Core course for B.Sc. (Research) Mathematics. Not available as UWE.
Credits (Lec:Tut:Lab)= 3:1:0 (3 lectures and 1 tutorial weekly)
Overview: Introduction to modern mathematical language and reasoning: Sets and Logic, Proof strategies, Functions, Induction.
- 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.
- 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