Learn · NPTEL

Course11110608336 lectures

An Invitation to Mathematics

Prof. Sankaran Vishwanath · IMSc

Start with lecture 1 At NPTEL

Lectures

Week-1 Polynomials

  1. Introduction Video
  2. Long division Video
  3. Applications of Long division Video
  4. Lagrange interpolation Video
  5. The 0-1 idea in other contexts - dot and cross product Video
  6. Taylors formula Video
  7. The Chebyshev polynomials Video
  8. Counting number of monomials - several variables Video

Week-2 Combinatorics

  1. Permutations, combinations and the binomial theorem. Video
  2. Combinations with repetition, and counting monomials. Video
  3. Combinations with restrictions, recurrence relations Video
  4. Fibonacci numbers; an identity and a bijective proof. Video
  5. Permutations and cycle type Video
  6. The sign of a permutation, composition of permutations Video
  7. Rules for drawing tangle diagrams Video
  8. Signs and cycle decompositions Video
  9. Sorting lists of numbers, and crossings in tangle diagrams Video

Week-3 Polynomials in Combinatorics

  1. Real and integer valued polynomials Video
  2. Integer valued polynomials revisited. Video

Week-4 Functions

  1. Functions on the real line, continuity Video
  2. The intermediate value property. Video
  3. Visualizing functions. Video
  4. Functions on the plane, Rigid motions. Video
  5. More examples of functions on the plane, dilations. Video
  6. Composition of functions Video
  7. Affine and Linear transformations Video
  8. Length and Area dilation, the derivative Video

Week-5 Conservation principles

  1. Examples-I Video
  2. Examples-II Video

Week-6 Matrices

  1. Linear equations, Lagrange interpolation revisited Video
  2. Completed Matrices in combinatorics Video
  3. Polynomials acting on matrices Video

Week-7 Number theory

  1. Divisibility, prime numbers Video
  2. Congruences, Modular arithmetic Video
  3. The Chinese remainder theorem Video
  4. The Euclidean algorithm, the 0-1 idea and the Chinese remainder theorem Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IMSc
Department
Mathematics
Teacher
Prof. Sankaran Vishwanath
Level
Undergraduate
Language
English
Subjects
Mathematics
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
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
NPTEL gives no rating. Invisible Network shows it to Tweens profiles and older, judged from what the source says about it. How courses are placed