1 
Integers 
Prof. Shripad M. Garge , IIT Bombay 

Monday 

2 
Divisibility and Primes 
Prof. Shripad M. Garge , IIT Bombay 

Monday 

3 
Integers 
Prof. Shripad M. Garge , IIT Bombay 

Monday 

4 
Divisibility and Primes 
Prof. Shripad M. Garge , IIT Bombay 

Monday 

5 
Integers 
Prof. Shripad M. Garge , IIT Bombay 

Monday 

6 
Divisibility and Primes 
Prof. Shripad M. Garge , IIT Bombay 

Monday 

7 
Integers 
Prof. Shripad M. Garge , IIT Bombay 

Tuesday 

8 
Divisibility and Primes 
Prof. Shripad M. Garge , IIT Bombay 

Tuesday 

9 
Integers 
Prof. Shripad M. Garge , IIT Bombay 

Wednesday 

10 
Divisibility and Primes 
Prof. Shripad M. Garge , IIT Bombay 

Wednesday 

11 
Infinitude of primes 
Prof. Shripad M. Garge , IIT Bombay 


Thursday 


12 
Division algorithm and the GCD 
Prof. Shripad M. Garge , IIT Bombay 


Thursday 


13 
Infinitude of primes 
Prof. Shripad M. Garge , IIT Bombay 


Friday 


14 
Division algorithm and the GCD 
Prof. Shripad M. Garge , IIT Bombay 


Friday 


15 
Infinitude of primes 
Prof. Shripad M. Garge , IIT Bombay 


Saturday 


16 
Division algorithm and the GCD 
Prof. Shripad M. Garge , IIT Bombay 


Saturday 


17 
Computing the GCD and Euclid's lemma 
Prof. Shripad M. Garge , IIT Bombay 

Monday 

18 
Fundamental Theorem of Arithmetic 
Prof. Shripad M. Garge , IIT Bombay 

Monday 

19 
Computing the GCD and Euclid's lemma 
Prof. Shripad M. Garge , IIT Bombay 

Tuesday 

20 
Fundamental Theorem of Arithmetic 
Prof. Shripad M. Garge , IIT Bombay 

Tuesday 

21 
Computing the GCD and Euclid's lemma 
Prof. Shripad M. Garge , IIT Bombay 

Wednesday 

22 
Fundamental Theorem of Arithmetic 
Prof. Shripad M. Garge , IIT Bombay 

Wednesday 

23 
Stories around primes 
Prof. Shripad M. Garge , IIT Bombay 

Thursday 

24 
Winding Upon'primes'and introducing 'congruences' 
Prof. Shripad M. Garge , IIT Bombay 

Thursday 

25 
Stories around primes 
Prof. Shripad M. Garge , IIT Bombay 

Friday 

26 
Winding Upon'primes'and introducing 'congruences' 
Prof. Shripad M. Garge , IIT Bombay 

Friday 

27 
Stories around primes 
Prof. Shripad M. Garge , IIT Bombay 

Saturday 

28 
Winding Upon'primes'and introducing 'congruences' 
Prof. Shripad M. Garge , IIT Bombay 

Saturday 

29 
Dasic result in congruences 
Prof. Shripad M. Garge , IIT Bombay 


Monday 


30 
Residue classes modulo n 
Prof. Shripad M. Garge , IIT Bombay 


Monday 


31 
Dasic result in congruences 
Prof. Shripad M. Garge , IIT Bombay 


Tuesday 


32 
Residue classes modulo n 
Prof. Shripad M. Garge , IIT Bombay 


Tuesday 


33 
Dasic result in congruences 
Prof. Shripad M. Garge , IIT Bombay 


Wednesday 


34 
Residue classes modulo n 
Prof. Shripad M. Garge , IIT Bombay 


Wednesday 


35 
Arithmetic modulo n,theory and examples 
Prof. Shripad M. Garge , IIT Bombay 

Thursday 

36 
Arithmetic modulo n more Examples 
Prof. Shripad M. Garge , IIT Bombay 

Thursday 

37 
Arithmetic modulo n,theory and examples 
Prof. Shripad M. Garge , IIT Bombay 

Friday 

38 
Arithmetic modulo n more Examples 
Prof. Shripad M. Garge , IIT Bombay 

Friday 

39 
Arithmetic modulo n,theory and examples 
Prof. Shripad M. Garge , IIT Bombay 

Saturday 

40 
Arithmetic modulo n more Examples 
Prof. Shripad M. Garge , IIT Bombay 

