Learn · An Invitation to Mathematics
Lecture 33 of 36Week-7 Number theory
Divisibility, prime numbers
Prof. Sankaran Vishwanath · IMSc
Credits and licence
- From
- An Invitation to Mathematics, IMSc (at NPTEL)
- Licence
- CC BY-NC-SA, as NPTEL states it. Non-commercial use only.
- Attribution
- NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge. Coordinated by IIT Madras.
- Who can watch
- Tweens profiles and older. How courses are placed
All the lectures
- Introduction
- Long division
- Applications of Long division
- Lagrange interpolation
- The 0-1 idea in other contexts - dot and cross product
- Taylors formula
- The Chebyshev polynomials
- Counting number of monomials - several variables
- Permutations, combinations and the binomial theorem.
- Combinations with repetition, and counting monomials.
- Combinations with restrictions, recurrence relations
- Fibonacci numbers; an identity and a bijective proof.
- Permutations and cycle type
- The sign of a permutation, composition of permutations
- Rules for drawing tangle diagrams
- Signs and cycle decompositions
- Sorting lists of numbers, and crossings in tangle diagrams
- Real and integer valued polynomials
- Integer valued polynomials revisited.
- Functions on the real line, continuity
- The intermediate value property.
- Visualizing functions.
- Functions on the plane, Rigid motions.
- More examples of functions on the plane, dilations.
- Composition of functions
- Affine and Linear transformations
- Length and Area dilation, the derivative
- Examples-I
- Examples-II
- Linear equations, Lagrange interpolation revisited
- Completed Matrices in combinatorics
- Polynomials acting on matrices
- Divisibility, prime numbers
- Congruences, Modular arithmetic
- The Chinese remainder theorem
- The Euclidean algorithm, the 0-1 idea and the Chinese remainder theorem