1 
Integers 
Prof. Shripad Garge , IIT Bombay 

Monday 

2 
Integers 
Prof. Shripad Garge , IIT Bombay 

Tuesday 

3 
Integers 
Prof. Shripad Garge , IIT Bombay 

Wednesday 

4 
Divisibility and primes 
Prof. Shripad Garge , IIT Bombay 

Thursday 

5 
Infinitude of primes 
Prof. Shripad Garge , IIT Bombay 

Thursday 

6 
Divisibility and primes 
Prof. Shripad Garge , IIT Bombay 

Friday 

7 
Infinitude of primes 
Prof. Shripad Garge , IIT Bombay 

Friday 

8 
Divisibility and primes 
Prof. Shripad Garge , IIT Bombay 

Saturday 

9 
Infinitude of primes 
Prof. Shripad Garge , IIT Bombay 

Saturday 

10 
Division Algorithm 
Prof. Shripad Garge , IIT Bombay 


Monday 


11 
Division Algorithm 
Prof. Shripad Garge , IIT Bombay 


Tuesday 


12 
Division Algorithm 
Prof. Shripad Garge , IIT Bombay 


Wednesday 


13 
Computing the GCD and Euclidâ€™s lemma 
Prof. Shripad Garge , IIT Bombay 


Thursday 


14 
Fundamental theorem of arithmetic 
Prof. Shripad Garge , IIT Bombay 

Thursday 

15 
Computing the GCD and Euclidâ€™s lemma 
Prof. Shripad Garge , IIT Bombay 


Friday 


16 
Fundamental theorem of arithmetic 
Prof. Shripad Garge , IIT Bombay 

Friday 

17 
Computing the GCD and Euclidâ€™s lemma 
Prof. Shripad Garge , IIT Bombay 


Saturday 


18 
Fundamental theorem of arithmetic 
Prof. Shripad Garge , IIT Bombay 

Saturday 

19 
Stories Around Primes 
Prof. Shripad Garge , IIT Bombay 


Monday 


20 
Stories Around Primes 
Prof. Shripad Garge , IIT Bombay 


Tuesday 


21 
Stories Around Primes 
Prof. Shripad Garge , IIT Bombay 


Wednesday 


22 
Arithmetic modulo n, theory and examples 
Prof. Shripad Garge , IIT Bombay 


Monday 


23 
Arithmetic modulo n, more examples 
Prof. Shripad Garge , IIT Bombay 


Monday 


24 
Solving linear polynomials modulo n  I 
Prof. Shripad Garge , IIT Bombay 

Monday 

25 
Arithmetic modulo n, theory and examples 
Prof. Shripad Garge , IIT Bombay 


Tuesday 


26 
Arithmetic modulo n, more examples 
Prof. Shripad Garge , IIT Bombay 


Tuesday 


27 
Solving linear polynomials modulo n  I 
Prof. Shripad Garge , IIT Bombay 

Tuesday 

28 
Arithmetic modulo n, theory and examples 
Prof. Shripad Garge , IIT Bombay 


Wednesday 


29 
Arithmetic modulo n, more examples 
Prof. Shripad Garge , IIT Bombay 


Wednesday 


30 
Solving linear polynomials modulo n  I 
Prof. Shripad Garge , IIT Bombay 

Wednesday 

31 
Solving linear polynomials modulo n  IV 
Prof. Shripad Garge , IIT Bombay 

Monday 

32 
Chinese remainder theorem, the initial cases 
Prof. Shripad Garge , IIT Bombay 

Monday 

33 
Solving linear polynomials modulo n  IV 
Prof. Shripad Garge , IIT Bombay 

Tuesday 

34 
Chinese remainder theorem, the initial cases 
Prof. Shripad Garge , IIT Bombay 

Tuesday 

35 
Solving linear polynomials modulo n  IV 
Prof. Shripad Garge , IIT Bombay 

Wednesday 

36 
Chinese remainder theorem, the initial cases 
Prof. Shripad Garge , IIT Bombay 

Wednesday 

37 
Using the CRT, square roots of 1 in
Ã¢â€žÂ¤n 
Prof. Shripad Garge , IIT Bombay 


Monday 


38 
Wilson's theorem 
Prof. Shripad Garge , IIT Bombay 

Monday 

39 
Using the CRT, square roots of 1 in
Ã¢â€žÂ¤n 
Prof. Shripad Garge , IIT Bombay 


Tuesday 


40 
Wilson's theorem 
Prof. Shripad Garge , IIT Bombay 

Tuesday 

41 
Using the CRT, square roots of 1 in
Ã¢â€žÂ¤n 
Prof. Shripad Garge , IIT Bombay 


Wednesday 


42 
Wilson's theorem 
Prof. Shripad Garge , IIT Bombay 