Saturday 

41 
Solving Linear Polynomials modulo n â€“ I 
Prof. Shripad Garge , IIT Bombay 


Monday 


42 
Solving Linear Polynomials modulo n â€“ II 
Prof. Shripad Garge , IIT Bombay 


Monday 


43 
Solving Linear Polynomials modulo n â€“ I 
Prof. Shripad Garge , IIT Bombay 


Tuesday 


44 
Solving Linear Polynomials modulo n â€“ II 
Prof. Shripad Garge , IIT Bombay 


Tuesday 


45 
Solving Linear Polynomials modulo n â€“ I 
Prof. Shripad Garge , IIT Bombay 


Wednesday 


46 
Solving Linear Polynomials modulo n â€“ II 
Prof. Shripad Garge , IIT Bombay 


Wednesday 


47 
Solving Linear Polynomials modulo n â€“ IV 
Prof. Shripad Garge , IIT Bombay 

Thursday 

48 
Function spacesII 
Prof. Ramadevi , IIT Bombay 

Thursday 

49 
Solving Linear Polynomials modulo n â€“ IV 
Prof. Shripad Garge , IIT Bombay 

Friday 

50 
Function spacesII 
Prof. Ramadevi , IIT Bombay 

Friday 

51 
Solving Linear Polynomials modulo n â€“ IV 
Prof. Shripad Garge , IIT Bombay 

Saturday 

52 
Function spacesII 
Prof. Ramadevi , IIT Bombay 

Saturday 

53 
Chinese remainder theorem, the initial cases 
Prof. Shripad Garge , IIT Bombay 

Monday 

54 
Chinese remainder theorem, the general case and
examples 
Prof. Shripad Garge , IIT Bombay 

Monday 

55 
Chinese remainder theorem, the initial cases 
Prof. Shripad Garge , IIT Bombay 

Tuesday 

56 
Chinese remainder theorem, the general case and
examples 
Prof. Shripad Garge , IIT Bombay 

Tuesday 

57 
Chinese remainder theorem, the initial cases 
Prof. Shripad Garge , IIT Bombay 

Wednesday 

58 
Chinese remainder theorem, the general case and
examples 
Prof. Shripad Garge , IIT Bombay 

Wednesday 

59 
Chinese remainder theorem, more examples 
Prof. Shripad Garge , IIT Bombay 

Thursday 

60 
Using the CRT, square roots of 1 in Zn 
Prof. Shripad Garge , IIT Bombay 

Thursday 

61 
Chinese remainder theorem, more examples 
Prof. Shripad Garge , IIT Bombay 

Friday 

62 
Using the CRT, square roots of 1 in Zn 
Prof. Shripad Garge , IIT Bombay 

Friday 

63 
Chinese remainder theorem, more examples 
Prof. Shripad Garge , IIT Bombay 

Saturday 

64 
Using the CRT, square roots of 1 in Zn 
Prof. Shripad Garge , IIT Bombay 

Saturday 

65 
Wilson's Theorem 
Prof. Shripad Garge , IIT Bombay 

Monday 

66 
Roots of polynomials over Zp 
Prof. Shripad Garge , IIT Bombay 

Monday 

67 
Wilson's Theorem 
Prof. Shripad Garge , IIT Bombay 

Tuesday 

68 
Roots of polynomials over Zp 
Prof. Shripad Garge , IIT Bombay 

Tuesday 

69 
Wilson's Theorem 
Prof. Shripad Garge , IIT Bombay 

Wednesday 

70 
Roots of polynomials over Zp 
Prof. Shripad Garge , IIT Bombay 

Wednesday 

71 
Euler Ï†function  I 
Prof. Shripad Garge , IIT Bombay 

Thursday 

72 
Euler Ï†function  II 
Prof. Shripad Garge , IIT Bombay 

Thursday 

73 
Euler Ï†function  I 
Prof. Shripad Garge , IIT Bombay 

Friday 

74 
Euler Ï†function  II 
Prof. Shripad Garge , IIT Bombay 

Friday 

75 
Euler Ï†function  I 
Prof. Shripad Garge , IIT Bombay 

Saturday 

76 
Euler Ï†function  II 
Prof. Shripad Garge , IIT Bombay 

Saturday 

77 
Primitive Roots  II 
Prof. Shripad Garge , IIT Bombay 

Monday 

78 
Primitive Roots  III 
Prof. Shripad Garge , IIT Bombay 

Monday 

79 
Primitive Roots  II 
