hammack.
*Mathematical Thinking*by Keith Devlin, Lightning Source.*How to Prove It*by Daniel J. Velleman, Cambridge University Press.*Mathematical Writing*by Franco Vivaldi, Springer.*Proofs and Fundamentals*by Ethan D. Bloch, Springer.*Introduction to Logic and to the Methodology of Deductive Sciences,*Alfred Tarski, Oxford University Press.

**Past Instructors**: Amber Habib, Priyanka Grover