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Classical Theorems and Proofs: An Introduction to Elegant Mathematics
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Introductory Lectures
Lecture 1: Why Mathematics is Worth Knowing (Preview Content)2 Topics|1 Quiz -
Lecture 2: What is Mathematics?3 Topics|1 Quiz
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ProofsLecture 3: Triangle Angle Sum Theorem (Preview Content)2 Topics|1 Quiz
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Lecture 4a: Polygonal Tilings2 Topics|1 Quiz
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Lecture 4b: Platonic Solids2 Topics|1 Quiz
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Lecture 5: Existence of Irrational Numbers2 Topics|1 Quiz
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Lecture 6: How Many Irrational Numbers are there?2 Topics|1 Quiz
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Theorems with Hard ProofsLecture 7: The Independence of the Parallel Postulate2 Topics|1 Quiz
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Lecture 8: Impossible Constructions2 Topics|1 Quiz
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Lecture 9: Three Fundamental Theorems2 Topics|1 Quiz
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Lecture 10: Euler’s Identity2 Topics|1 Quiz
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Lecture 11: Fermat’s Last Theorem2 Topics|1 Quiz
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Lecture 12: Gödel’s Incompleteness Theorems2 Topics|1 Quiz
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Unsolved ProblemsLecture 13a: A Handful of Unsolved Problems: The Infinite Depth of Mathematical Mystery2 Topics|1 Quiz
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Lecture 13b: A Handful of Unsolved Problems: The Infinite Depth of Mathematical Mystery2 Topics|1 Quiz
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End of Course TestEnd of Course Test: Classical Theorems and Proofs: An Introduction to Elegant Mathematics1 Quiz
Quiz 16 of 16
End of Course Test: Classical Theorems and Proofs: An Introduction to Elegant Mathematics
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Question 1 of 8
1. Question
The definition of _________ numbers is a number that cannot be written as a ratio of whole numbers.
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Question 2 of 8
2. Question
There are more irrational numbers than rational numbers.
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Question 3 of 8
3. Question
What is a regular polygon?
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Question 4 of 8
4. Question
The following theorem is which fundamental theorem: Any whole number greater than 1 is either prime or it is the product of primes, and its prime factorization is unique.
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Question 5 of 8
5. Question
It is possible to prove that something is impossible.
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Question 6 of 8
6. Question
What is Euclid’s fifth postulate called?
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Question 7 of 8
7. Question
Which of the following is the Triangle Angle Sum Theorem according to Euclid?
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Question 8 of 8
8. Question
In 250 to 350 words, summarize three proofs that were demonstrated in this course and describe how you would teach these three proofs to your students.
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