Wednesday 

43 
Roots of polynomials over Ã¢â€žÂ¤p 
Prof. Shripad Garge , IIT Bombay 


Thursday 


44 
Euler Ã°ÂÅ“â€˜function  I 
Prof. Shripad Garge , IIT Bombay 

Thursday 

45 
Roots of polynomials over Ã¢â€žÂ¤p 
Prof. Shripad Garge , IIT Bombay 


Friday 


46 
Euler Ã°ÂÅ“â€˜function  I 
Prof. Shripad Garge , IIT Bombay 

Friday 

47 
Roots of polynomials over Ã¢â€žÂ¤p 
Prof. Shripad Garge , IIT Bombay 


Saturday 


48 
Euler Ã°ÂÅ“â€˜function  I 
Prof. Shripad Garge , IIT Bombay 

Saturday 

49 
Euler Ã°ÂÅ“â€˜function  II 
Prof. Shripad Garge , IIT Bombay 

Monday 

50 
Primitive roots  I 
Prof. Shripad Garge , IIT Bombay 

Monday 

51 
Euler Ã°ÂÅ“â€˜function  II 
Prof. Shripad Garge , IIT Bombay 

Tuesday 

52 
Primitive roots  I 
Prof. Shripad Garge , IIT Bombay 

Tuesday 

53 
Euler Ã°ÂÅ“â€˜function  II 
Prof. Shripad Garge , IIT Bombay 

Wednesday 

54 
Primitive roots  I 
Prof. Shripad Garge , IIT Bombay 

Wednesday 

55 
Primitive roots  II 
Prof. Shripad Garge , IIT Bombay 

Thursday 

56 
Primitive roots  III 
Prof. Shripad Garge , IIT Bombay 

Thursday 

57 
Primitive roots  II 
Prof. Shripad Garge , IIT Bombay 

Friday 

58 
Primitive roots  III 
Prof. Shripad Garge , IIT Bombay 

Friday 

59 
Primitive roots  II 
Prof. Shripad Garge , IIT Bombay 

Saturday 

60 
Primitive roots  III 
Prof. Shripad Garge , IIT Bombay 

Saturday 

61 
Primitive roots  IV 
Prof. Shripad Garge , IIT Bombay 

Monday 

62 
Structure of Un  I 
Prof. Shripad Garge , IIT Bombay 

Monday 

63 
Primitive roots  IV 
Prof. Shripad Garge , IIT Bombay 

Tuesday 

64 
Structure of Un  I 
Prof. Shripad Garge , IIT Bombay 

Tuesday 

65 
Primitive roots  IV 
Prof. Shripad Garge , IIT Bombay 

Wednesday 

66 
Structure of Un  I 
Prof. Shripad Garge , IIT Bombay 

Wednesday 

67 
Structure of Un  II 
Prof. Shripad Garge , IIT Bombay 


Thursday 


68 
Quadratic residues 
Prof. Shripad Garge , IIT Bombay 

Thursday 

69 
Structure of Un  II 
Prof. Shripad Garge , IIT Bombay 


Friday 


70 
Quadratic residues 
Prof. Shripad Garge , IIT Bombay 

Friday 

71 
Structure of Un  II 
Prof. Shripad Garge , IIT Bombay 


Saturday 


72 
Quadratic residues 
Prof. Shripad Garge , IIT Bombay 

Saturday 

73 
The Legendre symbol 
Prof. Shripad Garge , IIT Bombay 

Monday 

74 
Quadratic reciprocity law  I 
Prof. Shripad Garge , IIT Bombay 


Monday 


75 
The Legendre symbol 
Prof. Shripad Garge , IIT Bombay 

Tuesday 

76 
Quadratic reciprocity law  I 
Prof. Shripad Garge , IIT Bombay 


Tuesday 


77 
The Legendre symbol 
Prof. Shripad Garge , IIT Bombay 

Wednesday 

78 
Quadratic reciprocity law  I 
Prof. Shripad Garge , IIT Bombay 


Wednesday 


79 
Quadratic reciprocity law  II 
Prof. Shripad Garge , IIT Bombay 


Thursday 


80 
Quadratic reciprocity law  II 
Prof. Shripad Garge , IIT Bombay 


Friday 


81 
Quadratic reciprocity law  II 
Prof. Shripad Garge , IIT Bombay 


Saturday 


82 
Quadratic reciprocity law III 
Prof. Shripad Garge , IIT Bombay 


Monday 


83 
Quadratic reciprocity law III 
Prof. Shripad Garge , IIT Bombay 


Tuesday 


84 
Quadratic reciprocity law III 
Prof. Shripad Garge , IIT Bombay 


Wednesday 


85 
Quadratic reciprocity law IV 
Prof. Shripad Garge , IIT Bombay 


Thursday 


86 
Quadratic reciprocity law IV 
Prof. Shripad Garge , IIT Bombay 


Friday 


87 
Quadratic reciprocity law IV 
Prof. Shripad Garge , IIT Bombay 


