ACADEMY OF MATHEMATICAL SCIENCES

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Firstly, I welcome to all my viewers on my You tube channel ACADEMY OF MATHEMATICAL SCIENCES. This channel ACADEMY OF MATHEMATICAL SCIENCES is created by AZMAT ALI. Currently, I am working as Lecturer in Mathematics at Govt. Shalimar Post Graduate College Baghbanpura, Lahore, Pakistan. I heartily welcome all of you in my You tube channel. Here you can find videos on higher Mathematics topics like as Real Analysis, Number Theory, Linear Algebra, Graph Theory, Mechanics, Group Theory, Ring Module and Ideal, Numerical Analysis, Operation Research, Complex Analysis, vector and Tensor Analysis, Advanced Analysis, General & Algebraic Topology, Functional Analysis, Measure Theory. Set Theory, Differential Geometry, Algebraic Topology, Quantum Mechanics, Mathematical Statistics, Calculus, Representation Theory. Algebraic geometry. Thanks Kindly Share and subscribe my channel 🤗 #highermathematics #ACADEMYOFMATHEMATICALSCIENCES EMAIL: [email protected]

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9. Rudin Real Analysis | Theorem 3.11 | Convergent Sequence, Cauchy Sequence & Compact Metric Spaces

9. Rudin Real Analysis | Theorem 3.11 | Convergent Sequence, Cauchy Sequence & Compact Metric Spaces ACADEMY OF MATHEMATICAL SCIENCES

8 hours ago

8. Rudin Real Analysis: Generalized Cantor Intersection Theorem (Complete Proof) | 3.10 b Theorem

8. Rudin Real Analysis: Generalized Cantor Intersection Theorem (Complete Proof) | 3.10 b Theorem ACADEMY OF MATHEMATICAL SCIENCES

2 views - 3 days ago

Proof of Theorem 3.10: diam(E) = diam(cl(E)) | Metric Space | Walter Rudin Real Analysis

Proof of Theorem 3.10: diam(E) = diam(cl(E)) | Metric Space | Walter Rudin Real Analysis ACADEMY OF MATHEMATICAL SCIENCES

8 views - 1 week ago

6.Cauchy Sequence & Diameter of a Set | Real Analysis | Walter Rudin |Numerical Sequences and Series

6.Cauchy Sequence & Diameter of a Set | Real Analysis | Walter Rudin |Numerical Sequences and Series ACADEMY OF MATHEMATICAL SCIENCES

33 views - 4 months ago

5.Bolzano Weierstrass Theorem in ℝᵏ | Proof | Real Analysis | Rudin | Numerical Sequences and series

5.Bolzano Weierstrass Theorem in ℝᵏ | Proof | Real Analysis | Rudin | Numerical Sequences and series ACADEMY OF MATHEMATICAL SCIENCES

45 views - 4 months ago

$4. Subsequences | A sequence converges to p iff its every subsequence {p_(n_k ) } converges to p$ 17:46

4. Subsequences | A sequence converges to p iff its every subsequence {p_(n_k ) } converges to p ACADEMY OF MATHEMATICAL SCIENCES

29 views - 4 months ago

3. Theorem 3.3 | Show that lim_(n→∞)⁡(s_n+t_n )=s+t, lim_(n→∞) ⁡s_n t_n=st | Rudin Real Analysis

3. Theorem 3.3 | Show that lim_(n→∞)⁡(s_n+t_n )=s+t, lim_(n→∞) ⁡s_n t_n=st | Rudin Real Analysis ACADEMY OF MATHEMATICAL SCIENCES

24 views - 4 months ago

2. Rudin Real Analysis | Theorem 3.2 Explained | Properties of Convergent Sequences | Chapter 3

2. Rudin Real Analysis | Theorem 3.2 Explained | Properties of Convergent Sequences | Chapter 3 ACADEMY OF MATHEMATICAL SCIENCES

21 views - 4 months ago

1. Convergent and Bounded Sequences | Real Analysis | Rudin Chapter 3 | Principles of Mathematical

1. Convergent and Bounded Sequences | Real Analysis | Rudin Chapter 3 | Principles of Mathematical ACADEMY OF MATHEMATICAL SCIENCES

