Objective: This course aims to help the students clear the fundamentals of mathematics and experience the joy of doing mathematics. It will let the students discover patterns and do various activities which will make them appreciate the beauty of mathematics.
Syllabus: The course will include but not be limited to the following topics.
Mathematical Pictures, Mathematical Sentences, Linear Equations, Perfect Squares, Rectangular Arrays, Divisors and Multiples, Eratosthenes Sieve, Divisibility, Prime Factorisation, GCD, LCM, Euclid’s Algorithm, Quadratic Equations, Pythagoras Theorem, Fibonacci Numbers, Golden Mean, Square and Square Roots, Continued Fractions, Telescoping, Geometric Series, Triangular Numbers, Sums of Powers of Natural Numbers, Mathematical Induction, Well Ordering Principle, Limits, Sequences, Pascal’s Triangle.
Schedule: There will be online lectures through Google Meet/Zoom. The exact schedule will be intimated to the students in advance.
Assignment: Problems will be uploaded to Moodle platform after each lecture. The students are expected to solve these problems and upload their solutions within a stipulated time.
- Teacher: Gaurav Bhatnagar
- Teacher: Ningombam Cha Cogent
Objective: This course aims to help the students develop elite problem solving skills. It will focus mainly on solving olympiad type problems.
Syllabus: The course will cover various topics from Number Theory, Algebra, Geometry and Combinatorics. It will include but not be limited to the following topics.
Number Theory: Divisibility, Congruences, Fermat’s Little Theorem, Euler’s Theorem, Wilson’s Theorem, Lagrange’s Theorem, Chinese Remainder The- orem, Basis Representation, Diophantine Equations.
Algebra: Polynomials, Inequalities, Functional Equations.
Geometry: Euler’s Line, Torricelli’s Point, Carnot’s Theorem, Appolonius Theorem, Thales’ Theorem, Ceva’s Theorem, Menelaus’ Theorem, Stewart’s Theorem, Ptolemy’s Theorem, Nine-Point Circle.
Combinatorics: Counting Principles, Permutations, Combinations, Pigeon- hole Principle, Inclusion-Exclusion Principle, Recurrence Relations.
Schedule: There will be online lectures through Google Meet or Zoom. The exact schedule will be intimated to the students in advance.
Assignment: Problems will be uploaded to Moodle platform. The students are expected to solve these problems within a stipulated time.
- Teacher: Gaurav Bhatnagar
- Teacher: Ningombam Cha Cogent