Saturday 


88 
The Jacobi symbol 
Prof. Shripad Garge , IIT Bombay 


Monday 


89 
The Jacobi symbol 
Prof. Shripad Garge , IIT Bombay 


Monday 


90 
The Jacobi symbol 
Prof. Shripad Garge , IIT Bombay 


Tuesday 


91 
The Jacobi symbol 
Prof. Shripad Garge , IIT Bombay 


Tuesday 


92 
The Jacobi symbol 
Prof. Shripad Garge , IIT Bombay 


Wednesday 


93 
The Jacobi symbol 
Prof. Shripad Garge , IIT Bombay 


Wednesday 


94 
Equivalence of binary quadratic forms 
Prof. Shripad Garge , IIT Bombay 


Thursday 


95 
Discriminant of a binary quadratic form 
Prof. Shripad Garge , IIT Bombay 


Thursday 


96 
Equivalence of binary quadratic forms 
Prof. Shripad Garge , IIT Bombay 


Friday 


97 
Discriminant of a binary quadratic form 
Prof. Shripad Garge , IIT Bombay 


Friday 


98 
Equivalence of binary quadratic forms 
Prof. Shripad Garge , IIT Bombay 


Saturday 


99 
Discriminant of a binary quadratic form 
Prof. Shripad Garge , IIT Bombay 


Saturday 


100 
Reduction theory of integral binary quadratic
forms 
Prof. Shripad Garge , IIT Bombay 


Monday 


101 
Reduced forms up to equivalence  I 
Prof. Shripad Garge , IIT Bombay 

Monday 

102 
Reduction theory of integral binary quadratic
forms 
Prof. Shripad Garge , IIT Bombay 


Tuesday 


103 
Reduced forms up to equivalence  I 
Prof. Shripad Garge , IIT Bombay 

Tuesday 

104 
Reduction theory of integral binary quadratic
forms 
Prof. Shripad Garge , IIT Bombay 


Wednesday 


105 
Reduced forms up to equivalence  I 
Prof. Shripad Garge , IIT Bombay 

Wednesday 

106 
Reduced forms up to equivalence  II 
Prof. Shripad Garge , IIT Bombay 

Thursday 

107 
Reduced forms up to equivalence  III 
Prof. Shripad Garge , IIT Bombay 

Thursday 

108 
Reduced forms up to equivalence  II 
Prof. Shripad Garge , IIT Bombay 

Friday 

109 
Reduced forms up to equivalence  III 
Prof. Shripad Garge , IIT Bombay 

Friday 

110 
Reduced forms up to equivalence  II 
Prof. Shripad Garge , IIT Bombay 

Saturday 

111 
Reduced forms up to equivalence  III 
Prof. Shripad Garge , IIT Bombay 

Saturday 

112 
Sums of squares  II 
Prof. Shripad Garge , IIT Bombay 

Monday 

113 
Sums of squares  II 
Prof. Shripad Garge , IIT Bombay 

Tuesday 

114 
Sums of squares  II 
Prof. Shripad Garge , IIT Bombay 

Wednesday 

115 
Sums of squares  III 
Prof. Shripad Garge , IIT Bombay 

Thursday 

116 
Sums of squares  III 
Prof. Shripad Garge , IIT Bombay 

Friday 

117 
Sums of squares  III 
Prof. Shripad Garge , IIT Bombay 

Saturday 

118 
Beyond sums of squares  I 
Prof. Shripad Garge , IIT Bombay 

Monday 

119 
Beyond sums of squares  I 
Prof. Shripad Garge , IIT Bombay 

Tuesday 

120 
Beyond sums of squares  I 
Prof. Shripad Garge , IIT Bombay 

Wednesday 

121 
Beyond sums of squares  II 
Prof. Shripad Garge , IIT Bombay 

Thursday 

122 
Continued fractions  basic results 
Prof. Shripad Garge , IIT Bombay 

Thursday 

123 
Beyond sums of squares  II 
Prof. Shripad Garge , IIT Bombay 

Friday 

124 
Continued fractions  basic results 
Prof. Shripad Garge , IIT Bombay 

Friday 

125 
Beyond sums of squares  II 
Prof. Shripad Garge , IIT Bombay 

Saturday 

126 
Continued fractions  basic results 
Prof. Shripad Garge , IIT Bombay 

Saturday 

127 
Dirichlet's approximation theorem 
Prof. Shripad Garge , IIT Bombay 

Monday 

128 
Dirichlet's approximation theorem 
Prof. Shripad Garge , IIT Bombay 

