Difference between revisions of "Real Numbers"
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Concepts Lectures on Real Numbers and Divisibility | Concepts Lectures on Real Numbers and Divisibility | ||
| − | =Concept | + | ==Concept Learning Sessions== |
Session # 1 [https://youtu.be/A7Xt-2CtzK4/ What are Real Numbers?] | Session # 1 [https://youtu.be/A7Xt-2CtzK4/ What are Real Numbers?] | ||
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Session # 9 [https://youtu.be/K1-b2hat-ME/ Euclid's Division Lemma - Applications] | Session # 9 [https://youtu.be/K1-b2hat-ME/ Euclid's Division Lemma - Applications] | ||
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| + | ==Problem Solving Sessions== | ||
| + | |||
| + | [https://youtu.be/KR4BRId5E7I/ Problem Solving Session # 1] Show that n^2-1 is divisible by 8 if n is an odd positive integer. | ||
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| + | [https://youtu.be/nvMBua1yNoE/ Problem Solving Session # 2] Show that the square of any positive integer is of the form of 3m or 3m+1 for some integer m. | ||
| + | |||
| + | [https://youtu.be/Rk5-XKjq1-U/ Problem Solving Session # 3] Prove that one of every three consecutive positive integers is divisible by 3 | ||
| + | |||
| + | ==Concept Learning Sessions== | ||
Session # 10 [https://youtu.be/VF4NtFu4Qgw/ Euclid's Division Algorithm] | Session # 10 [https://youtu.be/VF4NtFu4Qgw/ Euclid's Division Algorithm] | ||
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Session # 15 [https://youtu.be/sBGt9ncvd_I/ Expressing GCD of Two Positive Integers as a Linear Combination] | Session # 15 [https://youtu.be/sBGt9ncvd_I/ Expressing GCD of Two Positive Integers as a Linear Combination] | ||
| + | |||
| + | ==Problem Solving Sessions== | ||
| + | |||
| + | [https://youtu.be/s-PcZWhRCjQ/ Problem Solving Session # 4] Find the GCD/HCF of 237 and 81 and express it as a linear combination of 237 and 81 | ||
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| + | [https://youtu.be/6FwrDhqnjlU/ Problem Solving Session # 5] Find the GCD/HCF of 72 and 56 and express it as a linear combination of 72 and 56. Also show that the linear combination is not unique. | ||
| + | |||
| + | [https://youtu.be/E24re8lGdWc/ Problems Solving Session # 6] Word Problem | ||
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| + | [https://youtu.be/E24re8lGdWc/ Problems Solving Session # 7] Word Problem | ||
| + | |||
| + | ==Concept Lectures== | ||
Session # 16 [https://youtu.be/MvslTd4_xgw/ Fundamental Theorem of Arithmetic] | Session # 16 [https://youtu.be/MvslTd4_xgw/ Fundamental Theorem of Arithmetic] | ||
| − | =Problem Solving | + | ==Problems== |
| − | [https://youtu.be/ | + | |
| + | [https://youtu.be/lbv3wZwGuuI/ Problems Solving Session # 8] Express 168 and 234 as a product of prime factors | ||
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| + | [https://youtu.be/77wTxZg5pIM/ Problems Solving Session # 9] Prove that there is no natural number n for which 4^n ends with digit zero | ||
| + | |||
| + | [https://youtu.be/KsXrJ1RvrV4/ Problem Solving Session # 10] Prove that there are infinitely many prime numbers | ||
| + | |||
| + | [https://youtu.be/sAJyKNS3AXk/ Problem Solving Session # 11]Prove that a positive integer n is a prime number, if no prime less than or equal to square root of n, divides n | ||
Latest revision as of 17:59, 17 May 2019
Concepts Lectures on Real Numbers and Divisibility
Contents
Concept Learning Sessions
Session # 1 What are Real Numbers?
Session # 2 What is meant by divisibility?
Session # 3 Properties of divisibility : Part 1
Session # 4 Properties of divisibility : Part 2
Session # 5 Euclid's Division Lemma : Part 1
Session # 6 Euclid's Division Lemma : Part 2
Session # 7 Euclid's Division Lemma : Part 3
Session # 8 Proof of the Euclid's Division Lemma
Session # 9 Euclid's Division Lemma - Applications
Problem Solving Sessions
Problem Solving Session # 1 Show that n^2-1 is divisible by 8 if n is an odd positive integer.
Problem Solving Session # 2 Show that the square of any positive integer is of the form of 3m or 3m+1 for some integer m.
Problem Solving Session # 3 Prove that one of every three consecutive positive integers is divisible by 3
Concept Learning Sessions
Session # 10 Euclid's Division Algorithm
Session # 11 Euclid's Division Algorithm: What is GCD?
Session # 12 Euclid's Division Algorithm: What are co-prime numbers?
Session # 13 Euclid's Division Algorithm: Finding GCD of Two Positive Integers
Session # 14 Euclid's Division Algorithm: Theorem 1 and its proof
Session # 15 Expressing GCD of Two Positive Integers as a Linear Combination
Problem Solving Sessions
Problem Solving Session # 4 Find the GCD/HCF of 237 and 81 and express it as a linear combination of 237 and 81
Problem Solving Session # 5 Find the GCD/HCF of 72 and 56 and express it as a linear combination of 72 and 56. Also show that the linear combination is not unique.
Problems Solving Session # 6 Word Problem
Problems Solving Session # 7 Word Problem
Concept Lectures
Session # 16 Fundamental Theorem of Arithmetic
Problems
Problems Solving Session # 8 Express 168 and 234 as a product of prime factors
Problems Solving Session # 9 Prove that there is no natural number n for which 4^n ends with digit zero
Problem Solving Session # 10 Prove that there are infinitely many prime numbers
Problem Solving Session # 11Prove that a positive integer n is a prime number, if no prime less than or equal to square root of n, divides n