Prof. Shripad Garge , IIT Bombay 

Tuesday 

80 
Primitive Roots  III 
Prof. Shripad Garge , IIT Bombay 

Tuesday 

81 
Primitive Roots  II 
Prof. Shripad Garge , IIT Bombay 

Wednesday 

82 
Primitive Roots  III 
Prof. Shripad Garge , IIT Bombay 

Wednesday 

83 
Primitive Roots  III 
Prof. Shripad Garge , IIT Bombay 

Thursday 

84 
Primitive Roots  IV 
Prof. Shripad Garge , IIT Bombay 

Thursday 

85 
Primitive Roots  III 
Prof. Shripad Garge , IIT Bombay 

Friday 

86 
Primitive Roots  IV 
Prof. Shripad Garge , IIT Bombay 

Friday 

87 
Primitive Roots  III 
Prof. Shripad Garge , IIT Bombay 

Saturday 

88 
Primitive Roots  IV 
Prof. Shripad Garge , IIT Bombay 

Saturday 

89 
Structure of Un  I 
Prof. Shripad Garge , IIT Bombay 

Monday 

90 
Structure of Un  II 
Prof. Shripad Garge , IIT Bombay 

Monday 

91 
Structure of Un  I 
Prof. Shripad Garge , IIT Bombay 

Tuesday 

92 
Structure of Un  II 
Prof. Shripad Garge , IIT Bombay 

Tuesday 

93 
Structure of Un  I 
Prof. Shripad Garge , IIT Bombay 

Wednesday 

94 
Structure of Un  II 
Prof. Shripad Garge , IIT Bombay 

Wednesday 

95 
Quadratic residues 
Prof. Shripad Garge , IIT Bombay 

Thursday 

96 
The Legender symbol 
Prof. Shripad Garge , IIT Bombay 

Thursday 

97 
Quadratic residues 
Prof. Shripad Garge , IIT Bombay 

Friday 

98 
The Legender symbol 
Prof. Shripad Garge , IIT Bombay 

Friday 

99 
Quadratic residues 
Prof. Shripad Garge , IIT Bombay 

Saturday 

100 
The Legender symbol 
Prof. Shripad Garge , IIT Bombay 

Saturday 

101 
Quadratic reciprocity law  I 
Prof. Shripad Garge , IIT Bombay 


Monday 


102 
Quadratic reciprocity law  II 
Prof. Shripad Garge , IIT Bombay 


Monday 


103 
Quadratic reciprocity law  I 
Prof. Shripad Garge , IIT Bombay 


Tuesday 


104 
Quadratic reciprocity law  II 
Prof. Shripad Garge , IIT Bombay 


Tuesday 


105 
Quadratic reciprocity law  I 
Prof. Shripad Garge , IIT Bombay 


Wednesday 


106 
Quadratic reciprocity law  II 
Prof. Shripad Garge , IIT Bombay 


Wednesday 


107 
Quadratic reciprocity law  III 
Prof. Shripad Garge , IIT Bombay 


Thursday 


108 
Quadratic reciprocity law  III 
Prof. Shripad Garge , IIT Bombay 


Friday 


109 
Quadratic reciprocity law  III 
Prof. Shripad Garge , IIT Bombay 


Saturday 


110 
Quadratic reciprocity law  IV 
Prof. Shripad Garge , IIT Bombay 


Monday 


111 
The Jacobi symbol 
Prof. Shripad Garge , IIT Bombay 


Monday 


112 
Quadratic reciprocity law  IV 
Prof. Shripad Garge , IIT Bombay 


Tuesday 


113 
The Jacobi symbol 
Prof. Shripad Garge , IIT Bombay 


Tuesday 


114 
Quadratic reciprocity law  IV 
Prof. Shripad Garge , IIT Bombay 


Wednesday 


115 
The Jacobi symbol 
Prof. Shripad Garge , IIT Bombay 


Wednesday 


116 
Binary quadratic forms 
Prof. Shripad Garge , IIT Bombay 


Thursday 


117 
Equivalence of binary quadratic forms 
Prof. Shripad Garge , IIT Bombay 


Thursday 


118 
Binary quadratic forms 
Prof. Shripad Garge , IIT Bombay 


Friday 


119 
Equivalence of binary quadratic forms 
Prof. Shripad Garge , IIT Bombay 


Friday 


120 
Binary quadratic forms 
Prof. Shripad Garge , IIT Bombay 


Saturday 


121 
Equivalence of binary quadratic forms 
Prof. Shripad Garge , IIT Bombay 


Saturday 


122 
