Nature of Proof

This online course is developed to cover all the content required for HSC Mathematics Extension 2 students studying Proofs.

We will cover language of proof, some elementary number theory, proving inequalities and further mathematical induction.

While this course is developed for NSW HSC Mathematics Extension 2, it may also be suitable A-Level Further Mathematics, STEP Mathematics, and Honors Mathematics.

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- 1. Floor and Ceiling and Example 17
- 2. Example 18

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Meet Huan

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Meet Huan - -

Hello! I am Huan - founder of EIM Tuition.

Growing up in a first-generation immigrant family, I experienced first-hand the belief that education is the key to opportunity. Like many of the students I have helped, I went through the grind of preparing for the HSC, aiming for a top ATAR in a highly competitive selective high school environment.

That journey shaped how I teach (and EIM operates) today. Since 2010, I’ve helped 1,000+ students from 50+ schools across Sydney achieve outstanding results - including 99.95 ATARs, state ranks and countless Band 6’s.

Through these online courses, I hope to share the same clarity, structure and strategies that have helped so many students succeed - and help you achieve your own goals, wherever you’re studying from.

Course FAQ

Stay tuned!

1. Introduction to Proofs

2. Example 1

3. Example 2

4. Example 3

5. Example 4

1. Statements

2. Negation

3. Implications

4. Converse

5. Inverse

1. Even and Odd Integers

2. Example 16

3. Prime and Composite Integers

4. Example 17

5. Existential Statements

6. Example 18

7. Example 19

8. Example 20

9. Uniqueness

10. Universal Statements

11. Example 21

12. Example 22

13. Example 23

14. Example 24

15. Example 25

16. Example 26

17. Example 27

18. Example 28

19. Example 29

20. Example 30

21. Example 31

22. Example 32

23. Example 33

1. Example 34

2. Example 35

3. Example 36

4. Example 38

5. Example 39

6. Example 40

1. Example 1

2. Example 2

3. Example 3

4. Example 4

5. Example 5

6. Example 6

7. Unique Factorisation Theorem and Example 7

8. Example 8

9. Example 9

1. Quotient Remainder Theorem and Example 10

2. Example 11

3. Example 12

4. Example 13

5.Example 14

6. Example 15

7. Example 16

1. Floor and Ceiling and Example 17

2. Example 18

1. Proof by Contradiction and Example 19

2. Example 20

3. Example 21

4. Example 22

5. Example 23

6. Example 24

1. Proof by Contrapositive and Example 25

2. Example 26

3. Example 28

4. Example 29

1. Introduction to Inequalities

2. Example 1

3. Example 2

4. Example 3

5. Example 4

6. Example 5

1. Example 6

2. Example 7

3. Example 8

4. Example 9

1. Triangular Inequalities

2. Example 10

3. Example 11

Meet Huan - -