31 views - 4 months ago

1. Solution of Polynomial Congruences | Prime Power Modulo | Solve 2x≡5(mod27) | Number Theory

1. Solution of Polynomial Congruences | Prime Power Modulo | Solve 2x≡5(mod27) | Number Theory ACADEMY OF MATHEMATICAL SCIENCES

31 views - 5 months ago

4. Carmichael Number | Show that 561 is a Carmichael number | Number Theory by David M Burton

4. Carmichael Number | Show that 561 is a Carmichael number | Number Theory by David M Burton ACADEMY OF MATHEMATICAL SCIENCES

45 views - 5 months ago

3. Pseudoprimes | Show that 85 is a base 4 Pseudoprime but not base 2 | Number Theory by David

3. Pseudoprimes | Show that 85 is a base 4 Pseudoprime but not base 2 | Number Theory by David ACADEMY OF MATHEMATICAL SCIENCES

38 views - 5 months ago

2. Show that 341 and 561 are base 2 Fermat’s pseudoprimes | Number Theory by David M. Burton

2. Show that 341 and 561 are base 2 Fermat’s pseudoprimes | Number Theory by David M. Burton ACADEMY OF MATHEMATICAL SCIENCES

47 views - 5 months ago

13. How Many Integers Have Order d Modulo p? | Theorem 8.6 | Number Theory by David M Burton

13. How Many Integers Have Order d Modulo p? | Theorem 8.6 | Number Theory by David M Burton ACADEMY OF MATHEMATICAL SCIENCES

18 views - 5 months ago

12. Alternative Proof of Wilson’s Theorem Using Lagrange’s Theorem | Number Theory by David M Burton

12. Alternative Proof of Wilson’s Theorem Using Lagrange’s Theorem | Number Theory by David M Burton ACADEMY OF MATHEMATICAL SCIENCES

19 views - 5 months ago

11. Show that If p is a prime and d|p-1, then the congruence x^d-1≡0(modp) has exactly d solutions.

11. Show that If p is a prime and d|p-1, then the congruence x^d-1≡0(modp) has exactly d solutions. ACADEMY OF MATHEMATICAL SCIENCES

23 views - 5 months ago

10. Lagrange's Theorem for Polynomial congruence | Statement and Proof | primitive roots for primes.

10. Lagrange's Theorem for Polynomial congruence | Statement and Proof | primitive roots for primes. ACADEMY OF MATHEMATICAL SCIENCES

41 views - 5 months ago

9. Show that If a is primitive root of n then total number of primitive roots modulo n are ϕ(ϕ(n)).

9. Show that If a is primitive root of n then total number of primitive roots modulo n are ϕ(ϕ(n)). ACADEMY OF MATHEMATICAL SCIENCES

26 views - 6 months ago

8. Theorem 8.4 | Primitive Roots Modulo 𝑛 | Elementary Number Theory by David M Burton | M.sc Math

8. Theorem 8.4 | Primitive Roots Modulo 𝑛 | Elementary Number Theory by David M Burton | M.sc Math ACADEMY OF MATHEMATICAL SCIENCES

19 views - 6 months ago

7. Show that 2 is not a primitive root of Fermat number 𝐹_𝑛=2^(2^𝑛 )+1 | Number Theory by Burton

7. Show that 2 is not a primitive root of Fermat number 𝐹_𝑛=2^(2^𝑛 )+1 | Number Theory by Burton ACADEMY OF MATHEMATICAL SCIENCES

19 views - 6 months ago

6. Primitive Roots Modulo 𝑛 | Primitive Roots Modulo 50 and 100 | David M. Burton Chapter 8.

6. Primitive Roots Modulo 𝑛 | Primitive Roots Modulo 50 and 100 | David M. Burton Chapter 8. ACADEMY OF MATHEMATICAL SCIENCES

24 views - 6 months ago

5. Primitive Roots of an Integer modulo n | Number Theory by David M. Burton | B.SC Math | M.SC Math

5. Primitive Roots of an Integer modulo n | Number Theory by David M. Burton | B.SC Math | M.SC Math ACADEMY OF MATHEMATICAL SCIENCES