Quadratic reciprocity law  IV 
Prof. Shripad Garge , IIT Bombay 


Monday 


123 
The Jacobi symbol 
Prof. Shripad Garge , IIT Bombay 


Monday 


124 
Quadratic reciprocity law  IV 
Prof. Shripad Garge , IIT Bombay 


Tuesday 


125 
The Jacobi symbol 
Prof. Shripad Garge , IIT Bombay 


Tuesday 


126 
Quadratic reciprocity law  IV 
Prof. Shripad Garge , IIT Bombay 


Wednesday 


127 
The Jacobi symbol 
Prof. Shripad Garge , IIT Bombay 


Wednesday 


128 
Binary quadratic forms 
Prof. Shripad Garge , IIT Bombay 


Thursday 


129 
Equivalence of binary quadratic forms 
Prof. Shripad Garge , IIT Bombay 


Thursday 


130 
Binary quadratic forms 
Prof. Shripad Garge , IIT Bombay 


Friday 


131 
Equivalence of binary quadratic forms 
Prof. Shripad Garge , IIT Bombay 


Friday 


132 
Binary quadratic forms 
Prof. Shripad Garge , IIT Bombay 


Saturday 


133 
Equivalence of binary quadratic forms 
Prof. Shripad Garge , IIT Bombay 


Saturday 


134 
Discriminant of a Binary Quadratic Form 
Prof. Shripad Garge , IIT Bombay 


Monday 


135 
Reduction Theory of Integral Binary Quadratic
Forms 
Prof. Shripad Garge , IIT Bombay 


Monday 


136 
Discriminant of a Binary Quadratic Form 
Prof. Shripad Garge , IIT Bombay 


Tuesday 


137 
Reduction Theory of Integral Binary Quadratic
Forms 
Prof. Shripad Garge , IIT Bombay 


Tuesday 


138 
Discriminant of a Binary Quadratic Form 
Prof. Shripad Garge , IIT Bombay 


Wednesday 


139 
Reduction Theory of Integral Binary Quadratic
Forms 
Prof. Shripad Garge , IIT Bombay 


Wednesday 


140 
Reduced Forms up to Equivalence  II 
Prof. Shripad Garge , IIT Bombay 


Thursday 


141 
Reduced Forms up to Equivalence  III 
Prof. Shripad Garge , IIT Bombay 


Thursday 


142 
Reduced Forms up to Equivalence  II 
Prof. Shripad Garge , IIT Bombay 


Friday 


143 
Reduced Forms up to Equivalence  III 
Prof. Shripad Garge , IIT Bombay 


Friday 


144 
Reduced Forms up to Equivalence  II 
Prof. Shripad Garge , IIT Bombay 


Saturday 


145 
Reduced Forms up to Equivalence  III 
Prof. Shripad Garge , IIT Bombay 


Saturday 


146 
Sums of Squares  II 
Prof. Shripad Garge , IIT Bombay 

Monday 

147 
Sums of Squares  III 
Prof. Shripad Garge , IIT Bombay 

Monday 

148 
Beyond Sums of Squares  I 
Prof. Shripad Garge , IIT Bombay 

Monday 

149 
Sums of Squares  II 
Prof. Shripad Garge , IIT Bombay 

Tuesday 

150 
Sums of Squares  III 
Prof. Shripad Garge , IIT Bombay 

Tuesday 

151 
Beyond Sums of Squares  I 
Prof. Shripad Garge , IIT Bombay 

Tuesday 

152 
Sums of Squares  II 
Prof. Shripad Garge , IIT Bombay 

Wednesday 

153 
Sums of Squares  III 
Prof. Shripad Garge , IIT Bombay 

Wednesday 

154 
Beyond Sums of Squares  I 
Prof. Shripad Garge , IIT Bombay 

Wednesday 

155 
Beyond Sums of Squares  II 
Prof. Shripad Garge , IIT Bombay 

Thursday 

156 
Continued Fractions Basic Results 
Prof. Shripad Garge , IIT Bombay 

Thursday 

157 
Beyond Sums of Squares  II 
Prof. Shripad Garge , IIT Bombay 

Friday 

158 
Continued Fractions Basic Results 
Prof. Shripad Garge , IIT Bombay 

Friday 

159 
Beyond Sums of Squares  II 
Prof. Shripad Garge , IIT Bombay 

Saturday 

160 
Continued Fractions Basic Results 
Prof. Shripad Garge , IIT Bombay 

Saturday 

