Prof. Amritanshu Prasad
Professor , The Institute of Mathematical Science , Chennai
Amritanshu Prasad is a mathematician at The Institute of Mathematical Sciences, Chennai,
working in algebraic combinatorics and representation theory.
Degree Level Course
Mathematical Thinking
To introduce ideas of proofs and problem solving in mathematics and to help in the transition from learning basic mathematical methods to the learning of more advanced mathematical methods and ideas.
Code
BSMA2001
Credits
4 Credits
Type
Elective
Prerequisites
None
12-Week Roadmap
Course Structure & Syllabus
For details of standard term assessment timelines and exam structures, visit our Academics page.
WEEK 1
triangular numbers, Sigma Notation for Summation, Sequences, Peano's axioms for the natural numbers,
Set Theory: the language of Mathematics, Hilbert Hotel, Bijections and Cardinality, The Natural Numbers,
The Integers
WEEK 2
A Trip to Cantorsville, Cantor's Diagonalization Argument, Towards the Real Numbers, Ordered Field,
Completeness Axiom, The Least Upper Bound Property, Mathematical Logic and Statements
WEEK 3
Currency Game, Divisibility, Greatest Common Divisor, The Euclidean Algorithm, Proof of the Euclidean
Algorithm, Test for Divisibility
WEEK 4
Fermat's Little Theorem, Fundamental Theorem of Arithmetic, Modular Arithmetic, Arithmetic with
Congruences, Infinitude of Primes, Inclusion–Exclusion Principle
Reading List
Prescribed Books & References
- “Mathematical Thinking: Problem-solving and Proofs”, John D’Angelo and Douglas West, Pearson, 2000 (2nd edition)
- “Mathematical Proofs: A Transition to Advanced Mathematics”, G. Chartrand, A. D. Polimeni, P. Zhang, Pearson, 2012
Faculty & Experts
About the Instructors
Prof. Sankaran Viswanath
Professor , The Institute of Mathematical Science , Chennai
Sankaran Viswanath is a mathematician at The Institute of Mathematical Sciences, Chennai,
working in algebraic combinatorics and representation theory.