32 views - 6 months ago

17. Bounds, Supremum, Infimum & Completeness of ℝ | Real Analysis | Bartle & Sherbert

17. Bounds, Supremum, Infimum & Completeness of ℝ | Real Analysis | Bartle & Sherbert ACADEMY OF MATHEMATICAL SCIENCES

39 views - 6 months ago

16. Minimum, maximum, middle number | Exercise 2.2 | Question 18-19 | Real Analysis by R. G Bartle

16. Minimum, maximum, middle number | Exercise 2.2 | Question 18-19 | Real Analysis by R. G Bartle ACADEMY OF MATHEMATICAL SCIENCES

20 views - 6 months ago

15. Epsilon neighborhood of a point | Exercise 2.2 | Question 16-17 | Real Analysis by R. G Bartle

15. Epsilon neighborhood of a point | Exercise 2.2 | Question 16-17 | Real Analysis by R. G Bartle ACADEMY OF MATHEMATICAL SCIENCES

53 views - 6 months ago

14. Epsilon neighborhood of a point | Theorem 2.2.8 | Example 2.2.9 | Real Analysis by R. G Bartle

14. Epsilon neighborhood of a point | Theorem 2.2.8 | Example 2.2.9 | Real Analysis by R. G Bartle ACADEMY OF MATHEMATICAL SCIENCES

37 views - 6 months ago

13. Sketch the graph of |x|-|y|≥2 | Exercise 2.2, Question 14-15 | Real Analysis by Robert G Bartle

13. Sketch the graph of |x|-|y|≥2 | Exercise 2.2, Question 14-15 | Real Analysis by Robert G Bartle ACADEMY OF MATHEMATICAL SCIENCES

35 views - 7 months ago

33. gcd(a,b)=1⇒gcd(a^n,b^n )=1| gcd(a,b)=1⇒gcd(a+b,ab)=1 | Problems 2.4 | question 5, 6 and 11

33. gcd(a,b)=1⇒gcd(a^n,b^n )=1| gcd(a,b)=1⇒gcd(a+b,ab)=1 | Problems 2.4 | question 5, 6 and 11 ACADEMY OF MATHEMATICAL SCIENCES

41 views - 8 months ago

12. Sketch the graph of y=|x|-|x-1| | Exercise 2.2, Question 11 | Real Analysis by Robert G Bartle

12. Sketch the graph of y=|x|-|x-1| | Exercise 2.2, Question 11 | Real Analysis by Robert G Bartle ACADEMY OF MATHEMATICAL SCIENCES

66 views - 8 months ago

11. Solution of Inequalities | Exercise 2.2, Question 6 to 10 | Real Analysis by Robert G Bartle

11. Solution of Inequalities | Exercise 2.2, Question 6 to 10 | Real Analysis by Robert G Bartle ACADEMY OF MATHEMATICAL SCIENCES

97 views - 8 months ago

10. Ch # 2 The Real Numbers | Exercise 2.2, Question 1 to 5 | Real Analysis by Robert G Bartle

10. Ch # 2 The Real Numbers | Exercise 2.2, Question 1 to 5 | Real Analysis by Robert G Bartle ACADEMY OF MATHEMATICAL SCIENCES

157 views - 8 months ago

32. gcd⁡(𝑎+𝑏,𝑎^2+𝑏^2 )=1𝑜𝑟 2 | gcd⁡(𝑎+𝑏,𝑎^2−𝑎𝑏+𝑏^2 )=1 𝑜𝑟 3 | Problems 2.4 | question 4 | M. Burton

32. gcd⁡(𝑎+𝑏,𝑎^2+𝑏^2 )=1𝑜𝑟 2 | gcd⁡(𝑎+𝑏,𝑎^2−𝑎𝑏+𝑏^2 )=1 𝑜𝑟 3 | Problems 2.4 | question 4 | M. Burton ACADEMY OF MATHEMATICAL SCIENCES

63 views - 8 months ago

31. gcd (𝑎+𝑏,𝑎−𝑏)=1 𝑜𝑟 2 | gcd⁡(2𝑎+𝑏,𝑎+2𝑏)=1 𝑜𝑟 3 | Problems 2.4 | question 4 | David M. Burton