161 
Dirichlet's approximation theorem 
Prof. Shripad Garge , IIT Bombay 

Monday 

162 
Good rational approximations 
Prof. Shripad Garge , IIT Bombay 

Monday 

163 
Continued fraction expansion for real numbers  I 
Prof. Shripad Garge , IIT Bombay 

Monday 

164 
Dirichlet's approximation theorem 
Prof. Shripad Garge , IIT Bombay 

Tuesday 

165 
Good rational approximations 
Prof. Shripad Garge , IIT Bombay 

Tuesday 

166 
Continued fraction expansion for real numbers  I 
Prof. Shripad Garge , IIT Bombay 

Tuesday 

167 
Dirichlet's approximation theorem 
Prof. Shripad Garge , IIT Bombay 

Wednesday 

168 
Good rational approximations 
Prof. Shripad Garge , IIT Bombay 

Wednesday 

169 
Continued fraction expansion for real numbers  I 
Prof. Shripad Garge , IIT Bombay 

Wednesday 

170 
Convergents give better approximations 
Prof. Shripad Garge , IIT Bombay 

Thursday 

171 
Convergents are the best approximations  I 
Prof. Shripad Garge , IIT Bombay 

Thursday 

172 
Convergents give better approximations 
Prof. Shripad Garge , IIT Bombay 

Friday 

173 
Convergents are the best approximations  I 
Prof. Shripad Garge , IIT Bombay 

Friday 

174 
Convergents give better approximations 
Prof. Shripad Garge , IIT Bombay 

Saturday 

175 
Convergents are the best approximations  I 
Prof. Shripad Garge , IIT Bombay 

Saturday 

176 
Convergents are the best approximations  II 
Prof. Shripad Garge , IIT Bombay 


Monday 


177 
Quadratic irrationals as continued fractions 
Prof. Shripad Garge , IIT Bombay 


Monday 


178 
Convergents are the best approximations  II 
Prof. Shripad Garge , IIT Bombay 


Tuesday 


179 
Quadratic irrationals as continued fractions 
Prof. Shripad Garge , IIT Bombay 


Tuesday 


180 
Convergents are the best approximations  II 
Prof. Shripad Garge , IIT Bombay 


Wednesday 


181 
Quadratic irrationals as continued fractions 
Prof. Shripad Garge , IIT Bombay 


Wednesday 


182 
Some basics of algebraic number theory 
Prof. Shripad Garge , IIT Bombay 


Thursday 


183 
Units in quadratic fields: the imaginary case 
Prof. Shripad Garge , IIT Bombay 


Thursday 


184 
Some basics of algebraic number theory 
Prof. Shripad Garge , IIT Bombay 


Friday 


185 
Units in quadratic fields: the imaginary case 
Prof. Shripad Garge , IIT Bombay 


Friday 


186 
Some basics of algebraic number theory 
Prof. Shripad Garge , IIT Bombay 


Saturday 


187 
Units in quadratic fields: the imaginary case 
Prof. Shripad Garge , IIT Bombay 


Saturday 


188 
Units in quadratic fields: the real case 
Prof. Shripad Garge , IIT Bombay 

Monday 

189 
Units in quadratic fields: the real case 
Prof. Shripad Garge , IIT Bombay 

Tuesday 

190 
Units in quadratic fields: the real case 
Prof. Shripad Garge , IIT Bombay 

Wednesday 

191 
BrahmaguptaPell equations 
Prof. Shripad Garge , IIT Bombay 

Thursday 

192 
Tying some loose ends 
Prof. Shripad Garge , IIT Bombay 

Thursday 

193 
BrahmaguptaPell equations 
Prof. Shripad Garge , IIT Bombay 

Friday 

194 
Tying some loose ends 
Prof. Shripad Garge , IIT Bombay 

Friday 

195 
BrahmaguptaPell equations 
Prof. Shripad Garge , IIT Bombay 

Saturday 

196 
Tying some loose ends 
Prof. Shripad Garge , IIT Bombay 

Saturday 