Tuesday 

129 
Dirichlet's approximation theorem 
Prof. Shripad Garge , IIT Bombay 

Wednesday 

130 
Good rational approximations 
Prof. Shripad Garge , IIT Bombay 

Thursday 

131 
Continued fraction expansion for real numbers  I 
Prof. Shripad Garge , IIT Bombay 


Thursday 


132 
Good rational approximations 
Prof. Shripad Garge , IIT Bombay 

Friday 

133 
Continued fraction expansion for real numbers  I 
Prof. Shripad Garge , IIT Bombay 


Friday 


134 
Good rational approximations 
Prof. Shripad Garge , IIT Bombay 

Saturday 

135 
Continued fraction expansion for real numbers  I 
Prof. Shripad Garge , IIT Bombay 


Saturday 


136 
Continued fraction expansion for real numbers  II 
Prof. Shripad Garge , IIT Bombay 

Monday 

137 
Continued fraction expansion for real numbers  II 
Prof. Shripad Garge , IIT Bombay 

Tuesday 

138 
Continued fraction expansion for real numbers  II 
Prof. Shripad Garge , IIT Bombay 

Wednesday 

139 
Convergents give better approximations 
Prof. Shripad Garge , IIT Bombay 


Thursday 


140 
Convergents are the best approximations  I 
Prof. Shripad Garge , IIT Bombay 

Thursday 

141 
Convergents give better approximations 
Prof. Shripad Garge , IIT Bombay 


Friday 


142 
Convergents are the best approximations  I 
Prof. Shripad Garge , IIT Bombay 

Friday 

143 
Convergents give better approximations 
Prof. Shripad Garge , IIT Bombay 


Saturday 


144 
Convergents are the best approximations  I 
Prof. Shripad Garge , IIT Bombay 

Saturday 

145 
Convergents are the best approximations  II 
Prof. Shripad Garge , IIT Bombay 

Monday 

146 
Convergents are the best approximations  II 
Prof. Shripad Garge , IIT Bombay 

Tuesday 

147 
Convergents are the best approximations  II 
Prof. Shripad Garge , IIT Bombay 

Wednesday 

148 
Quadratic irrationals as continued fractions 
Prof. Shripad Garge , IIT Bombay 

Thursday 

149 
Some basics of algebraic number theory 
Prof. Shripad Garge , IIT Bombay 

Thursday 

150 
Quadratic irrationals as continued fractions 
Prof. Shripad Garge , IIT Bombay 

Friday 

151 
Some basics of algebraic number theory 
Prof. Shripad Garge , IIT Bombay 

Friday 

152 
Quadratic irrationals as continued fractions 
Prof. Shripad Garge , IIT Bombay 

Saturday 

153 
Some basics of algebraic number theory 
Prof. Shripad Garge , IIT Bombay 

Saturday 

154 
Units in quadratic fields: the imaginary case 
Prof. Shripad Garge , IIT Bombay 


Monday 


155 
Units in quadratic fields: the imaginary case 
Prof. Shripad Garge , IIT Bombay 


Tuesday 


156 
Units in quadratic fields: the imaginary case 
Prof. Shripad Garge , IIT Bombay 


Wednesday 


157 
Units in quadratic fields: the real case 
Prof. Shripad Garge , IIT Bombay 


Thursday 


158 
BrahmaguptaPell equations 
Prof. Shripad Garge , IIT Bombay 


Thursday 


159 
Units in quadratic fields: the real case 
Prof. Shripad Garge , IIT Bombay 


Friday 


160 
BrahmaguptaPell equations 
Prof. Shripad Garge , IIT Bombay 


Friday 


161 
Units in quadratic fields: the real case 
Prof. Shripad Garge , IIT Bombay 


Saturday 


162 
BrahmaguptaPell equations 
Prof. Shripad Garge , IIT Bombay 


Saturday 


163 
Tying some loose ends 
Prof. Shripad Garge , IIT Bombay 


Monday 


164 
Tying some loose ends 
Prof. Shripad Garge , IIT Bombay 


Tuesday 


165 
Tying some loose ends 
Prof. Shripad Garge , IIT Bombay 


Wednesday 