31. gcd (𝑎+𝑏,𝑎−𝑏)=1 𝑜𝑟 2 | gcd⁡(2𝑎+𝑏,𝑎+2𝑏)=1 𝑜𝑟 3 | Problems 2.4 | question 4 | David M. Burton ACADEMY OF MATHEMATICAL SCIENCES

108 views - 8 months ago

30. Properties of gcd | gcd is unique | gcd⁡(𝑘𝑎,𝑘𝑏)=|𝑘| gcd⁡(𝑎,𝑏) | gcd⁡(𝑎,𝑏)=𝑑⇔gcd⁡(𝑎/𝑑,𝑏/𝑑)=1

30. Properties of gcd | gcd is unique | gcd⁡(𝑘𝑎,𝑘𝑏)=|𝑘| gcd⁡(𝑎,𝑏) | gcd⁡(𝑎,𝑏)=𝑑⇔gcd⁡(𝑎/𝑑,𝑏/𝑑)=1 ACADEMY OF MATHEMATICAL SCIENCES

102 views - 8 months ago

29. Problems 2.3 | Solution of question 21-23 | Elementary Number Theory | David M. Burton

29. Problems 2.3 | Solution of question 21-23 | Elementary Number Theory | David M. Burton ACADEMY OF MATHEMATICAL SCIENCES

58 views - 8 months ago

28. Problems 2.3 | Solution of question 20 | Elementary Number Theory | David M. Burton

28. Problems 2.3 | Solution of question 20 | Elementary Number Theory | David M. Burton ACADEMY OF MATHEMATICAL SCIENCES

129 views - 8 months ago

Square Roots of a complex Number | Exercises| Solution of Question 10 | Real Analysis | Walter Rudin

Square Roots of a complex Number | Exercises| Solution of Question 10 | Real Analysis | Walter Rudin ACADEMY OF MATHEMATICAL SCIENCES

19 views - 8 months ago

27. Problems 2.3 | Solution of question 19 | Elementary Number Theory | David M. Burton

27. Problems 2.3 | Solution of question 19 | Elementary Number Theory | David M. Burton ACADEMY OF MATHEMATICAL SCIENCES

117 views - 9 months ago

9. Find Constant M such that |f(x)| ≤ M | Real Analysis Example 2.2.6(d) | Bartle, The Real Numbers

9. Find Constant M such that |f(x)| ≤ M | Real Analysis Example 2.2.6(d) | Bartle, The Real Numbers ACADEMY OF MATHEMATICAL SCIENCES

66 views - 9 months ago

8. Triangle Inequality | Absolute Value of real Number | Real Analysis by Robert G Bartle

8. Triangle Inequality | Absolute Value of real Number | Real Analysis by Robert G Bartle ACADEMY OF MATHEMATICAL SCIENCES

123 views - 9 months ago

7. Chapter # 2 The Real Numbers | Absolute Value of real Number | Real Analysis by Robert G Bartle

7. Chapter # 2 The Real Numbers | Absolute Value of real Number | Real Analysis by Robert G Bartle ACADEMY OF MATHEMATICAL SCIENCES

120 views - 9 months ago

6. Chapter # 2 The Real Numbers | Exercise 2.1, Question 23 to 26 | Real Analysis by Robert G Bartle

6. Chapter # 2 The Real Numbers | Exercise 2.1, Question 23 to 26 | Real Analysis by Robert G Bartle ACADEMY OF MATHEMATICAL SCIENCES

180 views - 9 months ago

26. Problems 2.3 | Solution of question 16-18 | Elementary Number Theory | David M. Burton

26. Problems 2.3 | Solution of question 16-18 | Elementary Number Theory | David M. Burton ACADEMY OF MATHEMATICAL SCIENCES

92 views - 9 months ago

Exercises| Solution of Question 6 | Real Analysis | Walter Rudin

Exercises| Solution of Question 6 | Real Analysis | Walter Rudin ACADEMY OF MATHEMATICAL SCIENCES

78 views - 9 months ago

25. Problems 2.3 | Solution of question 11-15 | Elementary Number Theory | David M. Burton

25. Problems 2.3 | Solution of question 11-15 | Elementary Number Theory | David M. Burton ACADEMY OF MATHEMATICAL SCIENCES

