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Course11110490048 lectures

An Introduction to Number Theory

Prof. Somnath Jha · IIT Kanpur

Start with lecture 1 At NPTEL

Lectures

Week 1

  1. Lecture 1: Abelian Groups - I Video
  2. Lecture2: Abelian Groups - II Video
  3. Lecture3: Abelian Groups - III Video
  4. Lecture 4: Abelian Groups - IV Video

Week 2

  1. Lecture 5: Abelian Groups - V Video
  2. Lecture 6: Abelian Groups - VI Video
  3. Lecture 7: Commutative Rings - I Video
  4. Lecture 8: Commutative Rings - II Video

Week 3

  1. Lecture 9: Commutative Rings -III Video
  2. Lecture 10: Chinese Reminder Theorem Video
  3. Lecture 11: Fermat's Little Theorem and Wilson's Theorem Video
  4. Lecture 12: Prime ideals and maximal ideals Video

Week 4

  1. Lecture 13: Ideals in a PID Video
  2. Lecture 14: Ideals in a UFD Video
  3. Lecture 15: Gauss Lemma Video
  4. Lecture 16: Field Extensions Video

Week 5

  1. Lecture 17: Finite Fields Video
  2. Lecture 18: Multiplicative groups of finite fields Video
  3. Lecture 19: Legendre Symbol Video
  4. Lecture 20: Quadratic Reciprocity Video

Week 6

  1. Lecture 21: Zero sets of polynomials Video
  2. Lecture 22 : Ring of quadratic integers - I Video
  3. Lecture 23 : Ring of quadratic integers - II Video
  4. Lecture 24 : Gaussian integers Video

Week 7

  1. Lecture 25: Ring of quadratic integers - III Video
  2. Lecture 26 : Ring of quadratic integers - IV Video
  3. Lecture 27: Ideal class group of quadratic fields Video
  4. Lecture 28: Binary quadratic forms Video

Week 8

  1. Lecture 29: Binary quadratic forms and ideal class group of imaginary quadratic fields – I Video
  2. Lecture 30: Binary quadratic forms and ideal class group of imaginary quadratic fields – II Video
  3. Lecture 31: Binary quadratic forms and ideal class group of imaginary quadratic fields – III Video
  4. Lecture 32: Binary quadratic forms and ideal class group of imaginary quadratic fields – IV Video

Week 9

  1. Lecture 33: Units in the rings of quadratic integers Video
  2. Lecture 34: Integral solutions of the equation 𝑥 2 − 2𝑦 2 = 1 Video
  3. Lecture 35: Dirichlet's approximation theorem Video
  4. Lecture 36: Brahmagupta - Pell's equation Video

Week 10

  1. Lecture 37: Congruent Numbers - I Video
  2. Lecture 38: Congruent Numbers - II Video
  3. Lecture 39: The n = 4 case of the Fermat's Last Theorem Video
  4. Lecture 40: Congruent Numbers and Elliptic Curves Video

Week 11

  1. Lecture 41: Sum of two squares theorem Video
  2. Lecture 42: Sum of four squares theorem Video
  3. Lecture 43: Sum of integer cubes Video
  4. Lecture 44: Rational cube sum problem Video

Week 12

  1. Lecture 45: Affine and Projective Spaces- I Video
  2. Lecture 46: Affine and Projective Spaces- II Video
  3. Lecture 47: Elliptic Curves - I Video
  4. Lecture 48: Elliptic Curves - II Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Kanpur
Department
Mathematics
Teacher
Prof. Somnath Jha
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
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