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Udemy – How to Write Proofs with Functions with the Math Sorcerer 2023-5

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Lecture 19/30

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Lecture 19 of 30

Proving a Piecewise Function is Bijective Example 1

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Course Content

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Section 1: Introductory Videos6 videos

Definition of a Surjective(Onto) Function

13m

The Image of a Set Under a Function

18m

Definition of a Function

11m

The Inverse Image of a Set Under a Function

22m

Defnition of an Injective(one to one) Function

12m

Intuitive Explanation for Injective, Surjective, and Bijective Functions

16m

Section 2: Proofs with Injections, Surjections, and Bijections10 videos

Proving a Function is Surjective Example 2

11m

Proving a Function is Surjective Example 1

20m

Proving a Function is Surjective Example 3

14m

Proving a Function is Surjective Example 4

11m

Proving a Function is Injective Example 2

Proving a Function is Injective Example 1

22m

Proving a Function is Surjective Example 5

Proving a Function is Injective Example 3

11m

Proving a Function is Not Surjective

14m

Proving a Piecewise Function is Bijective Example 1

37mNow Playing

Section 3: Two More Full Introductions with Sample Proofs2 videos

Full Introduction Condensed Into One Video(TONS of Knowledge)

54m

Bonus Full introduction with Audience Uncut and Unedited(TONS of Knowledge)

1h 30m

Section 4: Proofs of Key Properties of Surjective and Injective Functions4 videos

Injectivity and Function Composition Proof 1

Injectivity and Function Composition Proof 2

Surjectivity and Function Composition Proof 2

Surjectivity and Function Composition Proof 1

13m

Section 5: Direct Image and Inverse Image Proofs5 videos

Direct Image of Union Proof

26m

Inverse Image of Intersection Proof 2

13m

Inverse Image of Intersection Proof 1

18m

Direct Image of Intersection Under an Injection Proof

25m

Inverse Image of Union Proof

15m

Section 6: More Proofs3 videos

Proof 2

11m

Proof 1

34m

Proof 3

About this Lecture

Section: Proofs with Injections, Surjections, and Bijections • Size: 80.39 MB • Duration: 37m

Course Summary

How to Write Proofs with Functions with the Math Sorcerer is a training course on writing proofs with functions published by Udemy Online Academy. This course is a comprehensive guide designed to help people master the art of writing mathematical proofs involving functions. This course provides a step-by-step approach to understanding and constructing proofs, focusing on specific challenges and techniques associated with functions. Ideal for students, mathematicians, and anyone interested in deepening their proof writing skills, this course uses clear explanations and practical examples to demystify the process of proof construction. This course provides a structured and practical approach to mastering the art of mathematical proof involving functions.Focusing on fundamental concepts, step-by-step guidance, and interactive practice, this course is designed to help learners develop the skills needed to construct clear and accurate proofs. Whether for academic study or professional use, this guide provides the tools and knowledge necessary to excel in writing proofs with functions. The best way to learn a proof is to watch someone else give a detailed proof and then try to do it yourself. This is a great course for anyone who wants to write proofs and has some knowledge of basic proofs. After completing this course, you will be able to write different types of proofs and understand them well.

Course Content

0 / 30 completed

Section 1: Introductory Videos6 videos

Definition of a Surjective(Onto) Function

13m

The Image of a Set Under a Function

18m

Definition of a Function

11m

The Inverse Image of a Set Under a Function

22m

Defnition of an Injective(one to one) Function

12m

Intuitive Explanation for Injective, Surjective, and Bijective Functions

16m

Section 2: Proofs with Injections, Surjections, and Bijections10 videos

Proving a Function is Surjective Example 2

11m

Proving a Function is Surjective Example 1

20m

Proving a Function is Surjective Example 3

14m

Proving a Function is Surjective Example 4

11m

Proving a Function is Injective Example 2

Proving a Function is Injective Example 1

22m

Proving a Function is Surjective Example 5

Proving a Function is Injective Example 3

11m

Proving a Function is Not Surjective

14m

Proving a Piecewise Function is Bijective Example 1

37mNow Playing

Section 3: Two More Full Introductions with Sample Proofs2 videos

Full Introduction Condensed Into One Video(TONS of Knowledge)

54m

Bonus Full introduction with Audience Uncut and Unedited(TONS of Knowledge)

1h 30m

Section 4: Proofs of Key Properties of Surjective and Injective Functions4 videos

Injectivity and Function Composition Proof 1

Injectivity and Function Composition Proof 2

Surjectivity and Function Composition Proof 2

Surjectivity and Function Composition Proof 1

13m

Section 5: Direct Image and Inverse Image Proofs5 videos

Direct Image of Union Proof

26m

Inverse Image of Intersection Proof 2

13m

Inverse Image of Intersection Proof 1

18m

Direct Image of Intersection Under an Injection Proof

25m

Inverse Image of Union Proof

15m

Section 6: More Proofs3 videos

Proof 2

11m

Proof 1

34m

Proof 3