163 views - 10 months ago

5. Chapter # 2 Real Numbers || Exercise 2.1, Question 20 to 22 || Real Analysis by Robert G Bartle

5. Chapter # 2 Real Numbers || Exercise 2.1, Question 20 to 22 || Real Analysis by Robert G Bartle ACADEMY OF MATHEMATICAL SCIENCES

204 views - 10 months ago

4. Chapter # 2 Real Numbers || Exercise 2.1, Question 17 to 19 || Real Analysis by Robert G Bartle

4. Chapter # 2 Real Numbers || Exercise 2.1, Question 17 to 19 || Real Analysis by Robert G Bartle ACADEMY OF MATHEMATICAL SCIENCES

264 views - 10 months ago

24. Problems 2.3 | Solution of question 6-10 | Elementary Number Theory | David M. Burton

24. Problems 2.3 | Solution of question 6-10 | Elementary Number Theory | David M. Burton ACADEMY OF MATHEMATICAL SCIENCES

170 views - 10 months ago

23. Problems 2.3 | Solution of question 1-5 | Elementary Number Theory | David M. Burton

23. Problems 2.3 | Solution of question 1-5 | Elementary Number Theory | David M. Burton ACADEMY OF MATHEMATICAL SCIENCES

240 views - 10 months ago

22. Euclid's Lemma | Statement and proof | Elementary Number Theory | David M. Burton

22. Euclid's Lemma | Statement and proof | Elementary Number Theory | David M. Burton ACADEMY OF MATHEMATICAL SCIENCES

169 views - 10 months ago

21. Properties of GCD and Relatively Prime Integers | Elementary Number Theory | David M. Burton

21. Properties of GCD and Relatively Prime Integers | Elementary Number Theory | David M. Burton ACADEMY OF MATHEMATICAL SCIENCES

111 views - 10 months ago

Exercises| Solution of Question 1-5 | Real Analysis | Walter Rudin

Exercises| Solution of Question 1-5 | Real Analysis | Walter Rudin ACADEMY OF MATHEMATICAL SCIENCES

110 views - 10 months ago

Euclidean Spaces | Properties of Norm | Real Analysis | Walter Rudin

Euclidean Spaces | Properties of Norm | Real Analysis | Walter Rudin ACADEMY OF MATHEMATICAL SCIENCES

114 views - 10 months ago

Schwarz Inequality | Real Analysis | Walter Rudin

Schwarz Inequality | Real Analysis | Walter Rudin ACADEMY OF MATHEMATICAL SCIENCES

130 views - 10 months ago

Absolute Value of Complex Numbers and properties | Real Analysis | Walter Rudin

Absolute Value of Complex Numbers and properties | Real Analysis | Walter Rudin ACADEMY OF MATHEMATICAL SCIENCES

42 views - 10 months ago

Extended real number System | Real Analysis | Walter Rudin

Extended real number System | Real Analysis | Walter Rudin ACADEMY OF MATHEMATICAL SCIENCES

104 views - 10 months ago

20. Bezout's Lemma | Show that GCD can be expressed as the linear combination of integers a and b.

20. Bezout's Lemma | Show that GCD can be expressed as the linear combination of integers a and b. ACADEMY OF MATHEMATICAL SCIENCES

63 views - 11 months ago

19. GCD (Greatest Common Divisor) | Linear Combination | Elementary Number Theory | David M. Burton

19. GCD (Greatest Common Divisor) | Linear Combination | Elementary Number Theory | David M. Burton ACADEMY OF MATHEMATICAL SCIENCES

96 views - 11 months ago

18. Divisibility & Properties of Divisibility | Elementary Number Theory | David M. Burton

18. Divisibility & Properties of Divisibility | Elementary Number Theory | David M. Burton ACADEMY OF MATHEMATICAL SCIENCES

167 views - 11 months ago

3. Chapter # 2 Real Numbers || Exercise 2.1, Question 11 to 16 || Real Analysis by Robert G Bartle

3. Chapter # 2 Real Numbers || Exercise 2.1, Question 11 to 16 || Real Analysis by Robert G Bartle ACADEMY OF MATHEMATICAL SCIENCES

304 views - 11 months ago